Method and device for estimating angular transmission error of speed reducer, and method and device for controlling motor

Abstract

According to the present invention, in a plant having a motor, a load, and a speed reducer in which an input shaft is driven by the motor and the load is connected to an output shaft, when an angular transmission error of the speed reducer is estimated by a calculation amount, it is assumed that the plant is divided into a load-side plant composed of the speed reducer and the load, and a motor-side plant that is a portion from the motor to the input shaft of the speed reducer, including the motor. On the basis of the acceleration measured in the load and the angular velocity of the rotation of the motor, an observer (speed reducer ATE observer) corresponding to the load-side plant is used to calculate an estimated value of a vibration component of the load-side speed due to an angular transmission error of the speed reducer.

Description

Method and apparatus for estimating angular transmission error of a speed reducer, and method and apparatus for controlling a motor.

[0001] The present invention relates to the control of a plant comprising a motor, a reduction gear whose input shaft is driven by the motor, and a load connected to the output shaft of the reduction gear, and more particularly to an estimation method and apparatus for estimating the angular transmission error of the reduction gear, and a control method and apparatus for controlling the motor using the estimated angular transmission error.

[0002] A wide variety of devices and equipment are equipped with motors, and these devices and equipment are driven by servo-controlled motors. For example, industrial robots (hereinafter also referred to as "robots") are equipped with motors on each axis, such as robot arms and end effectors (or hands), and operate by receiving position commands or velocity commands from an external source and servo-controlling the motors on each axis based on those commands. End effectors are also called hands. Robot arms and end effectors are treated as loads from the perspective of the motors on each axis. The accuracy of a robot's operation can be expressed by the accuracy of the position and velocity of the load when control is performed based on the given commands. Generally, when servo-controlling a motor, an encoder that detects the motor's position, i.e., the current rotation angle, is attached to the motor's rotation axis, and the current position of the motor detected by the encoder is fed back to the controller that performs servo control of the motor. Since the derivative of position with respect to time is velocity, velocity may also be fed back from the encoder as needed.

[0003] When a motor is used in a controlled plant, the load is generally driven by transmitting the motor's driving force through a gearbox. There are various types of gearboxes; for example, cycloidal gearboxes and harmonic drive gearboxes are used in robots. In all types of gearboxes, there is an angular transmission error (ATE) due to manufacturing errors and elastic deformation of the components. Mechanical vibration occurs in the gearbox depending on the rotational speed of the gearbox's input shaft, and as a result, vibration occurs in the load at that position. Since what is detected by the encoder is the position on the motor's rotation axis, i.e., the rotation angle, and not the position of the load itself, simply performing servo control by feeding back the detection result from the encoder is not enough to cancel out the effect of the gearbox's angular transmission error and control the load with high precision. For high-precision control, it is necessary to measure the magnitude of the angular transmission error and determine the compensation amount, or to model the angular transmission error in some form and determine the compensation amount, and then perform control using these compensation amounts. For example, Patent Document 1 discloses a plant in which an arm is driven by a motor via a reduction gear, in which an inertial sensor for detecting the rotational angular velocity of the arm is attached to the arm, the rotational angular velocity output by the inertial sensor is measured while the arm is rotating, and the angular transmission error is calculated and correction data is obtained by comparing the measured rotational angular velocity with the ideal rotational angular velocity at the output shaft of the reduction gear calculated from the output data of the encoder.

[0004] Patent Document 2 discloses a method for compensating for angular transmission errors in a harmonic drive gear connected to a motor, in which the relative rotational synchronous component that occurs in synchronization with the motor position is treated as a vibration source, and the motor current command is compensated by a compensation current command calculated to compensate for the effect of this relative rotational synchronous component on the load position, and the motor position command is compensated by a motor position correction signal calculated to compensate for the effect of the relative rotational synchronous component. Non-Patent Document 1 proposes modeling of a controlled object that takes into account nonlinear friction and nonlinear spring characteristics in order to improve the positioning accuracy in a plant using a harmonic drive gear, and discloses modeling the angular transmission error of the harmonic drive gear using a relative rotational synchronous component and a nonlinear elastic deformation component.

[0005] The angular transmission error of a speed reducer can be considered a periodic disturbance applied to the plant. Therefore, a method has been proposed to estimate the angular transmission error using an extended state observer and calculate the compensation amount. For example, Non-Patent Document 2 discloses the estimation of velocity oscillations that appear as a periodic function of the mechanical angle in a speed reducer due to the angular transmission error of a cycloidal speed reducer, using an extended state observer. In the method shown in Non-Patent Document 2, the mechanism of the speed reducer and motor is modeled as a two-inertia resonant system, and the vibration is estimated in the extended state observer by formulating the vibration component of the angular transmission error input to the load-side velocity of the plant as a state variable represented by a sinusoidal function. The method shown in Non-Patent Document 2 does not take into account the angular transmission error that is proportional to the torque input to the speed reducer, but Non-Patent Document 3 and Patent Document 3 disclose an all-state extended state observer that can also estimate the vibration component due to the angular transmission error that is proportional to the torque of the speed reducer. In the methods described in Non-Patent Document 3 and Patent Document 3, the vibration component of the angular transmission error, which is proportional to the torque, is input to the torsional angle, and this is formulated as a state variable represented by a sinusoidal function.

[0006] Related to the present invention, Non-Patent Documents 4 and 5 disclose techniques for estimating and compensating for viscous friction and Coulomb friction on the motor side from the input shaft of a gearbox. In these techniques, a torque sensor is provided in addition to an encoder, and friction is estimated by an observer using the torsional torque detected by the torque sensor and the motor speed calculated from the detected value by the encoder. This observer is called a Force and Position Integrated Disturbance Observer (abbreviated as FPIDO) in Non-Patent Document 4 and a Motor-side Normalization Compensator (abbreviated as MNC) in Non-Patent Document 5. Furthermore, although it is difficult to estimate the angular transmission error of a gearbox, Patent Document 4 discloses a technique that uses two disturbance observers for two inertial systems consisting of a motor and a load. In the technique shown in Patent Document 4, disturbance observers are attached to both the motor side and the load side to estimate the load-side disturbance torque, thereby suppressing disturbance and vibration. A first disturbance observer, located on the motor side, takes the motor's speed response value and the current command value to the motor as inputs and outputs an estimated value of the motor's disturbance torque, which is the torsional torque. A second disturbance observer, located on the load side, takes the load's speed response value and the estimated motor's torsional torque as inputs and outputs an estimated value of the load's disturbance torque, separated from the motor's torsional torque.

