Vibration control device, vibration control method, and vibration control program

Abstract

The present invention provides a vibration control device, a vibration control method, and a vibration control program that compensate for rotational non-uniformity caused by the effects of angular transmission errors in the reduction mechanism. [Solution] The vibration control device is applied to a servo control system equipped with a reduction mechanism and is a vibration control device that compensates for rotational non-uniformity caused by the angle transmission error of the reduction mechanism, and includes a state estimation processing unit that estimates an estimated disturbance, which is an internal state quantity of the controlled object, based on observation information; an adaptive processing unit that uses the estimated disturbance as an evaluation signal and optimizes at least one of the evaluation signal or an objective function defined based on the evaluation signal; and an angle transmission error compensation unit that generates a compensation signal.

Description

[Technical Field]

[0001] This disclosure relates to a vibration control device, a vibration control method, and a vibration control program, and more particularly to a technique for compensating for angular transmission errors in a reduction mechanism. [Background technology]

[0002] In recent years, high-precision servo control systems for robots and machine tools have employed motors and compact, high-precision reduction mechanisms, particularly actuators using harmonic drive gears and planetary gear mechanisms. While these reduction mechanisms achieve both high reduction ratios and miniaturization, it is known that they can cause rotational angle deviations known as angular transmission errors due to structural tooth profile errors and assembly errors. Angular transmission error is the difference between the theoretical rotational output angle and the actual rotational output angle when a rotational input is applied to the reduction mechanism, and it repeats periodically in response to the rotational input. In particular, angular transmission errors that include periodic vibration components associated with motor rotation manifest as rotational non-uniformity (rotational unevenness, undulation, speed fluctuations, etc.) in the output shaft, causing deterioration in the motion accuracy and trajectory accuracy of robots and devices. Such phenomena are known as vibration phenomena caused by angular transmission errors. In compensation for rotational non-uniformity (vibration phenomenon), generally, a compensation signal is used to adjust the rotational input to the reduction mechanism in order to cancel out the periodic angular transmission error with respect to the motor rotational position (i.e., to bring the error in the rotational output of the reduction mechanism closer to zero) (see, for example, Patent Document 1). In addition, methods that apply correction to the motor speed, such as in Patent Document 2, are known. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Patent No. 2577713 [Patent Document 2] Patent No. 4837724 [Non-patent literature]

[0004] [Non-Patent Document 1] Toshiyuki Murakami, Ryo Nakamura, Fang Ming Iku, and Kohei Onishi: Force sensorless compliance control of a multi-degree-of-freedom robot based on a reaction force estimation observer, Journal of the Robotics Society of Japan, Vol. 11, No. 5, pp. 765-768, 1993. [Non-Patent Document 2] Toshiyuki Murakami, Kohei Onishi: A method for identifying the dynamic characteristics of multi-degree robots using disturbance observers, Journal of the Robotics Society of Japan, Vol. 11, No. 1, pp. 131-139, 1993. [Non-Patent Document 3] Kohei Onishi: Robust motion control using a disturbance observer, Journal of the Robotics Society of Japan, Vol. 11, No. 4, pp. 486-493, 1993. [Non-Patent Document 4] https: / / jp.mathworks.com / help / signal / ref / rpmordermap.html, accessed August 27, 2025. [Non-Patent Document 5] Yoshihide Kiyosawa, Xinyue Zhang, Hideo Asawa, Masana Kato, and Katsumi Inoue: A Study on Vibration Reduction in Harmonic Drive Gear Reducers (Part 1: Measurement of High-Precision Angular Transmission Error in Harmonic Drive Gear Reducers), Transactions of the Japan Society of Mechanical Engineers (Series C), Vol. 64, No. 9, pp. 348-354, 1998. [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] However, in the technologies described in Patent Documents 1 and 2, various factors can make it difficult to determine (or identify, estimate) appropriate parameters or to achieve sufficient compensation.

[0006] This disclosure is made in view of the above circumstances and aims to provide a vibration control device, a vibration control method, and a vibration control program that compensate for rotational non-uniformity caused by the influence of angular transmission errors in the reduction mechanism. [Means for solving the problem]

[0007] A first aspect of this disclosure is a vibration control device applied to a servo control system equipped with a reduction mechanism, which compensates for rotational non-uniformity caused by the influence of angular transmission error of the reduction mechanism, and includes: a state estimation processing unit that estimates an estimated disturbance, which is an internal state quantity of the controlled object, based on observation information; an adaptive processing unit that uses the estimated disturbance as an evaluation signal and optimizes at least one of the evaluation signal or an objective function defined based on the evaluation signal; and an angular transmission error compensation unit that generates a compensation signal.

[0008] A second aspect of the present disclosure is a vibration damping control method applied to a servo control system equipped with a reduction mechanism, which compensates for rotational non-uniformity caused by the influence of angular transmission error of the reduction mechanism, wherein a computer performs adaptive processing to optimize at least one of the evaluation signal or an objective function defined based on the evaluation signal, thereby generating a compensation signal.

[0009] A third aspect of this disclosure is a vibration damping control program applied to a servo control system equipped with a reduction mechanism, which compensates for rotational non-uniformity caused by the influence of angular transmission error of the reduction mechanism, and which causes a computer to perform adaptive processing to optimize at least one of the evaluation signal or an objective function defined based on the evaluation signal, based on observation information, an estimated disturbance which is an internal state variable of the controlled object, the estimated disturbance as an evaluation signal, and generate a compensation signal. [Effects of the Invention]

[0010] According to this disclosure, particularly in semi-closed control, it is possible to compensate for the rotational non-uniformity of the reduction mechanism without requiring additional sensors, by estimating the angular transmission error characteristics of the reduction mechanism, which are necessary for dynamic angular transmission error compensation and have individual product differences, through adaptive processing, and without requiring trial and error or optimization. Furthermore, it is possible to compensate for the rotational non-uniformity caused by the angular transmission error, regardless of whether the angular transmission error of the reduction mechanism is reproducible or not, and comprehensive suppression of rotational output errors considering various factors can be efficiently designed and implemented in a variety of systems. [Brief explanation of the drawing]

[0011] [Figure 1] Figure 1 shows a schematic diagram of the vibration control system. [Figure 2] Figure 2 shows a first example of the configuration of the control block for dynamic angle transmission error compensation of a vibration control device according to the present disclosure. [Figure 3] Figure 3 shows a second example of the configuration of the control block for dynamic angle transmission error compensation of the vibration control device according to the present disclosure. [Figure 4] Figure 4 shows a third configuration example of the control block for dynamic angle transmission error compensation of the vibration control device according to the present disclosure. [Figure 5] Figure 5 is a control block diagram when the compensator input is used as command information. [Figure 6] Figure 6 shows the response data of the motor speed in a constant speed interval when the motor is operated at a constant speed at multiple operating speeds. [Figure 7] Figure 7 shows the response data of the load speed in a constant speed interval when the system is operated at a constant speed at multiple operating speeds. [Figure 8] Figure 8 shows the order analysis results of the motor speed when the operating speed is 1600 r / min. [Figure 9] Figure 9 shows the order analysis results of the load speed when the operating speed is 1600 r / min. [Figure 10] Figure 10 shows the results of extracting the quadratic component of motor speed at multiple operating speeds. [Figure 11] Figure 11 shows the extraction results of the second-order component of the load velocity at multiple operating speeds. [Figure 12] Figure 12 shows the quadratic component of the motor position under condition A. [Figure 13] Figure 13 shows the second-order component of the load position under condition A. [Figure 14] Figure 14 shows the quadratic component of the motor speed under condition A. [Figure 15] Figure 15 shows the quadratic component of the load velocity under condition A. [Figure 16] Figure 16 shows the quadratic component of the motor position under condition B. [Figure 17] Figure 17 shows the second-order component of the load position under condition B. [Figure 18] Figure 18 shows the quadratic component of the motor speed under condition B. [Figure 19] Figure 19 shows the second-order component of the load velocity under condition B. [Figure 20] Figure 20 shows the quadratic component of the motor position under condition C. [Figure 21] Figure 21 shows the quadratic component of the load position under condition C. [Figure 22] Figure 22 shows the quadratic component of the motor speed under condition C. [Figure 23] Figure 23 shows the quadratic component of the load velocity under condition C. [Figure 24] Figure 24 shows the amplitude characteristics in the frequency response characteristics from angular transmission error to compensation current, and the compensation parameters corresponding to the motor speeds for the number of lookup tables. [Figure 25] Figure 25 shows the phase characteristics in the frequency response characteristics from angular transmission error to compensation current, and the compensation parameters corresponding to the motor speeds for the number of lookup table values. [Figure 26] Figure 26 shows the motor speed under condition D. [Figure 27] Figure 27 shows the load speed under condition D. [Figure 28]Figure 28 shows the motor speed vibration components under condition D. [Figure 29] Figure 29 shows the load velocity oscillation component under condition D. [Figure 30] Figure 30 shows the motor position vibration component under condition D. [Figure 31] Figure 31 shows the load position vibration component under condition D. [Figure 32] Figure 32 shows the motor speed under condition E. [Figure 33] Figure 33 shows the load speed under condition E. [Figure 34] Figure 34 shows the motor speed vibration components under condition E. [Figure 35] Figure 35 shows the load velocity oscillation component under condition E. [Figure 36] Figure 36 shows the motor position vibration component under condition E. [Figure 37] Figure 37 shows the load position vibration component under condition E. [Figure 38] Figure 38 shows the motor speed under condition F. [Figure 39] Figure 39 shows the load speed under condition F. [Figure 40] Figure 40 shows the motor speed vibration components under condition F. [Figure 41] Figure 41 shows the load velocity oscillation component under condition F. [Figure 42] Figure 42 shows the motor position vibration component under condition F. [Figure 43] Figure 43 shows the load position vibration component under condition F. [Figure 44] Figure 44 shows the motor speed under condition G. [Figure 45] Figure 45 shows the load speed under condition G. [Figure 46] Figure 46 shows the motor speed vibration components under condition G. [Figure 47] Figure 47 shows the load velocity vibration component under condition G. [Figure 48] Figure 48 shows the motor position vibration component under condition G. [Figure 49] Figure 49 shows the load position vibration component under condition G. [Figure 50] Figure 50 shows the motor speed under condition H. [Figure 51] Figure 51 shows the load speed under condition H. [Figure 52] Figure 52 shows the motor speed vibration components under condition H. [Figure 53] Figure 53 shows the load velocity vibration component under condition H. [Figure 54] Figure 54 shows the motor position vibration component under condition H. [Figure 55] Figure 55 shows the load position vibration component under condition H. [Figure 56] Figure 56 shows the amplitude characteristics and corresponding compensation parameters in the frequency response characteristics from the angular transmission error to the compensation position. [Figure 57] Figure 57 shows the phase characteristics and corresponding compensation parameters in the frequency response characteristics from the angular transmission error to the compensation position. [Figure 58] Figure 58 shows the motor speed under condition I. [Figure 59] Figure 59 shows the load speed under condition I. [Figure 60] Figure 60 shows the motor speed vibration components under condition I. [Figure 61] Figure 61 shows the load velocity oscillation component under condition I. [Figure 62] Figure 62 shows the motor position vibration component under condition I. [Figure 63] Figure 63 shows the load position vibration component under condition I. [Figure 64] Figure 64 shows the motor speed under condition J. [Figure 65] Figure 65 shows the load speed under condition J. [Figure 66]Figure 66 shows the motor speed vibration components under condition J. [Figure 67] Figure 67 shows the load velocity oscillation component under condition J. [Figure 68] Figure 68 shows the motor position vibration component under condition J. [Figure 69] Figure 69 shows the load position vibration component under condition J. [Figure 70] Figure 70 shows the motor speed under condition K. [Figure 71] Figure 71 shows the load speed under condition K. [Figure 72] Figure 72 shows the motor speed vibration components under condition K. [Figure 73] Figure 73 shows the load velocity oscillation component under condition K. [Figure 74] Figure 74 shows the motor position vibration component under condition K. [Figure 75] Figure 75 shows the load position vibration component under condition K. [Figure 76] Figure 76 shows the error between the motor position and the position command under condition K. [Figure 77] Figure 77 shows the error between the motor position and the approximate motor position under condition K. [Figure 78] Figure 78 shows the load position vibration component when the compensator input is command information and the servo control approximation characteristic is the dead time element. [Figure 79] Figure 79 shows the error between the motor position and the approximate motor position when the compensator input is command information and the servo control approximation characteristic is the dead time element. [Figure 80] Figure 80 shows the motor speed under condition L. [Figure 81] Figure 81 shows the load speed under condition L. [Figure 82] Figure 82 shows the motor speed vibration components under condition L. [Figure 83] Figure 83 shows the load velocity oscillation component under condition L. [Figure 84] Figure 84 shows the motor position vibration component under condition L. [Figure 85] Figure 85 shows the load position vibration component under condition L. [Figure 86] Figure 86 shows the motor speed under condition M. [Figure 87] Figure 87 shows the load speed under condition M. [Figure 88] Figure 88 shows the motor speed vibration components under condition M. [Figure 89] Figure 89 shows the load velocity vibration component under condition M. [Figure 90] Figure 90 shows the motor position vibration component under condition M. [Figure 91] Figure 91 shows the load position vibration component under condition M. [Figure 92] Figure 92 shows the motor speed under condition N. [Figure 93] Figure 93 shows the load speed under condition N. [Figure 94] Figure 94 shows the motor speed vibration components under condition N. [Figure 95] Figure 95 shows the load velocity oscillation component under condition N. [Figure 96] Figure 96 shows the motor position vibration component under condition N. [Figure 97] Figure 97 shows the load position vibration component under condition N. [Figure 98] Figure 98 shows the load moment of inertia fluctuation ratio. [Figure 99] Figure 99 shows the motor speed under condition O. [Figure 100] Figure 100 shows the load speed under condition O. [Figure 101] Figure 101 shows the motor speed vibration components under condition O. [Figure 102] Figure 102 shows the load velocity oscillation component under condition O. [Figure 103]Figure 103 shows the motor position vibration component under condition O. [Figure 104] Figure 104 shows the load position vibration component under condition O. [Figure 105] Figure 105 shows the motor speed under condition P. [Figure 106] Figure 106 shows the load speed under condition P. [Figure 107] Figure 107 shows the motor speed vibration components under condition P. [Figure 108] Figure 108 shows the load velocity oscillation component under condition P. [Figure 109] Figure 109 shows the motor position vibration component under condition P. [Figure 110] Figure 110 shows the load position vibration component under condition P. [Figure 111] Figure 111 shows the motor position vibration component under condition Q. [Figure 112] Figure 112 shows the load position vibration component under condition Q. [Figure 113] Figure 113 shows the motor position vibration component under condition R. [Figure 114] Figure 114 shows the load position vibration component under condition R. [Figure 115] Figure 115 shows the motor position vibration component under condition S. [Figure 116] Figure 116 shows the load position vibration component under condition S. [Figure 117] Figure 117 shows the motor position vibration component under condition T. [Figure 118] Figure 118 shows the load position vibration component under condition T. [Figure 119] Figure 119 shows the motor position vibration component under condition U. [Figure 120] Figure 120 shows the load position vibration component under condition U. [Figure 121] Figure 121 shows the motor position vibration component under condition V. [Figure 122] Figure 122 shows the load position vibration component under condition V. [Figure 123] Figure 123 is a magnified view of a portion of the motor speed vibration components shown in Figure 25. [Figure 124] Figure 124 is a flowchart of a vibration damping control program in a servo control system equipped with a reduction mechanism. [Figure 125] Figure 125 is a block diagram showing the estimation of angular transmission error characteristics. [Figure 126] Figure 126 is a block diagram showing the functional configuration of the vibration control device 100_5. [Figure 127] Figure 127 shows a first example configuration of the control block of the angle transmission error characteristic estimation device according to the present disclosure. [Figure 128] Figure 128 shows a block diagram of the lock-in amplifier used in calculating the evaluation index of this disclosure. [Figure 129] Figure 129 shows the motor speed under condition W. [Figure 130] Figure 130 shows the load speed under condition W. [Figure 131] Figure 131 shows the reaction torque under condition W. [Figure 132] Figure 132 shows the estimated disturbance under condition W. [Figure 133] Figure 133 shows the evaluation index (LIA output) under condition W. [Figure 134] Figure 134 shows the motor speed under condition X. [Figure 135] Figure 135 shows the load speed under condition X. [Figure 136] Figure 136 shows the reaction torque under condition X. [Figure 137] Figure 137 shows the estimated disturbance under condition X. [Figure 138] Figure 138 shows the evaluation metrics (LIA output) under condition X. [Figure 139] Figure 139 shows the motor speed under condition Y. [Figure 140] Figure 140 shows the load speed under condition Y. [Figure 141] Figure 141 shows the reaction torque under condition Y. [Figure 142] Figure 142 shows the estimated disturbance under condition Y. [Figure 143] Figure 143 shows the evaluation index (LIA output) under condition Y. [Figure 144] Figure 144 shows the motor speed under condition Z. [Figure 145] Figure 145 shows the load speed under condition Z. [Figure 146] Figure 146 shows the reaction torque under condition Z. [Figure 147] Figure 147 shows the estimated disturbance under condition Z. [Figure 148] Figure 148 shows the evaluation index (LIA output) under condition Z. [Figure 149] Figure 149 is a flowchart of an angular transmission error estimation program that estimates the effect of angular transmission error in a reduction mechanism. [Figure 150] Figure 150 is a flowchart of a vibration damping control program that compensates for rotational non-uniformity caused by the angular transmission error of the reduction mechanism. [Figure 151] Figure 151 is a block diagram showing the functional configuration of the vibration control device 100_6. [Figure 152] Figure 152 shows a first configuration example of the control block of a vibration control device according to an embodiment of the present disclosure. [Figure 153] Figure 153 shows the motor speed under condition AA. [Figure 154] Figure 154 shows the load speed under condition AA. [Figure 155] Figure 155 shows the reaction torque under condition AA. [Figure 156] Figure 156 shows the estimated disturbance under condition AA. [Figure 157] Figure 157 shows the estimated amplitude under condition AA. [Figure 158] Figure 158 shows the estimated phase under condition AA. [Figure 159] Figure 159 shows the motor speed under conditions AB. [Figure 160] Figure 160 shows the load speed under conditions AB. [Figure 161] Figure 161 shows the reaction torque under condition AB. [Figure 162] Figure 162 shows the estimated disturbance under conditions AB. [Figure 163] Figure 163 shows the estimated amplitude under condition AB. [Figure 164] Figure 164 shows the estimated phase under conditions AB. [Figure 165] Figure 165 shows the motor speed under AC conditions. [Figure 166] Figure 166 shows the load speed under condition AC. [Figure 167] Figure 167 shows the reaction torque under condition AC. [Figure 168] Figure 168 shows the estimated disturbance under condition AC. [Figure 169] Figure 169 shows the estimated amplitude under condition AC. [Figure 170] Figure 170 shows the estimated phase under condition AC. [Figure 171] Figure 171 shows the motor speed under condition AD. [Figure 172] Figure 172 shows the load speed under condition AD. [Figure 173] Figure 173 shows the reaction torque under condition AD. [Figure 174] Figure 174 shows the estimated disturbance under condition AD. [Figure 175] Figure 175 shows the estimated amplitude under condition AD. [Figure 176] Figure 176 shows the estimated phase under condition AD. [Figure 177] Figure 177 shows the motor speed under condition AE. [Figure 178] Figure 178 shows the load speed under condition AE. [Figure 179] Figure 179 shows the reaction torque under condition AE. [Figure 180] Figure 180 shows the estimated disturbance under condition AE. [Figure 181] Figure 181 shows the estimated amplitude under AE conditions. [Figure 182] Figure 182 shows the estimated phase under condition AE. [Figure 183] Figure 183 shows the motor speed under condition AF. [Figure 184] Figure 184 shows the load speed under condition AF. [Figure 185] Figure 185 shows the reaction torque under condition AF. [Figure 186] Figure 186 shows the estimated disturbance under condition AF. [Figure 187] Figure 187 shows the estimated amplitude under condition AF. [Figure 188] Figure 188 shows the estimated phase under condition AF. [Figure 189] Figure 189 shows the motor speed under condition AG. [Figure 190] Figure 190 shows the load speed under condition AG. [Figure 191] Figure 191 shows the reaction torque under condition AG. [Figure 192] Figure 192 shows the estimated disturbance under condition AG. [Figure 193] Figure 193 shows the estimated amplitude under condition AG. [Figure 194] Figure 194 shows the estimated phase under condition AG. [Figure 195] Figure 195 shows the motor speed under condition AH. [Figure 196] Figure 196 shows the load speed under condition AH. [Figure 197]Figure 197 shows the reaction torque under condition AH. [Figure 198] Figure 198 shows the estimated disturbance under condition AH. [Figure 199] Figure 199 shows the estimated amplitude under condition AH. [Figure 200] Figure 200 shows the estimated phase under condition AH. [Figure 201] Figure 201 shows the motor speed under AI conditions. [Figure 202] Figure 202 shows the load speed under the AI ​​conditions. [Figure 203] Figure 203 shows the reaction torque under AI conditions. [Figure 204] Figure 204 shows the estimated disturbances in the AI ​​under specific conditions. [Figure 205] Figure 205 shows the estimated amplitude under the AI ​​conditions. [Figure 206] Figure 206 shows the estimated phase under the AI ​​conditions. [Figure 207] Figure 207 shows the motor speed under condition AJ. [Figure 208] Figure 208 shows the load speed under condition AJ. [Figure 209] Figure 209 shows the reaction torque under condition AJ. [Figure 210] Figure 210 shows the estimated disturbance under condition AJ. [Figure 211] Figure 211 shows the motor position vibration component under condition AJ. [Figure 212] Figure 212 shows the load position vibration component under condition AJ. [Figure 213] Figure 213 shows the motor speed under condition AK. [Figure 214] Figure 214 shows the load speed under condition AK. [Figure 215] Figure 215 shows the reaction torque under condition AK. [Figure 216] Figure 216 shows the estimated disturbance under condition AK. [Figure 217] Figure 217 shows the motor position vibration components under condition AK. [Figure 218] Figure 218 shows the load position vibration component under condition AK. [Figure 219] Figure 219 shows the motor speed under condition AL. [Figure 220] Figure 220 shows the load speed under condition AL. [Figure 221] Figure 221 shows the reaction torque under condition AL. [Figure 222] Figure 222 shows the estimated disturbance under condition AL. [Figure 223] Figure 223 shows the motor position vibration component under condition AL. [Figure 224] Figure 224 shows the load position vibration component under condition AL. [Figure 225] Figure 225 shows the estimated amplitude under condition AL. [Figure 226] Figure 226 shows the estimated phase under condition AL. [Figure 227] Figure 227 shows the 1.96th order amplitude obtained from multiple angle transmission error measurements. [Figure 228] Figure 228 shows the second-order amplitude obtained from multiple angle transmission error measurements. [Figure 229] Figure 229 shows the 1.96th order phase obtained from multiple angle transmission error measurements. [Figure 230] Figure 230 shows the second phase obtained from multiple angle transmission error measurements. [Figure 231] Figure 231 shows the load speed during a constant-speed operation experiment without compensation. [Figure 232] Figure 232 shows the load speed during a constant-speed operation experiment with the first 1.96th-order adaptive compensation test. [Figure 233] Figure 233 shows the load speed during a constant-speed operation experiment in the second run of 1.96th-order adaptive compensation. [Figure 234]Figure 234 shows the load speed during a constant-speed operation experiment with 1.96th-order and 2nd-order adaptive compensation, first run. [Figure 235] Figure 235 shows the load speed during a constant-speed operation experiment with 1.96th-order and 2nd-order adaptive compensation, second time trial. [Figure 236] Figure 236 shows the results of the load speed order analysis during a constant speed operation experiment without compensation. [Figure 237] Figure 237 shows the results of the load speed order analysis during a constant-speed operation experiment using the second 1.96th-order adaptive compensation. [Figure 238] Figure 238 shows the results of the load speed order analysis during a constant-speed operation experiment with 1.96th order and 2nd order adaptive compensation (second trial). [Figure 239] Figure 239 is a flowchart of a vibration damping control program in a servo control system equipped with a reduction mechanism. [Modes for carrying out the invention]

[0012] The embodiments will be described in detail below with reference to the drawings.

