Angular transmission error estimation device, angular transmission error estimation method, angular transmission error estimation program, vibration damping control device, vibration damping control method, and vibration damping control program

Abstract

The present invention provides an angular transmission error estimation device, an angular transmission error estimation method, an angular transmission error estimation program, a vibration suppression control device, a vibration suppression control method, and a vibration suppression control program that compensate for rotational non-uniformity caused by the influence of angular transmission error in a reduction mechanism and are related to the compensation. [Solution] The angular transmission error estimation device is applied to a servo control system equipped with a reduction gear mechanism and estimates rotation non-uniformity caused by the influence of the angular transmission error of the reduction gear mechanism, and includes a state estimation processing unit that estimates an estimated disturbance, which is an internal state quantity of a controlled object, based on observation information, and an evaluation index calculation unit that calculates an evaluation index based on the estimated disturbance and on order components of a predetermined order that corresponds to the rotation non-uniformity.

Description

[Technical Field]

[0001] The present disclosure relates to a vibration control device, a vibration control method, and a vibration control program, and in particular to a technology for compensating for angular transmission error in a reduction gear mechanism, and further to an angular transmission error estimation device, an angular transmission error estimation method, and an angular transmission error estimation program related thereto. [Background technology]

[0002] In recent years, high-precision servo control systems for robots, machine tools, and other applications have adopted motors and actuators using compact, high-precision reduction mechanisms, particularly strain wave gearing and planetary gear mechanisms. While these reduction mechanisms offer both high reduction ratios and compact size, they are known to suffer from a rotational angle deviation known as angular transmission error (angular transmission error) due to structural tooth profile and assembly errors. Angular transmission error is the difference between the theoretical and actual rotational output angles when a rotational input is applied to a reduction mechanism, and it periodically repeats with respect to the rotational input. In particular, angular transmission error, which includes periodic vibration components associated with motor rotation, manifests itself in the output shaft as rotational nonuniformity (e.g., rotational irregularity, waviness, speed fluctuations), degrading the motion and trajectory accuracy of robots and other equipment. This phenomenon is known as vibration caused by angular transmission error. In general, compensation for rotational non-uniformity (vibration phenomenon) involves adjusting the rotational input to the reduction mechanism using a compensation signal so as to cancel out periodic angular transmission errors relative to the motor rotation position (i.e., to bring the error in the rotational output of the reduction mechanism closer to zero) (see, for example, Patent Document 1). Also known is a method that adds correction to the motor speed, as in Patent Document 2. [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, Ming Iku, Kohei Onishi: Force Sensorless Compliance Control of Multi-DOF Robots Based on 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 and Kohei Onishi: Dynamics Identification Method for Multi-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 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 Summary of the Invention [Problem to be solved by the invention]

[0005] However, with the techniques described in Patent Documents 1 and 2, various factors can affect the determination (or identification or estimation) of appropriate parameters, or can make it difficult to achieve sufficient compensation.

[0006] The present disclosure has been made in consideration of the above circumstances, and aims to provide a vibration suppression control device, a vibration suppression control method, and a vibration suppression control program that compensate for non-uniformity in rotation caused by the influence of angular transmission error in a reduction gear mechanism. It is also an object of the present disclosure to provide an angular transmission error estimation device, an angular transmission error estimation method, and an angular transmission error estimation program related to the compensation. [Means for solving the problem]

[0007] A first aspect of the present disclosure is an angular transmission error estimation device that is applied to a servo control system equipped with a speed reduction mechanism and estimates rotation non-uniformity caused by the influence of angular transmission error of the speed reduction mechanism, the angular transmission error estimation device including: a state estimation processing unit that estimates an estimated disturbance, which is an internal state quantity of a controlled object, based on observation information; and an evaluation index calculation unit that calculates an evaluation index based on the estimated disturbance and on order components of a predetermined order that corresponds to the rotation non-uniformity.

[0008] A second aspect of the present disclosure is an angular transmission error estimation method that is applied to a servo control system equipped with a reduction gear mechanism and estimates rotation non-uniformity caused by the influence of angular transmission error of the reduction gear mechanism, the method being executed by a computer to estimate an estimated disturbance, which is an internal state quantity of a controlled object, based on observation information, and calculate an evaluation index based on the estimated disturbance and on an order component of a predetermined order that corresponds to the rotation non-uniformity.

[0009] A third aspect of the present disclosure is an angular transmission error estimation program that is applied to a servo control system equipped with a reduction gear mechanism and estimates rotation non-uniformity caused by the influence of angular transmission error of the reduction gear mechanism, the program comprising: estimating an estimated disturbance, which is an internal state quantity of a controlled object, based on observation information; and calculating an evaluation index based on the estimated disturbance and on a predetermined order component corresponding to the non-uniformity of rotation.

[0010] A fourth aspect of the present disclosure is a vibration suppression control device that includes the angular transmission error estimating device of the first aspect and an angular transmission error compensator that generates a compensation signal, and that optimizes at least one of the evaluation index or an objective function defined based on the evaluation index, and corrects the compensation signal.

[0011] A fifth aspect of the present disclosure is a vibration suppression control method that is applied to a servo control system equipped with a reduction gear mechanism and compensates for rotation non-uniformity caused by the influence of angular transmission error of the reduction gear mechanism, the vibration suppression control method being executed by a computer to estimate an estimated disturbance, which is an internal state quantity of a controlled object, based on observation information, calculate an evaluation index based on an order component of a predetermined order corresponding to the rotation non-uniformity based on the estimated disturbance, generate a compensation signal, optimize at least one of the evaluation index or an objective function defined based on the evaluation index, and correct the compensation signal.

[0012] A sixth aspect of the present disclosure is a vibration control program that is applied to a servo control system equipped with a reduction mechanism and compensates for rotational non-uniformity caused by the influence of angular transmission error of the reduction mechanism, the vibration control program causing a computer to execute the following steps: estimate an estimated disturbance, which is an internal state quantity of a controlled object, based on observation information; calculate an evaluation index based on an order component of a predetermined order corresponding to the rotational non-uniformity based on the estimated disturbance; generate a compensation signal; optimize at least one of the evaluation index or an objective function defined based on the evaluation index; and correct the compensation signal. [Effects of the Invention]

[0013] According to the present disclosure, particularly in semi-closed control, the influence of the angular transmission error of the reduction mechanism can be calculated as an evaluation index and the angular transmission error characteristics of the reduction mechanism can be estimated without requiring any additional sensors. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is a diagram showing a schematic configuration of a vibration suppression control system. [Figure 2] FIG. 2 is a diagram illustrating a first configuration example of a control block for dynamic angular transmission error compensation of a vibration damping control device according to an embodiment of the present disclosure. [Figure 3] FIG. 3 is a diagram illustrating a second configuration example of a control block for dynamic angular transmission error compensation of a vibration damping control device according to an embodiment of the present disclosure. [Figure 4]FIG. 4 is a diagram illustrating a third configuration example of a control block for dynamic angular transmission error compensation of a vibration damping control device according to an embodiment of the present disclosure. [Figure 5] FIG. 5 is a control block diagram in the case where the compensator input is used as command information. [Figure 6] FIG. 6 is a diagram showing response data of the motor speed in a constant speed section when the motor is operated at a constant speed at a plurality of operating speeds. [Figure 7] FIG. 7 is a diagram showing response data of the load speed in a constant speed section when the motor is operated at a constant speed at a plurality of operating speeds. [Figure 8] FIG. 8 is a diagram showing the results of an order analysis of the motor speed when the operating speed is 1600 r / min. [Figure 9] FIG. 9 is a diagram showing the results of order analysis of the load speed when the operating speed is 1600 r / min. [Figure 10] FIG. 10 is a diagram showing the extraction results of the motor speed secondary component at a plurality of operating speeds. [Figure 11] FIG. 11 is a diagram showing the extraction results of the load speed secondary component at a plurality of operating speeds. [Figure 12] FIG. 12 is a diagram showing the motor position secondary component under condition A. [Figure 13] FIG. 13 is a diagram showing the load position second-order component under condition A. [Figure 14] FIG. 14 is a diagram showing the motor speed secondary component under condition A. [Figure 15] FIG. 15 is a diagram showing the load speed second-order component under condition A. [Figure 16] FIG. 16 is a diagram showing the motor position secondary component under condition B. [Figure 17] FIG. 17 is a diagram showing the load position second-order component under condition B. [Figure 18] FIG. 18 is a diagram showing the motor speed secondary component under condition B. [Figure 19] FIG. 19 is a diagram showing the load speed second-order component under condition B. [Figure 20] FIG. 20 is a diagram showing the motor position second-order component under condition C. [Figure 21] FIG. 21 is a diagram showing the load position second-order component under condition C. [Figure 22] FIG. 22 is a diagram showing the motor speed second-order component under condition C. [Figure 23] FIG. 23 is a diagram showing the load speed second-order component under condition C. [Figure 24] FIG. 24 is a diagram showing the amplitude characteristics in the frequency response characteristics from the angle transmission error to the compensation current, and the compensation parameters corresponding to the motor speeds for the number of look-up tables. [Figure 25] FIG. 25 is a diagram showing the phase characteristics in the frequency response characteristics from the angular transmission error to the compensation current, and the compensation parameters corresponding to the motor speeds for the number of look-up tables. [Figure 26] FIG. 26 is a diagram showing the motor speed under condition D. [Figure 27] FIG. 27 is a diagram showing the load speed under condition D. [Figure 28] FIG. 28 is a diagram showing the motor speed vibration component under condition D. [Figure 29] FIG. 29 is a diagram showing the load speed vibration component under condition D. [Figure 30] FIG. 30 is a diagram showing the motor position vibration component under condition D. [Figure 31] FIG. 31 is a diagram showing the load position vibration component under condition D. [Figure 32] FIG. 32 is a diagram showing the motor speed under condition E. [Figure 33] FIG. 33 is a diagram showing the load speed under condition E. [Figure 34] FIG. 34 is a diagram showing the motor speed vibration component under condition E. [Figure 35] FIG. 35 is a diagram showing the load speed vibration component under condition E. [Figure 36] FIG. 36 is a diagram showing the motor position vibration component under condition E. [Figure 37] FIG. 37 is a diagram showing the load position vibration component under condition E. [Figure 38]FIG. 38 is a diagram showing the motor speed under condition F. [Figure 39] FIG. 39 is a diagram showing the load speed under condition F. [Figure 40] FIG. 40 is a diagram showing the motor speed vibration component under condition F. [Figure 41] FIG. 41 is a diagram showing the load speed vibration component under condition F. [Figure 42] FIG. 42 is a diagram showing the motor position vibration component under condition F. [Figure 43] FIG. 43 is a diagram showing the load position vibration component under condition F. [Figure 44] FIG. 44 is a diagram showing the motor speed under condition G. [Figure 45] FIG. 45 is a diagram showing the load speed under condition G. [Figure 46] FIG. 46 is a diagram showing the motor speed vibration component under condition G. [Figure 47] FIG. 47 is a diagram showing the load speed vibration component under condition G. [Figure 48] FIG. 48 is a diagram showing the motor position vibration component under condition G. [Figure 49] FIG. 49 is a diagram showing the load position vibration component under condition G. [Figure 50] FIG. 50 is a diagram showing the motor speed under condition H. [Figure 51] FIG. 51 is a diagram showing the load speed under condition H. [Figure 52] FIG. 52 is a diagram showing the motor speed vibration component under condition H. [Figure 53] FIG. 53 is a diagram showing the load speed vibration component under condition H. [Figure 54] FIG. 54 is a diagram showing the motor position vibration component under condition H. [Figure 55] FIG. 55 is a diagram showing the load position vibration component under condition H. [Figure 56] FIG. 56 is a diagram showing the amplitude characteristics in the frequency response characteristics from the angular transmission error to the compensation position and the corresponding compensation parameters. [Figure 57]FIG. 57 is a diagram showing the phase characteristics in the frequency response characteristics from the angular transmission error to the compensation position and the corresponding compensation parameters. [Figure 58] FIG. 58 is a diagram showing the motor speed under condition I. [Figure 59] FIG. 59 is a diagram showing the load speed under condition I. [Figure 60] FIG. 60 is a diagram showing the motor speed vibration component under condition I. [Figure 61] FIG. 61 is a diagram showing the load speed vibration component under condition I. [Figure 62] FIG. 62 is a diagram showing the motor position vibration component under condition I. [Figure 63] FIG. 63 is a diagram showing the load position vibration component under condition I. [Figure 64] FIG. 64 is a diagram showing the motor speed under condition J. [Figure 65] FIG. 65 is a diagram showing the load speed under condition J. [Figure 66] FIG. 66 is a diagram showing the motor speed vibration component under condition J. [Figure 67] FIG. 67 is a diagram showing the load speed vibration component under condition J. [Figure 68] FIG. 68 is a diagram showing the motor position vibration component under condition J. [Figure 69] FIG. 69 is a diagram showing the load position vibration component under condition J. [Figure 70] FIG. 70 is a diagram showing the motor speed under condition K. [Figure 71] FIG. 71 is a diagram showing the load speed under condition K. [Figure 72] FIG. 72 is a diagram showing the motor speed vibration component under condition K. [Figure 73] FIG. 73 is a diagram showing the load speed vibration component under condition K. [Figure 74] FIG. 74 is a diagram showing the motor position vibration component under condition K. [Figure 75] FIG. 75 is a diagram showing the load position vibration component under condition K. [Figure 76]FIG. 76 is a diagram showing the error between the motor position and the position command under condition K. [Figure 77] FIG. 77 is a diagram showing the error between the motor position and the approximate motor position under condition K. [Figure 78] FIG. 78 is a diagram showing load position vibration components when the compensator input is command information and the servo control approximation characteristic is a dead time element. [Figure 79] FIG. 79 is a diagram showing the error between the motor position and the approximate motor position when the compensator input is the command information and the servo control approximate characteristic is the dead time element. [Figure 80] FIG. 80 is a diagram showing the motor speed under condition L. [Figure 81] FIG. 81 is a diagram showing the load speed under condition L. [Figure 82] FIG. 82 is a diagram showing the motor speed vibration component under condition L. [Figure 83] FIG. 83 is a diagram showing the load speed vibration component under condition L. [Figure 84] FIG. 84 is a diagram showing the motor position vibration component under condition L. [Figure 85] FIG. 85 is a diagram showing the load position vibration component under condition L. [Figure 86] FIG. 86 is a diagram showing the motor speed under condition M. [Figure 87] FIG. 87 is a diagram showing the load speed under condition M. [Figure 88] FIG. 88 is a diagram showing the motor speed vibration component under condition M. [Figure 89] FIG. 89 is a diagram showing the load speed vibration component under condition M. [Figure 90] FIG. 90 is a diagram showing the motor position vibration component under condition M. [Figure 91] FIG. 91 is a diagram showing the load position vibration component under condition M. [Figure 92] FIG. 92 is a diagram showing the motor speed under condition N. [Figure 93] FIG. 93 is a diagram showing the load speed under condition N. [Figure 94]FIG. 94 is a diagram showing the motor speed vibration component under condition N. [Figure 95] FIG. 95 is a diagram showing the load speed vibration component under condition N. [Figure 96] FIG. 96 is a diagram showing the motor position vibration component under condition N. [Figure 97] FIG. 97 is a diagram showing the load position vibration component under condition N. [Figure 98] FIG. 98 is a diagram showing the load inertia moment variation ratio. [Figure 99] FIG. 99 is a diagram showing the motor speed under condition O. [Figure 100] FIG. 100 is a diagram showing the load speed under condition O. [Figure 101] FIG. 101 is a diagram showing the motor speed vibration component under condition O. [Figure 102] FIG. 102 is a diagram showing the load speed vibration component under condition O. [Figure 103] FIG. 103 is a diagram showing the motor position vibration component under condition O. [Figure 104] FIG. 104 is a diagram showing the load position vibration component under condition O. [Figure 105] FIG. 105 is a diagram showing the motor speed under condition P. [Figure 106] FIG. 106 is a diagram showing the load speed under condition P. [Figure 107] FIG. 107 is a diagram showing the motor speed vibration component under condition P. [Figure 108] FIG. 108 is a diagram showing the load speed vibration component under condition P. [Figure 109] FIG. 109 is a diagram showing the motor position vibration component under condition P. [Figure 110] FIG. 110 is a diagram showing the load position vibration component under condition P. [Figure 111] FIG. 111 is a diagram showing the motor position vibration component under condition Q. [Figure 112] FIG. 112 is a diagram showing the load position vibration component under condition Q. [Figure 113]FIG. 113 is a diagram showing the motor position vibration component under condition R. [Figure 114] FIG. 114 is a diagram showing the load position vibration component under condition R. [Figure 115] FIG. 115 is a diagram showing the motor position vibration component under condition S. [Figure 116] FIG. 116 is a diagram showing the load position vibration component under condition S. [Figure 117] FIG. 117 is a diagram showing the motor position vibration component under condition T. [Figure 118] FIG. 118 is a diagram showing the load position vibration component under condition T. [Figure 119] FIG. 119 is a diagram showing the motor position vibration component under condition U. [Figure 120] FIG. 120 is a diagram showing the load position vibration component under condition U. [Figure 121] FIG. 121 is a diagram showing the motor position vibration component under condition V. [Figure 122] FIG. 122 is a diagram showing the load position vibration component under condition V. [Figure 123] FIG. 123 is an enlarged view of a part of the motor speed vibration component shown in FIG. [Figure 124] FIG. 124 is a flowchart of a vibration suppression control program in a servo control system equipped with a speed reducing mechanism. [Figure 125] FIG. 125 is a block diagram showing the angular transmission error characteristic estimation. [Figure 126] FIG. 126 is a block diagram showing the functional configuration of the vibration damping control device 100_5. [Figure 127] FIG. 127 is a diagram illustrating a first configuration example of a control block of an angular transmission error characteristic estimation device according to an embodiment of the present disclosure. [Figure 128] FIG. 128 is a diagram showing a block diagram of a lock-in amplifier in the calculation of the evaluation index of the present disclosure. [Figure 129] FIG. 129 is a diagram showing the motor speed under condition W. [Figure 130]FIG. 130 is a diagram showing the load speed under condition W. [Figure 131] FIG. 131 is a diagram showing the reaction torque under condition W. [Figure 132] FIG. 132 is a diagram showing an estimated disturbance under condition W. [Figure 133] FIG. 133 is a diagram showing the evaluation index (LIA output) under condition W. [Figure 134] FIG. 134 is a diagram showing the motor speed under condition X. [Figure 135] FIG. 135 is a diagram showing the load speed under condition X. [Figure 136] FIG. 136 is a diagram showing the reaction torque under condition X. [Figure 137] FIG. 137 is a diagram showing an estimated disturbance under condition X. [Figure 138] FIG. 138 is a diagram showing the evaluation index (LIA output) under condition X. [Figure 139] FIG. 139 is a diagram showing the motor speed under condition Y. [Figure 140] FIG. 140 is a diagram showing the load speed under condition Y. [Figure 141] FIG. 141 is a diagram showing the reaction torque under condition Y. [Figure 142] FIG. 142 is a diagram showing an estimated disturbance under condition Y. [Figure 143] FIG. 143 is a diagram showing the evaluation index (LIA output) under condition Y. [Figure 144] FIG. 144 is a diagram showing the motor speed under condition Z. [Figure 145] FIG. 145 is a diagram showing the load speed under condition Z. [Figure 146] FIG. 146 is a diagram showing the reaction torque under condition Z. [Figure 147] FIG. 147 is a diagram showing an estimated disturbance under condition Z. [Figure 148] FIG. 148 is a diagram showing the evaluation index (LIA output) under condition Z. [Figure 149]FIG. 149 is a flowchart of an angular transmission error estimation program for estimating the influence of the angular transmission error of the reduction mechanism. [Figure 150] FIG. 150 is a flowchart of a vibration suppression control program that compensates for non-uniformity in rotation due to the influence of angular transmission error in the reduction mechanism. DETAILED DESCRIPTION OF THE INVENTION