[0007] Japanese Patent Publication No. 2022-117610, Japanese Patent Publication No. 2010-244343, Japanese Patent Publication No. 2016-53914, Japanese Patent Publication No. 2008-228484

[0008] Junbun Yamamoto, Makoto Iwasaki, Yoshifumi Okitsu, Kozo Sasaki, Toshio Yajima, "Modeling and Compensation for Angular Transmission Error in Wave Drive Gears," Journal of the Japan Society for Precision Engineering, Vol. 76, No. 10, pp. 1206-1211, 2010. Shota Kawahara, Takashi Yoshioka, Kiyoshi Ohishi, Nguyen Hien, Toshimasa Miyazaki, Yuki Yokokura, "Suppression Method for Velocity Oscillation Caused by Angular Transmission Error in Cycloidal Reducers Using an Extended State Observer," Transactions of the Institute of Electrical Engineers of Japan, Vol. 134, No. 3, pp. 241-251, 2014. Yosei Hirano, Takashi Yoshioka, Kiyoshi Ohishi, Toshimasa Miyazaki, Yuki Yokokura, Masataka Sato, “Vibration Suppression Control Method for Trochoidal Reduction Gears under Load Conditions,” IEEJ Journal of Industry Application, Vol. 5, No. 3, pp. 267-275. 2016Yusuke Kawai, Yuki Yokokura, Kiyoshi Ohishi, Pattawan Boonwong, "High-robust acceleration control using force and position sensors integrated disturbance observer," IECON 2016 - 42nd Annual Conference. of the IEEE Industrial Electronics Society, pp. 5802-5807, 2016Yusuke Kawai, Yuki Yokokura, Kiyoshi Ohishi, Toshimasa Miyazaki, "Smooth Human Interaction Control using Torsion Torque Controller and Motor-side Normalization Compensator Focusing on Back-forward Drivability," IEEJ Journal of Industry Applications, Vol. 8, No. 2, pp.322-333, 2019Masayoshi Tomizuka, "Zero Phase Error Tracking Algorithm for Digital Control," Trans. ASME, Journal of Dynamic Systems, Measurement, and Control, vol. 109, pp. 65-68, Mar. 1987.

[0009] The methods disclosed in Non-Patent Documents 2-3, etc., use a state observer to estimate the vibration component of the angular transmission error input to the load-side speed in a plant. Since the input variables for the state observer to estimate the vibration component of the angular transmission error are the motor torque current and the motor angular velocity, the state equation of the state observer becomes a sixth- or eighth-order differential equation. The computational cost required to solve such high-order differential equations is large, and the computation time for the state observer becomes long. Furthermore, because the order is high, the robustness of the encoder to sensor noise deteriorates, making it difficult to design a pole arrangement for rapid estimation.

[0010] The object of the present invention is to provide an estimation method and apparatus that are robust and can estimate the angular transmission error of a speed reducer with a small amount of computation, and a control method and control apparatus that control a motor using such an estimation method.

[0011] According to one aspect of the present invention, a method for estimating the angular transmission error of a speed reducer in a plant having a motor, a load, and a speed reducer whose input shaft is driven by the motor and whose output shaft is connected to the load, is to consider the plant as being composed of a motor-side plant, which includes the motor and extends from the motor to the input shaft of the speed reducer, and a load-side plant, which consists of the speed reducer and the load, and to calculate an estimated value of the angular transmission error using a first observer corresponding to the load-side plant based on the acceleration obtained with respect to the load and the angular velocity of the motor's rotation.

[0012] According to one aspect of the present invention, a method for controlling the position or speed of a load in a plant consisting of a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, based on a command input from an external source, involves: generating a current command value for the motor by feeding back at least one of the rotational position and angular velocity of the motor; assuming that the plant consists of a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant consisting of the reduction gear and the load; calculating an estimated value of the angular transmission error of the reduction gear using a first observer corresponding to the load-side plant based on the measured acceleration and the rotational angular velocity of the motor obtained with respect to the load; using an inverse transfer function which calculates a first compensation current to compensate for the angular transmission error from the angular transmission error; calculating the first compensation current by applying the estimated value of the angular transmission error to the inverse transfer function; and compensating for the angular transmission error in the current command value using the calculated first compensation current.

[0013] According to one aspect of the present invention, an estimation device for estimating the angular transmission error of a speed reducer in a plant having a motor, a load, and a speed reducer whose input shaft is driven by the motor and whose output shaft is connected to the load, comprises, assuming the plant is composed of a motor-side plant which includes the motor and extends from the motor to the input shaft of the speed reducer, and a load-side plant which consists of the speed reducer and the load, an acceleration detection means for detecting the acceleration of the load, an angular velocity detection means for detecting the angular velocity of the motor's rotation, and a first observer represented by a state variable which includes at least the angular transmission error and a state equation corresponding to the load-side plant, wherein the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means are input to the first observer to calculate an estimated value of the angular transmission error.

[0014] According to one aspect of the present invention, a control device for controlling the position or speed of a load in a plant consisting of a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, based on a command input from an external source, comprises: a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant consisting of the reduction gear and the load, a controller which generates a current command value for the motor by feeding back at least one of the rotational position and angular velocity of the motor; acceleration detection means for detecting the acceleration of the load; angular velocity detection means for detecting the rotational angular velocity of the motor; a first observer represented by a state variable which includes at least the angular transmission error of the reduction gear and a state equation corresponding to the load-side plant; and an inverse transfer function calculation unit which receives an estimated value of the angular transmission error obtained by inputting the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means to the first observer, The inverse transfer function calculation unit calculates a first compensation current from an estimated value of the angular transfer error using an inverse transfer function configured to calculate a first compensation current that compensates for the angular transfer error from the angular transfer error, and performs compensation for the angular transfer error in the current command value using the calculated first compensation current.