[0013] [Vibration damping control system configuration and the effect of angular transmission error] (Vibration control system configuration) Figure 1 shows a schematic diagram of the vibration control system. The vibration control system 1000 includes, for example, a vibration control device 100_1, a motor 200, a reduction mechanism 300, a load 400, and an encoder 500. The vibration control device 100_1 is a computer device equipped with one or more processors, memory, etc. The vibration control system 1000 may also include vibration control devices 100_2, 100_3, 100_4, 100_5, or 100_6, which will be described later, instead of vibration control device 100_1. Hereafter, when vibration control devices 100_1, 100_2, 100_3, 100_4, 100_5, and 100_6 are not distinguished, they may be referred to as vibration control devices or simply as control devices. Furthermore, below, the motor 200, reduction mechanism 300, load 400, encoder 500, and vibration damping control system 1000 may be simply referred to as the motor, reduction mechanism, load, encoder, and vibration damping control system. The vibration damping control device may consist of one control unit or two or more control units (for example, a combination of a PLC (programmable logic controller) and, for example, a servo driver and a servo control unit). The control device performs target trajectory calculation of the load to generate a position command, generates a speed command, a torque command or drive current based on the position command, and supplies the drive current to the motor. The control device generates a position command, a speed command, and a torque command or drive current as command values ​​(target values). Depending on the purpose of the control device, the command value may be a position command, a speed command or a torque command. Since many control devices are so-called embedded systems, the computer resources of the control device, such as processing power (e.g., CPU performance) and memory resource usage (e.g., ROM capacity or RAM capacity), may be limited.

[0014] The motor rotates its motor shaft using a drive current supplied from the control device. The motor (e.g., a servo motor) may be equipped with a position detector (e.g., an encoder) that detects the rotational position of the motor shaft. The position detector outputs a rotational position signal (motor position) of the motor shaft to the control device. It may also be equipped with a speed detector (e.g., a tachogenerator) that detects the rotational speed of the motor shaft, and the speed detector outputs a rotational speed signal to the control device.

[0015] The reduction gear mechanism has a motor rotation shaft connected to its input shaft, reduces the motor rotation at a predetermined reduction ratio, and drives the load via the output shaft of the reduction gear mechanism. The motor rotation shaft may also be connected to the input shaft of the reduction gear mechanism via, for example, a belt mechanism. The load is a robot arm or the like connected to the output shaft of the reduction gear mechanism. The output shaft of the reduction gear mechanism may also be equipped with a position sensor. The position information of the output shaft of the reduction gear mechanism is sometimes called the load position. The reduction gear mechanism may also be equipped with a torque sensor to detect the load torque for driving the load. The torque sensor can output a load torque signal representing the load torque to a control device. The reduction gear mechanism may be, for example, a harmonic drive gear, a belt pulley mechanism, an RV reducer, or a planetary gear mechanism.

[0016] A servo control system is a system for precisely controlling the output (position, speed, or torque (current)) in relation to a command value, and may be a control system using a servo motor. The controlled variable is a state variable of the controlled object 1 to be controlled, and may be observed by various detectors (e.g., position detectors) and used in feedback control. Position control controls the position with the command value as the target position (angle) and the controlled variable as the position. Speed ​​control controls the speed with the command value as the target speed (rotational speed) and the controlled variable as the speed. Torque control controls the torque with the command as the target torque (current) and the controlled variable as the torque. Note that the output torque of the motor is controlled in proportion to the current flowing through the motor, so this is sometimes called current control.

[0017] Position control, speed control, and torque control (current control) may be configured in a multi-loop structure. In a multi-loop structure, the trade-off between the responsiveness (control performance) and computational load of each loop may be considered, and the processing cycle of the outer loop (speed control or position control) may be changed compared to the inner loop (current control), or the processing cycle of the target trajectory calculation (e.g., command unit, command generation unit) may be further slowed down.

[0018] Semi-closed control refers to a method where the control variable is the output shaft of the reduction gear mechanism, a position detector is installed on the motor side, and feedback control is performed using the rotational position of the motor. In this method, the actual position of the output shaft of the reduction gear mechanism is not directly detected, but control is performed based on information from the motor side.

[0019] (Effect of angular transmission error) This section summarizes the definition of angular transmission error and its impact on servo control systems.

[0020] Angular transmission error is defined as the difference between the theoretical rotation angle of the output and the actual rotation angle of the output. The characteristics of angular transmission error are mainly determined by machining errors in the reduction mechanism (e.g., dimensional errors of the reduction mechanism components and gear errors) and assembly errors (e.g., deformation of parts). Therefore, there are individual differences in the product, and the angular transmission error characteristics differ depending on the rotation direction of the reduction mechanism.

[0021] The effects of angular transmission errors can be broadly categorized into the following two types. Static: Deterioration of positioning accuracy Dynamic: Fluctuations in rotational speed (operating speed) during operation (non-uniformity of rotation)

[0022] As can be seen from the definition of angular transmission error, static effects do not result in the rotation angle of the theoretically rotating output, leading to a deterioration in positioning accuracy.

[0023] Regarding dynamic effects, for example, the technical documentation concerning harmonic drive gears (Harmonic Drive®) explains it as follows: When the natural frequency of the vibration system including the harmonic drive gear matches the natural frequency caused by the inertia of the housing or load, a resonance state occurs, and the angular transmission error component in the harmonic drive gear is amplified. In this case, the rotational non-uniformity behaves as a vibration phenomenon caused by the angular transmission error.

[0024] For example, in a harmonic drive gear, due to its structural characteristics, two main angular error components are generated for each rotation of the input shaft. Therefore, the frequency of the main component of the angular error corresponds to twice the input frequency. Consequently, if resonance occurs in the frequency range corresponding to twice the input frequency, the angular transmission error may be significantly amplified.

[0025] Furthermore, the actual vibration frequency is affected by servo control and is not the natural frequency mentioned above, but rather the vibration frequency of the entire system including the servo control, amplifying the effect of angular transmission error. As a result, the effect of angular transmission error behaves differently depending on the motor speed (input frequency).

[0026] Static effects tend to be a problem mainly during PTP (Point-to-Point) operation, while dynamic effects tend to be a problem during CP (Continuous Path) operation. For example, in the configuration shown in Figure 1, the angular transmission error can be understood as the difference between the load position and the motor position divided by the reduction ratio. The angular transmission error can be expressed by equation (1), taking into account the harmonic order with respect to the motor position.

number

[0027] (1) The symbols in the equation are as follows: θ Sync :Angular transmission error, unit is angular-second (arc-sec). θ m Motor position, unit is radians (rad). k: harmonic order O C : A coefficient determined by the structure of the reduction mechanism (a real number, not limited to integers) A k :Each order amplitude, in arc-seconds (arc-sec). φ k Each phase is expressed in radians (rad). The arc-sec is a unit of angle equivalent to 1 / 3600th of a degree (°), and is used to express very small angles.

[0028] Note that while there may be components in the actual angular transmission error that cannot be expressed by equation (1), it is known that the above components are often dominant and that these components are often reproducible. Therefore, from here on, the angular transmission error will be expressed as θ. Sync It shall be treated as such. Furthermore, to distinguish it from the definition of angular transmission error, it is expressed as synchronization with respect to motor position (Synchronous: Sync).

[0029] Furthermore, vibration components with two periods per rotation of the input shaft (motor position) are represented as "second-order components," and vibrations with n periods per rotation of the input shaft are represented as n-th-order components. Note that depending on the structure of the reduction mechanism, the components may be of an order other than integer.

[0030] [Vibration control method (dynamic angular transmission error compensation)] (Dynamic angle transmission error compensation) The vibration control system according to the embodiment of this disclosure will be described below with reference to the drawings. Furthermore, the effect of suppressing rotational non-uniformity (vibration suppression effect) of this disclosure will be quantitatively demonstrated by numerical simulations described later.

[0031] Figure 2 shows a control block diagram for dynamic angle transmission error compensation. The control system configuration here is a multi-loop configuration consisting of position control, speed control, and current control, with position control being the control device.

[0032] The symbols in Figure 2 are as follows: θ *m : Position command θ m : Motor position ω m : Motor speed θ l : Load position K p : Position loop gain K v : Speed loop gain T v : Speed loop integral time constant T t : Torque filter time constant V Fil : Speed feedback filter Delay: Delay element in current control system etc. C ATE : Angle transfer error compensator i ATEComp : Compensation signal (compensation current) R: Reduction ratio J m : Motor inertia moment K t : Torque constant J l : Load inertia moment K g : Spring constant of reduction mechanism θ Sync : Angle transfer error Delay = e -Tds approximated by second-order Padé as expressed by JPEG0007870027000003.jpg1742 [[ID=7३]]T d : Delay time JPEG0007870027000004.jpg1126 T V : Speed feedback filter time constant

[0033] The control device outputs a drive current to the motor based on the position command generated by the command generation unit (not shown) and the motor position acquired from the position detector (not shown). The control device comprises a position control unit (not shown), a speed control unit (not shown), a torque control unit (not shown), and an angle transmission error compensator. The position control unit generates a speed command by performing proportional control (P control) on the position deviation between the position command and the motor position. The speed control unit generates a current command (torque command) by performing proportional-integral control (PI control) and a torque filter on the speed deviation between the speed command and the motor speed. The torque control unit generates a drive current based on a command obtained by adding the current command and the compensation signal (compensation current) output from the angle transmission error compensator. The motor speed is obtained by passing the motor speed information, which is the result of a differential calculation with respect to the motor position, through a speed feedback filter.

[0034] The motor is driven based on a drive current from the control device. When torque is applied to the motor via a torque constant from the drive current, the rotational position of the motor changes with acceleration corresponding to the motor's moment of inertia, and this is integrated over time and converted into the motor's position.

[0035] The reduction mechanism reduces the motor's rotation by a predetermined reduction ratio and drives the load via the output shaft of the reduction mechanism. In this case, an angular transmission error is added to the difference between the motor position and the load position, and this is converted into torque that drives the load via the reduction mechanism's spring constant (stiffness). The torque that drives the load acts as a reaction force on the motor.

[0036] The load is driven by torque applied from the reduction gear mechanism, and, similar to a motor, the load position is determined according to the load's moment of inertia.

[0037] The drive system, including the motor, reduction gear, and load, can be modeled as a so-called two-inertia frame of reference.

[0038] The angular transmission error compensator generates a sinusoidal compensation signal, including compensation model 3, which will be described later. This compensation signal suppresses vibration phenomena caused by angular transmission errors. Hereafter, compensation model 3 may be simply referred to as the compensation model.

[0039] The terms used in this disclosure are defined as follows:

[0040] The control system configuration refers to the configuration of the control method in a control device. For example, in Figure 2, it shows the configuration of a feedback control system consisting of position proportional control, velocity proportional-integral control, and a filter.

[0041] Control parameters refer to parameters used to determine the response characteristics of various controls in a control system configuration. For example, in Figure 2, these include the position loop gain, velocity loop gain, velocity loop integral time constant, torque filter time constant, velocity feedback filter time constant, and delay time. Note that the content, type, and set values ​​of control parameters may differ depending on the control system configuration.

[0042] Motor characteristics refer to the characteristics that determine the dynamic characteristics of a motor. For example, in the case of Figure 2, these include the torque constant and the characteristics of a second-order integral system including the motor moment of inertia. Furthermore, if the motor is connected to a reduction mechanism, for example via a belt mechanism, these characteristics are treated as part of the dynamic characteristics.

[0043] Dynamic angular transmission error compensation refers to a vibration control method that compensates for the dynamic effects of angular transmission errors (vibration phenomena caused by angular transmission errors).

[0044] Position information refers to the motor position or position command, and speed information refers to the motor speed or position command speed.

[0045] Frequency response characteristics refer to the changes in amplitude and phase of the output signal for each frequency when sinusoidal waves of various frequencies are input to a given transfer function or system.

[0046] (Dynamic angle transmission error compensation, automatic setting of compensation parameters) This section describes the compensation method for the dynamic effects of angular transmission error shown in equation (1). In particular, it describes the angular transmission error compensator in the dynamic angular transmission error compensation, whose configuration is shown in Figure 2. In Figure 2, reference numeral 1 denotes the controlled object, reference numeral 200 denotes the motor, reference numeral 300 denotes the reduction mechanism, reference numeral 400 denotes the load, and reference numeral 100_1 denotes the vibration control device.

[0047] [composition] In this configuration, the compensation signal generated by the angle transmission error compensator is the compensation current i ATEComp This is shown in equations (2) through (5).

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[0048] The symbols in equations (2) through (5) are as follows: i: Compensation order A i Each compensation order amplitude is expressed in arcseconds (arc-sec). φ i Each compensation order phase is expressed in radians (rad). A Ci :Angle transmission error compensator amplitude at each compensation order, in units of amperes per angle-second (A / arc-sec). φ Ci :Angle transmission error compensator phase at each compensation order, in radians (rad). ω m Motor speed, in revolutions per minute (r / min). ωmi : Motor speed angular frequency relative to i The image is JPEG0007870027000009.jpg927, and the unit is radians per second (rad / s). j: Imaginary unit

[0049] Furthermore, the formula takes into account the comparison with the angular transmission error shown in equation (1), and also considers the handling of multiple compensation orders described later.

[0050] Hereafter, A corresponds to the angular transmission error in the controlled object 1. i , φ i This is called the angular transmission error characteristic. This characteristic uses values ​​that have been measured in advance or measured or identified on the system.

[0051] The angular transmission error compensator amplitude and phase at each compensation order are given by the transfer function from the angular transmission error to the compensation current. Using JPEG0007870027000010.jpg923, the frequency response characteristics at frequencies corresponding to the system's operating speed range are calculated and constructed as a compensation model. In equation (4), π corresponds to compensation in reverse phase, and equation (3) may be multiplied by "-1". This configures the system to automatically set the parameters of the compensation model and register them in the compensation model.

[0052] Hereafter, the information necessary for the angular transmission error characteristics and compensation model, which are parameters in an angular transmission error compensator, will be collectively referred to as compensation parameters. For example, if the reduction mechanism is a harmonic drive gear, the coefficient O is determined by the structure of the reduction mechanism. c This is shown by equation (5).

[0053] In this configuration, the summing unit 2 adds the compensation signal to the current command. Hereafter, the summing unit 2 may be simply referred to as the summing unit. Here, the current command is the target of the compensation signal addition, and in this disclosure, this is called the compensation addition point. In this configuration, in order to unify the compensation addition point regardless of the control mode (position control, speed control, or torque control selected), the compensation addition point is set to the current command.

[0054] The dynamic influence of the angular transmission error of the speed reduction mechanism is affected by various structural or control factors other than the motor position. Therefore, the angular transmission error compensator generates a compensation current, which is a sinusoidal compensation signal based on the angular transmission error characteristic of a separately determined compensation order and the motor position. At this time, in order to perform compensation considering the influence of control factors, the amplitude and phase calculated from the frequency response characteristic at the frequency corresponding to the motor speed using the transfer function from the angular transmission error to the compensation current are used as the angular transmission error compensator amplitude at each compensation order and the angular transmission error compensator phase at each compensation order, and the amplitude and phase used for generating the compensation signal are corrected using a compensation model. The realization of the sine wave at the time of generating the compensation signal may be realized, for example, as a sine wave function or a table reference for the position.

[0055] The transfer function from the angular transmission error to the compensation current is represented by Equation (6).

Equation

[0056] Each symbol in Equation (6) is as shown in Equations (7) and (8).

Equation

Equation

[0057] As shown in Equation (6), the transfer function from the angular transmission error to the compensation current is not proper, and generally properization is required for realization. However, in this case, there is a limit to the effect of suppressing the non-uniformity of rotation due to the influence of properization.

[0058] This disclosure utilizes the fact that angular transmission error can be expressed as a sum of sinusoidal waves, and uses a compensation model that has amplitude and phase calculated from frequency response characteristics. By correcting the amplitude and phase used to generate sinusoidal compensation signals of each compensation order using this compensation model, a desired compensation signal is generated. As a result, by correcting the amplitude and phase from frequency response characteristics rather than as a transfer function, properization is not required, and rotational non-uniformity can be suppressed.

[0059] An angle transmission error compensator compensates for the effects of angle transmission errors based on the control system configuration and angle transmission error characteristics, and thus has aspects of feedforward control. It is described as feedforward control because it calculates the compensation signal using motor position and motor speed.

[0060] Furthermore, since this is a feedforward control, the compensation is for the reproducible component of the angular transmission error.

[0061] For the sake of explanation, we are using a transfer function G(s) in the continuous-time domain, but this is not the only way to explain it; it also includes cases where the transfer function G[z] is in the discrete-time domain.

[0062] [effect] As mentioned above, in an angle transmission error compensator, rotational non-uniformity can be suppressed by utilizing frequency response characteristics rather than transfer functions to account for the influence of control system characteristics (characteristics from angle transmission error to compensation current).

[0063] The transfer function from angular transmission error to compensation current can be calculated from the control system configuration, control parameters, and motor characteristics, and can be set based on a clear mathematical formula derived theoretically. Therefore, the optimal parameters can be uniquely derived without the need for trial-and-error adjustments. This streamlines the design process, reduces variability and judgment errors by eliminating reliance on the designer's experience and subjectivity, and enables the construction of a highly reliable angular transmission error compensator in a short period of time.

[0064] Furthermore, it clearly distinguishes between angular transmission error characteristics, which vary from product to product, and control system characteristics, which do not. As a result, the design content and its operation are systematically structured and logically consistent, making it easy to handle at each stage of design, analysis, and maintenance, and resulting in excellent designability and implementability of the control device.

[0065] (Flexibility of control system configuration) [composition] The angle transmission error compensator can accommodate various control system configurations, not just the one shown in Figure 2. Figure 3 is a control block diagram where the compensation addition point is a position command (the compensation signal is added to the position command), and Figure 4 is a control block diagram where the compensation addition point is a speed feedback signal (motor speed) (the compensation signal is added to the speed feedback signal). In each case, the compensation signal is the compensation position command θ. ATEComp , compensation speed feedback signal ω ATEComp In addition, in Figures 3 to 5, including Figure 5 which will be described later, reference numeral 1 represents the controlled object, reference numeral 200 represents the motor, reference numeral 300 represents the reduction mechanism, and reference numeral 400 represents the load, while reference numerals 100_2, 100_3, and 100_4 represent the vibration control devices, respectively. The transfer function used when constructing the compensation model is, in the case of Figure 3, the transfer function from the angular transmission error to the position command. In the case of JPEG0007870027000014.jpg1022, Figure 4, the transfer function from angular transmission error to velocity feedback signal. You should use the filename JPEG0007870027000015.jpg925.

[0066] For example, the transfer function from the angular transmission error to the position command is given by equation (9).

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[0067] The symbols in equation (9) are as follows:

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[0068] When adding the compensation signal to the current command, similar to equation (6), the transfer function is not proper and has the same problems as described above, but it can be compensated similarly. Note that the same applies when the compensation addition point is the speed feedback signal.

[0069] Note that the above relates to the control system structure in position control. However, the present disclosure can similarly configure dynamic angular transfer error compensation for speed control and torque control based on the control system configuration and compensation addition point. Further, it is applicable not only to the configuration of the feedback control system but also to the control system configuration using feedforward control in combination.

[0070] [Effect] Since the uses of systems or devices using a reduction mechanism are various, the preferred control system configurations for systems or devices also vary. For example, in addition to general PID control, I-PD control with a modified derivative term structure, P-PI control, P-IP control, state quantity feedback control based on optimal regulator theory, and further H∞ control considering robustness, etc., various feedback control algorithms can be mentioned.