[0015] Hereinafter, the embodiments will be described in detail with reference to the drawings.

[0016] [Vibration suppression control system configuration and the effect of angular transmission error] (Vibration control system configuration) 1 shows a schematic configuration diagram of a vibration damping control system. The vibration damping control system 1000 includes, for example, a vibration damping control device 100_1, a motor 200, a speed reduction mechanism 300, a load 400, and an encoder 500. The vibration damping control device 100_1 is a computer device including one or more processors, memories, etc. Note that the vibration damping control system 1000 may include a vibration damping control device 100_2, a vibration damping control device 100_3, a vibration damping control device 100_4, or a vibration damping control device 100_5, which will be described later, instead of the vibration damping control device 100_1. Hereinafter, when the vibration damping control device 100_1, the vibration damping control device 100_2, the vibration damping control device 100_3, the vibration damping control device 100_4, and the vibration damping control device 100_5 are not to be distinguished from one another, they may be referred to as vibration damping control devices or simply as control devices. In the following, the motor 200, the speed reduction mechanism 300, the load 400, the encoder 500, and the vibration suppression control system 1000 may be simply referred to as the motor, the speed reduction mechanism, the load, the encoder, and the vibration suppression control system. The vibration suppression control device may be a single control unit or may be composed of two or more control units (e.g., a combination of a PLC (programmable logic controller) and, for example, a servo driver and a servo control unit). The control device calculates a target trajectory of the load to generate a position command, generates a speed command, a torque command, or a 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 a drive current as command values ​​(target values). Note that the command value may be a position command, a speed command, or a torque command depending on the purpose of the control device. Many control devices are so-called embedded systems, and therefore may have limited computer resources, such as the processing power (e.g., CPU performance) and the amount of storage resources used (e.g., ROM capacity and RAM capacity) of the control device.

[0017] The motor rotates its shaft by a drive current supplied from the control device. The motor (e.g., a servo motor) may include 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. The motor may also include 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.

[0018] The reduction mechanism has a motor rotating shaft connected to an input shaft of the reduction mechanism, reduces the motor rotation at a predetermined reduction ratio, and drives a load via an output shaft of the reduction mechanism. The motor rotating shaft may be connected to the input shaft of the reduction mechanism via, for example, a belt mechanism. The load is a robot arm or the like connected to the output shaft of the reduction mechanism. The output shaft of the reduction mechanism may also be equipped with a position detector. Position information of the output shaft of the reduction mechanism is sometimes referred to as load position. The reduction mechanism may also be equipped with a torque sensor for detecting load torque for driving the load. The torque sensor is capable of outputting a load torque signal representing the load torque to a control device. The reduction mechanism may also be, for example, a harmonic gear device, a belt pulley mechanism, a RV reducer, or a planetary gear mechanism.

[0019] A servo control system is a system for accurately controlling output (position, speed, or torque (current)) according to a command value, and may be a control system using a servo motor. The control amount is the state quantity of the control target 1 to be controlled, and may be observed by various detectors (for example, a position detector) and used for feedback control. Position control controls the control amount as a position using a command value as a target position (angle). Speed ​​control controls the control amount as a speed using a command value as a target speed (rotational speed). Torque control controls the control amount as a torque using a command as a target torque (current). Note that the output torque of a motor is controlled in proportion to the current flowing through the motor, so it is sometimes called current control.

[0020] Position control, speed control, and torque control (current control) may be configured as a multi-loop structure. In a multi-loop structure, the processing cycle of the outer loop speed control or position control may be changed compared to the inner loop current control, taking into account the trade-off between the responsiveness (control performance) and calculation load of each loop, and the processing cycle of the target trajectory calculation (for example, command unit, command generation unit) may be further slowed down.

[0021] Semi-closed loop control is a method in which the control variable is the output shaft of the reduction mechanism, a position detector is installed on the motor side, and feedback control is performed using the rotational position of the motor.This does not directly detect the actual position of the output shaft of the reduction mechanism, but rather controls based on information from the motor side.

[0022] (effect of angular transmission error) Here, we will summarize the definition of angular transmission error and the effect that angular transmission error has on servo control systems.

[0023] Angular transmission error is defined as the difference between the rotation angle of the theoretically rotating output and the rotation angle of the actually rotated output. The characteristics of angular transmission error are determined mainly by the processing errors of the reduction mechanism (for example, dimensional errors and gear errors of the reduction mechanism components) and assembly errors (for example, deformation of parts). As a result, there are individual differences between products, and the angular transmission error characteristics differ depending on the rotation direction of the reduction mechanism.

[0024] The effects of angular transmission error can be broadly divided into the following two types: Static: Deterioration of positioning accuracy Dynamic: Fluctuations in rotation speed (operation speed) during operation (unevenness of rotation)

[0025] As can be seen from the definition of angular transmission error, the static effect does not result in a rotation angle that is the theoretically rotating output, which leads to a deterioration in accuracy during positioning.

[0026] Regarding dynamic effects, for example, technical materials on strain wave gearing (Harmonic Drive (registered trademark)) explain them as follows: When the natural frequency of a vibration system including a strain wave gearing 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 strain wave gearing is amplified. In this case, the non-uniformity of rotation behaves as a vibration phenomenon caused by angular transmission error.

[0027] For example, in a strain wave gearing, due to its structural characteristics, angular error components are generated mainly twice per rotation of the input shaft, so the frequency of the main component of the angular error corresponds to twice the input frequency. Therefore, if resonance occurs in a frequency range corresponding to twice the input frequency, there is a risk that the angular transmission error will be significantly amplified.

[0028] The actual vibration frequency is affected by servo control, and is not the natural frequency mentioned above, but the vibration frequency of the system including servo control, amplifying the effect of the angular transmission error.As a result, the effect of the angular transmission error behaves differently depending on the motor speed (input frequency).

[0029] Static effects tend to be an issue mainly during PTP (Point To Point) operation, while dynamic effects tend to be an issue 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. Taking into account the harmonic order relative to the motor position, the angular transmission error can be expressed by equation (1).

number

[0030] The symbols in formula (1) are as follows: θ Sync : Angular transmission error, unit is arc-seconds (arc-sec). θ m : Motor position, unit is radians (rad). k: harmonic order O C : Coefficient determined by the structure of the reduction mechanism (real number, not limited to integer) A k : Amplitude of each order, unit is arc-seconds (arc-sec). φ k : Each order phase, unit is radian (rad). The arc-sec is a unit of angle equivalent to 1 / 3600 of a degree (°) and is used to express very small angles.

[0031] In actual angular transmission error, there may be components that cannot be expressed by equation (1). However, it is known that the above components are often dominant and often reproducible. Therefore, in the following, the angular transmission error will be expressed as θ Sync In order to distinguish it from the definition of angular transmission error, it is expressed as synchronous (Sync) with respect to the motor position.

[0032] Additionally, the vibration component with two cycles per rotation of the input shaft (motor position) is called the "second-order component," and the vibration with n cycles per rotation of the input shaft is called the nth-order component. Note that depending on the structure of the reduction mechanism, there may be cases where the order of the components is not integer.

[0033] [Vibration suppression control method (dynamic angular transmission error compensation)] (Dynamic Angular Transmission Error Compensation) Hereinafter, a vibration suppression control system according to an embodiment of the present disclosure will be described with reference to the drawings. The effect of suppressing rotation non-uniformity (vibration suppression effect) of the present disclosure will be quantitatively demonstrated by a numerical simulation described later.

[0034] A control block diagram of dynamic angular transmission error compensation is shown in Figure 2. The control system here is a multi-loop configuration consisting of position control, speed control, and current control, and the control device is configured as a position control.

[0035] 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 : Velocity feedback filter Delay: Delay element in current control systems, etc. C ATE :Angular transmission error compensator i ATEComp :Compensation signal (compensation current) R: Reduction ratio J m :Motor moment of inertia K t : Torque constant J l : Load moment of inertia K g : Reduction mechanism spring constant θ Sync :Angular transmission error Delay=e -Tds as a second-order Padé approximation Represented as JPEG0007800877000003.jpg1742 T d : Delay time JPEG0007800877000004.jpg1126 T V : Velocity feedback filter time constant

[0036] The control device outputs a drive current to the motor based on a position command generated by a command generation unit (not shown) and a motor position acquired from a position detector (not shown). The control device is equipped with a position control unit (not shown), a speed control unit (not shown), a torque control unit (not shown), and an angular 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 a compensation signal (compensation current) output from the angular transmission error compensator. The motor speed is obtained by passing the motor speed information, which is the result of a differential operation with respect to the motor position, through a speed feedback filter.

[0037] The motor is driven based on a drive current from a control device, and when torque is applied to the motor from the drive current via a torque constant, the rotational position of the motor changes with an acceleration according to the motor's moment of inertia, and is integrated over time and converted into the motor position.

[0038] The reduction mechanism reduces the motor rotation speed at 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 spring constant (rigidity) of the reduction mechanism. The torque that drives the load acts as a reaction force on the motor.

[0039] The load is applied with a torque output from the reduction mechanism for driving the load, and the load position is obtained according to the load moment of inertia, similar to a motor.

[0040] A drive system including a motor, a reduction mechanism, and a load can be modeled as a so-called two-inertia system.

[0041] The angular transmission error compensator generates a sinusoidal compensation signal, including a compensation model 3 (described later). This compensation signal suppresses vibration caused by the angular transmission error. Hereinafter, the compensation model 3 may be simply referred to as the compensation model.

[0042] Terms used in this disclosure are defined as follows:

[0043] The control system configuration refers to the configuration of the control method in the control device. For example, in the case of Figure 2, it shows the configuration of a feedback control system made up of position proportional control, speed proportional integral control, and a filter.

[0044] Control parameters refer to parameters that determine the response characteristics of various controls in a control system configuration, and in the case of Fig. 2, for example, they indicate the position loop gain, speed loop gain, speed loop integral time constant, torque filter time constant, speed feedback filter time constant, and delay time. Note that the content, type, set value, etc. of the control parameters may differ depending on the control system configuration.

[0045] Motor characteristics refer to the characteristics that determine the dynamic characteristics of a motor, and for example, in the case of Figure 2, they include the characteristics of a second-order integral system including the torque constant and the motor moment of inertia. Note that if the motor is connected to a reduction mechanism via a belt mechanism, for example, these characteristics are treated as part of the dynamic characteristics.

[0046] Dynamic angular transmission error compensation refers to a vibration suppression control method for compensating for the dynamic effects of angular transmission error (vibration phenomena caused by angular transmission error).

[0047] The position information refers to the motor position or the position command, and the speed information refers to the motor speed or the position command speed.

[0048] The frequency response characteristic refers to the change in amplitude and phase of the output signal for each frequency when sine waves of various frequencies are input to a certain transfer function or system.

[0049] (Dynamic angular transmission error compensation, automatic setting of compensation parameters) Here, we will describe a method for compensating for the dynamic effects of the angular transmission error shown in equation (1). In particular, we will describe an angular transmission error compensator for dynamic angular transmission error compensation, the configuration of which is shown in Figure 2. In Figure 2, reference numeral 1 represents the controlled object, reference numeral 200 represents the motor, reference numeral 300 represents the reduction mechanism, reference numeral 400 represents the load, and reference numeral 100_1 represents the vibration suppression control device.

[0050] [composition] In this configuration, the compensation signal generated by the angular transmission error compensator is the compensation current i ATEComp is shown in equations (2) to (5).

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[0051] The symbols in equations (2) to (5) are as follows: i: Compensation order A i : Amplitude of each compensation order, unit is arc-seconds (arc-sec). φ i : Each compensation order phase, unit is radian (rad). A Ci : Angular transmission error compensator amplitude at each compensation order, in amperes per arc-second (A / arc-sec). φ Ci : Angular transmission error compensator phase for each compensation order, unit is radian (rad). ω m : Motor speed, in revolutions per minute (r / min). ωmi : Motor speed angular frequency for i JPEG0007800877000009.jpg927, units are radians per second (rad / s). j: imaginary unit

[0052] Note that this formula takes into consideration the comparison with the angular transmission error shown in equation (1) and also takes into account support for multiple compensation orders, which will be described later.

[0053] Hereafter, we will use A corresponding to the angular transmission error in the controlled object 1. i , φ i is called the angular transmission error characteristic. This characteristic uses a value that is measured in advance or measured or identified on the system.

[0054] The amplitude and phase of the angular transmission error compensator at each compensation order are expressed as the transfer function from the angular transmission error to the compensation current. JPEG0007800877000010.jpg923 is used to calculate the frequency response characteristics at frequencies corresponding to the system's operating speed range, and this is configured as a compensation model. π in equation (4) corresponds to compensation in antiphase, and equation (3) can be multiplied by "-1". This automatically sets the parameters of the compensation model and registers them in the compensation model.

[0055] Hereinafter, the parameters in the angular transmission error compensator, namely, the angular transmission error characteristics and the information required for the compensation model, will be collectively referred to as the compensation parameters. For example, if the reduction mechanism is a strain wave gearing, the coefficient O, determined by the structure of the reduction mechanism, c is shown in equation (5).