[0015] According to the present invention, the angular transmission error of the speed reducer can be estimated robustly with a small amount of computation.

[0016] This figure shows an example of a plant configuration to which the estimation method and control method according to the present invention can be applied. This is a block diagram representing the plant shown in Figure 1. This is a block diagram illustrating the estimation method of the first embodiment. This is a block diagram illustrating a control method using the estimation method of the first embodiment. This is a block diagram illustrating the estimation method of the second embodiment. This is a block diagram illustrating a control method using the estimation method of the second embodiment. This is a block diagram illustrating a control method of the third embodiment. This is a block diagram representing the system used in the simulation. This is a graph showing the simulation results. This is a graph showing the simulation results.

[0017] Next, embodiments of the present invention will be described with reference to the drawings. Before describing each embodiment of the present invention, a plant to which the estimation method and control method according to the present invention can be applied will be described. Figure 1 shows an example of such a plant. This plant rotates a load 30, which is an arm-shaped member, in a horizontal plane. A motor 15 and a reduction gear 20 are mounted, for example, on the side of a base 10. An encoder 17 and a pulley 18 are attached to the rotation shaft 16 of the motor 15 to detect the rotation angle, i.e., the position of the motor 15. A pulley 22 is also attached to the input shaft 21 of the reduction gear 20, and a belt 25 is stretched between the pulley 18 on the motor 15 side and the pulley 22 on the reduction gear 20 side. One end of the load 30 is connected to the output shaft 23 of the reduction gear 20. The rotation shaft 16 of the motor 15 and the input shaft 21 and output shaft 23 of the reduction gear 20 all extend in the vertical direction. As the motor 15 rotates, the rotational driving force of the motor 15 is input to the reduction gear 20 via the belt 25, and the rotation of the motor 15 is reduced by a predetermined reduction ratio, and the load 30 rotates at a rotational speed slower than the rotational speed of the motor 15, with the output shaft 23 of the reduction gear 20 as the center of rotation, as shown by the arrows in the figure. It is preferable to use a toothed belt as the belt 25 so that the load 30 can move to the desired position without displacement when the motor 15 is servo controlled based on a command. An acceleration sensor 31 that detects the acceleration applied to the load 30 is provided, for example, at the other end of the load 30, which is configured as an arm-shaped member. In the figure, reference numeral 35 denotes the motor and belt portion, which is the part of the plant that includes the motor 15 and the belt 25.

[0018] In the plant shown in Fig. 1, the load 30 is constituted by a single arm-shaped member. However, a plurality of arms may be connected so as to have a hand (or an end effector) at the tip, and this may be used as the load 30. When a plant is configured by connecting a connection body composed of a hand and a plurality of arms to the output shaft 23 of the speed reducer 20 in this way, it can be said that the plant is a horizontal articulated robot. In the case of a horizontal articulated robot, acceleration sensors 31 are provided for each of the arms and the hand, and motors 15 and speed reducers 20 are provided for each joint, whereby the estimation method and the control method according to the present invention can be executed for each axis of the robot.

[0019] Fig. 2 shows the plant shown in Fig. 1 in a block diagram. In the figure, s is a Laplace operator. The plant shown in Fig. 1 is assumed to be a two-inertia system composed of a motor 15 and a load 30. Further, it is assumed that an angular transmission error in the speed reducer 20, a belt periodic disturbance by the belt 25, and a disturbance by Coulomb friction are applied to the plant. Let the reduction ratio of the speed reducer 20 be R g and the reduction ratio by the belt 25 be R b Then, the total reduction ratio R by the belt 25 and the speed reducer 20 is R = R b ·R g which is expressed as. Let the vibration component of the load-side speed due to the angular transmission error of the speed reducer 20 be ω err The vibration component ω err of the load-side speed due to the angular transmission error is sometimes simply called the angular transmission error ω err In the following description, for a variable x, one dot symbol added, two dot symbols added, and a hat symbol added, that is,

[0020]

[0021] represent the first derivative of x, the second derivative of x, and the estimated value of x, respectively. As an example, regarding the vibration component ω err of the load-side speed due to the angular transmission error and the torsional angle θ s of the speed reducer 20, what meanings they have by adding dot symbols and hat symbols will be described using Table 1.

[0022]

[0023] For motor 15, the q-axis current i q Given this, this is the torque constant K of the motor 15. t This is converted into torque. The inertia and viscosity of the motor 15 are J, respectively. m and D m Let's assume that the torque drives the inertia of the motor 15, generating angular acceleration. Integrating the angular acceleration (1 / s) gives the angular velocity ω of the motor 15. m The position θ of motor 15 is obtained by integrating once more. m The following is obtained. The motor 15 has a belt disturbance torque τ, which is a periodic disturbance torque caused by the belt 25. belt and step disturbance torque τ due to Coulomb friction step In addition, the torsional torque τ in the reduction gear 20 is also increased. s This is applied via the overall reduction ratio R. Belt disturbance torque τ belt and step disturbance torque τ step The sum of these is taken as the motor-side disturbance torque τ m dis Let us express it as follows: That is to say, τ m dis =τ belt +τ step In practice, in motor 15, the q-axis current i q Torque constant K t The torque obtained by conversion is then applied to the reduction gear 20 via the overall reduction ratio R, which is the torsional torque τ. s and viscous resistance torque and motor-side disturbance torque τ m dis The torque obtained by subtracting the torque expressed as the sum of is the inertia J. m It acts on and generates acceleration. The viscous resistance torque in motor 15 is D m ・ω m It is represented as follows.