[0071] According to the present disclosure, a vibration control (suppression of rotational non-uniformity) function can be added based on feedforward control that adds a compensation signal without making a structural change to the existing feedback control system described above. As described above, since the compensation parameters can be set based on clear mathematical formulas derived theoretically, it can be easily applied to various systems. From the perspective of industrial applications, there are cases where it is difficult to modify the existing control system structure from the perspective of achievements and reliability. It has an excellent effect of obtaining a vibration control function while maintaining the existing control system structure.

[0072] (Compensation Model Based on Speed Information) [Configuration] The angle transmission error compensator is configured as a compensation model in which the angle transmission error compensator amplitude and the angle transmission error compensator amplitude phase for each compensation order are set as a linear interpolation lookup table (hereinafter referred to as LUT) based on speed information. For compensation order i, the compensation model has angle transmission error compensator amplitude and angle transmission error compensator phase corresponding to multiple discrete motor speeds.

[0073] The angular transmission error compensator amplitude for each compensation order is shown in equation (12). The same applies to the angular transmission error compensator phase for each compensation order.

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[0074] The symbols in equation (12) are as follows: n i : Number of LUTs for compensation order i ω mil :ith LUT input is the lth motor speed A cil :Angle transmission error compensator amplitude at each l-th compensation order, which is the i-th LUT output.

[0075] For example, it can be set in increments of 200 r / min within the range of 0 to 3000 r / min to match the operating speed range of the system (0, 200, 400, ..., 3000). In this case, n i =16 corresponds to this. In this case, for example, ω m =ω mi2 In the case of A ci (ω m )=A ci2 This is the result. Note that the motor speeds do not need to be at equal intervals. Also, the angular transmission error compensator amplitude and the angular transmission error compensator phase at each compensation order are different n i This may also be done. For example, the number of amplitude LUTs n for compensation order i. iA =20, number of phase LUTs n for compensation order i iφ n can also be set to =10. iThis involves a trade-off between the amount of memory resources needed to store the necessary data and the compensation performance, so the balance between the two can be flexibly adjusted based on the requirements of the control device.

[0076] Specifically, in speed ranges where the corresponding frequency response characteristics change steeply, a balance between compensation performance and computing resources can be considered by setting more closely spaced (or more) motor speeds, and in speed ranges where the corresponding frequency response characteristics change gradually, a looser (or less) motor speed setting can be considered.

[0077] Furthermore, various algorithms exist for LUTs, including not only linear interpolation but also nearest neighbor interpolation, polynomial interpolation, and spline interpolation, so the choice should be made considering implementation constraints. From the viewpoint of the continuity of the compensation signal, it is preferable that the output of the LUT be a continuous output obtained by linear interpolation, but a discrete output method is also acceptable. In addition, if the operating speed exceeds the LUT consideration range (corresponding to extrapolation), the speed may be set to the maximum speed value set in the LUT (corresponding to clipping), or a warning may be issued from a display device or the like to prompt the user to reset the operating speed range.

[0078] Alternatively, another method for realizing the compensation model is to create a regression function (approximation function) for the amplitude and phase of the frequency response characteristics and use it to calculate the angular transmission error compensator amplitude and phase. Alternatively, the frequency response characteristics may be calculated sequentially to calculate the angular transmission error compensator amplitude and phase for each compensation order.

[0079] While the frequency response characteristics are calculated using the control system configuration, control parameters, and motor characteristics, if some or all of these are unknown, compensation parameters may be identified and set experimentally. For example, compensation parameters capable of reducing vibration when operating at a certain constant speed can be identified at multiple operating speeds. In this case, however, the compensation parameters will need to be identified again as the control parameters are adjusted.

[0080] [effect] In this disclosure, multiple configurations or computation methods can be selected as implementation methods for the compensation model, such as LUTs, regression functions, and sequential calculation of frequency response characteristics. The optimal implementation method can be flexibly selected according to the constraints of computing resources and design requirements of the control device. Therefore, this disclosure offers excellent industrial applicability, is easily applicable to various control devices in diverse industrial fields, and provides a compensation method with excellent versatility and scalability.

[0081] (Setting of compensation speed range) [Background and Challenges] Compensation is necessary depending on the operating speed at which rotational non-uniformity becomes a problem due to the effects of angular transmission errors. Furthermore, since the operating speed at which rotational non-uniformity becomes a problem differs depending on the compensation order, compensation that considers a wide range of operating speeds for various situations is preferable. Moreover, while rotational non-uniformity decreases above the operating speed at which resonance occurs, the frequency of the compensation signal becomes high and the amplitude also becomes large, resulting in a large power load relative to the compensation performance, which is undesirable from an energy saving perspective.

[0082] [composition] In an angular transmission error compensator, compensation speed bands may be additionally set to achieve compensation according to the operating speed at which rotational non-uniformity becomes a problem. Specifically, the degree of compensation influence can be set according to the operating speed by multiplying the angular transmission error compensator amplitude at each compensation order of the compensation model by a weighting coefficient. This is equivalent to adjusting (controlling) the effectiveness of the compensation signal according to a predetermined speed range. An example of setting the compensation speed band is shown in equation (13). In this case, for example, ω m =ω mi2 In the case of A ci (ω m )=W ci2 *A ci2 This is the result.

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[0083] The symbols in equation (13) are as follows: W cil: Weighting coefficients for angular transmission error compensator amplitude at each l-th compensation order

[0084] As for the weighting coefficient, for example, it is conceivable to set it to "1" near the operating speed assumed to be in the frequency band where the resonance state occurs, and to "0" everywhere else. Note that the weighting coefficient may be a value other than 1 or 0, and by appropriately setting the weighting coefficient according to the characteristics of the system, it is possible to handle various situations. To avoid compensation at low speeds, for example, the weighting coefficient may be set to "0" below 100 r / min. Similarly, to avoid compensation at high speeds, for example, the weighting coefficient may be set to "0" above the operating speed where vibration becomes a problem. In addition to multiplying the compensation model by the weighting coefficient, a weighting coefficient for the compensation speed band may also be constructed. Note that from the viewpoint of the continuity of the compensation signal, it is preferable for the weighting coefficient to be continuous, but a discrete method is also acceptable.

[0085] [effect] With this configuration, at low speeds, processing is performed that takes into account quantization errors in position detectors such as encoders, discretization errors associated with digital control, and the processing cycle of compensation processing. This makes it possible to prevent minute positioning movements, instability of control in the low-speed range, and excessive effects of compensation.

[0086] Furthermore, by configuring the system to suppress or stop the compensation operation under conditions where rotational non-uniformity is not a problem at high speeds, it is possible to avoid overloading the control device due to excessive compensation signals. This reduces unnecessary calculations and power consumption, enabling high efficiency and stability for the control device as a whole.

[0087] In particular, in a configuration where the compensation model is multiplied by a weighting coefficient, the compensation model based on velocity information and the consideration of the compensation velocity range can be implemented in a single process, making it simple and allowing for efficient use of computing resources.

[0088] (Information used for compensation) [composition] In the example shown in Figure 2, the inputs to the angle transmission error compensator (hereinafter referred to as compensator inputs) are motor position and motor speed, which are actual information derived from measured values ​​from the position detector. However, depending on the configuration of the control device, it may not be possible to use actual information. In such cases, the angle transmission error compensator may use command information (position command, position command speed) instead of actual information in the compensation calculation.

[0089] Figure 5 is a control block diagram when the compensator input is used as command information. In this case, the servo control approximate characteristics are Approximate motor position calculated via JPEG0007870027000021.jpg722 JPEG0007870027000022.jpg716 and approximate motor speed JPEG0007870027000023.jpg718 will be used as the compensator input.

[0090] The following describes in detail the case where position commands are used as position information. To derive an approximate motor position, which is information equivalent to the motor position, we use characteristics that approximate the servo control characteristics of the control device. The servo control approximation characteristics can be, for example, the first-order lag in equation (14) or the dead time element in equation (15). The approximate motor position can be calculated using equation (16) with the respective transfer functions.

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[0091] The symbols in equations (14) through (16) are as follows: ω approx : Estimated angular frequency for servo control, unit is radians per second (rad / s). Lapprox : Estimated dead time for servo control, in seconds (s).

[0092] The P-PI control system, which has the control system configuration shown in Figure 2, can approximate the response globally with the position loop gain, so ω approx =K p It can be done in the same way. The file can be named JPEG0007870027000027.jpg634. The approximate motor speed, which is the speed information, may also be the derivative (difference) of the approximate motor position.

[0093] Servo control characteristics vary depending on the system, and approximation requires consideration of servo control characteristics, operating speed range, control parameter settings, and management. To approximate the characteristics from position command to motor position, it is generally sufficient to determine the configuration of the servo control approximation characteristics and their parameters. For example, the objective function can be the sum of the squared errors or the mean squared error between the motor position and the position command. Alternatively, a curve fitting process of the frequency response characteristics may be used. This curve fitting can be achieved, for example, by estimating parameters using regression methods such as the least squares method based on a predefined transfer function model for the gain characteristics and phase characteristics on the Bode plot. The same applies to speed control and torque control.

[0094] Furthermore, it is necessary to consider the approximation accuracy of the position information and velocity information, which are inputs to the compensator. Errors in position information have a significant impact because they directly affect the period and phase of the sinusoidal compensation signal, while errors in velocity information affect the amplitude and phase values ​​of the compensation parameters, but the impact of errors is smaller compared to that of position information. Therefore, as an approximation characteristic that prioritizes the error of position information, the approximate motor speed may be calculated from the approximate motor position.

[0095] [effect] Depending on the configuration of the control device, it may be difficult to use real information due to physical wiring constraints, or it may be difficult to achieve the desired accuracy due to factors such as the resolution and processing cycle of the obtained information. In this disclosure, the information used for compensation can be flexibly selected according to the control device's requirements, enabling optimal compensation processing according to the system configuration and operating conditions. This makes it possible to apply to a variety of systems with different configuration requirements, improving the design flexibility of the system and expanding its scope of application and practicality.

[0096] (Non-interference with static components) [Background and Challenges] When compensating for rotational non-uniformity, which is a dynamic effect of angular transmission error, there is a problem in that, especially when adding a compensation signal to the position command, if the compensation signal is not set to zero when the system stops, it directly affects the static characteristics of the angular transmission error, leading to a deterioration in positioning accuracy. A similar problem exists when adding a compensation signal to something other than the position command, as it affects the behavior during operation start and positioning.

[0097] [composition] To achieve non-interference with static components, the angle transmission error compensator is configured to correct the compensation signal to zero when the velocity information is zero, i.e., when the system is stopped. Even when the compensation signal is added to components other than the position command, a similar configuration is preferable if it affects the static characteristics. Alternatively, the compensation model may be set so that the compensation signal is zero when the velocity information is zero.

[0098] Specifically, for example, by utilizing the compensation speed range setting, the weighting coefficient corresponding to the case where the motor speed is 0 can be set to 0, or each compensation order amplitude can be multiplied by the sign function sgn(x) (for details of the sign function, see the definition in the part that reflects the rotational direction characteristics).

[0099] [effect] In particular, when a compensation signal is added to a position command, it can lead to a deterioration of positioning accuracy. Therefore, this configuration allows for compensation of the dynamic effects of angular transmission error without affecting the static characteristics of the angular transmission error. Furthermore, by considering this in conjunction with the setting of the compensation speed band using a LUT, multiple functions can be implemented at once, making it simple and efficient use of computer resources. This makes it possible to achieve compensation that clearly distinguishes between dynamic and static compensation. Note that the dynamic compensation described in this disclosure may be used in combination with other static compensation methods.

[0100] (Reflection of rotational direction characteristics) [composition] In the angular transmission error compensator, the amplitude and phase of each compensation order, taking into account the direction of rotation, and the angular transmission error compensator phase at each compensation order are as shown in equations (17), (18), and (19).

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[0101] The symbols in equations (17) through (19) are as follows: A F i : The amplitude of each compensation order during forward rotation; the unit is arcseconds (arc-sec). A R i : The amplitude of each compensation order during reversal, in arc-sec units. φ F i : The phase of each compensation order during forward rotation; the unit is radians (rad). φ R i : The phase of each compensation order during reversal, in units of radians (rad). sgn(x): This is a sign function, defined as +1 when x > 0, 0 when x = 0, and -1 when x < 0. Alternatively, it may be defined as +1 when x = 0. This is to suppress the effects of chattering when the sign of x changes and to clearly correspond to the two values ​​of forward and reverse rotation. The superscript F indicates the characteristic of forward rotation, and the superscript R indicates the characteristic of reverse rotation.

[0102] [effect] Because angular transmission errors have different characteristics depending on the direction of rotation due to their generation principle, effective compensation is possible by considering the direction of rotation. In particular, when considering operation in which the direction of rotation reverses, by configuring it in conjunction with the non-interference with the static component mentioned above, the compensation signal changes continuously and smoothly without requiring complex processing even when the direction of rotation reverses, thus enabling stable operation. Furthermore, since the characteristics of the direction of rotation can be set separately in advance, parameters can be determined easily and efficiently, simplifying adjustment work in the design process, improving the efficiency of the design process, and suppressing rotational non-uniformity.

[0103] (Multiple compensation orders) [composition] As shown in equations (2) to (4), the angle transmission error compensator can support multiple compensation orders, and a compensation model corresponding to each compensation order is constructed. Alternatively, the following configuration, which is a modification of equation (2), may also be used.

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[0104] The symbols in equations (20) through (23) are as follows: ω mCi :ith motor speed, unit is radians per second (rad / s). ω m1 : The motor speed angular frequency relative to the primary, in units of radians per second (rad / s).

[0105] As a single compensation model (corresponding to a compensation model with a first-order compensation), the compensation model is referenced using motor speed and compensation order as equation (23). In contrast to the aforementioned pre-calculation configuration (equation (2)) in which the effect of the compensation order is calculated and stored in advance, this is a sequential calculation configuration (equation (20)) in which the effect of the compensation order is calculated sequentially. Furthermore, the compensation speed band may be set based on speed or based on (angular) frequency. When dealing with multiple compensation orders, the configuration can be simplified by using frequency as the basis.

[0106] [effect] When there are multiple components that dynamically influence the angular transmission error determined by the structure of the reduction mechanism, the configuration of the angular transmission error compensator can be designed according to certain rules without becoming overly complex.

[0107] Furthermore, when the compensation order and the number of lookup tables are large, a flexible configuration can be selected to suit the computing resources available. For example, if there is ample memory resources, a pre-calculation configuration can be used to reduce the sequential calculation process for compensation signal generation. Conversely, if the control unit has sufficient processing power, a sequential calculation configuration can be used to reduce the amount of memory resources used.

[0108] Multiple configurations or calculation methods are available, allowing for flexible selection of the optimal implementation method according to the design requirements and computing resource constraints of the control device.

[0109] Therefore, this disclosure provides a compensation method that is highly industrially applicable, easily applicable to various control devices in diverse industrial fields, and offers excellent versatility and expandability.

[0110] (Moment of inertia under load) [composition] In an angle transmission error compensator, for example, the frequency response characteristics from the angle transmission error to the compensation current can be calculated from the control system configuration, control parameters, and motor characteristics, and the configuration does not require information on the load inertia moment. Furthermore, if the control parameters are changed in accordance with changes in the load inertia moment (for example, gain scheduling), compensation can be achieved by changing the compensation parameters accordingly.

[0111] (Spring constant of the reduction mechanism) [composition] In an angle transmission error compensator, for example, the frequency response characteristics from the angle transmission error to the compensation current can be calculated from the control system configuration, control parameters, and motor characteristics, and the configuration does not require information on the reduction mechanism spring constant.

[0112] [effect] In a two-inertia frame, the vibration frequency and degree of influence of vibration phenomena are determined by the moment of inertia and the (deceleration mechanism) spring constant. However, in this disclosure, compensation parameters can be determined without requiring information on both. Regarding the load moment of inertia, for example, even if the load moment of inertia is unknown, or if the load moment of inertia changes depending on the posture of a vertical or horizontal articulated robot, and the vibration frequency changes, compensation is possible without being affected by this. Furthermore, the spring constant of the deceleration mechanism often has individual product differences, and various measures have been taken to address this, but in this disclosure, vibration damping control can be achieved without being affected by differences in the spring constant or its fluctuations.

[0113] In summary, this disclosure enables the design of an angular transmission error compensator regardless of the load moment of inertia and the reduction mechanism spring constant, thereby improving the efficiency of the design process and suppressing rotational non-uniformity regardless of these characteristics.

[0114] (Load torque compatible) [Background and Challenges] The angular transmission error characteristics may change depending on the load torque applied to the reduction mechanism (gravity torque, acceleration / deceleration torque (torque that drives the load)). For example, in robotic systems, the effect of load torque due to gravity can be significant.

[0115] [composition] To account for the effect of load torque, the angle transmission error compensator uses the load torque τ. l The system is configured to correct the amplitude and phase of each compensation order accordingly. Specifically, equations (24) and (25) are used instead of equations (3) and (4).

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[0116] [effect] Compensation that takes into account the effect of load torque on angular transmission error can be easily configured. The effect of load torque on fluctuations in angular transmission error characteristics can be compensated for, and rotational non-uniformity can be suppressed.

[0117] (Temperature fluctuation compatible) [Background and Challenges] The angular transmission error characteristics may vary depending on the temperature of the reduction mechanism and the ambient temperature surrounding it, as these characteristics are derived from the temperature characteristics of the components of the reduction mechanism.

[0118] [composition] To account for the effects of temperature, the angle transmission error compensator is configured to correct the amplitude and phase of each compensation order according to the temperature information T. Specifically, equations (26) and (27) and subsequent equations are used for equations (3) and (4).

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[0119] [effect] Compensation that takes into account the effect of temperature on angular transmission error can be easily configured. The effect of temperature on fluctuations in angular transmission error characteristics can be compensated for, and rotational non-uniformity can be suppressed.

[0120] (Compensation model configuration) [composition] This section describes an alternative configuration of the angle transmission error compensator, as mentioned in the sections on dynamic angle transmission error compensation and automatic setting of compensation parameters.

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[0121] The symbols in equations (28) through (30) are as follows: A Mi : The integrated amplitude of each compensation order, in amperes (A). φ Mi : The integrated compensation order phases, in units of radians (rad).

[0122] This configuration uses a merged (integrated) compensation model that combines the angular transfer error characteristics and the angular transfer error compensator characteristics. By considering the angular transfer error characteristics when creating the compensation model, the compensation signal calculation can be simplified. This is based on the same concept as the pre-calculation configuration described above.

[0123] [effect] In this disclosure, the implementation method of the compensation model allows for flexible configuration by selecting a configuration according to the available computing resources. For example, if there is sufficient memory resource usage, a pre-calculation configuration can be used to reduce the sequential calculation process for generating compensation signals, and if the control device has sufficient processing power, a sequential calculation configuration can be used to reduce the amount of memory resource usage.

[0124] (Combination of functions) As mentioned above, various factors can be considered when designing an angle transmission error compensator. For example, by appropriately selecting and combining configurations that consider setting the compensation speed band and non-interference with static components, or configurations that consider non-interference with static components, rotational direction characteristics, and support for multiple compensation orders, it is possible to easily configure embodiments that support a variety of functions. Furthermore, multiple functions can be considered collectively as a compensation model, reducing the redundancy of computational processing and enabling efficient use of computing resources.

[0125] These combinations of functions are not mutually exclusive; by appropriately selecting and combining them according to the purpose and constraints of each system, it is possible to efficiently design and implement comprehensive suppression of rotational output errors that take various factors into account in a variety of systems.

[0126] [Numerical example] (Simulation conditions) To verify the operation and effects of this disclosure, a numerical simulation is performed using the configuration shown in Figure 2. The various parameters used in the numerical example are shown in Table 1.

[0127] [Table 1]

[0128] Furthermore, in order to convert the control parameter units from SI units to the processing unit system, a normalization coefficient is considered for the velocity loop gain. JPEG0007870027000043.jpg743, JPEG0007870027000044.jpg736 is the nominal load inertia value, K tn This is the nominal torque constant.

[0129] The compensation parameters were designed under the following conditions: Compensation order i:2 Lookup table count n i :16 Lookup table for a number of minutes Motor speed ω m2l [r / min]: 0, 200, 400, 600, ..., 2800, 3000 (16 equally spaced data points)

[0130] The load speed is expressed as a value multiplied by the reduction ratio, taking into consideration comparison with the motor speed. In this case, the unit is expressed as "Mr / min". The motor position and load position are both values ​​on the load side, expressed in "arc-sec" units. Here, in order to consider the responsiveness of the servo control, the control parameters are evaluated in two ways: "low" and "high" (corresponding to "low" and "high" in Table 1). Hereafter, the low case will be referred to as "low gain setting" and the high case as "high gain setting". In general, control parameters are set according to the rigidity of the device (for example, the spring constant of the reduction mechanism). The higher the responsiveness, the better the tracking of commands and the shorter the settling time, but the more likely vibrations are to occur. Therefore, for example, the parameters are set so that the desired responsiveness is obtained within a range where vibrations do not occur.

[0131] (Constant speed operation) To evaluate the dynamic effects of angular transmission error and the effects of this disclosure, the vibration characteristics during constant-speed operation are evaluated. In constant-speed operation, the vibration characteristics are evaluated by performing an order analysis on the response data of the section in which constant-speed operation is performed after a time has elapsed during which the effects of transient response can be ignored. Hereafter, for example, the second-order component of the order analysis result for the constant-speed section of the motor speed will be referred to as the "second-order component of the motor speed." Here, the characteristics at an operating speed equal to the motor speed set in the LUT are evaluated.

[0132] As a vibration characteristic analysis, the motor is operated at a constant speed at multiple operating speeds (e.g., 1000, 1200, ..., 2400 r / min), and the quadratic components of the motor speed and load speed at each operating speed are extracted from the response data within the constant speed interval. Furthermore, position information is calculated by integral calculation of the speed information within the constant speed interval, and the quadratic components of the motor position and load position are also extracted.