[0056] In this configuration, the adder 2 adds the compensation signal to the current command. Hereinafter, the adder 2 may be simply referred to as the adder. Here, the current command is the target to which the compensation signal is added, and in this disclosure this is referred to as the compensation addition point. In this configuration, the compensation addition point is the current command in order to unify the compensation addition point regardless of the control mode (selection of one of position control, speed control, or torque control).

[0057] The dynamic influence of the angular transmission error of the reduction gear mechanism is affected by various structural and control factors in addition to motor position. Therefore, the angular transmission error compensator generates a compensation current, which is a sinusoidal compensation signal, based on the angular transmission error characteristics of a separately determined compensation order and the motor position. To compensate for the influence of control factors, the amplitude and phase used to generate the compensation signal are corrected using a compensation model that uses a transfer function from the angular transmission error to the compensation current and calculates the amplitude and phase from the frequency response characteristics at a frequency corresponding to the motor speed as the angular transmission error compensator amplitude and phase for each compensation order. The sine wave generated when generating the compensation signal can be achieved, for example, by table lookup for a sinusoidal function or position.

[0058] The transfer function from the angular transmission error to the compensation current is expressed by equation (6).

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[0059] The symbols in equation (6) are as in equations (7) and (8).

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[0060] As shown in equation (6), the transfer function from the angular transmission error to the compensation current is not proper, and generally needs to be made proper for realization. However, in this case, the effect of making it proper is limited in suppressing the rotation non-uniformity.

[0061] In this disclosure, by utilizing the fact that the angular transmission error can be expressed as the sum of sine waves, a compensation model has amplitude and phase calculated from frequency response characteristics, and the amplitude and phase used to generate a sine wave compensation signal of each compensation order are corrected using the compensation model to generate a desired compensation signal. As a result, by correcting the amplitude and phase from the frequency response characteristics rather than as a transfer function, it is possible to suppress non-uniformity of rotation without the need for properization.

[0062] The angular transmission error compensator compensates for the effects of angular transmission error based on the control system configuration and angular transmission error characteristics, and has an aspect of feedforward control.It is called feedforward control because it calculates a compensation signal using the motor position and motor speed.

[0063] Since this is feedforward control, compensation is made for reproducible components of the angular transmission error.

[0064] For convenience of explanation, the transfer function G(s) in the continuous time domain is used in the explanation, but this is not limited to this and also includes the case where the transfer function G[z] in the discrete time domain is used.

[0065] [effect] As mentioned above, in the angular transmission error compensator, the influence of the control system characteristics (characteristics from angular transmission error to compensation current) can be suppressed by utilizing the frequency response characteristics rather than the transfer function, thereby making it possible to suppress non-uniformity of rotation.

[0066] 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, theoretically derived formula, making it possible to derive uniquely optimal parameters without the need for trial-and-error adjustment work.This not only improves the efficiency of the design process, but also reduces variability and judgment errors without relying on the designer's experience or subjectivity, making it possible to build a highly reliable angular transmission error compensator in a short period of time.

[0067] In addition, a clear distinction is made between the angular transmission error characteristics, which vary between individual products, and the control system characteristics, which do not vary between individual products.As a result, the design content and its operation are systematically structured and have logical consistency, making it easy to handle at each stage of design, analysis, and maintenance, and providing excellent designability and implementability for the control device.

[0068] (Flexibility of control system configuration) [composition] The angular transmission error compensator can be adapted to various control system configurations, not limited to the configuration shown in Fig. 2. Fig. 3 is a control block diagram in which the compensation summing point is a position command (a compensation signal is added to a position command), and Fig. 4 is a control block diagram in which the compensation summing point is a speed feedback signal (motor speed) (a compensation signal is added to a speed feedback signal), and the compensation signals are respectively a compensated position command θ ATEComp , the compensation speed feedback signal ω ATEComp 3 to 5, including FIG. 5 described later, reference numeral 1 denotes a controlled object, reference numeral 200 denotes a motor, reference numeral 300 denotes a speed reduction mechanism, reference numeral 400 denotes a load, and reference numerals 100_2, 100_3, and 100_4 denote vibration control devices, respectively. In the case of FIG. 3, the transfer function for constructing the compensation model is the transfer function from the angle transmission error to the position command. JPEG0007800877000014.jpg1022,In the case of Fig. 4, the transfer function from the angular transmission error to the velocity feedback signal Just use JPEG0007800877000015.jpg925.

[0069] For example, the transfer function from the angular transmission error to the position command is expressed by equation (9).

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[0070] The symbols in equation (9) are as follows in equations (10) and (11).

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[0071] As with equation (6), which is the case when the compensation signal is added to the current command, the transfer function is not proper and there are the same issues as mentioned above, but compensation is possible in the same way.The same applies when the compensation addition point is the speed feedback signal.

[0072] Although the above relates to a control system structure for position control, the present disclosure can also be used to configure dynamic angular transmission error compensation for speed control and torque control, taking into account the control system configuration and compensation addition point. Furthermore, the present disclosure can be applied not only to feedback control system configurations, but also to control system configurations that use feedforward control in combination.

[0073] [effect] Since systems or devices using reduction gears have a wide variety of applications, there are also a wide variety of preferable control system configurations for the systems or devices. For example, in addition to general PID control, various feedback control algorithms are available, such as I-PD control with a modified differential term structure, P-PI control, P-IP control, state variable feedback control based on optimal regulator theory, and H∞ control that takes robustness into consideration.

[0074] According to the present disclosure, it is possible to add a vibration suppression control function (suppression of rotation non-uniformity) based on feedforward control that adds a compensation signal without making any structural changes to the existing feedback control system described above. As described above, the compensation parameters can be set based on a clear mathematical formula derived theoretically, and therefore can be easily applied to a variety of systems. From the viewpoint of industrial applications, it may be difficult to modify the existing control system structure from the standpoint of track record and reliability, and this has the excellent effect of providing a vibration suppression control function while maintaining the existing control system structure.

[0075] (Compensation model based on speed information) [composition] The angular transmission error compensator is configured as a compensation model in which the angular transmission error compensator amplitude and angular transmission error compensator amplitude phase for each compensation order are calculated as a linear interpolation lookup table (hereinafter referred to as LUT) based on speed information. In the compensation model, for the compensation order i, angular transmission error compensator amplitudes and angular transmission error compensator phases corresponding to a plurality of discrete motor speeds are set.

[0076] The amplitude of the angular transmission error compensator for each compensation order is shown in equation (12). The same applies to the phase of the angular transmission error compensator for each compensation order.

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[0077] The symbols in equation (12) are as follows: n i : Number of LUTs for compensation order i ω mil : the lth motor speed, which is the i-th LUT input A cil : the amplitude of the angular transmission error compensator at each lth compensation order, which is the i-th LUT output

[0078] For example, it can be set to a range of 0 to 3000 r / min in increments of 200 r / min (0, 200, 400, ..., 3000) according to the operating speed range of the system. i = 16. In this case, for example, ω m =ω mi2 In this case, A ci (ω m )=A ci2 The motor speeds do not have to be at equal intervals. Also, the angular transmission error compensator amplitude and the angular transmission error compensator phase for each compensation order are different. i For example, the number of amplitude LUTs for the compensation order i is n iA = 20, the number of phase LUTs for compensation order i is n iφ = 10. iSince there is a trade-off between the amount of storage resources required to store the necessary data and the compensation performance, the balance between the two can be flexibly adjusted based on the convenience of the control device.

[0079] Specifically, it is possible to consider the balance between compensation performance and computer resources by setting the motor speed more densely (or more) in a speed range where the corresponding frequency response characteristics change sharply, and by setting the motor speed more sparsely (or less) in a speed range where the corresponding frequency response characteristics change slowly.

[0080] Note that the LUT can be determined taking into consideration various algorithms, such as linear interpolation, nearest neighbor interpolation, polynomial interpolation, and spline interpolation, in addition to linear interpolation. From the viewpoint of continuity of the compensation signal, it is preferable that the output of the LUT be a continuous output by linear interpolation or the like, but a method that produces a discrete output may also be used. Furthermore, when the operating speed exceeds the range considered by the LUT (corresponding to extrapolation), the maximum speed value set in the LUT (corresponding to clipping) may be used, or a warning may be issued from a display device or the like to prompt the user to reset the operating speed range.

[0081] As another method for realizing the compensation model, a regression function (approximation function) may be created for the amplitude and phase of the frequency response characteristic, and the amplitude and phase of the angular transmission error compensator may be calculated using this. Alternatively, the frequency response characteristic may be calculated sequentially to calculate the amplitude and phase of the angular transmission error compensator for each compensation order.

[0082] Note that the control system configuration, control parameters, and motor characteristics are used to calculate the frequency response characteristics, but if some or all of these are unknown, the compensation parameters may be identified and set experimentally. For example, compensation parameters that can reduce vibration when operating at a certain constant speed may be identified at multiple operating speeds. In this case, it is necessary to re-identify the compensation parameters as the control parameters are adjusted.

[0083] [effect] In the present disclosure, a plurality of configurations or calculation methods can be selected as a method for realizing a compensation model, such as an LUT, a regression function, or sequential calculation of frequency response characteristics, and the optimum implementation method can be flexibly selected depending on the constraints of computer resources and design requirements of the control device. Therefore, the present disclosure can provide a compensation method that is highly industrially applicable, can be easily applied to various control devices in various industrial fields, and is highly versatile and scalable.

[0084] (Setting the compensation speed band) [Background and Issues] Compensation is required according to the operating speed at which rotational non-uniformity caused by the influence of angular transmission error becomes a problem. Also, because the operating speed at which rotational non-uniformity becomes a problem varies depending on the compensation order, compensation that takes into account the operating speed range for a variety of situations is preferable. Furthermore, although rotational non-uniformity becomes smaller at operating speeds above the resonance state, the frequency of the compensation signal becomes high and the amplitude also becomes large, which results in a large power load compared to the compensation performance and is not desirable from the perspective of energy conservation.

[0085] [composition] In the angular transmission error compensator, a compensation speed band may be additionally set to realize compensation according to the operating speed at which rotation non-uniformity becomes a problem. Specifically, by multiplying the amplitude of the angular transmission error compensator at each compensation order of the compensation model by a weighting coefficient, the influence of compensation can be set according to the operating speed. 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 this case, A ci (ω m )=W ci2 *A ci2 This becomes:

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[0086] The symbols in equation (13) are as follows: W cil:Weighting coefficient for the amplitude of the angular transmission error compensator at each lth compensation order

[0087] The weighting coefficient may be set to "1" near the operating speed assumed for the frequency band where the above-mentioned resonance occurs, and "0" at other speeds. Note that the weighting coefficient may be a value other than 1 or 0, and various situations can be handled by appropriately setting the weighting coefficient according to the characteristics of the system. To prevent compensation at low speeds, for example, the weighting coefficient may be set to "0" at speeds below 100 r / min. To prevent compensation at high speeds, for example, the weighting coefficient may be set to "0" above the operating speed at which 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 configured. Note that from the perspective of continuity of the compensation signal, it is preferable that the weighting coefficient be continuous, but a discrete method is also acceptable.

[0088] [effect] With this configuration, at low speeds, processing is performed taking into account quantization errors in position detectors such as encoders, discretization errors associated with digital control, and the processing cycle of compensation processing, making it possible to prevent minute positioning operations, control instability in low-speed areas, excessive effects of compensation, etc.

[0089] Furthermore, by configuring the system to suppress or stop compensation operation when non-uniformity of rotation is not a problem at high speeds, it is possible to avoid overloading the control device due to excessive compensation signals. This reduces unnecessary calculation processing and power consumption, enabling the control device to achieve high efficiency and stability as a whole.

[0090] In particular, in the configuration in which the compensation model is multiplied by a weighting coefficient, the compensation model based on speed information and the compensation speed band can be considered at the same time, which is simple and allows for effective use of computer resources.

[0091] (Information used for compensation) [composition] In the example shown in FIG. 2, the inputs to the angular transmission error compensator (hereinafter referred to as compensator inputs) are the motor position and motor speed, which are actual information derived from actual measured values ​​from a position detector. However, depending on the configuration of the control device, it may be possible that the actual information cannot be used. In such cases, the angular transmission error compensator may use command information (position command, position command speed) in place of the actual information for compensation calculations.

[0092] FIG. 5 is a control block diagram when the compensator input is used as command information. In this case, the servo control approximation characteristic Approximate motor position calculated via JPEG0007800877000021.jpg722 JPEG0007800877000022.jpg716 and approximate motor speed JPEG0007800877000023.jpg718 is the compensator input.

[0093] Below, we will explain in detail the case where a position command is used as position information. In order to derive an approximate motor position, which is information equivalent to the motor position as position information, we use characteristics that approximate the servo control characteristics of the control device. The approximate servo control characteristics can be, for example, the first-order lag in equation (14) or the dead time element in equation (15). Furthermore, the approximate motor position can be calculated using equation (16) using the respective transfer functions.

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[0094] The symbols in equations (14) to (16) are as follows: ω approx : Servo control approximate angular frequency, unit is radians per second (rad / s). Lapprox : Servo control approximate dead time, unit is seconds (s).

[0095] The P-PI control system shown in Figure 2 can globally approximate the response with the position loop gain, so ω approx =K p Similarly, JPEG0007800877000027.jpg634. The approximate motor speed, which is the speed information, may be a differential value (difference value) of the approximate motor position.

[0096] Servo control characteristics vary depending on the system, and approximation requires consideration of the servo control characteristics, operating speed range, control parameter settings, management, etc. To approximate the characteristics from a position command to a motor position, it is generally necessary to determine the configuration of the servo control approximation characteristics and their parameters. For example, the sum of squared errors or the mean squared error between the motor position and the position command may be minimized as an objective function. Alternatively, curve fitting of frequency response characteristics may be performed. This curve fitting can be achieved by estimating parameters using a regression method such as the least squares method based on a predefined transfer function model for the gain and phase characteristics on a Bode diagram. The same applies to speed control and torque control.

[0097] It is also necessary to consider the approximation accuracy of the position information and speed information that are input to the compensator. Errors in the position information have a large impact because they are directly linked to the period and phase of the sinusoidal compensation signal, while errors in the speed information affect the amplitude and phase values ​​of the compensation parameters, but the impact of errors is smaller than that of the position information. Therefore, an approximate motor speed can be calculated from an approximate motor position as an approximation characteristic that prioritizes errors in the position information.

[0098] [effect] Depending on the configuration of the control device, for example, it may be difficult to use actual information due to physical wiring, or it may be difficult to achieve the desired accuracy due to the influence of the resolution and processing cycle of the obtained information. In the present disclosure, the information to be used for compensation can be flexibly selected according to the convenience of the control device, thereby enabling optimal compensation processing according to the system configuration and operating conditions. This enables application to a variety of systems with different configuration requirements, improving the degree of freedom in system design and expanding the scope of application and practicality.

[0099] (No interference with static components) [Background and Issues] When compensating for rotational non-uniformity, which is the dynamic effect of angular transmission error, there is an issue that if a compensation signal is added to a position command in particular and the compensation signal is not set to 0 when stopped, it will have a direct effect on the static characteristics of the angular transmission error, leading to a deterioration in positioning accuracy. Similar issues arise even when a compensation signal is added to something other than a position command, as it will affect behavior during the start of operation and positioning.

[0100] [composition] To achieve non-interference with static components, the angular transmission error compensator is configured so that the compensation signal is set to 0 when the speed information is 0, i.e., when the motor is stopped. Note that even when the compensation signal is added to something other than the position command, a similar configuration is preferable if it affects static characteristics. Note that the compensation model may be set so that the compensation signal is 0 when the speed information is 0.

[0101] Specifically, for example, by utilizing the setting of the compensation speed band, the weighting coefficient corresponding to the case where the motor speed is 0 may be set to 0, or each compensation order amplitude may be multiplied by a sign function sgn(x) (for details of the sign function, see the definition in the section reflecting the rotation direction characteristics).

[0102] [effect] In particular, when a compensation signal is added to a position command, this can lead to a deterioration in positioning accuracy. Therefore, this configuration makes it possible to compensate for the dynamic effects of angular transmission error without affecting the static characteristics of the angular transmission error. Furthermore, by taking this into consideration in conjunction with the setting of the compensation speed band using an LUT, multiple functions can be realized collectively, making it possible to simply and effectively utilize computer resources. This makes it possible to realize compensation that clearly distinguishes between dynamic compensation and static compensation. Note that the dynamic compensation disclosed herein may be used in combination with other static compensation.

[0103] (Reflecting rotation direction characteristics) [composition] In the angular transmission error compensator, as shown in equations (17), (18), and (19), 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 used.