[0024] The inertia and viscosity of the load 30 are both J. l and D l The angular transmission error ω of the reduction gear 20 is expressed as follows: err The acceleration and velocity of the load 30 before the addition of α are respectively l1 and ωl1 The angular transmission error ω of the reduction gear 20 is expressed by the following: err The speed of load 30 after the addition of ω l Let's assume that at load 30, a torsional torque τ is generated from the reduction gear 20. s The input is: Angle transmission error ω err Speed ​​ω of load 30 before the addition of load l1 Viscosity D l The viscous resistance torque obtained by multiplying by the torsional torque τ of the reduction gear 20 is s The torque obtained by subtracting from is the inertia J l Acting on this, the angular transmission error ω of the reduction gear 20 err Acceleration α of load 30 before the addition of load 30 l1 This acceleration α is obtained. l1 By integrating, the velocity ω l1 This velocity ω is obtained, l1 For angular transmission error ω err The addition of this results in the actual speed ω of a load of 30. l This can be obtained.

[0025] The reduction gear 20 receives the angular velocity ω generated by the motor 15. m This is input via belt 25. As described above, the twist angle of the reduction gear 20 is θ s The torsional rigidity and torsional viscosity of the reduction gear 20 are K, respectively. s and D s This is expressed as follows: The torsional angular velocity of the output shaft 23 of the reduction gear 20 is equal to the angular velocity ω of the motor. m The speed ω of a load of 30 is obtained by applying the total reduction ratio R to the result. l This is the result of subtracting [a certain factor]. By integrating this torsional angular velocity, the torsional angle θ of the reduction gear 20 is obtained. s The resulting twist angle θ s Torsional rigidity K s The torsional torque τ in the reduction gear 20 is obtained by adding the viscous resistance torque to the torque obtained by applying the torque. s The viscous resistance torque in the reduction gear 20 is the torsional angular velocity of the output shaft 23 multiplied by the viscosity D. s It is obtained by multiplying by .

[0026] The vibration component ω of the load-side speed due to the angular transmission error of the reduction gear 20 errThis is thought to be a combination of a fundamental component, whose phase is the value obtained by multiplying the angle of the input shaft 21 of the reduction gear 20 by a constant μ, and its harmonic components. The rotational speed of the input shaft 21 of the reduction gear 20 is determined by the reduction ratio R of the belt 25. b The rotation speed of motor 15 is ω by that amount. m Because it is smaller, the angular transmission error ω err The error amplitude is δ a With the phase difference being φ, it can be expressed as shown in equation (1a). In equation (1a), n is the highest order when considering the angular transmission error. In a harmonic drive gear reducer, the constant μ is 2.

[0027]

[0028] Regarding the angular transmission error, the contribution of higher-order components where k is 2 or greater is small, so below, the angular transmission error ω err The current position θ of the motor 15 is expressed by equation (1b). m Based on the angular transmission error ω err This represents the angular velocity, but angular velocity can be used instead of position, in which case the angular transmission error ω is shown in equation (1c). err It can represent this.

[0029]

[0030] On the other hand, the periodic disturbance caused by belt 25 is belt disturbance torque τ belt This is expressed by the angular velocity ω of the motor 15. m This disturbance is considered to have a frequency that is a constant multiple of k. Let this constant be k. The belt disturbance torque τ is composed of superimposed components of different frequencies. belt This is also a possibility, but here we consider the belt disturbance torque τ, which is a periodic disturbance caused by belt 25. belt Let it be represented by equation (2).

[0031]

[0032] In each embodiment described below, in order to have robustness with respect to the plant shown in Figure 1 and to estimate the angular transmission error of the reducer 20 with a small amount of computation, the plant shown in Figure 1 is divided into a load-side plant 41 consisting of the reducer 20 and load 30, and a motor-side plant 42 which includes the motor 15 and is the part from the motor 15 to the input shaft 21 of the reducer 20. That is, the plant shown in Figure 1 is composed of a load-side plant 41 and a motor-side plant 42. Focusing on the load-side plant 41, an observer corresponding to the load-side plant 41, i.e., a reducer ATE observer 51 (see Figure 3), is constructed, and the angular transmission error ω err We will make an estimate.

[0033] [First Embodiment] Figure 3 shows the angular transmission error ω of the reduction gear 20. err This is a block diagram illustrating the estimation method of the first embodiment of the present invention, which estimates the angular transmission error ω. In this embodiment, the load-side plant 41 is focused on and the angular transmission error ω err To estimate this, Figure 3 shows the portion of the load-side plant 41 in the block diagram shown in Figure 2 and the reduction gear ATE observer 51 corresponding to the load-side plant 41. The load-side plant 41 measures the angular velocity ω of the motor 15. m The input is the acceleration α of load 30 before the angular transmission error is added. l1 It can be considered that this is the output. The load-side plant 41 is represented by equation (3a), and the acceleration α of the load 30 l1 This is expressed by equation (3b).

[0034]

[0035] A Ruwenberger state observer is designed to correspond to the load-side plant 41, and this state observer, or observer, is designated as the reduction gear ATE observer 51. The reduction gear ATE observer 51 is connected to the angular velocity ω of the motor 15. m and acceleration α with load 30 l1 The following needs to be provided. Input variable u of the speed reducer ATE observer 51 a This can be expressed as shown in equation (4). The angular velocity ω of motor 15 m For example, the position θ of the motor 15 output by the encoder 17. mIt is obtained by differentiating with a differentiator 61 (see FIG. 4). Alternatively, an angular velocity sensor is attached to the rotation shaft 16 of the motor 15 instead of the encoder 17, and the angular velocity ω m obtained by this angular velocity sensor may be input to the reduction gear ATE observer 51. In any case, it is sufficient if some speed detection means for detecting the angular velocity of the rotation of the motor 15 is provided. On the other hand, the acceleration α l1 of the load 30 is obtained from an acceleration sensor 31 attached to the load 30. The acceleration α l1 of the load 30 here may be any acceleration obtained with respect to the load 30. For example, a gyro sensor may be attached to the load 30, and the value obtained by differentiating the angular velocity obtained by the gyro sensor may be used, or the acceleration detected by software may be used. An acceleration can also be obtained by providing a position sensor on the load 30 to detect the position of the load 30 and calculating the second derivative thereof. However, when a position sensor is used, it is likely to be affected by noise, etc. by repeating differentiation. Specifically, torque vibration and torque ripple occur due to angular transmission error, etc. Therefore, in order to suppress these, state quantities in the acceleration dimension, that is, the torque dimension are required. However, even if the position is obtained with a position sensor and the position is second-differentiated to obtain a state quantity in the acceleration dimension, it is impossible to obtain the state quantity with sufficient accuracy due to the influence of noise, etc. Therefore, it becomes difficult to obtain a sufficient effect in suppressing torque vibration and torque ripple.