[0133] (Explanation of order analysis content under constant speed operation) Figures 6 and 7 show the motor speed response data and load speed response data in the constant speed section when the motor is operated at a constant speed at multiple operating speeds, while Figures 8 and 9 show the order analysis results of the motor speed and load speed when the operating speed is 1600 r / min, respectively, with a low gain setting and no compensation.

[0134] Figures 6 to 11 show the case with a low gain setting and no compensation. In Figure 6, the horizontal axis represents time and the vertical axis represents motor speed. In Figure 7, the horizontal axis represents time and the vertical axis represents load speed.

[0135] Figures 6 and 7 show that although the operation command is set to a constant speed, periodic speed fluctuations are superimposed on the motor speed and load speed due to the effect of angular transmission errors. In particular, when the operating speed is set to 1600 r / min, the amplitude of the vibration component is shown to be larger compared to other speeds.

[0136] Figure 8 shows the order of the motor speed on the horizontal axis and the order of the motor speed on the vertical axis. Figure 9 shows the order of the load speed on the horizontal axis and the order of the load speed on the vertical axis. Figures 8 and 9 show that the effect is due to the second-order component of the angular transmission error, which was considered in the simulation model.

[0137] In Figures 10 and 11, the horizontal axis represents the operating speed, and the vertical axis represents the extraction results of the second-order component of the motor speed and the extraction results of the second-order component of the load speed at multiple operating speeds, respectively. Figures 10 and 11 show that the degree of influence of equal angular transmission error differs depending on the operating speed, and that the influence of angular transmission error on load speed is significant.

[0138] (Vibration characteristics due to differences in control parameters) Figures 12 to 15 show the characteristics of the motor position quadratic component, load position quadratic component, motor speed quadratic component, and load speed quadratic component under low gain setting, high gain setting, and no compensation (hereinafter referred to as condition A). The solid lines represent the characteristics under low gain setting, the dashed lines represent the characteristics under high gain setting, the horizontal axis represents operating speed, and the vertical axis represents each quadratic component.

[0139] Figures 12 to 15 show that differences occur in each of the secondary components depending on the control parameters, indicating that they are affected by servo control. In particular, when the operating speed is 1600 r / min, the load position is 35.8 arc-sec with low gain setting and 59.0 arc-sec with high gain setting, and the load speed is 27.8 Mr / min with low gain setting and 45.7 Mr / min with high gain setting, showing a difference of 1.6 times and 1.7 times depending on the control parameters.

[0140] (Vibration characteristics with and without compensation (low gain setting)) Figures 16 to 19 show the characteristics of the motor position quadratic component, load position quadratic component, motor speed quadratic component, and load speed quadratic component, respectively, under low gain settings and with or without compensation (hereinafter referred to as Condition B). The solid lines represent the characteristics with compensation, the dashed lines represent the characteristics without compensation, the horizontal axis represents the operating speed, and the vertical axis represents each quadratic component.

[0141] Figures 16 to 19 show that the second-order component of the load position and load speed is reduced to zero by compensation. Furthermore, the motor position and motor speed are shown to have characteristics with a predetermined amplitude due to the compensation. Figure 16 shows that the motor position oscillates at 10 arc-sec, corresponding to the amplitude of the second-order component of the angular transmission error, regardless of the operating speed. This cancels out (compensates for) the effects of the second-order component of the angular transmission error in the load position and load speed. From the second-order components of the load position and load speed shown in Figures 17 and 19, it is clear that this disclosure can effectively compensate for the effects of angular transmission error.

[0142] (Vibration characteristics with and without compensation (high gain setting)) Figures 20 to 23 show the characteristics of the motor position quadratic component, load position quadratic component, motor speed quadratic component, and load speed quadratic component, respectively, under high gain settings and with and without compensation (hereinafter referred to as condition C). The solid lines represent the characteristics with compensation, the dashed lines represent the characteristics without compensation, the horizontal axis represents the operating speed, and the vertical axis represents each quadratic component.

[0143] Figures 20 to 23 show that, similar to the low-gain setting, the load position and load speed have their second-order components reduced to zero by compensation. Furthermore, the motor position and motor speed are shown to have characteristics with a predetermined amplitude due to the compensation. Figure 20 shows that the motor position oscillates at 10 arc-sec, which corresponds to the amplitude of the second-order component of the angular transmission error, regardless of the operating speed.

[0144] Simulation results under conditions A to C clearly demonstrate that the influence of the second-order component of angular transmission error, which exhibits different vibration characteristics depending on the control parameters, can be suppressed.

[0145] (Compensation parameters) Figures 24 and 25 show the amplitude and phase characteristics of the frequency response from angular transmission error to compensation current, with solid lines representing low-gain settings and dotted lines representing high-gain settings. The circles represent the compensation parameters for low-gain settings and the crosses represent the compensation parameters for high-gain settings.

[0146] The amplitude at motor speed = 0 indicates that the amplitude is set to 0 to avoid compensation when stopped in order to achieve non-interference with the static component. Figures 24 and 25 show that the amplitude and phase differ depending on the control parameter in order to compensate for the fact that the angular transmission error has different vibration characteristics depending on the control parameter. This means that once the control parameter is determined, the compensation parameter can be uniquely determined without trial and error. The motor speed and the number of compensation tables to be set in the compensation model may be determined from the amplitude and phase characteristics in the frequency response characteristics shown in Figures 24 and 25. Alternatively, as mentioned above, a regression function may be created for these characteristics.

[0147] (Acceleration and deceleration) As mentioned above, the effect of angular transmission error changes depending on the change in motor speed. Here, we examine the effect of angular transmission error and the effectiveness of this disclosure when the motor speed changes continuously due to acceleration and deceleration. During acceleration and deceleration, we evaluate the vibration characteristics when the effect of angular transmission error changes sequentially with the change in speed. Note that, unlike constant speed operation, it is difficult to evaluate vibration characteristics by order analysis during acceleration and deceleration. Therefore, in order to remove components associated with acceleration and deceleration other than the effect of angular transmission error, the output of the high-pass filter (HPF) shown in equation (31) is used as each vibration component.

number

[0148] The symbols in equation (31) are as follows: ω HPF :HPF cutoff angle frequency, in radians per second (rad / s). o HPF :HPF order Here, ω HPF =2π*5, o HPF =6

[0149] Figures 26 to 31 show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, and load position vibration component, respectively, under low gain settings and no compensation (hereinafter referred to as condition D). The horizontal axis represents time, and the vertical axis represents each component. Note that in the vibration component graphs such as Figure 28, the graphs are solid-colored because continuous vibration is occurring. As an example, an enlarged view of Figure 28 is shown in Figure 123.

[0150] Figures 32 to 37 show the characteristics under high gain setting with no compensation (hereinafter referred to as condition E), Figures 38 to 43 show the characteristics under low gain setting with compensation (hereinafter referred to as condition F), and Figures 44 to 49 show the characteristics under high gain setting with compensation (hereinafter referred to as condition G).

[0151] Since it is difficult to discuss the magnitude of vibration from the motor speed and load speed shown in Figures 26, 27, 32, 33, 38, 39, and 44, 45, the influence of angular transmission error and the effectiveness of this disclosure will be confirmed from each vibration component using the HPF described above.

[0152] In the uncompensated load speed vibration components and load position vibration components shown in Figures 29, 31 and 35, 37, the vibration characteristics due to the influence of angular transmission error change sequentially with differences in operating speed, and the differences in control parameters show a similar trend to the constant speed operation described above. Note that the components around 0 and 10 s in each vibration component are due to the transient response associated with the start of acceleration and deceleration.

[0153] Figures 41, 43 and 47, 49 show the compensated load speed vibration components and load position vibration components, demonstrating that the vibration characteristics associated with changes in operating speed can be suppressed by this disclosure.

[0154] Figures 28, 30, 34, 36, 40, 42, 45, 48 show the motor speed vibration components and motor position vibration components with and without compensation, demonstrating that, even with different control parameters, the effect of angular transmission error at the load position is reduced by vibrating the motor position, similar to the constant speed operation described above.

[0155] From the simulation results under conditions D to G, it is clear that the present disclosure can suppress the effects of vibration even when the operating speed changes continuously.

[0156] (Compensation due to differences in compensation points) The simulation results for the configuration shown in Figure 3, where the compensation addition point is the position command, are shown. Figures 50 to 55 show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, and load position vibration component, respectively, when the compensation addition point is the position command, low gain setting, and compensation is enabled (hereinafter referred to as condition H). The horizontal axis represents time, and the vertical axis represents each component.

[0157] Figures 50 to 55 demonstrate that rotational non-uniformity can be suppressed even when the compensation addition point is a position command.

[0158] Figures 56 and 57 show the amplitude and phase characteristics of the frequency response from the angular transmission error to the compensation position, with the compensation parameters indicated by circles. Note that the amplitude at motor speed = 0 is set to 0 to ensure non-interference with static components and to avoid compensation when stopped.

[0159] Figures 58 to 63 show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, and load position vibration component, respectively, under the configuration of Figure 4, with compensation added at the speed feedback, low gain setting, and compensation enabled (hereinafter referred to as Condition I). The horizontal axis represents the operating speed, and the vertical axis represents each component.

[0160] Figures 58 to 63 demonstrate that equivalent compensation can be achieved regardless of compensation bonus points.

[0161] From the simulation results under conditions H to I, it is clear that compensation points can be flexibly set in this disclosure.

[0162] (Setting of compensation speed range) The simulation results when a compensation speed range is set are shown. Low gain setting, and the compensation summation point is the current command. As an example of compensation only in the resonant operating speed range, the weighting coefficient between 1000 and 2000 r / min was set to "1", and the weighting coefficient at other motor speeds was set to "0". The weighting coefficient for the angular transmission error compensator amplitude is shown in equation (32).

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[0163] Figures 64 to 69 show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, and load position vibration component, respectively, when the compensation summation point is set to current command, low gain setting, and compensation is enabled (hereinafter referred to as condition J). The horizontal axis represents time, and the vertical axis represents each component.

[0164] Compared to Figures 26-31, which do not consider weighting coefficients, Figures 67 and 69, in particular, show that the vibration components at the specified operating speed range are compensated for in the load speed vibration components and load position vibration components, demonstrating that rotational non-uniformity can be suppressed only in that specific operating speed range. Similar trends are observed in the other figures as well.

[0165] From the simulation results under condition J, it is clear that rotational non-uniformity can be flexibly suppressed in a configuration with a set compensation speed range.

[0166] (Configuration using compensator input as command information) The simulation results for the configuration shown in Figure 5, where command information is used as the information for compensation, are shown. Figures 70 to 77 show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, load position vibration component, error between motor position and position command, and error between motor position and approximate motor position, respectively, for the configuration in Figure 5, with the servo control approximation characteristics set to equation (14), low gain setting, and compensation enabled (hereinafter referred to as condition K). The horizontal axis represents time, and the vertical axis represents each component.

[0167] Compared to Figures 26-31, which use actual information (motor position, motor speed), Figures 74 and 75 show that equivalent compensation performance is obtained for the load speed vibration component and load position vibration component.

[0168] The error between the motor position and the position command shown in Figure 76 has a maximum error of approximately -3.2 rad, which corresponds to half a motor rotation. This indicates that simply using the position command as the compensator input will not generate a proper compensation signal.

[0169] Figure 77 shows that the error between the motor position and the approximate motor position is kept small compared to the actual motor position, demonstrating that vibration reduction at load speed and load position is achievable. A similar trend is observed in other figures.

[0170] Figures 78 and 79 show the servo control approximation characteristics using equation (15), low gain setting, and compensation, as well as the load position vibration component and the error between the motor position and the approximation motor position, respectively, with the configuration of Figure 5. The horizontal axis represents time, and the vertical axis represents each component.

[0171] Figures 78 and 79 demonstrate that even with different approximation methods, rotational non-uniformity can be suppressed if the error between the motor position and the approximate motor position is kept small.

[0172] From the simulation results under condition K, it is clear that even in configurations using command information, the present disclosure can suppress rotational non-uniformity.

[0173] (compensation order) The angular transmission error characteristics were investigated under conditions that considered both the second-order and fourth-order components. The fourth-order angular transmission error characteristics were set to A4 = 5 arc-sec and φ4 = -10 deg. The number of lookup tables and the motor speed for each lookup table were set to be equivalent to those for the second-order component. The fourth-order component resonates at approximately 750 r / min (approximately 2.5 s). Note that the low gain setting and compensation summation point are current commands.

[0174] Figures 80 to 85 show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, and load position vibration component for the case without compensation (hereinafter referred to as condition L), Figures 86 to 91 show the case with secondary compensation (hereinafter referred to as condition M), and Figures 92 to 97 show the motor speed, load speed, motor speed vibration component, load speed vibration component, and load position vibration component for the cases of secondary and quaternary compensation (hereinafter referred to as condition N), respectively. The horizontal axis represents time, and the vertical axis represents each component.

[0175] Figures 83 and 85 show that, by considering the fourth-order component, the fourth-order component reaches a resonant state at approximately 750 r / min (approximately 2.5 s), and that the combination of the amplitudes and phases of the second-order and fourth-order angular transmission errors results in a complex vibration waveform. Similar trends are observed in other figures as well.

[0176] Figures 89 and 91 show that even if a fourth-order component exists, the second-order component can be compensated for by the second-order compensation. A similar trend is observed in the other figures as well.

[0177] Figures 95 and 97 demonstrate that non-uniformity of rotation due to both order components can be suppressed by second-order and fourth-order compensation. Similar trends are observed in other figures.

[0178] From the simulation results under conditions L to N, it is clear that even when multiple orders of angular transmission error exist, rotational non-uniformity can be suppressed by compensating for only the second-order component, or for multiple order components such as the second-order and fourth-order components.

[0179] (Load moment of inertia fluctuation) The vibration characteristics during load moment of inertia fluctuations are evaluated. Figure 98 shows the load moment of inertia fluctuation ratio, which is set to decrease in accordance with the acceleration and deceleration operations described above. Note that the low gain setting and compensation addition point are current commands.

[0180] Figures 99 to 104 show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, and load position vibration component, respectively, under the case without compensation (hereinafter referred to as condition O), while Figures 105 to 110 show the motor speed, load speed, motor speed vibration component, load position vibration component, and load position vibration component under the case with compensation (hereinafter referred to as condition P). The horizontal axis represents time, and the vertical axis represents each component.

[0181] Figures 102 and 104 show that the resonant frequency changes due to fluctuations in the load moment of inertia, resulting in a lower operating speed at which resonance occurs. This corresponds to a change in the time period when the vibration reaches its maximum value. Similar trends are observed in the other figures as well.

[0182] Figures 108 and 110 demonstrate that the vibration characteristics associated with load moment of inertia fluctuations can be suppressed by this disclosure, thereby reducing rotational non-uniformity. Similar trends are observed in the other figures as well.

[0183] From the simulation results under conditions O to P, it is clear that even when the load moment of inertia fluctuates, the non-uniformity of rotation can be suppressed by this disclosure without changing the compensation parameters.

[0184] Furthermore, in a configuration where the compensator input is used as command information, when load moment of inertia fluctuations occur, the characteristics from the position command to the motor position change. Therefore, if the effect of load moment of inertia fluctuations is significant, it is necessary to consider load moment of inertia fluctuations in the approximation characteristics. In this case, for example, the approximation characteristics can be changed to match the load moment of inertia fluctuations, or the characteristics can be made to minimize the objective function when the expected load moment of inertia fluctuations occur, or the approximation error in the operating speed range where resonance occurs can be minimized.

[0185] (Difference in reduction mechanism spring constant) To evaluate the vibration characteristics when the reduction gear spring constant differs, the vibration characteristics are evaluated using three different values: nominal, 0.8 times the nominal, and 1.2 times the nominal. Here, the case where the reduction gear spring constant differs is assumed to be due to individual differences in the reduction gear. Note that the low gain setting and compensation addition point are current commands.

[0186] Figures 111 and 112 show the case where the reduction mechanism spring constant is nominal and there is no compensation (hereinafter referred to as condition Q). Figures 113 and 114 show the case where the reduction mechanism spring constant is 0.8 times the nominal and there is no compensation (hereinafter referred to as condition R). Figures 115 and 116 show the case where the reduction mechanism spring constant is 1.2 times the nominal and there is no compensation (hereinafter referred to as condition S). Figures 117 and 118 show the case where the reduction mechanism spring constant is nominal and there is compensation (hereinafter referred to as condition T). Figures 119 and 120 show the case where the reduction mechanism spring constant is 0.8 times the nominal and there is compensation (hereinafter referred to as condition U). Figures 121 and 122 show the case where the reduction mechanism spring constant is 1.2 times the nominal and there is compensation (hereinafter referred to as condition V). Each figure shows the motor position vibration component and the load position vibration component, respectively, with the horizontal axis representing time and the vertical axis representing each component.

[0187] Figures 111 to 116 show that the resonant frequency changes due to the different spring constants of the reduction gear mechanism, resulting in different operating speeds at which resonance occurs. This corresponds to a change in the time period when the vibration reaches its maximum value. Furthermore, the peak value also changes along with the change in vibration frequency.

[0188] Figures 117 to 122 demonstrate that the vibration characteristics resulting from different spring constants in the reduction gear mechanism can be suppressed by this disclosure.

[0189] From the simulation results under conditions Q to V, it is clear that even when the spring constants of the reduction mechanism differ, the non-uniformity of rotation can be suppressed by this disclosure without changing the compensation parameters.

[0190] Furthermore, in configurations where the compensator input is used as command information, if the fluctuation in the reduction mechanism spring constant has a significant impact, the same measures as those for load inertia moment fluctuations will be necessary.

[0191] Figure 124 is a flowchart of a vibration damping control program in a servo control system equipped with a reduction mechanism.

[0192] Step S1: Initial setup. Perform the initial settings necessary for executing the vibration control program. This includes initial settings for the predetermined compensation order, amplitude, and phase for generating the compensation signal. Dynamic angle transmission error compensator (C ATE The compensation model referenced by (for example, the lookup table) reads amplitude and phase information corresponding to each compensation order, rotation direction, etc. These compensation parameters may be configured to automatically set the amplitude and phase according to the frequency or compensation order corresponding to a predetermined speed range based on the servo control system configuration, control parameters, and motor characteristics that target at least one of the motor position, speed, and current, and to be registered in the compensation model.

[0193] Step S2: Information acquisition. The system acquires the current position information of the controlled object (e.g., motor position or position command) and the current speed information of the controlled object (e.g., motor speed or position command speed). This information can be used by selecting either real-world information (motor position / motor speed) or command information (position command / position command speed).

[0194] Step S3: Amplitude and phase correction. Based on the speed information acquired in step S2, the amplitude and phase of the compensation signal are determined and corrected by referring to the compensation model. The dynamic angular transmission error compensator is configured so that the compensation signal is 0 when the speed information is 0, so adjustments are made so that the compensation signal is 0 when stopped (when the speed information is 0). The compensation model may be set to correct the compensation signal using a weighting coefficient that controls the effectiveness of the compensation signal according to a predetermined range of speed information. Consideration is given to generating the compensation signal from a preset amplitude and phase according to the rotation direction of the motor. If necessary, sinusoidal compensation signals are generated for each compensation order based on preset amplitude and phase for each different compensation order, and these are added together to generate a compensation signal. The compensation signal is corrected by referring to the compensation model regardless of the inertia of the load connected to the output shaft of the reduction mechanism with respect to rotation. The compensation signal is also corrected by referring to the compensation model regardless of the spring constant of the reduction mechanism. It is also possible to correct the compensation signal according to the load torque acting on the reduction mechanism. Furthermore, it is also possible to correct the compensation signal according to the temperature of the reduction mechanism, the temperature around the reduction mechanism, or the temperature assumed based on the operating conditions.

[0195] Step S4: Compensation signal generation. A sinusoidal compensation signal is generated based on the compensation order set in step S1, the amplitude and phase corrected in step S3, and the position information acquired in step S2. The sinusoidal wave can be realized as a sinusoidal function or by using a table reference to the position.

[0196] Step S5: Signal addition. The compensation signal generated in step S4 is added to either the position command, speed command, current command, or a control signal associated with these. According to the source, the compensation addition point is often the current command value because compensation is performed regardless of the control mode (position control, speed control, torque control). However, this compensation method can be implemented with any control system configuration, and the compensation addition point does not have an essential meaning; it is an element that can be designed according to the characteristics of the system. It has been confirmed that adding to the position command or speed feedback also yields a similar compensation effect.

[0197] Step S6: Servo control. A servo control system equipped with a reduction mechanism performs its operation based on a control signal to which a compensation signal has been added. This compensates for rotational non-uniformity caused by the angular transmission error of the reduction mechanism, resulting in a vibration damping effect.

[0198] [Summary of vibration control effects] As described above, this disclosure shows that when compensating for rotational non-uniformity due to the effects of angular transmission errors, the influence of various factors such as motor speed and parameter settings within the control device (e.g., various gains in feedback control) can be taken into consideration. This makes it possible to compensate for individual differences in the reduction mechanism and variations in operating conditions. Furthermore, even if the configuration and control method of the control device that implements the compensation are diverse, flexible compensation suitable for each configuration is possible, and adjustments can also be made according to the constraints of computer resources. Moreover, it is clear that the design and adjustment of control parameters of the control device that take various factors into consideration are easy.

[0199] [Estimation of angular transmission error characteristics using a reaction force estimation observer] (Understanding the characteristics of angular transmission error) The following terms are used in the context of control engineering. In the field of control engineering, the term "estimation" is widely used to describe the estimation of system state variables, and is particularly common in technologies such as observers. On the other hand, "identification" is often used to describe methods for clarifying system parameters.

[0200] On the other hand, the term "identification" in general understanding can give the impression that a parameter is definitively determined. In the field of control engineering, "identification" is often used even for parameters that change sequentially, but in this disclosure, in order to facilitate technical understanding, the term "estimation" is used to clarify the meaning of an estimated value that includes uncertainty.

[0201] The technical background of this disclosure is explained below. As mentioned above, the angular transmission error is affected by assembly errors, and its characteristics are determined at the stage when various robots and devices are assembled, and there are individual differences in the products. Therefore, in order to understand the angular transmission error characteristics, after assembling various robots and devices, for example, the motor position and load position are measured, and the characteristic is determined using the reduction ratio and a defining formula.