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[0104] The symbols in equations (17) to (19) are as follows: A F i : Amplitude of each compensation order during normal rotation, unit is arc-seconds (arc-sec). A R i : Amplitude of each compensation order during reversal, unit is arc-seconds (arc-sec). φ F i : Each compensation order phase during normal rotation, unit is radian (rad). φ R i : Each compensation order phase during reversal, unit is radian (rad). sgn(x): A function that indicates the sign (sign function), which is +1 when x>0, 0 when x=0, and -1 when x<0. Note that it can also 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 is the characteristic for forward and the superscript R is the characteristic for reverse.

[0105] [effect] Because angular transmission error has different characteristics depending on the direction of rotation due to the principles behind its occurrence, compensation that takes the direction of rotation into consideration allows for effective compensation. In particular, when considering operations in which the direction of rotation is reversed, by combining this with the non-interference with static components described above, the compensation signal changes continuously and smoothly even when the direction of rotation is reversed, without the need for complex processing, enabling stable operation. Furthermore, because the characteristics of the direction of rotation can be separated and set 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 non-uniformity in rotation.

[0106] (Multiple compensation orders) [composition] As shown in equations (2) to (4), the angular transmission error compensator can accommodate multiple compensation orders, and compensation models corresponding to each compensation order are configured. Furthermore, the following configuration, which is a modification of equation (2), may also be used.

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[0107] The symbols in equations (20) to (23) are as follows: ω mCi : ith motor speed, in radians per second (rad / s). ω m1 : The motor speed angular frequency for the first order, in radians per second (rad / s).

[0108] The compensation model is referenced as equation (23) using the motor speed and compensation order as one compensation model (equivalent to a compensation model with a first-order compensation order). As opposed to the pre-calculation configuration (equation (2)) described above, in which the influence of the compensation order is calculated and stored in advance, this is a sequential calculation configuration (equation (20)) in which the influence of the compensation order is calculated sequentially. Furthermore, the compensation speed band may be set based on the speed or the (angular) frequency. When dealing with multiple compensation orders, the configuration can be simplified by using the frequency as the reference.

[0109] [effect] Even when there are multiple components that have a dynamic effect on the angular transmission error, which is determined by the structure of the reduction gear mechanism, the angular transmission error compensator can be designed according to certain rules without the structure becoming complicated.

[0110] Furthermore, when the number of compensation orders and lookup tables is large, a flexible configuration can be selected according to the availability of computer resources. For example, when there is a margin in the amount of storage resource usage, a pre-calculation configuration can be used to reduce the sequential calculation processing for generating compensation signals, and when there is a margin in the processing capacity of the control device, a sequential calculation configuration can be used to reduce the amount of storage resource usage.

[0111] Multiple configurations or calculation methods can be selected, and the optimal implementation method can be flexibly selected depending on the design requirements of the control device and the constraints of computer resources.

[0112] Therefore, the present disclosure can provide a compensation method that is highly industrially applicable, can be easily applied to various control devices in a variety of industrial fields, and is highly versatile and expandable.

[0113] (load moment of inertia) [composition] In an angular transmission error compensator, for example, the frequency response characteristics from the angular transmission error to the compensation current can be calculated from the control system configuration, control parameters, and motor characteristics, and are configured without requiring information on the load moment of inertia. Note that if the control parameters are changed in accordance with changes in the load moment of inertia (for example, gain scheduling), compensation can be achieved by changing the compensation parameters as well.

[0114] (reduction mechanism spring constant) [composition] In the angular transmission error compensator, for example, the frequency response characteristics from the angular transmission error to the compensation current can be calculated from the control system configuration, control parameters and motor characteristics, and is configured without requiring information on the spring constant of the reduction mechanism.

[0115] [effect] In a two-inertia system, the vibration frequency and influence of vibration phenomena are determined from the moment of inertia and the (reduction mechanism) spring constant, but this disclosure makes it possible to determine compensation parameters without requiring information on either. Regarding the load moment of inertia, for example, when the load moment of inertia is unknown, or in a vertical articulated robot or horizontal articulated robot system, the load moment of inertia changes depending on the robot's posture, causing a change in vibration frequency, but compensation is possible without being affected by these factors. Furthermore, the spring constant of the reduction mechanism often varies between individual products, and various measures have been taken to address this issue. However, this disclosure makes it possible to achieve vibration suppression control without being affected by differences in spring constants or their fluctuations.

[0116] As described above, the present disclosure makes it possible to design an angular transmission error compensator regardless of the load moment of inertia and the spring constant of the reduction mechanism, thereby improving the efficiency of the design process and suppressing non-uniformity in rotation regardless of these characteristics.

[0117] (Load torque compatible) [Background and Issues] The angular transmission error characteristics may change depending on the load torque (gravity torque, acceleration / deceleration torque (torque that drives the load)) applied to the reduction gear mechanism. For example, in a robot system, the load torque due to gravity torque may have a large effect.

[0118] [composition] To consider the effect of the load torque, the angular transmission error compensator uses the load torque τ l Specifically, the equations (3) and (4) are replaced by the equations (24) and (25).

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[0119] [effect] It is possible to easily configure compensation that takes into account the effect of load torque on angular transmission error. The effect of fluctuations in angular transmission error characteristics due to the effect of load torque can be compensated for, and non-uniformity of rotation can be suppressed.

[0120] (Temperature fluctuation resistant) [Background and Issues] The angular transmission error characteristics may fluctuate depending on the temperature characteristics of the components of the reduction mechanism, the temperature of the reduction mechanism, and the temperature around the reduction mechanism (environmental temperature).

[0121] [composition] To take into account the influence of temperature, the angular transmission error compensator is configured to correct each compensation order amplitude and each compensation order phase according to the temperature information T. Specifically, the following equations (26) and (27) are used in place of equations (3) and (4).

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[0122] [effect] It is possible to easily configure compensation that takes into account the effect of temperature on angular transmission error. It is possible to compensate for the effect of fluctuations in angular transmission error characteristics due to the effect of temperature, and to suppress non-uniformity of rotation.

[0123] (Compensation model configuration) [composition] Here, another configuration of the angular transmission error compensator will be described in the section on dynamic angular transmission error compensation and automatic setting of compensation parameters.

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[0124] The symbols in equations (28) to (30) are as follows: A Mi : The integrated amplitude of each compensation order, in amperes (A). φ Mi : The integrated phase of each compensation order, in radians (rad).

[0125] In this configuration, the angular transmission error characteristics and the angular transmission error compensator characteristics are integrated (merged) into the compensation model. By taking the angular transmission error characteristics into consideration when creating the compensation model, it is possible to simplify the calculation of the compensation signal. This is based on the same idea as the pre-calculation configuration described above.

[0126] [effect] In the present disclosure, a configuration can be selected flexibly according to the availability of computer resources as a method for realizing a compensation model. For example, when there is a surplus in the amount of storage resource usage, a pre-calculation configuration can be used to reduce the sequential calculation processing for generating a compensation signal, and when there is a surplus in the processing capacity of the control device, a sequential calculation configuration can be used to reduce the amount of storage resource usage.

[0127] (Combination of functions) As described above, various elements can be taken into consideration when designing an angular transmission error compensator. In this case, by appropriately selecting and combining, for example, a configuration that takes into consideration the setting of a compensation speed band and non-interference with static components, or a configuration that takes into consideration non-interference with static components, rotational direction characteristics, and support for multiple compensation orders, it is possible to easily configure an embodiment that supports a variety of functions. Furthermore, multiple functions can be considered collectively as a compensation model, reducing redundancy in calculation processing and enabling efficient use of computer resources.

[0128] 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 rotation output error that takes into account various factors can be efficiently designed and realized in a variety of systems.

[0129] [Numerical example] (Simulation conditions) In order to explain the operation and confirm the effects of the present disclosure, a numerical simulation is performed using the configuration shown in Fig. 2. Table 1 shows various parameters used in the numerical example.

[0130] [Table 1]

[0131] In addition, in order to convert the control parameter units from SI units to the processing unit system, a normalization coefficient is taken into consideration for the speed loop gain. JPEG0007800877000043.jpg743, JPEG0007800877000044.jpg736 is the nominal load inertia value, K tn is the nominal torque constant.

[0132] The compensation parameters were designed under the following conditions: Compensation order i:2 Number of lookup tables n i :16 Motor speed ω for the number of lookup tables m2l [r / min]: 0, 200, 400, 600, ..., 2800, 3000 (16 equally spaced data)

[0133] The load speed is expressed as a value multiplied by the reduction ratio to take into account comparison with the motor speed. The unit is "Mr / min." The motor position and load position are expressed in arc-seconds, both on the load side. 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). Hereinafter, the "low" setting will be referred to as the "low gain setting," and the "high" setting will be referred to as the "high gain setting." Generally, control parameters are set according to the rigidity of the device (e.g., the spring constant of the reduction mechanism). Higher responsiveness improves command tracking and shortens settling time, but also increases the likelihood of vibration. Therefore, the parameters are set to obtain the desired responsiveness within a range that does not generate vibration.

[0134] (constant speed operation) To evaluate the dynamic influence of angular transmission error and the effects of the present disclosure, vibration characteristics during constant speed operation (constant speed operation) are evaluated. In constant speed operation, order analysis is performed on response data from the section where constant speed operation is performed after a period of time has passed during which the influence of transient response can be ignored, and vibration characteristics are evaluated. Hereinafter, 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 "motor speed second-order component." Note that here, the characteristics are evaluated at an operating speed equal to the motor speed set in the LUT.

[0135] As vibration characteristics, the motor is operated at multiple constant speeds (for example, 1000, 1200, ..., 2400 r / min), and the motor speed second-order component and load speed second-order component at each operating speed are extracted from the response data in the constant speed section. In addition, the speed information in the constant speed section is integrated to calculate position information, and the motor position second-order component and load position second-order component are also extracted.

[0136] (Explanation of order analysis at constant speed) Fig. 6 and Fig. 7 show the motor speed response data and load speed response data in the constant speed section when the motor was operated at a constant speed at multiple operating speeds. Fig. 8 and Fig. 9 show the motor speed order analysis results and load speed order analysis results when the operating speed was 1600 r / min, with low gain settings and no compensation.

[0137] 6 to 11 show the case where low gain is set and no compensation is performed. The horizontal axis of Fig. 6 represents time, and the vertical axis represents motor speed. The horizontal axis of Fig. 7 represents time, and the vertical axis represents load speed.

[0138] 6 and 7 show that, although a constant speed operation command is used, periodic speed fluctuations are superimposed on the motor speed and load speed due to the influence of angular transmission error. In particular, when the operating speed is set to 1600 r / min, the amplitude of the vibration component is larger than at other speeds.

[0139] The horizontal axis of Fig. 8 shows the order, and the vertical axis shows the results of the order analysis of the motor speed. The horizontal axis of Fig. 9 shows the order, and the vertical axis shows the results of the order analysis of the load speed. Figs. 8 and 9 show that this is the effect of the second-order component of the angular transmission error, which was taken into account in the simulation model.

[0140] 10 and 11, the horizontal axis represents the operating speed, and the vertical axis represents the results of extracting the motor speed second-order component and the load speed second-order component at multiple operating speeds. Figures 10 and 11 show that the degree of influence of an equal angular transmission error varies depending on the operating speed, and that the influence of the angular transmission error on the load speed is significant.

[0141] (Vibration characteristics due to differences in control parameters) Figures 12 to 15 show the characteristics of the motor position second-order component, load position second-order component, motor speed second-order component, and load speed second-order component, respectively, when the gain is set to low or high and there is no compensation (hereinafter referred to as condition A). The solid line represents the characteristics when the gain is set to low, the dashed line represents the characteristics when the gain is set to high, the horizontal axis represents the operating speed, and the vertical axis represents each second-order component.

[0142] 12 to 15 show that differences occur in each second-order component depending on the control parameters, and 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 when set to low gain and 59.0 arc-sec when set to high gain, and the load speed is 27.8 Mr / min when set to low gain and 45.7 Mr / min when set to high gain, showing differences of 1.6 times and 1.7 times depending on the control parameters.

[0143] (Vibration characteristics with and without compensation (low gain setting)) Figures 16 to 19 show the characteristics of the motor position second-order component, load position second-order component, motor speed second-order component, and load speed second-order component, respectively, when the gain is set to low and compensation is provided or not (hereinafter referred to as condition B). The solid lines show the characteristics with compensation, the dashed lines show the characteristics without compensation, the horizontal axis shows the operating speed, and the vertical axis shows each second-order component.

[0144] 16 to 19 show that the second-order components of the load position and load speed are reduced to zero through compensation. Furthermore, it is also shown that the motor position and motor speed have characteristics with a predetermined amplitude through compensation. The motor position shown in FIG. 16 is shown to be in a state where it vibrates at 10 arc-sec, which corresponds to the amplitude of the second-order component of the angular transmission error, regardless of the operating speed. This cancels out (compensates for) the influence of the second-order component of the angular transmission error on the load position and load speed. It is clear from the second-order components of the load position and load speed shown in FIGS. 17 and 19 that the present disclosure can effectively compensate for the influence of the angular transmission error.

[0145] (Vibration characteristics with and without compensation (high gain setting)) Figures 20 to 23 show the characteristics of the motor position second-order component, load position second-order component, motor speed second-order component, and load speed second-order component, respectively, when high gain is set and compensation is provided or not (hereinafter referred to as condition C). The solid lines show the characteristics with compensation, the dashed lines show the characteristics without compensation, the horizontal axis shows the operating speed, and the vertical axis shows each second-order component.

[0146] 20 to 23 show that, similar to the low gain setting, the second-order components of the load position and load speed are reduced to zero through compensation. Also, it is shown that the motor position and motor speed have characteristics with a predetermined amplitude through compensation. The motor position shown in FIG. 20 shows that, regardless of the operating speed, it vibrates at 10 arc-sec, which corresponds to the amplitude of the second-order component of the angular transmission error.

[0147] From the simulation results under conditions A to C, it is clear that it is possible to suppress the influence of the second-order component of angular transmission error, which has different vibration characteristics depending on the control parameters.

[0148] (Compensation parameters) 24 and 25 show the amplitude and phase characteristics in the frequency response characteristics from the angular transmission error to the compensation current at the low gain setting (solid line) and the high gain setting (dotted line), and the circles and crosses show the compensation parameters at the low gain setting and the high gain setting, respectively.

[0149] The amplitude when the motor speed is 0 indicates that no compensation is performed when the motor is 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 parameters in order to compensate for the fact that the angular transmission error has different vibration characteristics depending on the control parameters. This means that once the control parameters are determined, the compensation parameters 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 set from the amplitude and phase characteristics in the frequency response characteristics shown in Figures 24 and 25. Furthermore, as mentioned above, a regression function may be created for these characteristics.

[0150] (Acceleration / deceleration operation) As described above, the influence of angular transmission error changes according to changes in motor speed. Here, we confirm the influence of angular transmission error when the motor speed changes continuously due to acceleration / deceleration operation, and the effectiveness of the present disclosure. During acceleration / deceleration operation, we evaluate vibration characteristics when the influence of angular transmission error changes sequentially due to speed changes. Note that, unlike constant speed operation, it is difficult to evaluate vibration characteristics using order analysis during acceleration / deceleration operation. Therefore, in order to remove components associated with acceleration / deceleration other than the influence of angular transmission error, the output of a high-pass filter (HPF) shown in equation (31) is used as each vibration component.

number

[0151] The symbols in equation (31) are as follows: ω HPF :HPF cutoff angular frequency, unit is radians per second (rad / s). o HPF :HPF order Here, ω HPF =2π*5,o HPF =6.

[0152] 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, for a low gain setting and no compensation (hereinafter referred to as condition D), with the horizontal axis representing time and the vertical axis representing each component. Note that in the vibration component diagrams such as Figure 28, the graphs are solidly colored because continuous vibration is occurring. As an example, an enlarged view of Figure 28 is shown in Figure 123.

[0153] Figures 32 to 37 show the characteristics when a high gain setting is used and no compensation is performed (hereinafter referred to as condition E), Figures 38 to 43 show the characteristics when a low gain setting is used and compensation is performed (hereinafter referred to as condition F), and Figures 44 to 49 show the characteristics when a high gain setting is used and compensation is performed (hereinafter referred to as condition G).

[0154] Since it is difficult to determine the magnitude of vibration from the motor speeds and load speeds shown in Figures 26 and 27, Figures 32 and 33, Figures 38 and 39, and Figures 44 and 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.