[0036]

[0037] As the state variable x a of the reduction gear ATE observer 51, the twist angle θ s of the reduction gear 20, the speed ω l1 of the load 30 before the angular transmission error is added, the vibration component ω err of the load-side speed due to the angular transmission error, and the differential value of ω err are used. Therefore, the state variable x a is expressed as in equation (5).

[0038]

[0039] As described above, the input variable u a and state variable x a By defining this, the state equation of the speed reducer ATE observer 51 is expressed by equation (6). Matrix A in equation (6) a , B a These are expressed by equations (7a) and (7b), respectively.

[0040]

[0041] k1 to k4 in equations (7a) and (7b) are observer gains, which are expressed by equations (8a) to (8d), respectively. d is expressed by equation (8e), and p a This represents the designated pole of the speed reducer ATE observer 51.

[0042]

[0043] ω d ω is the angular velocity of motor 15. m Since it is proportional to the angular velocity ω, m When ω is close to 0, the observer gains k1 to k4 become extremely large, which can lead to unstable control. d Lower limit ω with respect to the absolute value dl Determined, |ω d | <ω dl When ω d ga ω dl It is preferable to perform the calculation assuming that it is true.

[0044] The angular velocity ω of the motor 15 is measured relative to the reduction gear ATE observer 51. m and acceleration α with load 30 l1 By inputting this, the state variable x a Estimated value

[0045]

[0046] This allows us to obtain such a state variable x a Based on the estimated values, the torsional torque τ of the reduction gear 20 is calculated using equation (9). s An estimated value can be calculated.

[0047]

[0048] As is clear from the above explanation, the angular velocity ω of motor 15 m and acceleration α with load 30 l1 By providing a reduction gear ATE observer 51 that receives input, the vibration component ω of the load-side speed due to the angular transmission error of the reduction gear 20 can be detected. err And an estimated value of its derivative can be obtained, and the torsional torque τ of the reduction gear 20 s An estimated value can also be obtained. The speed reducer ATE observer 51 can be said to be an estimation device for estimating the angular transmission error.

[0049] Next, a control method for servo-controlling the plant shown in Figure 1 based on externally input position commands, while performing compensation based on the angle transmission error estimated in this way, will be explained using the block diagram shown in Figure 4. The block diagram shown in Figure 4 is the same as the block diagram shown in Figure 2, but with the elements necessary for control added, and shows the configuration of the control device that performs servo control of the plant. The encoder 17 attached to the rotating shaft of the motor 15 controls the position of the motor 15, i.e., the rotation angle θ. m The output is the speed of motor 15, i.e., the angular velocity ω m To obtain this, a differentiator 61 is connected to the output of encoder 17. In order to perform servo control based on position command, the position θ of motor 15 is connected. m and speed ω m The q-axis current command i is fed back. q ref A position and speed controller 62 is provided to generate the following. A compensation current i is provided in the subtraction element 63 to compensate for the angular transmission error. cmps q-axis current command i q ref Subtracting from this will result in the q-axis current i q This is obtained, and the motor 15 controls this q-axis current i q It is actually driven by.

[0050] Next, the compensation current i for angle transmission error compensation. cmps Let's explain how to calculate the angle transmission error ω. err From load 30 speed ω l Transfer function ω l / ω err And, compensation current i cmpsFrom speed ω l Transfer function ω l / i cmps Considering this, by dividing the former by the latter, the angle transmission error ω err Compensation current i cmps The inverse transfer function T for calculating the inverse transfer function m (s) can be calculated as shown in equation (10).

[0051] Here,

[0052] (10) Equation i is the compensation current i cmps It includes the inverse transfer function T m In (s), the numerator has a higher order than the denominator, so in this form the compensation current i cmps It is not possible to determine this. Therefore, a first-order low-pass filter (LPF) is applied to equation (10), and the angular transfer error ω is added to the input of the transfer function. err The differential value of the estimated value, i.e.

[0053]

[0054] Using this, the inverse transfer function T m Make (s) proper. With respect to equation (10), we can perform the transformation shown in equation (11). Here, ω n This is the cutoff angle frequency of the low-pass filter. Compensation current icmps This can be found using equation (11).

[0055]

[0056] In the block diagram shown in Figure 4, the inverse transfer function calculation unit 64 calculates the angular transfer error ω from the output of the reduction gear ATE observer 51. err Estimated value and angular transmission error ω err The inverse transfer function T' above is obtained using the estimated derivative of the above. m The calculation is performed using (s), and the compensation current i is used to compensate for the angle transmission error. cmps The calculated compensation current i is calculated. cmps This is sent to the subtraction element 63. Therefore, by performing the control shown using Figure 4, the angular transmission error ω of the reducer 20 in the plant shown in Figure 1 is reduced. errCompensation is provided for this, reducing the impact of the angle transmission error of the reduction gear 20, and allowing the load 30 to be accurately moved to the position indicated by the position command. In the control method described here, the acceleration sensor 31 measures the acceleration α on the load 30 side. l1 By using this information as an input variable for the speed reducer ATE observer 51, the structure of the speed reducer ATE observer 51 can be simplified, and the observer order can be reduced to the fourth order. As a result, the computational load on the speed reducer ATE observer 51 can be reduced. Because it is not a high-order observer structure, the sensitivity to noise in the encoder 17 and acceleration sensor 31 is also reduced, and it becomes possible to specify the pole arrangement, which enables quick estimation of the angle transmission error.