[0202] On the other hand, various robots and devices using reduction gears generally employ a semi-closed control system that controls the output of the reduction gear using a motor position encoder at the motor end. In some research applications, a load position encoder may be incorporated to enable fully closed-loop control, but due to cost, size, and other factors, load position encoders are not commonly installed.

[0203] Furthermore, industrial robots and collaborative robots sometimes incorporate force sensors in their end-effectors and torque sensors in each joint to achieve force control. By measuring the load torque from the torque sensors in each joint, the angular transmission error can be indirectly calculated. However, understanding the angular transmission error characteristics requires conversion from the torque dimension to the position dimension, which can be difficult to achieve with high accuracy. Note that torque sensors are not installed in each joint if they are integrated with the reduction mechanism, or in devices that do not require force control, as torque sensors are not necessary and therefore are not installed.

[0204] When considering how to determine angle transmission errors, similar to load position encoders, sensor implementation is often difficult due to industrial constraints such as device size, cost, and wiring.

[0205] Given the above background, it is difficult to directly measure angular transmission errors in various robots, etc. Therefore, angular transmission errors can sometimes be measured or identified indirectly by measuring the robot's tip using separate measuring instruments (e.g., laser trackers, laser distance sensors, camera systems, acceleration sensors, inertial measurement units (IMUs)). On the other hand, the need for separate measuring instruments can pose challenges in terms of handling and cost. Furthermore, if the reduction mechanism is replaced due to a malfunction, on-site measurements are necessary, but this can be time-consuming and costly, and the environment may not be suitable for measurement due to lack of space or other factors.

[0206] Another aspect of this approach involves proposing methods for estimating and compensating for angle transmission errors without requiring separate measuring instruments (external sensors), but these methods sometimes fail to provide sufficient compensation.

[0207] Furthermore, there are two aspects to consider: understanding the angular transmission error characteristics and understanding the parameters for compensating for the effects of angular transmission error. In dynamic angular transmission error compensation, these two aspects coincide, so here, it is expressed as understanding the angular transmission error characteristics.

[0208] As described above, various situations exist, but there are four main patterns for understanding angular transmission error characteristics: (pre-)measuring, trial and error exploration, using identification algorithms, and using optimization algorithms.

[0209] Furthermore, in the case of pre-measurements, the angular transmission error characteristics may change due to the influence of assembly errors. Also, even with pre-measurements, experimental exploration, identification algorithms, and optimization algorithms, setting appropriate parameters requires a considerable amount of time, resulting in high adjustment costs during the design phase and implementation.

[0210] On the other hand, since angular transmission errors vary from product to product, there are cases where, for example, if the impact of angular transmission errors is small, it may be desirable to reduce the effort and cost by not even attempting to identify them. Therefore, a method for calculating evaluation indicators to determine the magnitude of the impact of angular transmission errors is necessary.

[0211] (Estimation of Angular Transmission Error Characteristics) To supplement the technical background of the present disclosure, the following describes methods related to measurement and estimation in the prior art. Fig. 125 shows a control block diagram of angular transmission error characteristic estimation. In Fig. 125, reference numeral 30 denotes an angular transmission error measuring device, reference numeral 31 denotes an angular transmission error estimator, and reference numeral 32 represents a feedback control system. Each symbol is as follows. θ * m: Position command θm: Motor position θ l : Load position i ref : Current command C(s): Feedback compensator R: Reduction ratio K t : Torque constant J m : Motor inertia moment D m : Motor damping coefficient J l : Load inertia moment D l : Load damping coefficient K g : Spring constant of the reduction mechanism D g : Damping coefficient of the reduction mechanism θ Sync : Angular transmission error ATE Mea.: Angular transmission error measuring device 30 ATE Est.: Angular transmission error estimator 31

[0212] In actuality, not only the viscous friction term due to the influence of the damping coefficient but also effects such as Coulomb friction are involved, but here they are omitted for simplicity of explanation. Also, delay elements such as the current control system are omitted.

[0213] Angular transmission error measurement is, for example, to measure the motor position θm and the load position θ l and, using the definition formula θ Sync =θ l -θ mCalculated from / R

[0214] On the other hand, the angle transmission error estimation is performed using the motor position θm and the current command i ref Measure the angular transmission error θ Sync Let's consider estimating this. The current command affected by angular transmission error is modeled below.

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[0215] The angle transmission error characteristic estimation is given by A in equation (1). k and φ k This is estimated using equation (33). Note that motor speed may be used, or current command and motor speed may be used in combination. The effect of angular transmission error on the current command, and the estimation of angular transmission error from the current command, can be expressed as follows.

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[0216] As shown in Figure 125, in the transfer function from angular transmission error to current command, in addition to the feedback compensator and motor characteristics, J l ,D l ,K g ,D g ,D m The following information (hereinafter referred to as "information required for analysis") is necessary.

[0217] In this estimation principle, the behavior of the reduction mechanism and the load side are considered as disturbance components on the motor side and detected as a component (current command) to compensate for them. Therefore, for example, it is preferable that the effect of angular transmission error appears in the current command when operating in the operating speed range where resonance occurs. In this estimation principle, the controlled object is defined as consisting of a two-inertia model and angular transmission error, and the angular transmission error characteristics are estimated assuming that everything except the angular transmission error is known. Therefore, when considering the estimation of angular transmission error characteristics, the error in the information required for analysis directly affects the estimation accuracy. In other words, accurate understanding of the information required for analysis is necessary for estimating angular transmission error characteristics.

[0218] On the other hand, it is known that various damping coefficients, in particular, are affected by individual differences and temperature characteristics, making it difficult to understand their properties.

[0219] As described above, analytical angle transmission error characteristic estimation faces the practical challenge of accurately grasping the necessary information for analysis. Based on the above, this disclosure presents an angle transmission error characteristic estimation method that takes this perspective into account.

[0220] Figure 126 shows a schematic diagram of an embodiment for estimating and compensating for angular transmission error characteristics in this disclosure. As shown in Figure 126, the vibration control device 100_5 comprises a servo control system 10, an angular transmission error compensation unit 11, a state estimation processing unit 12, an evaluation index calculation unit 13, and an optimization processing unit 14. The servo control system 10 is, for example, the feedback control system shown in Figure 2, and consists of position proportional control, velocity proportional integral control, and a filter, and outputs a drive current to the motor. The angular transmission error compensation unit 11 generates a compensation signal to compensate for the angular transmission error in the servo control system 10. The state estimation processing unit 12 is configured, for example, as a reaction force estimation observer as shown in Figure 127, which will be described later, and calculates an estimated disturbance. The evaluation index calculation unit 13 uses the estimated disturbance as an evaluation signal and is configured, for example, as a lock-in amplifier as shown in Figure 128, which will be described later, and calculates an evaluation index. The angular transmission error estimation device 35 consists of the state estimation processing unit 12 and the evaluation index calculation unit 13, and estimates the angular transmission error characteristics. The optimization processing unit 14 optimizes the amplitude and phase used by the angle transmission error compensation unit 11 by using methods such as random search, gradient descent, Bayesian optimization, and genetic algorithms to optimize at least one of the objective function defined based on the evaluation index or evaluation signal. Alternatively, the system may be configured to manually search (adjust) through trial and error instead of using the optimization processing unit 14. The angle transmission error compensation unit 11 is, for example, a dynamic angle transmission error compensation unit, which generates a compensation signal that compensates for the rotational non-uniformity of the angle transmission error. The vibration control device consists of an angle transmission error estimation device 35, an angle transmission error compensation unit 11, and an optimization processing unit 14, which compensate for the rotational non-uniformity of the angle transmission error. Hereinafter, the angle transmission error compensation unit 11, state estimation processing unit 12, evaluation index calculation unit 13, optimization processing unit 14, and angle transmission error estimation device may be simply referred to as the angle transmission error compensation unit, state estimation processing unit, evaluation index calculation unit, optimization processing unit, and angle transmission error estimation device.

[0221] (Estimation of angular transmission error characteristics by reaction force estimation observer) The following describes the relevant technical background and the approach to estimating angular transmission error characteristics to aid in understanding this disclosure, followed by the logical background leading to the configuration of the embodiments of this disclosure. Furthermore, the effectiveness of the angular transmission error characteristic estimation in this disclosure will be quantitatively demonstrated by numerical simulations described later.

[0222] The terms used in this disclosure are defined as follows: An evaluation index refers to a value used to quantitatively assess the degree to which an objective has been achieved. Various methods exist for calculating evaluation indexes, and the appropriate method is selected depending on the equipment and operating environment. An objective function is a function defined using evaluation metrics to determine a particular optimization target (e.g., parameters, structure, processing conditions). An optimization method refers to a computational technique that searches for or determines the optimal combination of parameters or structure, for example, to minimize or maximize the value of an objective function. It includes not only determining the exact optimal value, but also iteratively or exploratory processing to improve the value of an evaluation metric or objective function. Angular transmission error characteristic estimation refers to the estimation of angular transmission error characteristics, including the estimation of the degree of influence of angular transmission error (the degree of influence of the difference between the actual angular transmission error characteristics and the angular transmission error characteristics used for compensation).

[0223] As an example of a specific configuration for estimating angular transmission error characteristics, Figure 127 shows a block diagram of the angular transmission error characteristic estimation by the Reaction Force Observer (RFOB), which is the state estimation processing unit 33. In Figure 127, reference numeral 32 denotes the feedback control system, and reference numeral 33 denotes the state estimation processing unit (reaction force observation observer). Plant: A controlled object consisting of delay elements such as motors, reduction mechanisms, loads, and current control systems. τ re : Reaction torque RFOB: Reaction Force Estimation Observer K tn : Nominal torque constant J mnNominal motor moment of inertia Delay n : Nominal delay elements in current control systems, etc. F: Reaction force estimation filter τ^ d Estimated disturbance (estimated torque of reaction force)

[0224] The notation indicates that the dynamic angle transmission error compensation is added to the current command. Furthermore, the control system includes delays from current control systems, etc., as part of the control target.

[0225] Focusing on the dynamic angular transmission error compensation mentioned above, the influence of the compensation-order angular transmission error can be reduced to zero, thereby reducing vibration at the load position. In this state, the torque that drives the load and the reaction torque to the motor does not include the influence of the compensation-order angular transmission error. Specifically, the reaction torque τ in Figure 127 re However, this means that the effect of the compensation order's angular transmission error is not included. Therefore, if it is found that the effect of the compensation order's angular transmission error on the reaction torque is zero, then the angular transmission error characteristics used for dynamic angular transmission error compensation will match the angular transmission error characteristics of the controlled object, and the angular transmission error characteristics can be estimated.

[0226] Reaction torque is an internal state variable of the controlled object and is not usually measured. However, as mentioned above, there are cases where a torque sensor is installed and it is measured directly. As a method for estimating reaction torque without a torque sensor, a reaction force estimation observer is known. The reaction force estimation observer estimates the reaction force by separately modeling various disturbance components and subtracting them from the estimated value, and is mainly used to realize force (torque) control. For example, it is a method for estimating the force (reaction force or reaction force) applied to the tip of a robot arm. For details on the reaction force estimation observer, please refer to Non-Patent Documents 1 and 2. In the calculation process of the reaction force estimation observer, an "estimated disturbance" is calculated which includes various components such as the torque driving the load, the reaction torque, the friction torque, and the torque due to the effect of angular transmission error.

[0227] This disclosure considers the estimation of angular transmission error characteristics using estimated disturbances in a reaction force estimation observer. Estimated disturbances are torque dimension (acceleration dimension) information, and angular transmission error is position dimension information. Therefore, conversion is necessary to estimate angular transmission error characteristics, and simply obtaining estimated disturbances is insufficient. Furthermore, as mentioned above, estimated disturbances include the influence of various disturbance components, so some kind of ingenuity is necessary to estimate angular transmission error characteristics.

[0228] Based on the above, when considering the use of a reaction force estimation observer for estimating angular transmission error characteristics, the following two points present significant challenges. These two challenges also apply when a torque sensor integrated with the reduction mechanism is installed. Task 1: Equivalent processing for conversion from torque dimension to position dimension Task 2: Extraction of angular transmission error characteristics from estimated disturbances.

[0229] In this disclosure, the degree of influence of angular transmission error can be grasped by using the harmonic components of the estimated disturbance on motor rotation as an evaluation index. Furthermore, in this disclosure, the angular transmission error characteristics are estimated by performing dynamic angular transmission error compensation so that the value of the above evaluation index is set to 0, based on the characteristics of the dynamic angular transmission error and the reaction force estimation observer.

[0230] In this disclosure, to address Problem 1, dynamic angular transmission error compensation is utilized. When the influence of the compensation order of the angular transmission error in the estimated disturbance is zero, the angular transmission error characteristics used in dynamic angular transmission error compensation can be considered as the angular transmission error characteristics of the controlled object, making it possible to estimate the angular transmission error characteristics. By utilizing dynamic angular transmission error compensation, it is possible to indirectly estimate the angular transmission error characteristics without the need for direct conversion. Furthermore, although the details of the reaction force estimation observer design will be described later, both dynamic angular transmission error compensation and the reaction force estimation observer do not require analytical information for their design, thus indirectly solving Problem 1.

[0231] Furthermore, for problem 2, the estimated disturbance during constant-speed operation corresponding to the vibration frequency is used. Since the effect of angular transmission error can be considered as a constant frequency during constant-speed operation, the frequency component corresponding to the effect of angular transmission error in the Fourier analysis result of the estimated disturbance during constant-speed operation is used as the evaluation index. Then, using the Fourier analysis result of this estimated disturbance as the evaluation index, the angular transmission error characteristic used in dynamic angular transmission error compensation, where the effect of the compensation order of angular transmission error in the estimated disturbance becomes zero, becomes the angular transmission error characteristic of the controlled object. Note that, similar to the analytical angular transmission error characteristic estimation method, it is preferable that the effect of angular transmission error appears in the current command, for example, in the operating speed band where the resonance state occurs.

[0232] It should be noted that, unlike analytical angle transfer error characteristic estimation methods, it is not possible to definitively estimate the angle transfer error characteristics. Therefore, the angle transfer error characteristics can be estimated either by manually searching (adjusting) through trial and error using an evaluation index or an objective function defined based on the evaluation index, or by automatically estimating them using various optimization methods, such as random search, gradient descent, Bayesian optimization, or genetic algorithms. In determining the angle transfer error characteristics, the optimization process may be performed within the device, or an external computing device may be used to perform the optimization process, and the resulting angle transfer error characteristics may be set. In either configuration, the angle transfer error characteristics are determined based on an evaluation index or objective function. It should also be noted that it is possible to estimate the angle transfer error characteristics even when operating at a constant speed, and details of the relevant evaluation index will be described later.

[0233] Next, the configuration of the reaction force estimation observer will be described. A typical reaction force estimation observer is configured using a model of the moment of inertia that integrates the motor, reduction mechanism, and load. In contrast, this disclosure is characterized by configuring the reaction force estimation observer based on motor characteristics. One advantage of this is that it can be configured without requiring information on the load moment of inertia or the reduction mechanism spring constant, even in the design of dynamic angle transmission compensation. Furthermore, although it is possible to model and utilize the necessary information for analysis, including the load moment of inertia and the reduction mechanism spring constant, configuring it based on motor characteristics reduces the difficulty and effort required for modeling. In addition, motor characteristics can be easily obtained from nominal values ​​in catalogs, etc., and various methods for estimating them as needed are known, making it relatively easy to reduce parameter errors. It should be noted that reaction force estimation observers are often configured to feed back estimated disturbances, but in this disclosure, similar to dynamic angle transmission error compensation, estimated disturbances are not fed back in order to realize angle transmission error characteristic estimation without changing the existing feedback control system C(s). As mentioned above, the estimated disturbance includes the influence of various components, so it may be configured to remove unwanted components other than the effect of angular transmission error, similar to a normal reaction force estimation observer.

[0234] The estimated disturbance can be calculated as shown in equations (36) to (38) below, and if the parameter error is small, the reaction torque can be estimated as if it were filtered through the reaction torque estimation filter F.

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[0235] The reaction force estimation filter F is a second-order system of equation (39) shown below, in order to make the reaction force estimation observer proper.

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[0236] The estimated disturbance must include a vibration frequency component corresponding to the estimated order, taking into account the influence of the control system characteristics. Therefore, the reaction force estimation filter is designed to include the above vibration frequency component. For example, it should be set to a frequency band corresponding to the operating speed band considered in dynamic angle transmission error compensation, or approximately twice the vibration frequency. While it is necessary to take into account the influence of the motor encoder resolution, control period, operating pattern, noise, etc., the design difficulty is not as high as that of a normal reaction force estimation observer because the estimated disturbance is not directly fed back. The design of the reaction force estimation observer is closely related to that of the disturbance observer, and for design methods, please refer to, for example, Non-Patent Document 3.

[0237] While reaction force estimation observers are often configured as a first-order system using velocity information, this example shows a configuration using position information, assuming the absence of velocity feedback. Therefore, if velocity information is available, a configuration based on a general disturbance observer may be used instead of this one. Furthermore, the reaction force estimation observer may be configured using current values ​​instead of current commands, and the observational information used in the reaction force estimation observer can be composed of various elements such as current commands, current values, motor position, and motor speed.

[0238] Furthermore, estimated disturbances may be estimated using various state estimation methods such as Luenberger observers, disturbance observers, and Kalman filters. Depending on the configuration of the existing feedback control system, the estimated disturbances may be estimated by extending various state estimation methods. Specifically, in systems where the effects of disturbances are a problem, if a feedback control system utilizing a disturbance observer is configured, the estimated disturbances may be used in the calculation of the evaluation index of this disclosure. Also, if a feedback control system utilizing a Kalman filter is configured to address noise effects or achieve optimal control, the estimated disturbances may be considered in the state variables to be estimated during the design process. These are merely representative examples, and appropriate selections should be made depending on the configuration and application of the device.

[0239] If the torque driving the load during the estimated disturbance (acceleration / deceleration torque) and the effects of friction characteristics cannot be ignored, the system is configured to remove unwanted components using filtering such as low-pass or high-pass filters. Filtering may be performed in conjunction with various state estimation methods, or it may be performed when calculating evaluation metrics.

[0240] Furthermore, if a torque sensor is installed, a configuration is possible in which the torque sensor detection value is used as a substitute for the reaction force estimation observer. In this case as well, the challenges of estimating the angular transmission error characteristics using reaction force torque—conversion from torque dimension to position dimension and extraction of angular transmission error characteristics from reaction force torque—can be achieved through dynamic angular transmission error compensation. Here, an example of a torque sensor has been described in order to directly correspond to the reaction force estimation torque, but if sensors such as an acceleration sensor or an inertial measurement unit (IMU) are installed, the angular transmission error characteristics can be estimated by performing dynamic angular transmission error compensation to set the value of the harmonic components with respect to motor rotation in the various signals to 0, as in this disclosure. Alternatively, various sensor information may be used as observation information for the state estimation method.

[0241] Dynamic angular transmission error compensation requires understanding the angular transmission error characteristics, control system structure, and control parameters to determine the compensation parameters. The above method estimates the angular transmission error characteristics, which are difficult to understand, assuming the control system structure and control parameters are known. However, by utilizing this disclosure, it is possible to experimentally determine the compensation parameters necessary for dynamic angular transmission error compensation even when the control system structure and control parameters are unknown.

[0242] Here, Estimation 1: When estimating the angular transmission error characteristics under conditions where the control system structure and control parameters are known, Estimation 2: When estimating compensation parameters in a situation where the control system structure and control parameters are unknown, This section will describe the characteristics of both methods, including dynamic angular transmission error compensation. As mentioned above, Estimation 1 estimates the angular transmission error characteristics based on equation (2). On the other hand, Estimation 2 estimates the compensation parameters, including the control system structure and control parameter characteristics, based on equation (28).

[0243] Given the advantages of dynamic angular transmission error compensation, which clearly considers the influence of the control system structure and control parameters, it is preferable to implement it as Estimation 1, which estimates only the angular transmission error characteristics. On the other hand, for example, when a servo system is configured by combining commercially available products, the control system structure and control parameters may be unknown. In this case, Estimation 2 can be used to estimate compensation parameters including angular transmission error characteristics, and the non-uniformity of rotation due to the influence of angular transmission error can be compensated by dynamic angular transmission error compensation. In the case of Estimation 2, for example, compensation parameters that can reduce vibration when operating at a certain constant speed can be estimated at multiple operating speeds. In this case, if the control parameters are adjusted, it will be necessary to re-estimate the compensation parameters.

[0244] Since angular transmission errors have characteristics that differ depending on the direction of rotation, the estimation of angular transmission error characteristics is performed separately for forward and reverse rotation.

[0245] This disclosure estimates angle transmission error characteristics through dynamic angle transmission error compensation. However, the dynamic angle transmission error, the calculation of estimated disturbances by the reaction force estimation observer, and the calculation of evaluation metrics are all independent processes and do not necessarily need to be operated synchronously within the same processing cycle. In particular, the calculation of estimated disturbances by the reaction force estimation observer and the calculation of evaluation metrics may be implemented as offline processes, and the processing cycle and timing can be flexibly configured according to the device configuration.

[0246] Furthermore, while dynamic angular transmission error compensation was used in conjunction with the angular transmission error characteristic estimation by the reaction force estimation observer, it is also possible to apply known configurations described in prior art documents, etc., as the angular transmission error compensation method, and is not limited to dynamic angular transmission error compensation. Therefore, the parameters that determine the output of each compensation method (corresponding to the compensation signal in the case of dynamic angular transmission error compensation) may be manually explored (adjusted) through trial and error using an evaluation index or an objective function defined based on the evaluation index, or optimization may be performed by utilizing various optimization methods.