[0155] In the load speed vibration components and load position vibration components without compensation shown in Figures 29, 31 and Figures 35, 37, the vibration characteristics due to the influence of angular transmission error change successively depending on the difference in operating speed, and the difference in control parameters also shows the same tendency as the constant speed operation described above. Note that the components around 0 and 10 s in each vibration component are the influence of the transient response accompanying the start of acceleration and deceleration.

[0156] The load speed vibration component and load position vibration component with compensation shown in FIGS. 41, 43 and 47, 49 show that the present disclosure can suppress vibration characteristics accompanying changes in operating speed.

[0157] The motor speed vibration components and motor position vibration components with and without compensation shown in Figures 28 and 30, Figures 34 and 36, Figures 40 and 42, and Figures 45 and 48 show that, even with different control parameters, the effects of angle transmission error at the load position are reduced by vibrating the motor position, just as with the constant speed operation described above.

[0158] As described above, from the simulation results under conditions D to G, it is clear that the present disclosure can suppress the influence of vibrations even when the operating speed changes continuously.

[0159] (Compensation due to difference in compensation points) The following shows the simulation results for the configuration of Figure 3, where the compensation addition point is set to a position command. Figures 50 to 55 respectively show the motor speed, load speed, motor speed vibration component, load speed vibration component, motor position vibration component, and load position vibration component when the compensation addition point is set to a position command, low gain is set, and compensation is present (hereinafter referred to as condition H), with the horizontal axis representing time and the vertical axis representing each component.

[0160] 50 to 55 show that even if the compensation addition point is a position command, it is possible to suppress non-uniformity in rotation.

[0161] Figures 56 and 57 show the amplitude and phase characteristics of the frequency response characteristics from the angular transmission error to the compensation position, with the compensation parameters indicated by circles. Note that the amplitude when the motor speed is 0 indicates that no compensation is performed when the motor is stopped in order to achieve non-interference with the static component.

[0162] 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, for the configuration of Figure 4, with the compensation addition point set to speed feedback, low gain, and with compensation (hereinafter referred to as condition I), with the horizontal axis representing the operating speed and the vertical axis representing each component.

[0163] 58 to 63 show that equivalent compensation can be achieved regardless of the compensation addition point.

[0164] From the above simulation results under conditions H to I, it is clear that the compensation addition point can be flexibly set in the present disclosure.

[0165] (Setting the compensation speed band) The simulation results are shown below when a compensation speed band is set. The low gain setting and compensation addition point are current commands. As an example of compensation only in the operating speed band in a resonant state, the weighting coefficient between 1000 and 2000 r / min is set to "1," and the weighting coefficient at other motor speeds is set to "0." The weighting coefficient for the angular transmission error compensator amplitude is shown in equation (32).

number

[0166] 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 addition point is a current command, low gain setting, and compensation is present (hereinafter referred to as condition J), with the horizontal axis representing time and the vertical axis representing each component.

[0167] 26 to 31, which do not take weighting coefficients into consideration, the load speed vibration components and load position vibration components in Figures 67 and 69 in particular show that the vibration components in the specified operating speed range are compensated for, making it possible to suppress non-uniformity of rotation only in a specific operating speed range. Similar trends are also confirmed in the other figures.

[0168] From the above simulation results under condition J, it is clear that in a configuration in which a compensation speed band is set, it is possible to flexibly suppress non-uniformity of rotation.

[0169] (Compensator input is used as command information) The simulation results for the configuration of Fig. 5 when command information is used as the information used for compensation are shown. Figs. 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 of Fig. 5, with the servo control approximation characteristics set to equation (14), low gain setting, and compensation present (hereinafter referred to as condition K), with the horizontal axis representing time and the vertical axis representing each component.

[0170] Compared with Figures 26 to 31 when actual information (motor position, motor speed) is used, it is shown that the load speed vibration components and load position vibration components in Figures 74 and 75 have equivalent compensation performance.

[0171] The error between the motor position and position command shown in Figure 76 has a maximum error of approximately -3.2 rad, equivalent to half a motor rotation, which indicates that if the compensator input is simply set as a position command, an appropriate compensation signal will not be generated.

[0172] In the error between the motor position and the approximate motor position shown in Figure 7, the error in the approximate motor position is kept small relative to the motor position, which indicates that it is possible to reduce vibrations in the load speed and load position. Similar trends are also observed in other figures.

[0173] Figures 78 and 79 show the load position vibration component and the error between the motor position and the approximate motor position when the servo control approximation characteristics are expressed by equation (15), the gain is set low, and compensation is applied, using the configuration of Figure 5. The horizontal axis represents time, and the vertical axis represents each component.

[0174] 78 and 79 show that even if the approximation method is different, if the error between the motor position and the approximate motor position is kept small, it is possible to suppress non-uniformity of rotation.

[0175] From the above simulation results under condition K, it is clear that the present disclosure can suppress non-uniformity of rotation even in a configuration using command information.

[0176] (compensation order) The angular transmission error characteristics were examined under conditions that considered the fourth-order component in addition to the second-order component. The fourth-order angular transmission error characteristics were set to A4 = 5 arc-sec, φ4 = -10 deg. The number of lookup tables and the motor speed for the number of lookup tables were set to the same as the second-order component. The fourth-order component reaches resonance at approximately 750 r / min (approximately 2.5 s). Note that the low gain setting and compensation addition point are current commands.

[0177] 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 in the case of no compensation (hereinafter referred to as condition L), Figures 86 to 91 show those in the case of second-order compensation (hereinafter referred to as condition M), and Figures 92 to 97 show those in the cases of second-order compensation and fourth-order compensation (hereinafter referred to as condition N), respectively. The horizontal axis represents time and the vertical axis represents each component.

[0178] In Figures 83 and 85, by taking the fourth-order component into consideration, it is shown that the fourth-order component is in a resonant state at approximately 750 r / min (approximately 2.5 s), and that the combination of the amplitude and phase of the second-order and fourth-order components of the angular transmission error results in a complex vibration waveform. Similar trends are also confirmed in the other figures.

[0179] 89 and 91 show that even if a fourth-order component is present, the second-order component can be compensated for by second-order compensation. Similar trends are also observed in the other figures.

[0180] 95 and 97 show that second-order and fourth-order compensation can suppress the non-uniformity of rotation due to both order components. Similar trends are also observed in the other figures.

[0181] From the simulation results under conditions L to N, it is clear that even when there are multiple orders of angular transmission error, it is possible to suppress non-uniformity of rotation by compensating for only the second-order component or multiple order components such as the second-order and fourth-order components.

[0182] (Load moment of inertia fluctuation) Evaluate the vibration characteristics when the load moment of inertia fluctuates. Figure 98 shows the load moment of inertia fluctuation ratio, which is set so that the load moment of inertia is small in accordance with the acceleration / deceleration operation described above. Note that the low gain setting and compensation addition point are current commands.

[0183] 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 in the case without compensation (hereinafter referred to as condition O), and Figures 105 to 110 show the motor speed, load speed, motor speed vibration component, load position vibration component, and motor position vibration component in the case with compensation (hereinafter referred to as condition P), respectively. The horizontal axis represents time and the vertical axis represents each component.

[0184] Figures 102 and 104 show that the operating speed at which the resonance state occurs is lower because the resonance frequency has changed due to fluctuations in the load moment of inertia. This corresponds to a change in the time period when the vibration reaches its maximum value. Similar trends are also confirmed in the other figures.

[0185] 108 and 110 show that the present disclosure can suppress non-uniformity in rotation due to the vibration characteristics caused by fluctuations in the load moment of inertia. Similar trends are also observed in the other figures.

[0186] As described above, from the simulation results under conditions O to P, it is clear that even when the load moment of inertia fluctuates, the present disclosure can suppress non-uniformity of rotation without changing the compensation parameters.

[0187] In a configuration where the compensator input is command information, when a load inertia moment fluctuation occurs, the characteristics from the position command to the motor position change, and therefore if the impact of the load inertia moment fluctuation is significant, it is necessary to take the load inertia moment fluctuation into consideration in the approximation characteristics. In this case, for example, the approximation characteristics can be changed in accordance with the load inertia moment fluctuation, or the characteristics can be set to minimize the objective function when the load inertia moment is expected to fluctuate, or the approximation error can be minimized in the operating speed range where a resonance state occurs.

[0188] (Different spring constants for reduction gears) In order to evaluate vibration characteristics when the spring constant of the reduction gear mechanism is different, the spring constant of the reduction gear mechanism is set to three values: nominal (nominal value), 0.8 times nominal, and 1.2 times nominal. Here, cases where the spring constant of the reduction gear mechanism is different are assumed to be due to individual differences in the reduction gear mechanism. Note that the low gain setting and compensation addition point are current commands.

[0189] Figures 111 and 112 show the case where the reduction gear 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 gear 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 gear 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 gear 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 gear 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 gear mechanism spring constant is 1.2 times the nominal and there is compensation (hereinafter referred to as condition V). Each diagram shows the motor position vibration component and the load position vibration component, with the horizontal axis representing time and the vertical axis representing each component.

[0190] Figures 111 to 116 show that the operating speed at which the resonance state occurs changes because the resonance frequency changes due to the influence of different reduction mechanism spring constants. This corresponds to a change in the time period when the vibration reaches its maximum value. It also shows that the peak value changes as the vibration frequency changes.

[0191] 117 to 122 show that the present disclosure can suppress vibration characteristics caused by differences in the spring constant of the reduction mechanism.

[0192] As described above, from the simulation results under conditions Q to V, it is clear that even when the spring constant of the reduction mechanism is different, the present disclosure can suppress non-uniformity of rotation without changing the compensation parameters.

[0193] In addition, in a configuration in which the compensator input is used as command information, if the influence of fluctuations in the spring constant of the reduction mechanism is large, it is necessary to take the same measures as for fluctuations in the load moment of inertia.

[0194] FIG. 124 is a flowchart of a vibration suppression control program in a servo control system equipped with a speed reducing mechanism.

[0195] Step S1: Initial setting. The initial settings required for the execution of the vibration suppression control program are performed. This includes the initial settings of the predetermined compensation order, amplitude, and phase for generating the compensation signal. The dynamic angular transmission error compensator (C ATE The information on amplitude and phase corresponding to each compensation order, rotation direction, etc. is read into a compensation model (for example, a look-up table ( )) referred to by the compensation model. These compensation parameters may be configured so that the amplitude and phase are automatically set according to the frequency or compensation order corresponding to a predetermined speed range based on the configuration of a servo control system that targets at least one of the position, speed, and current of the motor, the control parameters, and frequency response characteristics based on the motor characteristics, and are registered in the compensation model.

[0196] Step S2: Information acquisition. Obtain current position information of the controlled object (for example, motor position or position command). Obtain current speed information of the controlled object (for example, motor speed or position command speed). Either actual information (motor position / motor speed) or command information (position command / position command speed) can be selected and used.

[0197] Step S3: Amplitude and phase correction. Based on the speed information acquired in step S2, the compensation model is referenced to determine and correct the amplitude and phase of the compensation signal. Since the dynamic angular transmission error compensator is configured so that the compensation signal is 0 when the speed information is 0, the compensation signal is adjusted so that it is 0 when the motor is stopped (when the speed information is 0). The compensation model may be configured 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. The compensation signal is generated from a preset amplitude and phase according to the direction of rotation of the motor. If necessary, a sinusoidal compensation signal is generated for each compensation order based on the preset amplitude and phase for each different compensation order, and a compensation signal is generated by adding these signals. The compensation signal is corrected by reference to the compensation model regardless of the inertia relative to the rotation of the load connected to the output shaft of the reduction mechanism. The compensation signal is also corrected by reference to the compensation model regardless of the spring constant of the reduction mechanism. The compensation signal can also be corrected according to the load torque acting on the reduction mechanism. Furthermore, the compensation signal can also be corrected according to the temperature of the reduction mechanism, the temperature around the reduction mechanism, or a temperature estimated based on the operating conditions.

[0198] Step S4: Compensation signal generation. A sine wave 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 sine wave can be realized by a sine wave function or by table lookup for position.

[0199] Step S5: Signal addition. The compensation signal generated in step S4 is added to the position command, speed command, current command, or any of the control signals related to these. According to the source, the compensation addition point is often set to the current command value, since compensation is performed regardless of the control mode (position control, speed control, torque control). However, this compensation method can be realized with any control system configuration, and the compensation addition point does not have an essential meaning; it is an element that can be designed to suit the characteristics of the system. It has been confirmed that adding it to the position command or speed feedback can also achieve the same compensation effect.

[0200] Step S6: Servo control. A servo control system equipped with a speed reducing mechanism operates based on the control signal to which the compensation signal has been added, thereby compensating for the non-uniformity of rotation caused by the effect of the angular transmission error of the speed reducing mechanism and achieving vibration damping.

[0201] [Summary of vibration control effects] As described above, this disclosure makes it possible to consider the influence of various factors, such as motor speed and parameter settings within the control device (e.g., various gains in feedback control), when compensating for rotation non-uniformity due to the influence of angular transmission error. This enables compensation that takes into account individual differences in reduction mechanisms and variations in operating conditions. Furthermore, even if the configuration and control method of the control device that achieves compensation are diverse, flexible compensation appropriate for each configuration is possible, and adjustments can also be made in accordance with computer resource constraints. Furthermore, it is clear that it is easy to design and adjust the control parameters of the control device, taking into account various factors.

[0202] [Angular transmission error characteristic estimation using reaction force estimation observer] (Understanding angular transmission error characteristics) The following explains the terms used. In the field of control engineering, the term "estimation" is widely used to estimate the state of a system, and is particularly common in technologies such as observers. On the other hand, the term "identification" is often used to describe methods for clarifying system parameters.

[0203] On the other hand, the term "identification" as generally understood may give the impression that a parameter is determined deterministically. In the field of control engineering, "identification" is often used for parameters that change sequentially, but in this disclosure, in order to facilitate technical understanding, the term "estimation" is used from the viewpoint of clarifying the meaning of an estimated value that includes uncertainty.

[0204] The technical background of the present disclosure is described below. As described above, the characteristics of angular transmission error are determined at the stage when various robots and devices are assembled due to the influence of assembly errors, and there are also individual differences between 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 angular transmission error characteristics are found from a definition formula using the reduction ratio.

[0205] On the other hand, various robots and devices that use reduction mechanisms are generally configured with semi-closed control, which uses a motor position encoder at the motor end to control the output of the reduction mechanism. In some research applications, a load position encoder is incorporated to use full-closed control, but due to factors such as cost and size, load position encoders are not often installed.

[0206] Additionally, some industrial robots and collaborative robots have built-in force sensors in their hands and torque sensors in each joint to achieve force control. Measuring the load torque from the torque sensors in each joint makes it possible to indirectly calculate the angular transmission error. However, in order to grasp the angular transmission error characteristics, it is necessary to convert from torque dimensions to position dimensions, which can be difficult to achieve with high accuracy. Note that torque sensors are not installed in some cases, such as in devices that are integrated with the reduction mechanism and are not installed in each joint, or in devices that do not require force control, where torque sensors are not necessary and therefore are not installed.

[0207] When considering grasping the angle transmission error, similar to the load position encoder, it is often difficult to mount a sensor due to industrial constraints such as device size, cost, and wiring.

[0208] Given the above background, it is difficult to directly measure angular transmission error in various robots, etc., and angular transmission error can be measured or identified indirectly by measuring the robot tip, etc. using a separate measuring device (e.g., laser tracker, laser distance sensor, camera system, acceleration sensor, inertial measurement unit (IMU)). However, since a separate measuring device is required, issues such as its handling and the cost of the measuring device can arise. Furthermore, if the reduction mechanism is replaced due to a malfunction or other reason, on-site measurement is required, which is time-consuming and costly, and there may also be cases where the environment is not suitable for measurement, such as a lack of space in the surrounding area.

[0209] On the other hand, a method has been proposed to estimate and compensate for angular transmission error without requiring a separate measuring device (external sensor), but there are cases where sufficient compensation cannot be achieved.

[0210] There are two perspectives 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 are the same, so here it is expressed as understanding the angular transmission error characteristics.

[0211] As mentioned above, there are various situations, but there are four main patterns for grasping the angular transmission error characteristics: (pre-)measurement, trial and error search, use of an identification algorithm, and use of an optimization algorithm.

[0212] In the case of advance measurement, the angular transmission error characteristics may change due to the influence of assembly errors.In addition, whether advance measurement is used or a method using experimental search, identification algorithms, or optimization algorithms is used, it takes a considerable amount of time to set appropriate parameters, which increases the adjustment costs during the design stage and at the time of implementation.