[0057] Furthermore, by configuring a reduction gear ATE observer 51 using an acceleration sensor 31 attached to the load, and by dividing the plant, which is configured as two inertial systems consisting of the motor 15 and the load 30, into a load-side plant 41 and a motor-side plant 42, it becomes unnecessary to consider the motor-side plant 42 when estimating the angular transmission error. As a result, the number of parameters in the observer's state equation is reduced, making it less susceptible to parameter fluctuations and modeling errors compared to conventional methods that do not divide the plant. Specifically, while conventional methods are affected by fluctuations in Coulomb friction and viscous friction (kinetic friction) in the motor-side plant 42, the method in this embodiment is not affected at all by fluctuations in Coulomb friction and viscous friction (kinetic friction) in the motor-side plant 42. In addition, the moment of inertia J of the motor 15 is included in the parameters of the reduction gear ATE observer 51. mSince it does not include the resonant and anti-resonant frequencies in the two inertial frames, it is not affected by fluctuations in the resonant and anti-resonant frequencies in the two inertial frames. Therefore, the gearbox ATE observer 51 can be said to have a robust structure against fluctuations in Coulomb friction and viscous friction (kinetic friction) on the motor side and fluctuations in the resonant and anti-resonant frequencies in the two inertial frames. This also enables the specification of pole placement to quickly estimate the observer. Note that the estimation method of this embodiment is intended for estimating the angular transmission error, which is a periodic disturbance, and the gearbox ATE observer 51 is configured to estimate the angular transmission error with a small amount of computation. For this reason, the gearbox ATE observer 51 may not be able to estimate step-like disturbance torque applied to the load side. Therefore, the estimation method of this embodiment is particularly suitable for estimating the angular transmission error of a gearbox in a system where no large disturbances such as gravity are applied on the load side.

[0058] The method described in Patent Document 4 also uses two disturbance observers and estimates the torsional torque, but the value estimated in Patent Document 4 is the torsional torque of the motor. The torsional torque of the motor is converted to the torsional torque τ of the gearbox via the reduction ratio. s Although it can be converted to torsional torque, the estimation method of this embodiment differs from the method described in Patent Document 4 in terms of the principle of calculating torsional torque. That is, in this embodiment, the load-side observer, the reduction gear ATE observer 51, measures the angular velocity ω of the motor 15. m and acceleration α with load 30 l1 Based on this, the angular transmission error ω err Estimated value and angular transmission error ω err The estimated derivative of the torsional torque τ of the reduction gear 20 is also s This is estimated. In contrast, in the method described in Patent Document 4, the first disturbance observer, which is an observer on the motor side, takes the motor's speed response value and the current command value to the motor as input and outputs an estimated value of the torsional torque, which is the disturbance torque of the motor. In this embodiment, the acceleration sensor 31 provided on the load 30 measures the acceleration α of the load 30. l1This method detects the torque and, compared to the method described in Patent Document 4 which uses a speed sensor or position sensor to determine the speed, it can reduce the influence of noise and other factors on the estimation of torsional torque. In the method described in Patent Document 4, since the acceleration on the load side is not used, it is difficult to estimate the torque due to periodic disturbances on the load side, such as the angular transmission error of the reduction gear 20, as is clear from the explanation of the angular transmission error estimation procedure above.

[0059] [Second Embodiment] Next, in the second embodiment, the angular transmission error of the reduction gear 20 is estimated based on the first embodiment, and the disturbance torque τ input to the motor 15 is... m dis We will explain how to estimate the disturbance torque τ. m dis The belt disturbance torque τ is due to belt 25. belt and step disturbance torque τ due to Coulomb friction step This is a combination of the two, and the belt disturbance torque τ belt Let it be represented by equation (2).

[0060] Figure 5 shows the motor-side disturbance torque τ. m dis This is a block diagram illustrating the estimation method of a second embodiment of the present invention for estimating the motor-side disturbance torque τ. Here, we focus on the motor-side plant 42 and m dis To estimate this, Figure 5 shows the motor-side plant 42 portion of the block diagram shown in Figure 2 and the motor-side disturbance observer 52 corresponding to the motor-side plant 42. The motor-side plant 42 controls the q-axis current i for the motor 15. q And the torsional torque τ of the reduction gear 20, which is input from the reduction gear 20 via the overall reduction ratio R. s The inputs are and and the angular velocity ω of motor 15. m It can be considered that this outputs the following. The motor-side plant 42 is expressed by equation (12), and the angular velocity ω of the motor 15 m is expressed by equation (13). In the equation, ω b ω is the angular frequency of the vibration due to the periodic disturbance on the motor side, and the angular velocity of the motor 15. mIt is a constant multiple of and T represents the transpose of the matrix. When the motor-side periodic disturbance is a periodic disturbance caused by belt 25, the belt disturbance torque τ belt Since this is expressed by equation (2), using k in equation (2), ω b = k・ω m It is expressed as follows.