[0247] [effect] According to this disclosure, by utilizing a reaction force estimation observer, the influence of angular transmission error can be quantitatively grasped from evaluation indicators without requiring additional sensors such as load position encoders, torque sensors, and laser distance sensors, which are particularly problematic in semi-closed control. Furthermore, by utilizing dynamic angular transmission error, the characteristics of angular transmission error can be grasped. The collaborative action of the reaction force estimation observer in the state estimation process and the calculation of evaluation indicators for the influence of angular transmission error enables a configuration that does not require additional sensors. In addition, by configuring the reaction force estimation observer based on motor characteristics, similar to dynamic angular transmission error compensation, the number of design parameters can be reduced, eliminating the need to model parameters in advance and streamlining the design process. By utilizing various optimization methods with an objective function based on evaluation indicators, angular transmission error characteristics can be automatically estimated. Therefore, this disclosure has excellent industrial applicability and can be easily applied to various control devices in diverse industrial fields, including existing equipment, and has excellent effects such as simplifying equipment, reducing costs, and facilitating introduction and maintenance.

[0248] (Angle transmission error characteristic estimation evaluation index) This section describes the evaluation metrics used to estimate angular transmission error characteristics. Evaluation metrics can be broadly classified into offline processing and online processing, and each will be explained. Offline processing refers to a processing method in which the data to be processed is collected and stored in advance, and then analyzed and parameter estimated all at once, meaning that detailed analysis and optimization can be performed without time constraints. Online processing refers to a processing method in which the data to be processed is input sequentially, and processing is carried out quickly, and the results are immediately reflected in control and decision-making.

[0249] (Evaluation metrics based on offline processing) Here, we will discuss two representative methods for calculating evaluation metrics based on offline processing. • Fourier transform during constant-speed operation ·Vibration order analysis (during variable speed operation)

[0250] As mentioned above, the Fourier transform for constant-speed operation allows for the calculation of evaluation metrics simply because the effect of angular transmission error can be considered as a constant frequency. An example of an evaluation metric for variable-speed operation, vibration order analysis, involves estimating and interpolating the phase angle according to the rotational speed, and then applying a short-time Fourier transform to map the amplitude of each order component onto the rotational speed axis. This process makes it possible to visually and quantitatively grasp the frequency characteristics of vibrations associated with changes in rotational speed. A concrete example of implementation is the rpmordermap function from MathWorks, which is described in Non-Patent Document 4.

[0251] While the evaluation metrics in this disclosure are not limited to a specific algorithm, it is preferable to use the Fourier transform under constant speed operation from the viewpoint of processing content and analysis accuracy.

[0252] (Evaluation metrics based on online processing) Here, we will discuss three representative methods for calculating evaluation metrics based on online processing. • Synchronous detection: Lock-in amplifier (LIA) DFT: Goertzel method • Bandbus filter

[0253] A lock-in amplifier, an example of synchronous detection, is a device or algorithm for accurately measuring very weak signals, capable of detecting the amplitude and phase of specific known frequency components. It has the advantage of being able to extract the target signal through "synchronous detection" even in noisy environments. The Goertzel method is an algorithm for efficiently calculating only specific frequency components of the Discrete Fourier Transform (DFT). It calculates the inner product of sine waves using a recursive difference equation. A bandpass filter is a filter used to extract frequency components in a specific frequency band.

[0254] As mentioned above, the estimated disturbance is composed of various components, so here we will outline a method using a lock-in amplifier with excellent noise immunity. In a lock-in amplifier, the target signal becomes a DC component when the dot product of the target signal and the reference signal is obtained, and the other components become high-frequency components. A low-pass filter is used to remove the high-frequency components, extracting the target component and calculating its amplitude.

[0255] Figure 128 shows a block diagram of the lock-in amplifier, which is the evaluation index calculation unit 34 for calculating the evaluation index. The target signal is used to estimate the disturbance τ^ d By using the reference signal as a sine wave and cosine wave corresponding to the compensation order component of the angular transmission error (exemplified as the second-order component in Figure 128), and calculating the amplitude A from the signal passed through a low-pass filter (LPF), the value of the compensation order component can be obtained. The dot product of the target signal (the second-order component in the estimated disturbance) and the reference signal can be calculated as follows.

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[0256] Since the target signal components are a DC component (in this case, a component independent of θm) and a high-frequency component (in this case, 4θm), the LPF can be used to extract only the DC component and calculate its amplitude. The LPF should be designed taking into account the frequencies of the harmonic components. Furthermore, since the evaluation metric only needs to be able to determine the magnitude of the effect of the compensation order angle transmission error, only the amplitude needs to be known.

[0257] (Effects on evaluation indicators) [effect] The evaluation metrics used in this disclosure have multiple embodiments for both offline and online processing, and these can be appropriately selected or combined depending on the situation. The above are merely representative examples, and can be appropriately selected or combined depending on the configuration and application of the device. Therefore, the optimal implementation method can be flexibly selected according to the constraints of computing resources and design requirements of the control device, and parameter estimation can be performed flexibly and effectively without being limited to a specific method. For this reason, this disclosure has excellent versatility, as it can flexibly respond to diverse device situations and is easily applicable to various control devices in diverse industrial fields.

[0258] (Numerical example) In the following sections, the operation of the characteristic components of this disclosure will be quantitatively evaluated through numerical simulations, and their usefulness will be objectively demonstrated. The simulation conditions will be the same as those for the dynamic angular transmission error compensation described above. As mentioned above, in this case, the resonant vibration is maximum at 1600 r / min, so the simulation will be performed as constant-speed operation at 1600 r / min. The system will accelerate to 1600 r / min in 0 to 0.5 s, and then operate at a constant speed of 1600 r / min. Based on the correspondence with the second-order component of the angular transmission error, the vibration frequency is 1600 / 60 × 2 = 53.3 Hz. The design parameter of the reaction force estimation filter is ω RFOB = 2π × 100 [rad / s], ζ RFOB We set it to =1. Other design parameters can be determined from the motor characteristics shown in Table 1.

[0259] The results of simulations performed under the following four conditions are shown below. 1. No dynamic angle transmission error compensation (hereinafter referred to as condition W) 2. Dynamic angle transmission error compensation is enabled (hereinafter referred to as Condition X). 3. Dynamic angle transmission error compensation is enabled (with compensation parameter error) (hereinafter referred to as condition Y). 4. Dynamic angle transmission error compensation is included, and friction characteristics are considered in the controlled object (hereinafter referred to as condition Z).

[0260] The conditions for compensation parameter errors were as follows: • Second-order characteristics of the angle transmission error of the controlled object (as shown in Table 1) Amplitude: 10 arc-sec Phase: 15 degrees • Compensation for angular transmission error characteristics Amplitude: 5 arc-sec Phase: 15 degrees

[0261] The conditions for considering friction characteristics in the controlled system were as follows: Motor damping coefficient D m 4.5×10 -4 Nm / (rad / s) • Load damping coefficient D l 1.4 Nm / (rad / s) • Gear reducer damping coefficient D g 10 Nm / (rad / s)

[0262] As an example of an evaluation metric, we calculate an evaluation metric using a lock-in amplifier in online processing. The design parameters were as follows. • LPF for lock-in amplifier: 1st order, cutoff frequency 5 Hz • Estimated disturbance high-pass filter (HPF): 1st order, cutoff frequency 5 Hz *The signal passed through the above HPF for the estimated disturbance was used as the target signal for the lock-in amplifier.

[0263] Figures 129 to 133 show the motor speed, load speed, reaction torque, estimated disturbance, and evaluation index (LIA output) under condition W, respectively, with the horizontal axis representing time and the vertical axis representing each component. It is shown that the motor speed, load speed, reaction torque, and estimated disturbance have oscillatory components due to the influence of angular transmission error. For the reaction torque, the estimated disturbance is affected by the reaction estimation filter, and the amplitude in the steady state is... It has been shown that JPEG0007870027000057.jpg will be 638 times larger. The evaluation metrics will be discussed later, along with the compensation.

[0264] (With dynamic angle transmission error compensation) Figures 134 to 138 show the motor speed, load speed, reaction torque, estimated disturbance, and evaluation index (LIA output) under condition X, respectively, with the horizontal axis representing time and the vertical axis representing each component. It is shown that when the angular transmission error is compensated by dynamic angular transmission error compensation, vibration at the load speed under constant speed conditions is reduced, and furthermore, the reaction torque and estimated disturbance become zero. As mentioned above, during the acceleration operation between 0 and 0.5 s, torque is generated to drive the load inertia, so the reaction torque and estimated disturbance do not become zero, and it is shown that the reaction torque consists only of the torque that drives the load. It is shown that the motor speed exhibits an oscillatory response in order to achieve vibration reduction at the load speed.

[0265] (With dynamic angle transmission error compensation (with compensation parameter error)) Figures 139 to 143 show the motor speed, load speed, reaction torque, estimated disturbance, and evaluation index (LIA output) under condition Y, with the horizontal axis representing time and the vertical axis representing each component. It is shown that when there is an error between the angular transmission error characteristics of the controlled object and the angular transmission error characteristics of the compensation parameter, the amplitude of the reaction torque and estimated disturbance can be reduced compared to no compensation, and the vibration of the load speed is also reduced. It is shown that the motor speed exhibits an oscillatory response to achieve vibration reduction at the load speed. However, it is shown that no vibration reduction effect is obtained compared to condition X.

[0266] (Dynamic angle transmission error compensation included; friction characteristics considered for the controlled object) Figures 144 to 148 show the motor speed, load speed, reaction torque, estimated disturbance, and evaluation index (LIA output) under condition Z, respectively, with the horizontal axis representing time and the vertical axis representing each component. Even when friction characteristics are considered, the effect of friction characteristics is almost negligible on the reaction torque, indicating that vibration at load speed is reduced by dynamic angular transmission error compensation. On the other hand, although the effect of friction characteristics is evident in the estimated disturbance, it remains constant at constant speed, indicating that no vibration component due to the angular transmission error is observed. The motor speed is shown to exhibit an oscillatory response in order to achieve vibration reduction at load speed.

[0267] Next, we compare the lock-in amplifier output, which is an evaluation index under conditions W to Z. Comparing Figures 133, 138, and 143, it is shown that the values ​​correspond to the vibration suppression performance. In particular, Figure 138 shows that the evaluation index is 0. Furthermore, Figure 148, which takes friction characteristics into account, also shows that the evaluation index is 0.

[0268] From the simulation results under conditions W to Z, it is clear that the angular transmission error characteristics can be determined by using the compensation order component for motor rotation during the estimated disturbance as an evaluation index, and suppressing rotational non-uniformity through dynamic angular transmission error compensation. As mentioned above, this will involve trial and error, but it is possible to estimate the optimal value by utilizing various optimization methods.

[0269] Figure 149 is a flowchart of an angle transmission error estimation program in a servo control system equipped with a reduction mechanism. This program estimates an estimated disturbance, which is an internal state variable of the controlled object, based on observational information, and calculates an evaluation index based on a predetermined order component corresponding to the rotational non-uniformity of the estimated disturbance, thereby quantitatively understanding the degree of influence of the angle transmission error. This process consists of a group of steps corresponding to the angle transmission error estimation method and the angle transmission error estimation program, and functions as a state estimation processing unit and an evaluation index calculation unit.

[0270] Step S21: Initial setup. Prior to running the angle transmission error estimation program, various initial settings are performed. Specifically, the design parameters of the state estimation method used to estimate the estimated disturbance (e.g., disturbance observer, reaction force estimation observer, Kalman filter, etc.) are set. Initial settings regarding the usage of the calculated evaluation index (monitoring, adjustment, optimization, etc.) may also be performed.

[0271] Step S22: Information acquisition. The control device acquires observational information necessary for estimating the estimated disturbance. Examples of observational information include current command, current value, motor position, and motor speed. Furthermore, signals measured by torque sensors, acceleration sensors, inertial measurement devices, etc., may also be used as observational information for the state estimation method.

[0272] Step S23: Estimation of estimated disturbances (state estimation process). Based on the acquired observational information, estimated disturbances, which are internal state variables of the controlled object, are estimated. State estimation methods such as disturbance observers, reaction force estimation observers, or Kalman filters can be used for estimation. Preferably, this state estimation processing unit does not require analytical information such as load inertia moment or reduction mechanism spring constant, and is configured based on motor characteristics (e.g., torque constant, motor inertia moment). Estimated disturbances may include components other than those originating from angular transmission errors (e.g., load drive torque and friction effects associated with acceleration and deceleration). Therefore, filtering may be applied to suppress components other than those of a predetermined order corresponding to rotational non-uniformity. As a typical example, processing can be done all at once without modeling with a high-pass filter (HPF) aimed at reducing inertia or friction effects, which is simple and cost-effective.

[0273] Step S24: Calculation of evaluation metrics. Based on the estimated disturbance, an evaluation index is calculated based on the amplitude of a predetermined order component corresponding to the rotational non-uniformity (e.g., a component with two periods per rotation of the input shaft), or based on the amplitude and phase. The evaluation index may consist only of the amplitude of the order component, or a combination of amplitude and phase. The calculation of the evaluation index can be performed offline or online. Offline examples include Fourier transform and vibration order analysis during constant-speed operation (estimation of the phase angle according to the rotational speed, interpolation processing, and then application of a short-time Fourier transform), while online examples include synchronous detection (lock-in amplifier), Goertzel method, and bandpass filter. The calculated evaluation index is used to determine the degree of influence of angular transmission error.

[0274] The calculated evaluation index can be used to monitor and diagnose the appropriateness of compensation as an evaluation index for compensation performance in dynamic angular transmission error compensation, and can also be used as an optimization index for determining and adjusting compensation parameters (amplitude and phase). Various algorithms such as random search, gradient descent, Bayesian optimization, and genetic algorithms may be applied as optimization methods.

[0275] Figure 150 is a flowchart of a vibration damping control program in a servo control system equipped with a reduction mechanism. This flowchart shows a process that suppresses rotational non-uniformity by determining and correcting the compensation signal (amplitude and phase) for dynamic angular transmission error compensation, even when the angular transmission error characteristics are unknown, by iteratively searching and updating evaluation indices calculated from estimated disturbances estimated based on observational information using an optimization method. This process corresponds to the vibration damping control method and the set of instructions for the vibration damping control program. This optimization method minimizes or maximizes the evaluation indices using algorithms such as random search, gradient descent, Bayesian optimization, and genetic algorithms.

[0276] Step S31: Initial setup. Initial settings necessary for executing the vibration damping control program are performed. This includes initial settings for predetermined compensation order, amplitude, and phase for generating compensation signals. Amplitude and phase information corresponding to each compensation order and rotation direction is loaded into the compensation model (e.g., lookup table) referenced by the dynamic angular transmission error compensator. These compensation parameters may be configured to automatically set the amplitude and phase according to the frequency or compensation order corresponding to a predetermined speed range, based on the servo control system configuration, control parameters, and motor characteristics for at least one of the motor's position, speed, and current, and to be registered in the compensation model.

[0277] Step S32: Information acquisition. The control device acquires observational information necessary for estimating the estimated disturbance. This observational information includes, for example, current command, current value, motor position, and motor speed. It also acquires the current position information of the controlled object (e.g., motor position or position command) and the current speed information of the controlled object (e.g., motor speed or position command speed). This information can be selected and used as either real-world information (motor position / motor speed) or command information (position command / position command speed).

[0278] Step S33: Estimation of estimated disturbances (state estimation process). Based on the acquired observational information, estimated disturbances, which are internal state variables of the controlled object, are estimated. State estimation methods such as disturbance observers, reaction force estimation observers (RFOBs), or Kalman filters can be used for estimation. RFOBs can be configured based on motor characteristics (e.g., torque constant, motor inertia) and are advantageous in that they do not require analytical parameters such as load inertia moment or spring constant of the reduction mechanism. Since the estimated disturbances may include components other than the order component of the angular transmission error (e.g., acceleration / deceleration torque, friction effects), filtering (e.g., a high-pass filter) to suppress these unwanted components may be applied in this step or a subsequent step.

[0279] Step S34: Calculation of evaluation metrics. Based on estimated disturbances, an evaluation index is calculated based on predetermined order components corresponding to rotational non-uniformity. The calculation of the evaluation index can be performed offline or online. Offline examples include Fourier transform and vibration order analysis during constant-speed operation (estimation of phase angle according to rotational speed, interpolation processing, and application of short-time Fourier transform), while online examples include synchronous detection (lock-in amplifier: LIA), Goertzel method, and bandpass filter. The calculated evaluation index is used to determine the degree of influence of angular transmission error.

[0280] Step S35: Optimization of compensation parameters. The amplitude and phase of the compensation signal can be optimized using methods such as random search, gradient descent, Bayesian optimization, or genetic algorithms to minimize the evaluation index obtained in step S34, or the objective function defined based on that evaluation index. Furthermore, if the angular transmission error has characteristics specific to the direction of rotation, the forward and reverse rotations may be optimized separately. If there are multiple compensation orders to be compensated, each order may be optimized independently.

[0281] Step S36: Amplitude and phase compensation. Based on the amplitude and phase optimized in step S35, the amplitude and phase of the compensation signal are corrected by referring to a compensation model (e.g., a lookup table). The compensation model may be configured and adjusted so that the compensation signal is zero when the velocity information is zero, in order to avoid interference with the static component.

[0282] Step S37: Compensation signal generation. A sinusoidal compensation signal is generated based on the compensation order set in step S31, the amplitude and phase corrected in step S36, and the position information acquired in step S32.

[0283] Step S38: Signal addition. The generated compensation signal is added to the control signal associated with the position command, speed command, current command, or any control signal related thereto.

[0284] Step S39: Servo control. Based on the control signal to which the compensation signal has been added, a servo control system equipped with a reduction mechanism is operated to compensate for rotational non-uniformity caused by the angular transmission error of the reduction mechanism.

[0285] [Summary of the effect of estimating angular transmission error characteristics using a reaction force estimation observer] According to this disclosure, by utilizing dynamic angle transmission error and reaction force estimation observers, it is possible to quantitatively grasp the influence of angle transmission error from evaluation indicators and understand the angle transmission error characteristics without requiring additional sensors such as load position encoders, torque sensors, and laser distance sensors, which are particularly problematic in semi-closed control. When designing the reaction force estimation observer, similar to dynamic angle transmission error compensation, the number of design parameters can be reduced and the design process can be made more efficient.

[0286] Furthermore, by using an objective function based on evaluation metrics and utilizing various optimization methods, the angular transmission error characteristics can be automatically estimated. Multiple embodiments exist for both offline and online processing in calculating the evaluation metrics, and these can be appropriately selected or combined depending on the situation.

[0287] Based on the above, this disclosure offers excellent industrial applicability, is easily applicable to various control devices in diverse industrial fields, including existing equipment, and has excellent effects such as simplifying the device, reducing costs, and facilitating installation and maintenance.

[0288] [Adaptive Dynamic Angular Transmission Error Compensation] (Technical background) The technical background of this disclosure is explained below. In the angle transmission error characteristic estimation using the reaction force estimation observer described above, the angle transmission error characteristic can be estimated without requiring additional sensors such as load position encoders, torque sensors, and laser distance sensors, especially in semi-closed control. On the other hand, although the angle transmission error characteristic can be estimated with a simple configuration without requiring additional sensors, it is not possible to definitively estimate the angle transmission error characteristic. Therefore, it has been necessary to manually adjust the angle transmission error characteristic through trial and error using an objective function based on evaluation indicators, or to estimate the angle transmission error characteristic using various optimization methods, which involves some trial and error. However, whether through trial and error or by using various optimization methods, there is a problem that estimating the angle transmission error characteristic can be time-consuming.

[0289] Furthermore, the angular transmission error consists of reproducible components, and its compensation is achieved through feedforward control. However, when pursuing even higher precision, the influence of non-reproducible components cannot be ignored, and a compensation method for non-reproducible components is required. It should be noted that dynamic angular transmission error compensation is a feedforward control method, and in principle, it is impossible to compensate for non-reproducible components.

[0290] (Adaptive algorithm) This disclosure outlines the underlying adaptive algorithms in the field of adaptive control technology. An adaptive algorithm refers to a sequential computation method for improving performance by successively optimizing processing content in response to changes in the environment. This makes it possible to perform adaptive control even under time-changing conditions.

[0291] Next, as a concrete example of the application of adaptive algorithms, we will explain the basic structure of an adaptive filter. An adaptive filter applies a weight coefficient vector w(k), which is a set of adaptively controlled parameters, to an input signal x(k) to estimate the output y(k) = w TA known configuration involves generating (k)x(k) and updating w(k) using an evaluation signal e(k)=d(k)-y(k), which is the difference between (k)x(k) and the target signal d(k). This configuration allows the estimation filter to respond flexibly to input characteristics and environmental changes.

[0292] One example of an adaptive algorithm that implements the updating of the weight coefficient vector of an adaptive filter is the Normalized Least Mean Squares (NLMS) method. In NLMS, the instantaneous value of the squared value of the evaluation signal is considered as the objective function, and the weight coefficient vector is updated by successively minimizing this function using gradient descent, as follows. In other words, the objective function is simplified based on the evaluation signal at a certain time, and the adaptive processing is performed directly.

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[0293] Another example of an adaptive algorithm is the recursive least squares (RLS) method. In RLS, the weighted sum of squares based on past values ​​of the evaluation signal is explicitly defined as the objective function J, and the weight coefficient vector is updated to minimize this function. RLS is structured to sequentially calculate the analytical minimum solution of this objective function using a sequential optimization algorithm, enabling highly accurate adaptive control that also takes past data into consideration.

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[0294] While both of these are control processes that adaptively update the weight coefficient vector, they differ in terms of optimization. NLMS aims to minimize the evaluation signal itself, while RLS uses an objective function that cumulatively evaluates the time-series error signal to perform a more indirect and overall optimization.

[0295] Representative algorithms that perform adaptive processing using evaluation signals directly or sequentially include the aforementioned normalized least mean squares method (NLMS), as well as stochastic gradient descent (SGD) based on gradient descent, variable step size NLMS (VSS-NLMS) which improves convergence characteristics using an adaptive step size, and Leaky NLMS which enhances the convergence stability of classical NLMS. These methods adaptively update the weight coefficients using instantaneous or sequential values ​​of the evaluation signal.