[0213] On the other hand, because angular transmission error varies between individual products, for example, if the impact of angular transmission error is small, it may be desirable to reduce the effort and cost by not grasping the error itself. Therefore, a method for calculating an evaluation index for determining the magnitude of the impact of angular transmission error is required.

[0214] (Analytical estimation of angular transmission error characteristics) To supplement the technical background of this disclosure, the following describes techniques for measurement and estimation in conventional technology. Fig. 125 shows a control block diagram for estimating angular transmission error characteristics. 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 denotes a feedback control system. The symbols are 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 moment of inertia D m :Motor damping coefficient J l : Load moment of inertia D l : Load damping coefficient K g : Reduction mechanism spring constant D g : Reduction mechanism damping coefficient θ Sync :Angular transmission error ATE Mea.: Angular Transmission Error Measuring Instrument 30 ATE Est.: Angular transmission error estimator 31

[0215] In reality, the system is affected not only by the viscous friction term due to the damping coefficient, but also by Coulomb friction, etc., but these are omitted here for simplicity. Delay elements in the current control system, etc. are also omitted.

[0216] The angular transmission error measurement is performed, for example, by measuring the motor position θm and the load position θ l Measure the value of the definition formula θ Sync =θ l -θ mCalculated from / R.

[0217] On the other hand, the angular transmission error estimation is performed using the motor position θm and the current command i ref Measure the angular transmission error θ Sync The current command due to the influence of the angular transmission error is modeled as follows:

number

[0218] The angular transmission error characteristic is estimated by A in Eq. (1). k and φ k is estimated using equation (33). Note that there are cases where the motor speed is used, or where the current command and motor speed are used together. The effect of the angular transmission error on the current command, and the estimation of the angular transmission error from the current command, can be expressed as follows:

number

number

[0219] From Figure 125, in the transfer function from the angle transmission error to the 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 necessary information for analysis) is required.

[0220] In this estimation principle, the behavior of the reduction gear mechanism and the load is considered as a disturbance component on the motor side and is detected as a component (current command) to compensate for it. Therefore, for example, when operating in a resonant operating speed range, it is preferable that the influence of angular transmission error is reflected in the current command. In this estimation principle, the controlled object is defined as consisting of a two-inertia model and angular transmission error, and angular transmission error characteristics are estimated with everything except angular transmission error as known. Therefore, when considering the estimation of angular transmission error characteristics, errors in the information required for analysis are directly related to the estimation accuracy. In other words, to estimate angular transmission error characteristics, it is necessary to accurately grasp the information required for analysis.

[0221] On the other hand, it is known that various attenuation coefficients in particular are affected by individual differences and temperature characteristics, and that it is difficult to grasp their characteristics.

[0222] As described above, analytical angular transmission error characteristic estimation has a practical problem of accurately grasping the information required for analysis. In light of the above, the present disclosure provides an angular transmission error characteristic estimation method that takes this point of view into account.

[0223] FIG. 126 shows a schematic diagram of an embodiment for estimating and compensating for angular transmission error characteristics according to the present disclosure. As shown in FIG. 126, a vibration suppression control device 100_5 includes 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 FIG. 2, and is configured with 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 for compensating 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 FIG. 127 (described later) and calculates an estimated disturbance. The evaluation index calculation unit 13 is configured, for example, as a lock-in amplifier as shown in FIG. 128 (described later) and calculates an evaluation index using the estimated disturbance as an evaluation signal. The angular transmission error estimation device 35 is configured with 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 at least one of the objective functions defined based on the evaluation index or the evaluation signal, using, for example, random search, gradient descent, Bayesian optimization, or genetic algorithm to optimize the amplitude and phase used in the angular transmission error compensator 11. Note that instead of using the optimization processing unit 14, manual search (adjustment) may be performed by trial and error. The angular transmission error compensator 11 is, for example, dynamic angular transmission error compensation, and generates a compensation signal that compensates for rotational non-uniformity of the angular transmission error. The vibration suppression control device is composed of the angular transmission error estimator 35, the angular transmission error compensator 11, and the optimization processing unit 14, and compensates for rotational non-uniformity of the angular transmission error. Hereinafter, the angular transmission error compensator 11, state estimation processing unit 12, evaluation index calculation unit 13, optimization processing unit 14, and angular transmission error estimator may be simply referred to as the angular transmission error compensator, state estimation processing unit, evaluation index calculation unit, optimization processing unit, and angular transmission error estimator.

[0224] (Angular transmission error characteristic estimation using a reaction force estimation observer) To facilitate understanding of the present disclosure, the following describes the related technical background and the concept of estimating the angular transmission error characteristic, followed by the logical background leading to the configuration of the embodiment of the present disclosure. Furthermore, the effect of the angular transmission error characteristic estimation of the present disclosure is quantitatively demonstrated by numerical simulations described below.

[0225] Terms used in this disclosure are defined as follows: An evaluation index refers to a value for quantitatively evaluating the degree of objective achievement, and there are various methods for calculating the evaluation index, and an appropriate method is selected depending on the device and the environment in which it is used. An objective function is a function defined using evaluation indices to determine an optimization target (for example, parameters, structure, or processing conditions). An optimization method refers to a calculation method for searching or determining the optimal combination of parameters or structures, for example, to minimize or maximize the value of an objective function. Note that this is not limited to determining the exact optimal value, but also includes iterative or exploratory processing to improve the value of an evaluation index or objective function. The angular transmission error characteristic estimation includes the estimation of the angular transmission error characteristic and the estimation of the influence of the angular transmission error (the influence of the difference between the actual angular transmission error characteristic and the angular transmission error characteristic used for compensation).

[0226] As an example of a specific configuration for estimating the angular transmission error characteristic, Fig. 127 shows a block diagram of angular transmission error characteristic estimation by a reaction force observer (RFOB), which is the state estimation processing unit 33. In Fig. 127, reference numeral 32 denotes a feedback control system, and reference numeral 33 denotes a state estimation processing unit (reaction force estimation observer). The symbols are as follows: Plant: A control 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 mn: Nominal motor moment of inertia Delay n : Nominal delay element of current control system, etc. F: Reaction force estimation filter τ^ d : Estimated disturbance (estimated reaction torque)

[0227] It is expressed as something that is added to the current command as dynamic angle transmission error compensation. In addition, delays in the current control system, etc. are also expressed as the controlled object.

[0228] Here, if we focus on the dynamic angular transmission error compensation mentioned above, the influence of the angular transmission error of the compensation order can be made zero, and vibration at the load position can be reduced. In this state, the torque that drives the load, which is the reaction torque to the motor, does not include the influence of the angular transmission error of the compensation order. Specifically, the reaction torque τ re This corresponds to not including the influence of the angular transmission error of the compensation order. Therefore, if it is known that the influence of the angular transmission error of the compensation order on the reaction torque is 0, it means that the angular transmission error characteristics used in dynamic angular transmission error compensation match the angular transmission error characteristics of the controlled object, and the angular transmission error characteristics can be estimated.

[0229] Reaction torque is an internal state quantity of the controlled object and is not usually measured. However, as mentioned above, a torque sensor may be installed and the reaction torque may be measured directly. A reaction torque estimation observer is known as a torque sensorless method for estimating reaction torque. A reaction torque estimation observer estimates reaction torque by separately modeling various disturbance components and subtracting them from the estimated value, and is primarily used to achieve force (torque) control. For example, this is a method for estimating the force (reaction force or reactive force) applied to the tip of a robot arm. For details about reaction torque estimation observers, see Non-Patent Documents 1 and 2. In the calculation process of the reaction torque estimation observer, an "estimated disturbance" is calculated, which includes various components such as the torque driving the load, reaction torque, friction torque, and torque due to the influence of angular transmission error.

[0230] In this disclosure, we consider estimating angular transmission error characteristics using an estimated disturbance in a reaction force estimation observer. The estimated disturbance is torque-dimensional (acceleration-dimensional) information, and the angular transmission error is position-dimensional information. Therefore, conversion is required to estimate the angular transmission error characteristics, and simply obtaining the estimated disturbance is insufficient. Furthermore, as mentioned above, the estimated disturbance includes the influence of various disturbance components, so some kind of ingenuity is required to estimate the angular transmission error characteristics.

[0231] From the above, when considering using a reaction force estimation observer to estimate angular transmission error characteristics, the following two main issues arise: Note that these two issues also apply when a torque sensor integrated with the reduction gear mechanism is installed. Task 1: Conversion from torque dimension to position dimension Task 2: Extraction of angular transmission error characteristics from estimated disturbance

[0232] In the present disclosure, the influence of angular transmission error can be grasped by using the harmonic components of the estimated disturbance with respect to motor rotation as an evaluation index. Also, in the present disclosure, the angular transmission error characteristics are estimated by performing dynamic angular transmission error compensation so as to set the value of the evaluation index to 0 based on the characteristics of the dynamic angular transmission error and the reaction force estimation observer.

[0233] In this disclosure, problem 1 is addressed by utilizing dynamic angular transmission error compensation. When the influence of the angular transmission error of the compensation order in the estimated disturbance is zero, the angular transmission error characteristic used in dynamic angular transmission error compensation can be regarded as the angular transmission error characteristic of the controlled object, making it possible to estimate the angular transmission error characteristic. By utilizing dynamic angular transmission error compensation, direct conversion is not necessary and it is possible to indirectly estimate the angular transmission error characteristic. Furthermore, although the design of the reaction force estimation observer will be described in detail later, the dynamic angular transmission error compensation and reaction force estimation observer do not require the necessary information for analysis in their design, making it possible to indirectly solve problem 1.

[0234] Furthermore, for problem 2, an estimated disturbance during constant speed operation that corresponds to the vibration frequency is used. Because the influence of angular transmission error can be considered to be a constant frequency during constant speed operation, the frequency component corresponding to the influence of angular transmission error in the results of Fourier analysis of the estimated disturbance during constant speed operation is used as the evaluation index. Then, using the results of Fourier analysis of this estimated disturbance as the evaluation index, the angular transmission error characteristic used in dynamic angular transmission error compensation, in which the influence of angular transmission error of the compensation order in the estimated disturbance is zero, becomes the angular transmission error characteristic of the controlled object. Note that, as with the analytical angular transmission error characteristic estimation method, it is preferable that the influence of angular transmission error appears in the current command, for example, when operating in an operating speed range that causes a resonance state.

[0235] Unlike analytical angular transmission error characteristic estimation methods, it is not possible to estimate the angular transmission error characteristic definitively. Therefore, it is possible to manually search (adjust) the angular transmission error characteristic by trial and error using an evaluation index or an objective function defined based on the evaluation index, or to automatically estimate the angular transmission error characteristic using various optimization techniques, such as random search, gradient descent, Bayesian optimization, and genetic algorithms. The angular transmission error characteristic may be determined by an optimization process performed within the device, or by an external computing device, and the resulting angular transmission error characteristic may be set. In either case, the angular transmission error characteristic is determined based on an evaluation index or an objective function. It is also possible to estimate the angular transmission error characteristic even when the motor is not operating at a constant speed. The details of the related evaluation indexes will be described later.

[0236] Next, the configuration of the reaction force estimation observer will be described. Conventional reaction force estimation observers are configured using a model of the moment of inertia of the motor, reduction gear mechanism, and load. In contrast, the present disclosure features a reaction force estimation observer configured based on motor characteristics. This is because, even in the design of dynamic angular transmission post-compensation, the observer can be configured without requiring information on the load moment of inertia or the reduction gear mechanism spring constant. While it is possible to model and utilize information required for analysis, including the load moment of inertia and the reduction gear mechanism spring constant, configuring the observer based on motor characteristics reduces the difficulty and man-hours required for modeling. Furthermore, nominal values ​​for motor characteristics are easily obtained from catalogs, etc., and various methods for estimating them as needed are known, making it relatively easy to reduce parameter errors. While reaction force estimation observers are often configured to feed back estimated disturbances, the present disclosure does not feed back estimated disturbances, as with dynamic angular transmission error compensation, in order to estimate angular transmission error characteristics without modifying the existing feedback control system C(s). As described above, the estimated disturbance includes the influence of various components, so it may be configured to remove unnecessary components other than the influence of the angular transmission error, similar to a normal reaction force estimation observer.

[0237] The estimated disturbance can be calculated as shown in the following equations (36) to (38). If the parameter error is small, the reaction torque can be estimated as having passed through the reaction force estimation filter F.

number

number

number

[0238] The reaction force estimation filter F is a second-order system of the following equation (39) in order to make the reaction force estimation observer proper.

number

[0239] The estimated disturbance must include a vibration frequency component corresponding to the order of the object to be estimated, 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, a frequency band corresponding to the operating speed range in dynamic angular transmission error compensation, or approximately twice the vibration frequency, may be used as a guideline. Note that the setting must take into account the influence of the motor encoder resolution, control period, operating pattern, noise, etc., but because the estimated disturbance is not directly fed back, the design is not as difficult as a conventional reaction force estimation observer. The design of a reaction force estimation observer is closely related to a disturbance observer, and for details on the design method, see, for example, Non-Patent Document 3.

[0240] In many cases, the reaction force estimation observer is configured as a first-order system using speed information, but here we have assumed a case where there is no speed feedback and have expressed it as configured from position information. Therefore, if speed information is available, it may be configured by referring to the configuration of a general disturbance observer rather than this configuration. Also, the reaction force estimation observer may be configured using current values ​​instead of current commands, and the observation information used in the reaction force estimation observer can be configured from a variety of sources, including current commands, current values, motor position, and motor speed.

[0241] Furthermore, the estimated disturbance may be estimated using various state estimation methods, such as a Luenberger observer, a disturbance observer, or a Kalman filter. Depending on the configuration of an existing feedback control system, the estimated disturbance may be estimated by extending various state estimation methods. Specifically, in a system where the influence of disturbances is an issue and a feedback control system utilizing a disturbance observer is configured, the estimated disturbance may be used to calculate the evaluation index of the present disclosure. Furthermore, in a feedback control system utilizing a Kalman filter to address the influence of noise or achieve optimal control, the estimated disturbance may be designed to be taken into account in the state quantity to be estimated. These are merely representative examples, and may be selected as appropriate depending on the configuration and application of the device.

[0242] When the torque (acceleration / deceleration torque) driving the load during the estimated disturbance and the influence of friction characteristics cannot be ignored, unnecessary components are removed using filtering such as a low-pass filter or a high-pass filter. Note that the filtering may be performed in conjunction with various state estimation methods, or may be performed when calculating the evaluation index.

[0243] Furthermore, if a torque sensor is installed, it is also possible to configure the system so that the torque sensor detection value is used instead of the reaction force estimation observer. In this case, too, the challenges of estimating the angular transmission error characteristic using the reaction torque—conversion from torque dimension to position dimension and extraction of the angular transmission error characteristic from the reaction torque—can be achieved through dynamic angular transmission error compensation. Here, the example of a torque sensor has been described because it directly corresponds to the reaction torque estimation torque. However, if sensors such as an acceleration sensor or an inertial measurement unit (IMU) are installed, the angular transmission error characteristic can be estimated by using the harmonic components of various signals with respect to motor rotation as evaluation indicators and performing dynamic angular transmission error compensation so that their values ​​become zero, as in the present disclosure. Furthermore, various sensor information may be used as observation information for the state estimation method.

[0244] Dynamic angular transmission error compensation uses angular transmission error characteristics, control system structure, and control parameters to determine compensation parameters, so it is necessary to understand these characteristics. The above method assumes that the control system structure and control parameters are known, and estimates angular transmission error characteristics, which are difficult to understand. By utilizing this disclosure, however, it is possible to experimentally determine the compensation parameters required for dynamic angular transmission error compensation even when the control system structure and control parameters are unknown.

[0245] Here, Estimation 1: When estimating the angular transmission error characteristics in a situation 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, The features of both, including dynamic angular transmission error compensation, will be described below. 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 the characteristics of the control parameters, based on equation (28).

[0246] Considering the advantage of dynamic angular transmission error compensation (ATEC), which can clearly consider the influence of the control system structure and control parameters, it is preferable to realize it as Estimation 1, which estimates only the angular transmission error characteristics. On the other hand, for example, when a servo system is configured using a combination of commercially available products, the control system structure and control parameters may not be known. In this case, Estimation 2 makes it possible to estimate compensation parameters including the angular transmission error characteristics, and dynamic angular transmission error compensation can compensate for rotation non-uniformity caused by the influence of angular transmission error. In the case of Estimation 2, for example, when operating at a certain constant speed, estimation of compensation parameters that can reduce vibration can be performed at multiple operating speeds. In this case, if the control parameters are adjusted, it is necessary to re-estimate the compensation parameters.