[0061]

[0062] A Ruenberger observer is designed to correspond to the motor-side plant 42 and designated as the motor-side disturbance observer 52. The motor-side disturbance observer 52 is configured to handle the q-axis current i q and the angular velocity ω of motor 15 m and the torsional torque τ of the reduction gear 20 s It is necessary to provide the following. As long as the motor 15 is being servo controlled, the current command value output from the servo control device is the q-axis current i q This can be obtained. However, the q-axis current i used to estimate the motor-side disturbance torque is q The current command value from the control device does not necessarily have to be the current command value itself; it may be the current value after various compensations have been applied to the current command value output by the device, or it may be the current value actually measured in the motor 15. Here, the control device is, for example, a position speed controller 62. The angular velocity ω of the motor 15 m For example, the position θ of the motor 15 output by the encoder 17. m It is obtained by differentiating it using the differentiator 61. Alternatively, instead of the encoder 17, an angular velocity sensor can be attached to the rotation shaft 16 of the motor 15, and the angular velocity ω obtained by this angular velocity sensor can be obtained. m The motor-side disturbance observer 52 may also be input to this. The reduction gear ATE observer 51 described in the first embodiment is a torsional torque τ s Since it outputs an estimated value, this estimated value is the torsional torque τ s This can be supplied to the motor-side disturbance observer 52. The input variable u of the motor-side disturbance observer 52 b This is expressed as shown in equation (14). The state variable x of the motor-side disturbance observer 52 b The torsional torque τ of the reduction gear 20 s Estimated value of belt disturbance torque τbelt , belt disturbance torque τ belt The derivative of and the step disturbance torque τ step We shall use the following. Therefore, the state variable x a It can be expressed as shown in equation (15).

[0063]

[0064] As described above, the input variable u b and state variable x b By defining this, the state equation of the motor-side disturbance observer 52 is expressed by equation (16), and the matrix A in equation (16) b , B b These are expressed by equations (17a) and (17b), respectively.

[0065]

[0066] In equations (17a) and (17b), g1 to g4 are observer gains, which are expressed by equations (18a) to (18d), respectively. b This represents the designated pole of the motor-side disturbance observer 52.

[0067]

[0068] ω b ω is the angular velocity of motor 15. m Since it is proportional to the angular velocity ω, m When ω is close to 0, the observer gains g1 to g4 become extremely large, which can make the control unstable. b Lower limit ω with respect to the absolute value bl Determined, |ω b | <ω bl When ω b ga ω bl It is preferable to perform the calculation assuming that it is true.

[0069] The motor-side disturbance observer 52 receives the q-axis current i q and the torsional torque τ of the reduction gear 20 s (Or its estimated value) and the angular velocity ω of motor 15 m By inputting this, the state variable x b Estimated value

[0070]

[0071] This can be obtained. From the motor-side disturbance observer 52, the belt disturbance torque τ belt Estimated values ​​and step disturbance torque τ step The estimated value and are output, and by adding these together in the addition element 66, the motor-side disturbance torque τ is obtained as shown in equation (19). m dis An estimate can be obtained.

[0072]

[0073] Thus, the q-axis current i q and the torsional torque τ of the reduction gear 20 s (Or its estimated value) and the angular velocity ω of motor 15 m By providing a motor-side disturbance observer 52 that receives input from the motor-side plant 42, the disturbance torque (τ) input to the motor 15 is reduced. belt , τ step , τ m dis The motor-side disturbance observer 52 can be described as an estimation device that estimates disturbances input to the motor 15.

[0074] Next, a control method for servo-controlling the plant shown in Figure 1 based on externally input position commands while performing compensation based on angular transmission error and motor-side disturbance torque will be explained using the block diagram shown in Figure 6. The block diagram shown in Figure 6 is different from the block diagram shown in Figure 4 in that it includes a motor-side disturbance observer 52 that estimates the motor-side disturbance torque, and a compensation current i based on the estimated motor-side disturbance torque. cmpm This adds a section that generates and compensates for the q-axis current, and shows the configuration of the control device that performs servo control of the plant shown in Figure 1. The motor-side disturbance observer 52 receives the q-axis current i supplied to the motor 15. q The angular velocity ω of the motor 15 is output by the differentiator 61 connected to the encoder 17. m The torsional torque τ output by the reduction gear ATE observer 51 s The estimated value and are input. The motor-side disturbance observer 52 is the belt disturbance torque τ beltEstimated values ​​and step disturbance torque τ step The estimated value of and are output, and these are added together in the summing element 66, thereby generating the motor-side disturbance torque τ m dis An estimated value of the motor-side disturbance torque τ is obtained. m dis For the estimated value, the torque constant K of motor 15 t By multiplying by the reciprocal of the above, a compensation current i is generated to compensate for the motor-side disturbance torque. cmpm The obtained compensation current i is obtained. cmpm This is added to the output of the subtraction element 63 in the addition element 67, and the output of the addition element 67 becomes the actual q-axis current i q This is supplied to the motor 15. In other words, in the control device shown in the block diagram of Figure 6, the angular transmission error ω of the reduction gear 20 err Compensation for and motor-side disturbance torque τ m dis Compensation for both will be provided.

[0075] In conventional methods, the influence of the belt 25 between the motor 15 and the reduction gear 20 is not considered when compensating for the angular transmission error of the reduction gear 20. As a result, when the angular transmission error is compensated, vibrations sometimes occur on the load 30 side due to the belt 25. In contrast, in the control method of the second embodiment, the periodic belt disturbance torque τ caused by the belt 25 is not considered. belt Since the effects of this can be compensated for, the occurrence of vibration at load 30 can be further suppressed. The disturbance torque applied to motor 15 is a step-shaped disturbance torque τ due to Coulomb friction. step While estimating the torsional torque τ is described in Non-Patent Documents 4-5, in this embodiment, s Without using a torque sensor to directly detect step-shaped disturbance torque τ step In addition, periodic belt disturbance torque τ belt This can be estimated and used for compensation. In the above example, the motor-side disturbance torque τ m dis The periodic disturbance torque included is the belt disturbance torque τ due to belt 25. beltWe are making an estimate of the belt disturbance torque τ, but the periodic disturbance torque that can be the target of the estimate is the belt disturbance torque τ belt It is not limited to this. Periodic disturbance torques that can be estimated by the method of this embodiment include belt disturbance torque τ belt Other examples include periodic disturbance torque generated in the motor bearings as the motor 15 rotates.