[0296] On the other hand, a representative algorithm that explicitly defines an objective function and performs adaptive processing through its minimization is the recursive least squares method (RLS). RLS achieves high-precision weight updates by analytically minimizing the weighted sum of squares based on past values ​​of the evaluation signal as the objective function. Fast RLS, aimed at speeding up and stabilizing RLS, and Robust RLS, which is more resistant to noise and disturbances, are also known as practical improvements. Furthermore, within the framework of state estimation, Kalman filters, extended Kalman filters (EKF), and successive Bayesian estimation methods are also applied to adaptive processing as methods that sequentially calculate the optimal estimate while minimizing the error evaluation corresponding to the objective function.

[0297] As described above, various adaptive algorithms are known, each with its own characteristics and advantages.

[0298] The terms used in this disclosure are defined as follows: An evaluation signal refers to an index signal used to evaluate the performance of the current adaptive mechanism. For example, in an adaptive filter, it is calculated as the difference between the target signal d(k) and the estimated output y(k). An objective function is a function defined based on an evaluation signal, which evaluates the performance of an adaptive mechanism through its optimization. Adaptive processing refers to the process of sequentially adjusting parameters based on evaluation signals and objective functions, and is implemented using adaptive algorithms. An adaptive mechanism refers to the component that performs adaptive processing.

[0299] Figure 151 shows a schematic diagram of the configuration for angular transmission error compensation in this disclosure. As shown in Figure 151, the vibration control device 100_6 comprises a servo control system 10, an angular transmission error compensation unit 11, a state estimation processing unit 12, and an adaptive processing unit 15. The servo control system 10 is, for example, the feedback control system in Figure 2, and consists of position proportional control, velocity proportional integral control, and a filter, and outputs a drive current to the motor. The state estimation processing unit 12 is configured, for example, as a reaction force estimation observer, and calculates estimated disturbances. The adaptive processing unit 15 uses the estimated disturbance as an evaluation signal and optimizes the amplitude and phase used in the angular transmission error compensation unit 11 by adaptive processing that optimizes at least one of the evaluation signal or an objective function defined based on the evaluation signal. The angular transmission error compensation unit 11 is, for example, dynamic angular transmission error compensation, and generates a compensation signal that compensates for the rotational non-uniformity of the angular transmission error. The vibration control device 100_6 is composed of the state estimation processing unit 12, the adaptive processing unit 15, and the angular transmission error compensation unit 11, and compensates for the rotational non-uniformity of the angular transmission error.

[0300] The vibration control system according to the embodiment of this disclosure will be described below with reference to the attached drawings. Furthermore, the estimation and compensation of angular transmission error characteristics by the adaptive algorithm of this disclosure will be quantitatively demonstrated by numerical simulations described later.

[0301] As an example of a specific configuration for estimating and compensating for angular transmission error characteristics, Figure 152 shows a block diagram of adaptive dynamic angular transmission error compensation. In Figure 152, reference numeral 40 denotes the reaction force estimation observer, reference numeral 41 denotes the adaptive processing unit, reference numeral 42 denotes the angular transmission error compensator, and reference numeral 43 denotes the feedback control system. Note that the configuration is based on a second-order component as an example, and the contents will be explained using a second-order component as an example from here on. Note that it is possible to extend it to a form that takes higher-order components into consideration, and the details will be described later.

[0302] The symbols are as follows: Plant: A controlled object consisting of delay elements such as motors, reduction mechanisms, loads, and current control systems. C(s): Feedback control system i ref :Current command θ m : Motor position θ l :Load position RFOB: Reaction Force Estimation Observer adaptive: adaptive mechanism (adaptive processing unit) C ATE :Angle transmission error compensator i ATEComp :Compensation current A^2: Estimated amplitude, in arc-seconds (arc-sec). φ^2: Estimated phase, in radians (rad). τ^ d Estimated disturbance, in units of Newton-meters (Nm).

[0303] Adaptive dynamic angular transmission error compensation eliminates the need for trial and error and optimization in the estimation of angular transmission error characteristics using a reaction force estimation observer. By estimating the angular transmission error characteristics using an adaptive method, it resolves the challenges of estimating angular transmission error characteristics using a reaction force estimation observer. More specifically, it constructs a system that reduces the influence of angular transmission error by adaptively estimating the amplitude and phase of each compensation order in dynamic angular transmission error compensation so that the influence of angular transmission error in the estimated disturbance is zero.

[0304] The following describes the processing steps in the adaptive processing unit.

[0305] Basic part (from the addition formulas of trigonometric functions)

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[0306] The second-order component of the angular transmission error is given by equation (44), and by applying the trigonometric addition formula, it can be expressed as equations (45) to (49). Furthermore, the coefficient vector is defined by equation (50), and the input signal vector by equation (51). The evaluation signal is also defined as the estimated disturbance as shown in equation (52).

[0307] In adaptive filters, which are one type of adaptive mechanism, the evaluation signal is the difference between the target signal, the coefficient vector, and the estimated output, which is the inner product of the input signal vector. However, this disclosure is characterized by not using the estimated output and instead using the estimated disturbance as the evaluation signal. This is because the estimated output in this configuration is the angular transmission error, and its characteristics are unknown. Furthermore, as mentioned above, setting the estimated disturbance to 0 reduces the influence of the angular transmission error. Therefore, the configuration indirectly optimizes the evaluation signal or target signal through dynamic angular transmission error compensation.

[0308] As an example of an adaptive algorithm for optimizing the evaluation signal, we will describe the case of NLMS. In NLMS, the optimization of the evaluation signal is achieved by updating the coefficient vector θ(k) in the direction of reducing the magnitude of the evaluation signal e(k) based on equation (53).

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[0309] The step size is a design parameter that controls the amount of change in coefficient updates; if it is too large, convergence becomes unstable, and if it is too small, convergence becomes slow. The normalization term also functions as a stabilization term to prevent division by zero and excessive updates when the energy of the input signal is extremely small, and plays a role in numerically stabilizing the coefficient vector.

[0310] Next, we will describe the case of RLS as an example of an adaptive algorithm for optimizing the objective function. In RLS, the objective function is the weighted sum of squares based on past values ​​of the evaluation signal shown in equation (43), and the coefficient vector is updated based on equations (54) to (56) in order to sequentially calculate the analytical minimum solution of this objective function.

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[0311] The initial value P(0) of the covariance matrix is ​​usually a matrix obtained by multiplying the identity matrix by its scalar values. A larger covariance matrix value leads to a larger range of variation in the coefficient vectors, and faster convergence can be expected. On the other hand, a smaller covariance matrix value results in slower parameter convergence, but increases stability against noise.

[0312] In adaptive algorithms, for example, the initial value of the coefficient vector in NLMS and RLS is often set to a zero vector (all elements are 0). The initial value of the coefficient vector is the initial value of the target to be estimated, and in this disclosure, it corresponds to the initial value of the estimated amplitude and estimated phase. It may be set based on some prior information, for example, the initial value of the estimated amplitude may be an approximate value based on past knowledge (for example, the average value for equivalent products), and the initial value of the estimated phase may be 0.

[0313] The operation suitable for the adaptive processing in this disclosure is preferably operation in the operating speed range where a resonant state occurs, and more preferably constant-speed operation in the operating speed range where a resonant state occurs. In this case, the adaptive processing is simplified and parameter estimation becomes easier. However, the operation pattern is not limited to this, and other operating conditions can also be used.

[0314] This disclosure estimates angle transmission error characteristics through dynamic angle transmission error compensation. However, the dynamic angle transmission error, estimated disturbance calculation by the reaction force estimation observer, and adaptive processing are independent processes and do not necessarily need to be operated synchronously with the same processing cycle. Adaptive processing is generally designed depending on the dynamic characteristics of the system and the rate of change of the external environment. In this disclosure, performance can often be obtained even when executed with a relatively slow processing cycle compared to dynamic angle transmission error compensation. The processing cycle and processing timing can be flexibly configured according to the device configuration, and efficient use of computer resources is possible by reducing the processing load.

[0315] In adaptive dynamic angular transmission error compensation, dynamic angular transmission error compensation was used in combination. However, it is also possible to apply known configurations described in prior art documents, etc., as methods for compensating for angular transmission errors, and the method is not limited to dynamic angular transmission error compensation.

[0316] [Adaptive extension considering the characteristics of dynamic angular transmission error compensation] (Setting the adaptive speed range) [composition] A weighting coefficient that takes into account the adaptive speed range may be used, and the system may be configured to adapt only in situations where the effect of angular transmission error is significant. Specifically, the evaluation signal may be multiplied by the weighting coefficient. This is similar to setting the compensation speed range in dynamic angular transmission error compensation, and the weighting coefficient changes the effectiveness of the evaluation signal based on speed information. For example, it may be changed using linear interpolation or spline interpolation, or it may be changed in steps, such as nearest neighbor interpolation. In addition, from the viewpoint of continuity of the adaptive processing, it is preferable that the weighting coefficient for the adaptive speed range is continuous, but a discrete method may also be used.

[0317] [effect] By performing adaptive processing under conditions where the effects of angle transmission errors are significant, it is possible to improve the convergence and stability of the adaptive processing. This prevents unnecessary or unstable coefficient updates when the input signal to the adaptive processing does not contain an appropriate amount of information, reduces the risk of erroneous learning or poor convergence that deviates from the optimal estimated parameters, and enables efficient use of computing resources by reducing unnecessary computational processing.

[0318] (Information used for compensation) [composition] As mentioned above, in dynamic angle transmission error compensation, command information may be used in the compensation calculation. In adaptive dynamic angle transmission error compensation, the system may also be configured to use command information in the compensation calculation, except for the calculation of estimated disturbances. Furthermore, the system may be configured to change the information used for compensation according to the adaptive processing control described later.

[0319] [effect] Because the information used for compensation can be flexibly selected to suit the control device, optimal compensation processing can be achieved according to the system configuration and operating conditions. This makes it possible to apply the system to a variety of systems with different configuration requirements, improving the design flexibility of the system and expanding its scope of application and practicality.

[0320] (Reflection of rotational direction characteristics) [composition] Since the angular transmission error has characteristics that differ depending on the direction of rotation, adaptive processing is performed separately for forward and reverse rotation.

[0321] [effect] Because angular transmission errors have different characteristics depending on the direction of rotation due to their generation principle, effective compensation is possible through estimation and compensation that takes the direction of rotation into account.

[0322] (Multiple compensation orders) [composition] When supporting multiple compensation order components, an adaptive mechanism equivalent to the adaptive processing for the second-order component described above is constructed for each compensation order. When supporting multiple compensation orders, instead of extending the coefficient vector and input signal vector, an adaptive mechanism targeting each order can be constructed and processed in parallel. For example, when targeting second-order and fourth-order components, adaptive mechanisms for the second-order and fourth-order components are constructed separately. In particular, RLS updates the coefficient vector considering the correlation (covariance) of all parameters, so the computational complexity and memory usage can be significantly reduced by partitioning or parallel processing. Alternatively, instead of parallel processing, the system can be configured to sequentially perform adaptive processing for each of the multiple compensation orders.

[0323] [effect] When handling multiple compensation orders, processing each compensation order separately and in parallel eliminates the need to process the correlations between all parameters at once, thereby reducing computational complexity. Furthermore, since the situations in which the influence of each order component becomes significant depend on the operating speed, there is little need to process them simultaneously. Processing them in parallel or individually allows for even more efficient use of computing resources.

[0324] (Effect of load moment of inertia) [composition] In this configuration, the torque driving the load (acceleration / deceleration torque) is included in the estimated disturbance. Therefore, if parameter estimation is performed by adaptive processing during acceleration and deceleration, it may result in inappropriate compensation. Typically, the frequency corresponding to acceleration / deceleration torque is in the low frequency band, and the frequency due to the effect of angular transmission error differs near the resonant frequency determined by the load inertia moment and the reduction mechanism spring constant (which is affected by the control system). Therefore, it may be possible to configure the system to address this by using filters or the like to separate the frequency components of the effect of angular transmission error from other frequency components.

[0325] Furthermore, as mentioned above regarding consideration of operating speed ranges, it is preferable to adapt the system in situations where the effect of angular transmission error becomes significant. Since there may be speed ranges during acceleration and deceleration where the effect of angular transmission error becomes significant, the system may be configured to use speed information and acceleration / deceleration information to construct weighting coefficients, thereby enabling adaptation in more appropriate situations. Specifically, the system is configured not to adapt when the absolute value of the acceleration / deceleration degree exceeds a certain threshold. In addition, the weighting coefficients may include those based on speed information, those based on acceleration information, and those based on both speed and acceleration information. Furthermore, the reaction force estimation observer may be configured to remove the acceleration / deceleration torque component.

[0326] Acceleration information refers to motor acceleration or position command acceleration.

[0327] [effect] If the estimated disturbance includes components other than the angle transmission error, the adaptive processing will include those components. By using an adaptive processing configuration that is unaffected by acceleration and deceleration torque, more effective compensation is possible through estimation and compensation.

[0328] (friction characteristics) [composition] In devices using reduction gears, friction characteristics often cannot be ignored due to the effects of lubrication in various sliding parts. Since friction characteristics, like the effects of acceleration and deceleration torque, are in the low-frequency range, their influence can be reduced by frequency separation using filters, as mentioned above. Furthermore, as mentioned above, the estimated disturbance includes the effects of various components, so, similar to a normal reaction force estimation observer, it may be configured to remove unnecessary components other than the effects of angular transmission error.

[0329] (Adaptive processing control) [composition] In this disclosure, as a control condition for adaptive processing, for example, adaptive processing may be performed only during specific operations, and if the aforementioned evaluation index falls below a threshold and appropriate angular transmission error characteristics are obtained, the adaptive processing may be stopped and dynamic angular transmission error compensation may be performed. Alternatively, if the evaluation index exceeds a threshold, the adaptive processing may be performed again. Furthermore, adaptive processing may be stopped under conditions unsuitable for adaptive processing, such as when the influence of acceleration / deceleration torque in the aforementioned estimated disturbance is large, when the influence of noise is large, or when abnormalities are observed in sensor signals, etc. Based on these, the system is configured to start, stop, and restart adaptive processing according to the control conditions for adaptive processing.

[0330] Alternatively, for example, the amplitude and phase of each compensation order may be determined by adaptive processing in accordance with the aging of the equipment during the final stages of product manufacturing, and the final product may not undergo adaptive processing. While continuously performing adaptive processing can mitigate the effects of time-dependent and aging factors such as temperature changes, this comes at the cost of increased system complexity.

[0331] [effect] By narrowing down the conditions for performing adaptive processing, the time required for parameter setting and verification in adaptive processing can be reduced. Furthermore, unnecessary adaptive processing calculations can be reduced, enabling efficient use of computing resources. Additionally, by integrating adaptive processing functionality into the shipment adjustment device, there is no need to incorporate adaptive processing as a separate product. This eliminates the need to allocate computing resources to implement adaptive processing, improving cost efficiency and allowing for application to a wider range of systems. This increases system design flexibility, expands the scope of application and practicality, and enables support for a broader range of environments and applications.

[0332] (Combination of functions) As mentioned above, various factors can be considered when designing an angle transmission error compensator. Similarly, various factors can be considered when designing an adaptive dynamic angle transmission error compensation. For example, a weighting coefficient that considers both the compensation speed band setting and the adaptive speed band setting together may be used. By leveraging the advantages of both and appropriately selecting and combining various configurations, it is possible to easily construct embodiments that support diverse functions. These combinations of functions are not mutually exclusive, and by appropriately selecting and combining them according to the purpose and constraints of each system, comprehensive suppression of rotational output errors that consider various factors can be efficiently designed and implemented in a variety of systems.

[0333] (Numerical example) In the following sections, we quantitatively evaluate the impact of the characteristic components of this disclosure on operation through numerical simulations and objectively demonstrate their usefulness. Here, the numerical simulation conditions for the following six types of comparisons are shown in Table 2. 1. Differences in adaptive algorithms 2. Weight coefficient not considered / considered 3. Differences in initial values ​​of the target of estimation 4. Consideration of frictional properties 5. Consideration of 4th order components 6. Operation Patterns

[0334] The simulation conditions are the same as those for the dynamic angle transmission error compensation described above. The design parameters for the reaction force estimation observer are the same as those described above (ω RFOB = 2π × 100 [rad / s], ζ RFOB =1) [Table 2]

[0335] Furthermore, the design parameters and initial values ​​for each adaptive algorithm were set as follows. NLMS μ = 0.02 ε = 1 × 10 -3 RLS P(0) = 0.01 × I λ = 0.99

[0336] The initial values ​​in the adaptive algorithm are denoted as estimated amplitude initial value [arc-sec] / estimated phase initial value [deg]. For example, the notation 10 / 15 corresponds to an estimated amplitude initial value of 10 arc-sec and an estimated phase initial value of 15 deg.

[0337] As an example of adapting to the operating speed range of the resonant state, as shown in equation (57), the weighting coefficient between 1000 and 2000 r / min was set to 1, the weights at other motor speeds were set to 0, and linear interpolation was performed between each speed.

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[0338] Figures 153 to 158 show the motor speed, load speed, reaction torque, estimated disturbance, estimated amplitude, and estimated phase, respectively, under condition AA. The horizontal axis represents time, and the vertical axis represents each component. Figures 159 to 206 are the corresponding figures for conditions AB to AI, which correspond to condition AA.

[0339] Figures 207 to 212 show the motor speed, load speed, reaction torque, estimated disturbance, motor position vibration component, and load position vibration component, respectively, under condition AJ. The horizontal axis represents time, and the vertical axis represents each component. Figures 213 to 218 are the corresponding figures under condition AK, which is the same as condition AJ.

[0340] Figures 219 to 226 show the motor speed, load speed, reaction torque, estimated disturbance, motor position vibration component, load position vibration component, estimated amplitude, and estimated phase, respectively, under condition AL. The horizontal axis represents time, and the vertical axis represents each component.

[0341] (Differences in adaptive algorithms and consideration of adaptive speed range (weighting coefficient)) Conditions AA and AD show that when the angular transmission error characteristics are set to be equal to the angular transmission error of the controlled object, and the adaptive algorithm is applied during acceleration and deceleration without considering a weighting coefficient that takes the adaptive speed range into account, the estimated amplitude and phase become inappropriate due to the influence of the acceleration and deceleration torque in the estimated disturbance, regardless of the adaptive algorithm, and oscillations occur in the load speed. Conditions AB and AE show that by considering a weighting coefficient that takes the adaptive speed range into account, the adaptive processing during acceleration is suppressed, and compensation is achieved regardless of the adaptive algorithm.

[0342] (Difference in initial adaptive values) Based on conditions AC and AF, when the initial values ​​are set to 0 / 0 (indeterminate), each state variable is oscillatory in the initial stage of constant velocity after acceleration. However, after the constant velocity is maintained, the estimated amplitude and estimated phase converge to the set values, regardless of the adaptive algorithm, demonstrating that oscillations at the load velocity can be reduced.

[0343] From the above, it is clear that even when the angular transmission error characteristics are unknown, the estimated amplitude and estimated phase can be estimated from the response during operation, and the effects of angular transmission error can be suppressed.

[0344] (Consideration of frictional properties) Condition AG shows that even when considering friction characteristics, vibrations at the load speed can be compensated, but the estimated amplitude and estimated phase exhibit an oscillatory response centered around the setpoint. Condition AH shows that when HPF is applied to the estimated disturbance, the influence of friction characteristics can be reduced, resulting in the same results as under conditions AB.

[0345] (Consideration of the fourth-order component) The AI ​​analysis of the conditions shows that even when considering a fourth-order component as the angular transmission error of the controlled object, the estimated amplitude and estimated phase remain at the set values, similar to when only the second-order component is considered, demonstrating that the second-order component can be compensated for. However, since the estimation and compensation of the fourth-order component were not performed, it is shown that vibrations due to the fourth-order component remain in the load velocity.

[0346] (Operation pattern) Conditions AJ and AK show that even during acceleration and deceleration, if vibration is compensated by dynamic angular transmission error compensation, the effect of angular transmission error is not observed in the reaction torque and estimated disturbance, indicating that vibration in the load speed and load position vibration components can be reduced.

[0347] Condition AL demonstrates that, similar to the case of constant-speed operation, even when the angular transmission error is unknown, the estimated amplitude and estimated phase can be estimated from the response during operation, thereby suppressing the effects of the angular transmission error.

[0348] From the simulation results under conditions AA to AL, it is clear that adaptive dynamic angular transmission error compensation can estimate the amplitude and phase based on the response during operation, even when the angular transmission error is unknown, thereby suppressing rotational non-uniformity caused by the angular transmission error.

[0349] (Expansion of the scope of application (presence or absence of reproducibility of angular transmission error characteristics)) As mentioned above, there are cases where the actual angular transmission error contains components that cannot be expressed by equation (1). Below, we consider further improvements in accuracy and vibration reduction in such cases. In angular transmission error, for example, in a harmonic drive gear, the repeatable and non-replicable components can be expressed as equations (58) and (59).

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[0350] The aforementioned equation (1) considers only the first term on the right-hand side of equation (58), and dynamic angular transmission error compensation is a feedforward control, meaning it compensates for reproducible components. On the other hand, the second term on the right-hand side of equation (58) is a component that is synchronized with the motor rotation but is not reproducible due to the influence of rotational speed, temperature, etc., and has been excluded from discussion until now. Note that the first term on the right-hand side of equation (58) is mainly a component caused by C / S, and the second term on the right-hand side of equation (58), W / G, is a component caused by the position of the outer ring. From equation (59), for example, when the reduction ratio is 50, it appears as a 2.04th order component relative to the second-order component. For details on each component, please refer to Non-Patent Document 5.