[0247] Since the angular transmission error has characteristics that differ depending on the direction of rotation, the angular transmission error characteristics are estimated for both forward and reverse rotations.

[0248] Although the present disclosure estimates angular transmission error characteristics through dynamic angular transmission error compensation, the dynamic angular transmission error, the calculation of an estimated disturbance by a reaction force estimation observer, and the calculation of an evaluation index are independent processes and do not necessarily need to be performed synchronously in the same processing cycle. In particular, the calculation of an estimated disturbance by a reaction force estimation observer and the calculation of an evaluation index may be realized by offline processing, and the processing cycle and processing timing can be flexibly configured depending on the device configuration.

[0249] Although dynamic angular transmission error compensation is used in estimating angular transmission error characteristics using a reaction force estimation observer, known configurations described in prior art documents, etc., can also be applied as a method of compensating for angular transmission error, and the method is not limited to dynamic angular transmission error compensation. Therefore, the parameters that determine the output of each compensation method (equivalent to the compensation signal in dynamic angular transmission error compensation) can be manually searched (adjusted) by trial and error using an evaluation index or an objective function defined based on the evaluation index, or optimized using various optimization methods.

[0250] [effect] According to the present disclosure, by utilizing a reaction force estimation observer, the influence of angular transmission error can be quantitatively grasped from an evaluation index without the need for additional sensors such as a load position encoder, torque sensor, or laser distance sensor, which are particularly problematic in semi-closed loop control. Furthermore, by utilizing dynamic angular transmission error, angular transmission error characteristics can be grasped. The cooperation between the reaction force estimation observer in the state estimation process and the calculation of an evaluation index for the influence of angular transmission error enables a configuration that does not require additional sensors. Furthermore, by designing the reaction force estimation observer based on motor characteristics, as with dynamic angular transmission error compensation, the number of design parameters can be reduced, eliminating the need to model the parameters in advance, and streamlining the design process. By utilizing various optimization techniques using an objective function based on the evaluation index, angular transmission error characteristics can be automatically estimated. Therefore, the present disclosure has excellent industrial applicability and can be easily applied to various control devices in various industrial fields, including existing equipment, and has excellent effects such as simplifying the device, reducing costs, and facilitating installation and maintenance.

[0251] (Angular transmission error characteristic estimation evaluation index) Here, we will explain the evaluation indexes used to estimate the angular transmission error characteristics. Evaluation indexes can be broadly divided into offline processing and online processing, and each will be explained below. Offline processing refers to a processing format in which data to be processed is collected and stored in advance, and then analyzed and parameter estimation is performed all at once, meaning detailed analysis and optimization without time constraints. Online processing refers to a processing format in which data to be processed is processed quickly as it is input sequentially, and the results are immediately reflected in control and judgment.

[0252] (Evaluation metrics based on offline processing) Here, we will discuss the following two representative methods for calculating evaluation indices based on offline processing. -Fourier transform at constant speed ·Vibration order analysis (during variable speed operation)

[0253] As mentioned above, the Fourier transform during constant speed operation allows the influence of angular transmission error to be considered as a constant frequency, making it possible to easily calculate evaluation indices. Vibration order analysis, an example of an evaluation indices compatible with variable speed operation, estimates and interpolates the phase angle according to the rotational speed, and then applies a short-time Fourier transform to map the amplitude of each order component onto the rotational speed axis. This processing makes it possible to visually and quantitatively grasp the frequency characteristics of vibrations that accompany changes in rotational speed. An example of a specific implementation is the rpmordermap function from MathWorks, which is described in Non-Patent Document 4.

[0254] The evaluation index in the present disclosure is not limited to a specific algorithm, but it is preferable to use a Fourier transform during constant speed operation from the viewpoint of processing content and analytical accuracy.

[0255] (Evaluation index based on online processing) Here, we will discuss the following three representative methods for calculating evaluation indicators based on online processing. Synchronous detection: Lock-in amplifier (LIA) DFT: Goertzel method Bandpass filter

[0256] A lock-in amplifier, an example of synchronous detection, is a device and algorithm for measuring extremely weak signals with high precision, and can detect the amplitude and phase of specific known frequency components. It has the advantage that it can extract the desired signal through "synchronous detection" even in the presence of large amounts of noise. 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 a sine wave using a recursive difference equation. A bandpass filter is a filter for extracting frequency components in a specific frequency band.

[0257] As mentioned above, the estimated disturbance is made up of various components, so here we will outline a method using a lock-in amplifier, which has excellent noise resistance. With a lock-in amplifier, the target signal becomes a DC component due to the dot product of the target signal and the reference signal, and other components become high-frequency components. Therefore, a low-pass filter is used to remove the high-frequency components, extract the target component, and calculate the amplitude.

[0258] FIG. 128 shows a block diagram of a lock-in amplifier, which is the evaluation index calculation unit 34 for calculating the evaluation index. d The value of the compensation order component can be obtained by calculating the amplitude A from the signal that passes through the low-pass filter LPF, with the reference signal being a sine wave and cosine wave corresponding to the compensation order component of the angular transmission error (illustrated as the second-order component in Figure 128). The inner product of the target signal (the second-order component in the estimated disturbance) and the reference signal can be calculated as follows:

number

number

[0259] Since the target signal components are DC components (in this case, components that are not dependent on θm) and high-frequency components (in this case, 4θm), it is possible to extract only the DC components using an LPF and calculate the amplitude. The LPF can be designed taking into account the frequencies of the harmonic components. Note that, since it is sufficient to determine the magnitude of the impact of the angular transmission error of the compensation order as an evaluation index, only the amplitude needs to be known.

[0260] (Effects on evaluation indicators) [effect] The evaluation indexes used in the present disclosure have multiple embodiments for both offline and online processing, and these can be selected or combined as appropriate depending on the situation. The above are merely representative examples, and they can be selected or combined as appropriate depending on the configuration and application of the device. Therefore, the optimal implementation method can be flexibly selected depending on the computer resource constraints and design requirements of the control device, and parameter estimation can be performed flexibly and effectively without being limited to a specific method. Therefore, the present disclosure has excellent versatility, such as being able to flexibly respond to various device situations and being easily applicable to various control devices in various industrial fields.

[0261] (Numerical example) Hereinafter, through numerical simulation, the operation of the characteristic components of the present disclosure will be quantitatively evaluated and its usefulness will be objectively demonstrated. The simulation conditions are the same as those for the dynamic angular transmission error compensation described above. As described above, in this case, the resonance vibration reaches a maximum at 1600 r / min, so the simulation is performed with constant speed operation at 1600 r / min. Acceleration is performed from 0 to 0.5 s to 1600 r / min, and then constant speed operation is performed at 1600 r / min. The vibration frequency is 1600 / 60×2=53.3 Hz based on the correspondence relationship with the second-order component of the angular transmission error. The design parameters of the reaction force estimation filter are ω RFOB =2π×100[rad / s], ζ RFOB = 1. Other design parameters can be determined from the motor characteristics shown in Table 1.

[0262] The results of a simulation performed under the following four conditions are shown below. 1. No dynamic angular transmission error compensation (hereinafter referred to as condition W) 2. With dynamic angular transmission error compensation (hereinafter referred to as condition X) 3. With dynamic angular transmission error compensation (with compensation parameter error) (hereinafter referred to as condition Y) 4. Dynamic angular transmission error compensation is enabled, and friction characteristics are considered in the controlled object (hereinafter referred to as condition Z).

[0263] The conditions for compensation parameter error are as follows: Second-order characteristics of the angle transmission error of the controlled object (see Table 1) Amplitude: 10 arc-sec Phase: 15 deg Angular transmission error characteristics for compensation Amplitude: 5 arc-sec Phase: 15 deg

[0264] The conditions for taking into consideration the friction characteristics of the controlled object are as follows: Motor damping coefficient D m 4.5×10 -4 Nm / (rad / s) Load damping coefficient D l 1.4 Nm / (rad / s) Reducer damping coefficient D g 10 Nm / (rad / s)

[0265] As an example of the evaluation index, the evaluation index is calculated using a lock-in amplifier in online processing. The design parameters are as follows: LPF for lock-in amplifier: 1st order, cutoff frequency 5 Hz High-pass filter (HPF) for estimated disturbance: 1st order, cutoff frequency 5 Hz *The signal that passes through the above HPF in response to the estimated disturbance is used as the target signal for the lock-in amplifier.

[0266] Figures 129 to 133 show the motor speed, load speed, reaction torque, estimated disturbance and evaluation index (LIA output) under condition W, with the horizontal axis representing time and the vertical axis representing each component. It shows that the motor speed, load speed, reaction torque and estimated disturbance have oscillatory components due to the influence of angular transmission error. The estimated disturbance for the reaction torque is affected by the reaction torque estimation filter, and the amplitude in the steady state is JPEG0007800877000057.jpg638 times. The evaluation index will be explained later together with the case with compensation.

[0267] (with dynamic angular 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. When angular transmission error can be compensated for by dynamic angular transmission error compensation, it is shown that vibration at load speed in a constant speed state is reduced, and furthermore, the reaction torque and estimated disturbance become zero. As mentioned above, during acceleration between 0 and 0.5 seconds, 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 torque to drive the load. It is shown that the motor speed has an oscillatory response to achieve vibration reduction at load speed.

[0268] (with dynamic angular 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, respectively, with the horizontal axis representing time and the vertical axis representing each component. When there is an error between the angular transmission error characteristics of the controlled object and the angular transmission error characteristics in the compensation parameters, it is shown that the amplitude of the reaction torque and estimated disturbance can be reduced compared to no compensation, and load speed vibration is also reduced. It is shown that the motor speed has an oscillatory response in order to achieve vibration reduction at the load speed. Furthermore, when compared with condition X, it is shown that no vibration reduction effect is obtained.

[0269] (Dynamic angular transmission error compensation included, friction characteristics considered for controlled object) Figures 144 to 148 show the motor speed, load speed, reaction torque, estimated disturbance, and evaluation index (LIA output) under condition Z, with the horizontal axis representing time and the vertical axis representing each component. Even when friction characteristics are taken into account, the reaction torque is hardly affected by the friction characteristics, indicating that vibration at load speed is reduced by dynamic angular transmission error compensation. On the other hand, although the estimated disturbance is affected by the friction characteristics, it remains a constant value at constant speeds, and no vibration components due to the influence of angular transmission error are observed. This shows that the motor speed exhibits an oscillatory response in order to achieve vibration reduction at load speed.

[0270] Next, we will compare the lock-in amplifier output, which is the evaluation index under conditions W to Z. Comparing Figures 133, 138, and 143, we can see that the values ​​correspond to vibration suppression performance. In particular, Figure 138 shows that the evaluation index is 0. Furthermore, Figure 148, which takes friction characteristics into consideration, also shows that the evaluation index is 0.

[0271] 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 components for motor rotation during an estimated disturbance as an evaluation index and suppressing rotation non-uniformity through dynamic angular transmission error compensation. Although this involves trial and error as mentioned above, it is possible to estimate optimal values ​​by utilizing various optimization methods.

[0272] Figure 149 is a flowchart of an angular transmission error estimation program for a servo control system equipped with a speed reduction mechanism. This program estimates an estimated disturbance, which is an internal state quantity of the controlled object, based on observation information, calculates an evaluation index based on a predetermined order component corresponding to the rotation non-uniformity of the estimated disturbance, and executes processing to quantitatively grasp the influence of the angular transmission error. Note that this processing is composed of a group of steps corresponding to the angular transmission error estimation method and angular transmission error estimation program, and functions as a state estimation processing unit and an evaluation index calculation unit.

[0273] Step S21: Initial setting. Prior to the execution of the angular transmission error estimation program, various initial settings are made. Specifically, design parameters for the state estimation method (e.g., disturbance observer, reaction force estimation observer, Kalman filter, etc.) used to estimate the estimated disturbance are set. In addition, initial settings may be made regarding the usage form (monitoring, adjustment, optimization, etc.) of the calculated evaluation index.

[0274] Step S22: Information acquisition. The control device acquires observation information necessary for estimating the estimated disturbance. Examples of the observation information include a current command, a current value, a motor position, and a motor speed. Furthermore, signals measured by a torque sensor, an acceleration sensor, an inertial measurement unit, etc. may be used as observation information for the state estimation method.

[0275] Step S23: Estimate the estimated disturbance (state estimation process). Based on the acquired observation information, an estimated disturbance, which is an internal state quantity of the controlled object, is estimated. State estimation techniques such as a disturbance observer, a reaction force estimation observer, or a Kalman filter can be used for the estimation. This state estimation processor is preferably configured based on motor characteristics (e.g., torque constant, motor inertia moment) without requiring analytical information such as the load inertia moment or the reduction gear mechanism spring constant. The estimated disturbance may include components other than those derived from angular transmission error (e.g., load drive torque due to acceleration / deceleration and friction effects). For this reason, filtering may be applied to suppress components other than those of a predetermined order corresponding to rotation nonuniformity. A typical example is a high-pass filter (HPF) designed to reduce inertia or friction effects. This method allows for batch processing without modeling, offering advantages in simplicity and cost.

[0276] Step S24: Calculation of evaluation indexes. Based on the estimated disturbance, an evaluation index is calculated based on the amplitude or amplitude and phase of a predetermined order component (e.g., a component with two cycles per rotation of the input shaft) corresponding to the rotation non-uniformity. The evaluation index may consist of only the amplitude of the order component, or a combination of the amplitude and phase. The calculation of the evaluation index can be performed offline or online. Offline examples include Fourier transform during constant speed operation and vibration order analysis (estimating the phase angle according to the rotation speed, performing interpolation, and then applying a short-time Fourier transform). Online examples include synchronous detection (lock-in amplifier), the Goertzel method, and band-pass filters. The calculated evaluation index is used to determine the degree of influence of the angular transmission error.

[0277] The calculated evaluation index can be used as an evaluation index of the compensation performance in dynamic angular transmission error compensation to monitor and diagnose the appropriateness of the compensation, and can also be used as an optimization index for determining and adjusting the compensation parameters (amplitude and phase).Various algorithms such as random search, gradient descent, Bayesian optimization, and genetic algorithm may be applied as the optimization method.

[0278] Figure 150 is a flowchart of a vibration suppression control program in a servo control system equipped with a speed reducer. This flowchart shows a process for determining and correcting the compensation signal (amplitude and phase) of dynamic angular transmission error compensation to suppress rotation non-uniformity by repeatedly searching and updating, using an optimization method, an evaluation index calculated from an estimated disturbance estimated based on observation information, even when the angular transmission error characteristics are unknown. This process corresponds to the vibration suppression control method and the vibration suppression control program command group. This optimization method minimizes or maximizes the evaluation index using algorithms such as random search, gradient descent, Bayesian optimization, and genetic algorithm.

[0279] Step S31: Initial setting. The initial settings required to execute the vibration suppression control program are performed. This includes initial settings for a predetermined compensation order, amplitude, and phase for generating a compensation signal. Amplitude and phase information corresponding to each compensation order, rotation direction, etc. is read into a compensation model (e.g., a look-up table) referenced by the dynamic angular transmission error compensator. These compensation parameters may be configured so that the amplitude and phase are automatically set according to the frequency or compensation order corresponding to a predetermined speed range based on the configuration of a servo control system for at least one of the motor position, speed, and current, the control parameters, and frequency response characteristics based on the motor characteristics, and then registered in the compensation model.

[0280] Step S32: Information acquisition. The control device acquires observation information necessary for estimating the estimated disturbance. Examples of the observation information include a current command, a current value, a motor position, and a motor speed. The control device also acquires current position information of the controlled object (for example, a motor position or a position command). It also acquires current speed information of the controlled object (for example, a motor speed or a position command speed). From this information, either actual information (motor position / motor speed) or command information (position command / position command speed) can be selected and used.

[0281] Step S33: Estimate the estimated disturbance (state estimation process). Based on the acquired observation information, an estimated disturbance, which is an internal state quantity of the controlled object, is estimated. For the estimation, a state estimation method such as a disturbance observer, a reaction force observer (RFOB), or a Kalman filter can be used. RFOB can be configured based on motor characteristics (e.g., torque constant, motor inertia), and is advantageous in that it does not require analytical parameters such as the load inertia moment or the spring constant of the reduction mechanism. Since the estimated disturbance may include components other than the order components of the angular transmission error (e.g., acceleration / deceleration torque, friction effects, etc.), filtering (e.g., a high-pass filter) to suppress these unnecessary components may be applied in this step or a subsequent step.

[0282] Step S34: Calculation of evaluation indexes. Based on the estimated disturbance, an evaluation index is calculated based on a predetermined order component corresponding to the non-uniformity of rotation. The calculation of the evaluation index can be performed offline or online. Offline examples include Fourier transform during constant speed operation and vibration order analysis (estimating the phase angle according to the rotation speed, performing interpolation processing, and then applying a short-time Fourier transform), while online examples include synchronous detection (lock-in amplifier: LIA), the Goertzel method, and bandpass filters. The calculated evaluation index is used to determine the degree of influence of the angular transmission error.

[0283] Step S35: Optimizing compensation parameters. The amplitude and phase of the compensation signal can be optimized using an optimization method such as random search, gradient descent, Bayesian optimization, or genetic algorithm to minimize the evaluation index obtained in step S34 or an objective function defined based on the evaluation index. Furthermore, if the angular transmission error has characteristics different from one direction of rotation to another, it may be optimized separately for forward and reverse rotation. If there are multiple orders of compensation to be compensated, each order may be optimized independently.

[0284] Step S36: Amplitude and phase correction. 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 (for example, a look-up table). The compensation model may be configured and adjusted so that the compensation signal is 0 when the speed information is 0, in order to prevent interference with the static component.

[0285] 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.

[0286] Step S38: Signal addition. The generated compensation signal is added to a position command, a speed command, a current command, or a control signal related to a control signal related to these.

[0287] Step S39: Servo control. A servo control system having a speed reducing mechanism is operated based on the control signal to which the compensation signal has been added, thereby compensating for non-uniformity of rotation caused by angular transmission error of the speed reducing mechanism.

[0288] [Summary of the effect of estimating angular transmission error characteristics using a reaction force estimation observer] According to the present disclosure, by utilizing a dynamic angular transmission error and reaction force estimation observer, it is possible to quantitatively grasp the influence of angular transmission error from an evaluation index and grasp angular transmission error characteristics without the need for additional sensors such as a load position encoder, torque sensor, or laser distance sensor, which are particularly problematic in semi-closed loop control. When designing the reaction force estimation observer, by configuring it based on motor characteristics, just like dynamic angular transmission error compensation, it is possible to reduce the number of design parameters and make the design process more efficient.

[0289] Furthermore, by utilizing various optimization techniques using an objective function based on the evaluation index, it is possible to automatically estimate the angular transmission error characteristics. There are multiple embodiments for both offline and online processing in the calculation of the evaluation index, and these can be selected or combined as appropriate depending on the situation.

[0290] As described above, the present disclosure has excellent industrial applicability, is easily applicable to various control devices in a variety of industrial fields, including existing equipment, and has excellent effects such as simplifying the device, reducing costs, and facilitating installation and maintenance.

[0291] In this embodiment, each process is executed by an arbitrary computer. Furthermore, the arbitrary computer may execute these processes by a processor as hardware, a program as software, or a combination thereof. In this case, the processor is configured to execute various processes in this embodiment in cooperation with the program, and may function as each unit or means in this embodiment. Furthermore, the order in which the processes are executed by the processor is not limited to the order described above and may be changed as appropriate. The arbitrary computer may be a general-purpose computer, a computer for specific applications, a workstation, or any other system capable of executing each process.

[0292] The processor may be composed of one or more pieces of hardware, and the type of hardware is not limited. For example, the processor may be composed of hardware such as a programmable logic device such as a CPU, an MPU (Micro Processing Unit), or an FPGA (Field Programmable Gate Array), a dedicated circuit for executing specific processes such as an ASIC (Application Specific Integrated Circuit), a GPU (Graphic Processing Unit), or an NPU (Neural Processing Unit). The type of hardware may also be a combination of different types of hardware. When multiple pieces of hardware are configured to execute one or more processes of a certain processor, the multiple pieces of hardware may exist in devices physically separated from each other or in the same device. 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. The hardware may be composed of an electric circuit or the like, which is a combination of circuit elements such as semiconductor elements.

[0293] Furthermore, the program may be software, such as firmware or 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 the respective function. The program may be program code or multiple code segments stored on one or more non-transitory computer-readable media (e.g., storage media or other storages). The program may be stored across multiple non-transitory computer-readable media that reside in physically separate devices. The program code or code segment may represent a procedure, a function, a subprogram, a routine, a subroutine, a module, a software package, a class, or any combination of instructions, data structures, or program statements. The program code or code segment may be connected to another code segment or a hardware circuit by transmitting or receiving information, data, arguments, parameters, or memory contents. The program of the present application may also be provided as a program product.

[0294] The angular transmission error estimation method and angular transmission error estimation program of the present disclosure include steps that implement the functions of each component of the angular transmission error estimation device of the present disclosure (such as the state estimation processing unit and the evaluation index calculation unit) or instructions that cause a computer to execute them. Therefore, the angular transmission error estimation method and angular transmission error estimation program can be configured into embodiments that include all of the additional features of the angular transmission error estimation device (such as a configuration based on motor characteristics) as method steps or program instructions, respectively.

[0295] The vibration suppression control method and vibration suppression control program of the present disclosure include steps that realize the functions of each component of the vibration suppression control device of the present disclosure (state estimation processing unit, evaluation index calculation unit, optimization processing unit, angular transmission error compensation unit, etc.) or instructions that cause a computer to execute them. Therefore, the vibration suppression control method and vibration suppression control program can be configured into an embodiment that includes all of the additional features of the vibration suppression control device (for example, automatic setting of a compensation model, etc.) as method steps or program instructions, respectively.

[0296] (Addendum) The following additional notes are provided regarding aspects of the present disclosure. (Appendix 1) An angular transmission error estimating device applied to a servo control system equipped with a speed reduction mechanism, for estimating rotation non-uniformity caused by the influence of angular transmission error of the speed reduction mechanism, the angular transmission error estimating device comprising: a state estimation processing unit that estimates an estimated disturbance, which is an internal state quantity of a controlled object, based on observation information; and an evaluation index calculation unit that calculates an evaluation index based on the estimated disturbance and on order components of a predetermined order that corresponds to the rotation non-uniformity. (Appendix 2) 2. The angular transmission error estimating device according to claim 1, wherein the state estimation processing unit is configured based on motor characteristics. (Appendix 3) 3. The angular transmission error estimating 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. (Appendix 4) 4. The angular transmission error estimating device according to any one of Supplementary Note 1 to Supplementary Note 3, wherein the evaluation index is defined based on offline processing including at least one of a Fourier transform and a vibration order analysis. (Appendix 5) 5. The angular transmission error estimating device according to any one of Supplementary Note 1 to Supplementary Note 4, wherein the evaluation index is defined based on online processing including at least one of synchronous detection, Goertzel's algorithm, and band-pass filtering. (Appendix 6) 6. The angular transmission error estimating device according to any one of Supplementary Note 1 to Supplementary Note 5, further comprising a filter for removing components other than the order components from the estimated disturbance. (Appendix 7) 7. The angular transmission error estimating device according to any one of Supplementary Note 1 to Supplementary Note 6, wherein the estimated disturbance is calculated from a signal measured by a sensor. (Appendix 10) 8. A vibration suppression control device comprising: the angular transmission error estimating device according to any one of Supplementary Note 1 to Supplementary Note 7; and an angular transmission error compensator that generates a compensation signal, wherein the vibration suppression control device optimizes at least one of the evaluation index and an objective function defined on the basis of the evaluation index, and corrects the compensation signal. (Appendix 11) 11. The vibration damping control device according to claim 10, wherein the angular transmission error compensator includes: an angular transmission error compensator that generates the sinusoidal compensation signal based on position information, the angular transmission error compensator having the order and amplitude and phase that are parameters in the optimization; 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 the phase based on speed information. (Appendix 12) 12. The vibration control device according to claim 10 or 11, wherein an optimization method including at least one of random search, gradient descent, Bayesian optimization, and genetic algorithm is used. (Appendix 13) 13. A vibration control device according to any one of appendix 10 to appendix 12, wherein the angular transmission error compensator is configured to automatically set amplitude and phase at a frequency corresponding to a predetermined speed range using a control system configuration in which one of motor position, motor speed, and current is a controlled variable, control parameters, and frequency response characteristics derived based on motor characteristics, and to register the amplitude and phase in the compensation model. (Appendix 14) 14. The vibration control device according to any one of Supplementary Note 10 to Supplementary Note 13, wherein the compensation model is a lookup table that references the amplitude and the phase based on the velocity information. (Appendix 15) 15. A vibration control device according to any one of appendices 10 to 14, wherein the compensation model is configured to correct the amplitude using a weighting coefficient that controls the effectiveness of the compensation signal in accordance with a predetermined speed range of the speed information. (Appendix 16) 16. The vibration damping control device according to any one of Supplementary Note 10 to Supplementary Note 15, wherein the position information is a position command or a motor position, and the speed information is a position command speed or a motor speed. (Appendix 17) 17. The vibration control device according to any one of claims 10 to 16, wherein the angular transmission error compensator is configured so that the compensation signal is 0 when the speed information is 0. (Appendix 18) 18. The vibration control device according to claim 10, wherein the angular transmission error compensator generates the compensation signal from the amplitude and the phase in accordance with a rotation direction of the reduction mechanism. (Appendix 19) 19. The vibration control device according to claim 10, wherein the angular transmission error compensator generates a sinusoidal compensation signal for each order based on the amplitude and the phase for each order, and generates the compensation signal by adding these signals together. (Appendix 20) 19. A vibration control device according to claim 10, wherein the angular transmission error compensator designs the compensation model and corrects the compensation signal regardless of the inertia with respect to rotation of a load connected to the output shaft of the reduction mechanism. (Appendix 21) 21. The vibration control device according to claim 10, wherein the angular transmission error compensator designs the compensation model and corrects the compensation signal regardless of a spring constant of the reduction mechanism. (Appendix 22) 22. The vibration control device according to claim 10, wherein the angular transmission error compensator corrects an amplitude and a phase of the compensation signal for generating the compensation signal based on a load torque acting on the reduction gear mechanism. (Appendix 23) 23. A vibration control device according to any one of claims 10 to 22, wherein the angular transmission error compensator corrects the amplitude and phase of the compensation signal generated based on the temperature of the reduction mechanism, the temperature around the reduction mechanism, or a temperature estimated based on operating conditions.

[0297] All publications, patent applications, and technical standards mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent application, or technical standard was specifically and individually indicated to be incorporated by reference. [Explanation of symbols]

[0298] 1. Control target 2 Addition section 3 Compensation Model 10 Servo control system 11 Angular transmission error compensation section 12 State estimation processing unit 13 Evaluation index calculation section 14 Optimization processing section 30 Angular transmission error measuring instrument 31 Angular transmission error estimator 32 Feedback Control System 33 State estimation processing unit 34 Evaluation index calculation section 35 Angular transmission error estimator 100_1, 100_2, 100_3, 100_4, 100_5 Vibration control device 200 motor 300 Reduction mechanism 400 load 500 Encoder 1000 Vibration Control System

Claims

1. 1. An angular transmission error estimating device applied to a servo control system equipped with a speed reduction mechanism, for estimating rotation non-uniformity caused by the influence of angular transmission error of the speed 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 the observation information; an evaluation index calculation unit that calculates an evaluation index based on an order component of a predetermined order corresponding to the non-uniformity of the rotation, based on the estimated disturbance; An angular transmission error estimating device comprising:

2. 2. The angular transmission error estimating device according to claim 1, wherein the state estimation processing unit is configured based on motor characteristics.

3. 2. The angular transmission error estimating 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. 2. The angular transmission error estimating device according to claim 1, wherein the evaluation index is defined based on offline processing including at least one of a Fourier transform and a vibration order analysis.

5. 2. The angular transmission error estimating device according to claim 1, wherein the evaluation index is defined based on online processing including at least one of synchronous detection, Goertzel's method, and band-pass filtering.

6. 2. The angular transmission error estimating device according to claim 1, further comprising a filter for removing components other than the order components from the estimated disturbance.

7. 2. The angular transmission error estimating device according to claim 1, wherein the estimated disturbance is calculated from a signal measured by a sensor.

8. 1. An angular transmission error estimation method applied to a servo control system equipped with a speed reduction mechanism, for estimating rotation non-uniformity caused by the influence of angular transmission error of the speed reduction mechanism, comprising: Based on the observed information, an estimated disturbance, which is an internal state quantity of the controlled object, is estimated; calculating an evaluation index based on a predetermined order component corresponding to the non-uniformity of the rotation based on the estimated disturbance; The angular transmission error estimation method is performed by a computer.

9. 1. An angular transmission error estimation program that is applied to a servo control system having a speed reduction mechanism and estimates rotation non-uniformity caused by the influence of an angular transmission error of the speed reduction mechanism, comprising: Based on the observed information, an estimated disturbance, which is an internal state quantity of the controlled object, is estimated; calculating an evaluation index based on a predetermined order component corresponding to the non-uniformity of the rotation based on the estimated disturbance; An angular transmission error estimation program that causes a computer to execute the above.

10. The angular transmission error estimating device according to any one of claims 1 to 7; an angular transmission error compensator that generates a compensation signal; A vibration control device that optimizes at least one of the evaluation index or an objective function defined based on the evaluation index, and corrects the compensation signal.

11. The angular transmission error compensation unit an angular transmission error compensator that has the order and amplitude and phase parameters used in the optimization and generates the sinusoidal compensation signal based on position information; an adder that adds the compensation signal to a position command, a speed command, a current command, or a control signal related thereto; the angular transmission error compensator includes a compensation model unit that corrects the compensation signal by referring to a compensation model that corrects the amplitude and the phase based on speed information; The vibration control device according to claim 10, comprising:

12. 11. The vibration damping control device according to claim 10, wherein an optimization method including at least one of random search, gradient descent, Bayesian optimization, and genetic algorithm is used.

13. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator is configured to automatically set amplitude and phase at a frequency corresponding to a predetermined speed range based on a control system configuration in which any one of motor position, motor speed, and current is a controlled variable, control parameters, and frequency response characteristics derived based on motor characteristics, and to register the amplitude and phase in the compensation model.

14. 12. The vibration damping control device according to claim 11, wherein the compensation model is a lookup table that references the amplitude and the phase based on the velocity information.

15. 12. The vibration damping control device according to claim 11, wherein the compensation model is set to correct the amplitude using a weighting coefficient that controls the effectiveness of the compensation signal in accordance with a predetermined speed range of the speed information.

16. the position information is a position command or a motor position; 12. The vibration damping control device according to claim 11, wherein the speed information is a position command speed or a motor speed.

17. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator is configured so that the compensation signal is zero when the speed information is zero.

18. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator generates the compensation signal from the amplitude and the phase in accordance with a rotation direction of the reduction mechanism.

19. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator generates a sinusoidal compensation signal for each order based on the amplitude and the phase for each order, and generates the compensation signal by adding these signals together.

20. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator designs the compensation model and corrects the compensation signal regardless of the inertia with respect to rotation of a load connected to the output shaft of the reduction mechanism.

21. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator designs the compensation model and corrects the compensation signal regardless of a spring constant of the reduction mechanism.

22. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator corrects the amplitude and phase of the compensation signal used to generate the compensation signal based on a load torque acting on the reduction gear mechanism.

23. 12. The vibration damping control device according to claim 11, wherein the angular transmission error compensator corrects the amplitude and phase of the compensation signal generated based on the temperature of the reduction mechanism, the temperature around the reduction mechanism, or a temperature estimated based on operating conditions.

24. 1. A vibration suppression control method applied to a servo control system equipped with a reduction mechanism, for compensating for non-uniformity of rotation caused by the influence of an angular transmission error of the reduction mechanism, comprising: An estimated disturbance, which is an internal state quantity of the controlled object, is estimated based on the observed information; calculating an evaluation index based on a predetermined order component corresponding to the non-uniformity of the rotation based on the estimated disturbance; generating a compensation signal; optimizing at least one of the evaluation index or an objective function defined based on the evaluation index, and correcting the compensation signal; This vibration suppression control method is implemented by a computer.

25. 1. A vibration suppression control program that is applied to a servo control system having a speed reduction mechanism and compensates for non-uniformity of rotation caused by the influence of an angular transmission error of the speed reduction mechanism, comprising: An estimated disturbance, which is an internal state quantity of the controlled object, is estimated based on the observed information; calculating an evaluation index based on a predetermined order component corresponding to the non-uniformity of the rotation based on the estimated disturbance; generating a compensation signal; optimizing at least one of the evaluation index or an objective function defined based on the evaluation index, and correcting the compensation signal; A vibration control program that causes a computer to execute the following:

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