[0351] On the other hand, adaptive dynamic angular transmission error compensation can track changes in characteristics even for components that are not reproducible due to environmental or condition fluctuations, and estimate and compensate for the corresponding angular transmission error characteristics. Furthermore, the angular transmission error of a reduction mechanism may change due to the load torque applied to the reduction mechanism, the temperature of the reduction mechanism, and age-related changes such as wear. In this disclosure, even in these situations, adaptive processing can track changes in characteristics and estimate and compensate for the corresponding angular transmission error characteristics. In this disclosure, compensation can be achieved by a configuration that considers multiple compensation orders corresponding to equation (58). Note that adaptive processing cannot be stopped for components that are not reproducible.

[0352] Furthermore, this disclosure can compensate for angular transmission errors if the component is synchronized with the motor rotation, and is not limited to the harmonic drive gear exemplified here, but can be applied to other reduction mechanisms as well, provided that they can be expressed in a form similar to equation (58).

[0353] [effect] According to this disclosure, by using adaptive processing to suppress rotational non-uniformity due to angular transmission errors in the reduction mechanism, even for components that are not reproducible due to fluctuations in the environment and conditions, it becomes possible to adjust parameters flexibly and easily. This simplifies the adjustment work that previously required a great deal of effort during the design phase, and compensation that encompasses changes in the equipment and environment is realized. Furthermore, due to its excellent versatility and expandability, it can be easily applied to various control devices in diverse industrial fields, and has excellent industrial applicability.

[0354] (Angle transmission error characteristics) Hereafter, the estimation and compensation of angular transmission error characteristics by the adaptive processing of this disclosure will be quantitatively shown based on an example following equation (58). Here, a system with a harmonic drive gear as a reduction mechanism, specifically our own SHA25A51SG, was used. In this case, JPEG0007870027000077.jpg425, O W =1, mainly k=2, JPEG0007870027000078.jpg416,n=2,nO w It is affected by the angular transmission error of =2. In other words, this occurs when the influence of the 1.96th order component of the reproducible angular transmission error and the 2nd order component of the non-reproducible angular transmission error is large.

[0355] Figures 227 to 230 show the results of multiple angle transmission error measurements, illustrating the 1.96th order amplitude, 2nd order amplitude, 1.96th order phase, and 2nd order phase, respectively. The horizontal axis represents the number of measurements, and the vertical axis represents each component. The figures show that the 1.96th order component is reproducible across multiple measurements, while the 2nd order component is not reproducible across multiple measurements.

[0356] The following shows experimental results from constant-speed operation at 1050 r / min, where the effects of rotational non-uniformity due to angular transmission errors are significant. For adaptive processing, RLS was used, with the initial estimated amplitude and phase for both orders set to 0, and the forgetting coefficient λ = 0.998 for both orders.

[0357] Figures 231 to 235 show the load speeds during constant-speed operation experiments, with the following results: no compensation, first 1.96th-order adaptive compensation, second 1.96th-order adaptive compensation, first 1.96th-order and second-order adaptive compensation, and second 1.96th-order and second-order adaptive compensation, respectively. The horizontal axis represents time, and the vertical axis represents load speed.

[0358] Figures 236 to 238 show the load speed order analysis results under constant speed conditions during a constant speed operation experiment. They show the results for no compensation, 1.96th-order adaptive compensation (2nd time), and 1.96th-order and 2nd-order adaptive compensation (2nd time), respectively. The horizontal axis represents the order, and the vertical axis represents the load speed.

[0359] Figure 231 shows how vibration occurs at the load speed due to the effect of angular transmission error. Figures 232 and 234 show that vibration at the load speed is reduced by estimating the estimated amplitude and estimated phase through adaptive processing. Figures 233 and 235 show that vibration at the load speed is reduced from the second operation onward. Figure 235 also shows that each order is compensated by multiple compensation orders.

[0360] Figure 236 shows that the effects of angular transmission error are largely due to the 1.96th and 2nd order components. Figure 237 shows that the 1.96th order component of the angular transmission error is compensated for. Figure 238 shows that both the 1.96th and 2nd order components of the angular transmission error are compensated for. In particular, it is shown that the non-reproducible 2nd order component is also reduced.

[0361] From the above, it is clear that adaptive dynamic angular transmission error compensation can suppress rotational non-uniformity caused by angular transmission errors, regardless of whether or not the angular transmission error is reproducible.

[0362] (Explanation of effects) In addition to the results of numerical simulations, similar trends have been confirmed in actual experimental results, demonstrating that this disclosure is effective in real-world operating environments. Therefore, it is clear that this disclosure is not merely a theoretical framework, but enables even higher-precision control than conventional technologies and is extremely useful in practice.

[0363] Figure 239 is a flowchart of a vibration damping control program in a servo control system equipped with a reduction mechanism, showing the main processing steps S41 to S48 of adaptive dynamic angle transmission error compensation. This program uses estimated disturbances as evaluation signals, adaptively determines and updates compensation parameters to minimize their effects, and realizes vibration damping control that compensates for rotational non-uniformity.

[0364] Step S41: Initial setup. This process performs the initial setup required for executing the vibration control program. Specifically, it loads amplitude and phase information corresponding to the compensation order and rotation direction into the compensation model (e.g., lookup table) referenced by the Dynamic Angle Transmission Error Compensator (ATEComp). It may also set initial values ​​for coefficients and covariance matrices used in adaptive algorithms (e.g., NLMS, RLS).

[0365] Step S42: Information acquisition. The system acquires the current position information (e.g., motor position) and speed information (e.g., motor speed) of the controlled object, and also acquires signals such as current commands as needed. This information can be selected and used as either measured information or command information.

[0366] Step S43: Estimation of estimated disturbances (state estimation process). Based on the acquired observational information, estimated disturbances, which are internal state variables of the controlled object, are estimated. The state estimation process can utilize a disturbance observer, a reaction force estimation observer, or a Kalman filter, and it is preferable to configure the system based on motor characteristics so that analytical information such as load-side parameters is not required.

[0367] Step S44: Optimization of compensation parameters. The estimated disturbance is used as an evaluation signal, and at least one of the evaluation signal or the objective function based thereon is optimized. An adaptive algorithm (NLMS, RLS, etc.) is used to sequentially update the estimated amplitude and phase values ​​that generate the compensation signal, and adjust them so that the angular transmission error component in the estimated disturbance is minimized. The amount of update is controlled using a weighting coefficient according to the operating state (suppressing updates in inappropriate situations such as during acceleration and deceleration), and optimization may be performed separately for forward and reverse rotation, taking into account the characteristics of each rotation direction. If there are multiple compensation orders, an independent adaptive mechanism may be configured for each order.

[0368] Step S45: Amplitude and phase correction. Based on the optimization parameters obtained in step S44 and the velocity information from step S42, the amplitude and phase of the compensation signal are determined and corrected by referring to the compensation model. The compensation model may be configured and adjusted so that the compensation signal is zero when the velocity information is zero, in order to avoid interference with the static component.

[0369] Step S46: Compensation signal generation. A sinusoidal compensation signal is generated based on the compensation order set in step S41, the amplitude and phase corrected in step S45, and the position information acquired in step S42.

[0370] Step S47: Addition of compensation signals. The generated compensation signal is added to the control signal associated with the position command, speed command, current command, or any control signal related thereto.

[0371] Step S48: Execute servo control. Based on the control signal to which the compensation signal has been added, servo control is performed to compensate for rotational non-uniformity caused by the angular transmission error of the reduction mechanism. If appropriate compensation parameters are obtained, the adaptive process may be stopped and the system may operate as normal dynamic angular transmission error compensation.

[0372] [Summary of Adaptive Dynamic Angular Transmission Error Compensation Effects] According to this disclosure, by utilizing a dynamic angular transmission error and reaction force estimation observer and an adaptive algorithm, particularly in semi-closed control, it is possible to estimate the angular transmission error characteristics of a reduction mechanism, which is necessary for dynamic angular transmission error compensation and has individual product differences, through adaptive processing, without requiring additional sensors, and to compensate for the rotational non-uniformity of the reduction mechanism without requiring trial and error or optimization. Furthermore, regardless of whether the angular transmission error of the reduction mechanism is reproducible or not, it is possible to compensate for the rotational non-uniformity caused by the influence of the angular transmission error, and comprehensive suppression of rotational output errors considering various factors can be efficiently designed and implemented in a variety of systems.

[0373] Based on the above, this disclosure has high industrial applicability and can be easily deployed in various fields utilizing existing equipment. This will result in significant benefits such as simplification of equipment, cost reduction, and increased efficiency in installation and maintenance. Furthermore, this technology can flexibly respond to conditions that were previously difficult to apply, thereby resulting in significant benefits such as expanded scope of application, improved operability, and deployment in new industrial fields.

[0374] In this embodiment, each process is executed on any computer. Furthermore, any computer may execute these processes using a processor as hardware, a program as software, or a combination thereof. In that case, the processor is configured to work in cooperation with the program to execute the various processes in this embodiment, and can function as a unit or means in this embodiment. Also, the execution order of the processes by the processor is not limited to the order described and may be changed as appropriate. Any computer may be a general-purpose computer, a computer designed for a specific purpose, a workstation, or any other system capable of executing each process.

[0375] A processor may consist of one or more hardware components, and the type of hardware is not limited. For example, a processor may consist of hardware such as a CPU, MPU (Micro Processing Unit), FPGA (Field Programmable Gate Array) or other programmable logic devices, ASIC (Application Specific Integrated Circuit) or other dedicated circuits for executing specific processes, GPU (Graphic Processing Unit), or NPU (Neural Processing Unit). Furthermore, the type of hardware may be a combination of different types of hardware. When multiple hardware components are configured to execute one or more processes of a given processor, these multiple hardware components may reside in physically separate devices or in the same device. Also, in any embodiment, the order of each process performed by the processor is not limited to the order described above and may be changed as appropriate. Hardware is composed of electrical circuits (circuitry) that combine circuit elements such as semiconductor elements.

[0376] Furthermore, the program may be firmware or software such as microcode. Alternatively, the program may be, for example, a group of program modules, each function of which may be implemented by a processor configured to perform its respective function. The program may be program code or multiple code segments stored on one or more non-temporary computer-readable media (e.g., storage media or other storage devices). The program may be divided and stored on multiple non-temporary computer-readable media located on physically separate devices. The program code or code segments may represent any combination of procedures, functions, subprograms, routines, subroutines, modules, software packages, classes, or instructions, data structures, or program statements. The program code or code segments may be connected to other code segments or hardware circuits by sending and receiving information, data, arguments, parameters, or memory contents. The program of this application may also be provided as a program product.

[0377] The vibration control method and vibration control program of this disclosure include steps or instructions to be executed by a computer that realize the functions of each component (state estimation processing unit, adaptive processing unit, angle transmission error compensation unit, etc.) of the vibration control device of this disclosure. Therefore, the vibration control method and vibration control program can be configured in an embodiment that includes all additional features of the vibration control device (e.g., configuration based on motor characteristics) as steps of the method or instructions of the program.

[0378] (Note) The following is an addendum regarding the nature of this disclosure. (Note 1) A vibration control device applied to a servo control system equipped with a reduction mechanism, which compensates for rotational non-uniformity caused by the influence of angular transmission error of the reduction mechanism, comprising: a state estimation processing unit that estimates an estimated disturbance, which is an internal state quantity of the controlled object, based on observation information; an adaptive processing unit that uses the estimated disturbance as an evaluation signal and optimizes at least one of the evaluation signal or an objective function defined based on the evaluation signal; and an angular transmission error compensation unit that generates a compensation signal. (Note 2) The vibration control device described in Appendix 1, wherein the state estimation processing unit is configured based on motor characteristics. (Note 3) The vibration control device according to Appendix 1 or Appendix 2, wherein the state estimation processing unit includes at least one of a disturbance observer, a reaction force estimation observer, and a Kalman filter. (Note 4) The vibration control device according to any one of Appendix 1 to Appendix 3, wherein the adaptive processing unit further includes a weighting unit that controls the effectiveness of the evaluation signal using at least one of a weighting coefficient based on a predetermined speed range and a weighting coefficient based on a predetermined acceleration range. (Note 5) The vibration control device according to any one of the appendices 1 to 4, wherein the adaptive processing unit individually optimizes according to the rotation direction of the reduction mechanism. (Note 6) The vibration control device according to any one of Appendix 1 to Appendix 5, wherein the adaptive processing unit individually optimizes the compensation order for the angular transmission error. (Note 7) The vibration control device according to any one of the appendices 1 to 6, wherein the adaptive processing unit optimizes the evaluation signal using an adaptive algorithm including normalized least mean squares (NLMS). (Note 8) The vibration control device according to any one of the appendices 1 to 7, wherein the adaptive processing unit optimizes the objective function using an adaptive algorithm including recursive least squares (RLS). (Note 9) The vibration control device according to any one of Appendix 1 to Appendix 8, further comprising an adaptive processing control unit that controls the optimization process in the adaptive processing unit based on predetermined processing control conditions. (Note 10) The vibration control device according to any one of appendices 1 to 9, further comprising a filter for removing components other than the compensation order component for the angular transmission error from the estimated disturbance. (Note 11) A vibration control device according to any one of the appendices 1 to 10, which calculates the estimated disturbance from the signal measured by the sensor. (Note 12) The vibration control device according to any one of Appendix 1 to Appendix 11, wherein the angle transmission error compensation unit includes an angle transmission error compensator that generates a sinusoidal compensation signal based on position information, having a compensation order for the angle transmission error, an amplitude and phase set by the adaptive processing unit; an adder that adds the compensation signal to a position command, a speed command, a current command, or a control signal related thereto; and a compensation model unit that corrects the compensation signal by referring to a compensation model that corrects the amplitude and phase based on speed information. (Note 13) The vibration control device described in any one of the appendices 1 to 12, wherein the angle transmission error compensator is configured to automatically set the amplitude and phase at frequencies corresponding to a predetermined speed range based on a control system configuration, control parameters, and frequency response characteristics derived from motor characteristics, with motor position, motor speed, or current as the control variable, and to register these settings in the compensation model. (Note 14) The vibration control device according to any one of Appendix 1 to Appendix 13, wherein the compensation model is a lookup table that references the amplitude and phase based on the velocity information. (Note 15) The vibration control device according to any one of Appendix 1 to Appendix 14, wherein the compensation model is set to correct the amplitude using a weighting coefficient that controls the effectiveness of the compensation signal according to a predetermined speed range of the speed information. (Note 16) The vibration control device according to any one of Appendix 1 to Appendix 15, wherein the position information is a position command or motor position, and the speed information is a position command speed or motor speed. (Note 17) The vibration control device according to any one of the appendices 1 to 16, wherein the angle transmission error compensator is configured such that the compensation signal becomes 0 when the speed information is 0. (Note 18) The vibration control device according to any one of Appendix 1 to Appendix 17, wherein the angle transmission error compensator generates the compensation signal from the amplitude and the phase according to the rotation direction of the reduction mechanism. (Note 19) The vibration control device according to any one of Appendix 1 to Appendix 18, wherein the angle transmission error compensator generates sinusoidal compensation signals for each compensation order based on the amplitude and phase for each compensation order, and generates the compensation signal by adding these together. (Note 20) The vibration control device according to any one of Appendix 1 to Appendix 19, wherein the angle transmission error compensator designs the compensation model and corrects the compensation signal regardless of the rotational inertia of the load connected to the output shaft of the reduction mechanism. (Note 21) The vibration control device according to any one of Appendix 1 to Appendix 20, wherein the angle transmission error compensator designs the compensation model and corrects the compensation signal regardless of the spring constant of the reduction mechanism. (Note 22) The vibration control device according to any one of Appendix 1 to Appendix 21, wherein the angle transmission error compensator corrects the amplitude and phase for generating the compensation signal based on the load torque acting on the reduction mechanism. (Note 23) The vibration control device according to any one of Appendix 1 to Appendix 22, wherein the angle transmission error compensator corrects the amplitude and phase for generating the compensation signal based on the temperature of the reduction mechanism, the temperature around the reduction mechanism, or a temperature assumed based on the operating conditions.

[0379] All documents, patent applications, and technical standards described herein are incorporated by reference to the same extent as if each individual document, patent application, and technical standard were specifically and individually noted to be incorporated by reference. [Explanation of symbols]

[0380] 1. Controlled object 2 Addition section 3. Compensation Models 10. Servo control system 11 Angle transmission error compensation unit 12 State Estimation Processing Unit 13. Evaluation Index Calculation Unit 14. Optimization Processing Unit 15 Adaptive Processing Unit 30 Angle transmission error measuring instrument 31. Angle transmission error estimator 32 Feedback control system 33 State Estimation Processing Unit 34. Evaluation Index Calculation Unit 35. Angle transmission error estimation device 40 Reaction force estimation observer 41 Adaptive Processing Unit 42. Angle transmission error compensator 43 Feedback control system 100_1, 100_2, 100_3, 100_4, 100_5, 100_6 Vibration control device 200 motor 300 Reduction mechanism 400 load 500 encoders 1000 Vibration Control System

Claims

1. A vibration damping control device applied to a servo control system equipped with a reduction mechanism, which compensates for rotational non-uniformity caused by the angle transmission error of the reduction mechanism, A state estimation processing unit that estimates the estimated disturbance, which is an internal state variable of the controlled object, based on observational information, An adaptive processing unit that uses the estimated disturbance as an evaluation signal and optimizes at least one of the evaluation signal or an objective function defined based on the evaluation signal, An angle transmission error compensation unit that generates a compensation signal, A vibration control device, including a vibration damping control device.

2. The vibration control device according to claim 1, wherein the state estimation processing unit is configured based on motor characteristics.

3. The vibration control device according to claim 1, wherein the state estimation processing unit includes at least one of a disturbance observer, a reaction force estimation observer, and a Kalman filter.

4. The vibration control device according to claim 1, wherein the adaptive processing unit further includes a weighting unit that controls the effectiveness of the evaluation signal using at least one of a weighting coefficient based on a predetermined speed range and a weighting coefficient based on a predetermined acceleration range.

5. The vibration control device according to claim 1, wherein the adaptive processing unit individually optimizes according to the rotation direction of the reduction mechanism.

6. The vibration control device according to claim 1, wherein the adaptive processing unit individually optimizes the compensation order for the angular transmission error.

7. The vibration control device according to claim 1, wherein the adaptive processing unit optimizes the evaluation signal using an adaptive algorithm including normalized least mean squares (NLMS).

8. The vibration control device according to claim 1, wherein the adaptive processing unit optimizes the objective function using an adaptive algorithm including recursive least squares (RLS).

9. The vibration control device according to claim 1, further comprising an adaptive processing control unit that controls the optimization process in the adaptive processing unit based on predetermined processing control conditions.

10. The vibration control device according to claim 1, further comprising a filter for removing components other than the compensation order component for the angular transmission error from the estimated disturbance.

11. The vibration control device according to claim 1, wherein the estimated disturbance is calculated from the signal measured by the sensor.

12. The angle transmission error compensation unit is, An angle transmission error compensator having a compensation order for the angle transmission error, an amplitude and phase set by the adaptive processing unit, and generating a sinusoidal compensation signal based on position information; An adder that adds the compensation signal to a position command, speed command, current command, or a control signal related thereto, The angle transmission error compensator includes a compensation model unit that corrects the compensation signal by referring to a compensation model that corrects the amplitude and phase based on velocity information, A vibration control device according to claim 1, including the following:

13. The vibration control device according to claim 12, wherein the angle transmission error compensator is configured to automatically set the amplitude and phase at frequencies corresponding to a predetermined speed range based on a control system configuration in which one of the motor position, motor speed, or current is the control variable, the control parameters, and the frequency response characteristics derived from the motor characteristics, and register these settings in the compensation model.

14. The vibration control device according to claim 12, wherein the compensation model is a lookup table that references the amplitude and the phase based on the velocity information.

15. The vibration control device according to claim 12, wherein the compensation model is set to correct the amplitude using a weighting coefficient that controls the effectiveness of the compensation signal according to a predetermined speed range of the speed information.

16. The position information is a position command or motor position. The vibration control device according to claim 12, wherein the speed information is a position command speed or motor speed.

17. The vibration control device according to claim 12, wherein the angle transmission error compensator is configured such that the compensation signal becomes 0 when the speed information is 0.

18. The vibration control device according to claim 12, wherein the angle transmission error compensator generates the compensation signal from the amplitude and the phase according to the rotation direction of the reduction mechanism.

19. The vibration control device according to claim 12, wherein the angle transmission error compensator generates sinusoidal compensation signals for each compensation order based on the amplitude and phase for each compensation order, and generates the compensation signal by adding these together.

20. The vibration control device according to claim 12, wherein the angle transmission error compensator designs the compensation model and corrects the compensation signal regardless of the rotational inertia of the load connected to the output shaft of the reduction mechanism.

21. The vibration control device according to claim 12, wherein the angle transmission error compensator designs the compensation model and corrects the compensation signal regardless of the spring constant of the reduction mechanism.

22. The vibration control device according to claim 12, wherein the angle transmission error compensator corrects the amplitude and phase for generating the compensation signal based on the load torque acting on the reduction mechanism.

23. The vibration control device according to claim 12, wherein the angle transmission error compensator corrects the amplitude and phase for generating the compensation signal based on the temperature of the reduction mechanism, the temperature around the reduction mechanism, or a temperature assumed based on the operating conditions.

24. A vibration damping control method applied to a servo control system equipped with a reduction mechanism, which compensates for rotational non-uniformity caused by the influence of angular transmission error of the reduction mechanism, Based on observational information, the estimated disturbance, which is an internal state variable of the controlled object, is estimated. The estimated disturbance is used as the evaluation signal, and an adaptive process is performed to optimize at least one of the evaluation signal or the objective function defined based on the evaluation signal. Generate a compensation signal. A vibration control method in which a computer performs the action.

25. A vibration damping control program applied to a servo control system equipped with a reduction mechanism, which compensates for rotational non-uniformity caused by the influence of angular transmission error of the reduction mechanism, Based on observational information, the estimated disturbance, which is an internal state variable of the controlled object, is estimated. The estimated disturbance is used as the evaluation signal, and an adaptive process is performed to optimize at least one of the evaluation signal or the objective function defined based on the evaluation signal. Generate a compensation signal. A vibration control program that instructs a computer to perform this action.

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