[0076] The estimation method of the second embodiment uses a gearbox ATE observer 51 and a motor-side disturbance observer 52, and is similar to the method disclosed in Patent Document 4 in that it uses two disturbance observers in a two-inertia system consisting of a motor and a load. However, in the method of this embodiment, by linking the gearbox ATE observer 51 and the motor-side disturbance observer 52 in series, it is possible to effectively estimate the angle transmission error and belt disturbance torque with a small amount of computation and suppress the generation of vibrations and the like based on them. In contrast, in the method described in Patent Document 4, in order to estimate the disturbance torque applied to the load side, the first disturbance observer, which is the motor-side observer, estimates the motor's torsional torque based on the motor's speed response value and current command value, and the second disturbance observer, which is the load-side observer, estimates the load's disturbance torque using the estimated motor's torsional torque and the load's speed response value. In other words, the coupling relationship between the motor-side disturbance observer and the load-side disturbance observer differs between the estimation method of this embodiment and the method described in Patent Document 4. Therefore, the input and output directions of the estimated torsional torque are completely different between the estimation method of this embodiment and the method described in Patent Document 4. There is also a difference in whether acceleration response values ​​or velocity response values ​​are used on the load side, so the disturbances that can be estimated differ between the method of this embodiment and the method described in Patent Document 4. Specifically, the method of this embodiment can estimate the angle transmission error of the reduction gear and the motor-side disturbance, while the method described in Patent Document 4 can estimate the load-side disturbance.

[0077] [Third Embodiment] In the methods described in the first and second embodiments, the angular transmission error ω err Load-side angular velocity ω l Compensation current i to compensate for fluctuationscmps The calculation was performed. In this invention, the angular transmission error ω err Acceleration α on the load side due to l1 A compensating current i is set to compensate for the fluctuations. cmps It is also possible to calculate and compensate for this. Below, as a third embodiment, in the plant shown in Figure 2, the acceleration α on the load side l1 Based on the angular transmission error ω err Estimate the compensation current i cmps A control method for calculating the belt disturbance torque τ will be described. Figure 7 is a block diagram illustrating the control method of the third embodiment. The model shown by the block diagram in Figure 7 is the same as the model shown in Figure 6, although the input parameters are different. In the model shown in Figure 6, the belt disturbance torque τ belt The input to is the motor speed ω m However, in the model shown in Figure 7, the belt disturbance torque τ belt The input to the motor is the rotation angle θ. m However, in the example shown in Figure 7, assuming that the reducer is a harmonic drive reducer, the contribution of higher-order components is also considered, and the angular transmission error ω shown in equation (20) is obtained. err The formula used was (20), which is the same as in (1a) but with the constant μ set to 2.

[0078]

[0079] Also, belt disturbance torque τ belt Regarding this, we assume that components of different frequencies are superimposed, as shown in equation (21).

[0080]

[0081] Belt disturbance torque τ belt When components of different frequencies overlap, the particularly prominent components are the frequency component corresponding to one rotation of the pulley supporting the belt and the frequency component corresponding to one turn of the belt, and these can be expressed as, for example, τ b1 , τ b2 It can be set as follows: Belt disturbance torque τ belt The frequency of each component contained in is the angular velocity ω of the motor 15. m It is proportional to.

[0082] The control method in the third embodiment will be explained with reference to Figure 7. Similar to the first embodiment, a Ruwenberger observer is considered to correspond to the load-side plant 41 and is designated as the gearbox ATE observer 51. The gearbox ATE observer 51 itself is the same as in the first embodiment, but in the third embodiment, the state variables of the two inertial systems consisting of the motor 15, the gearbox 20 and the load 30, and the feedback system consisting of the encoder 17 and the position-velocity controller 62 are set to x b2 It is expressed as follows, and the equation of state is the one shown in equations (22a) to (22b) below. Acceleration α of load 30 l1 This is expressed by equation (22c). In this example, it is assumed that the position speed controller 62 performs speed proportional control, and its speed proportional gain is K p Let's assume that.

[0083]

[0084] In the inverse transfer function calculation unit 64, the angular transfer error ω is calculated using the above state equation. err Acceleration α from load 30 l1 Transfer function α up to l1 / ω err And, compensation current i cmps From acceleration α l1 Transfer function α up to l1 / i cmps Considering this, the angle transmission error ω err Compensation current i cmps The inverse transfer function T for calculating the inverse transfer function m αl1 (s) is determined. By deriving it in the same manner as shown in the first embodiment, we obtain equation (23).

[0085]

[0086] The inverse transfer function T expressed by equation (23) m αl1 In (s), the order of the numerator is higher than that of the denominator, so in this form the compensation current i cmps It is not possible to obtain the angular transfer error ω in the input of the transfer function. err The differential value of the estimated value, i.e.

[0087]

[0088] Using the inverse transfer function T m αl1 Make (s) proper. Compensation current i cmps This can be found using equation (24).

[0089]

[0090] The compensation current i obtained in this way cmps Subtraction element 63 for q-axis current command i q ref Subtracting from this will result in the q-axis current i q This is obtained, and the motor 15 controls this q-axis current i q It is actually driven by this. This causes the angular transmission error ω err This means that compensation has been made. In addition, a motor-side disturbance observer 52, as described in the second embodiment, is provided, and in the motor-side disturbance observer 52, the q-axis current i q And the angular velocity ω of the motor 15 output by the differentiator 61 m The torsional torque τ output by the reduction gear ATE observer 51 s Based on the estimated value of the belt disturbance torque τ belt This allows for the estimation of the motor-side disturbance torque τ, similar to the case of the second embodiment. m dis Compensation can be provided for this.

[0091] As in the third embodiment, the acceleration α on the load side l1 Based on the angular transmission error ω err We will refer to the compensation performed in the acceleration dimension as compensation. In contrast to this, as in the first embodiment, the velocity ω on the load side l Compensation based on this will be called velocity-dimension compensation. In acceleration-dimension compensation, compared to velocity-dimension compensation, the addition of a first-order LPF and zero-phase error tracking control methods necessary to make the inverse transfer function proper are unnecessary, so the angular transfer error ω err Compensation current i to compensate for cmpsThe phase error is eliminated, improving vibration damping performance. Also, as can be seen by comparing equations (10) and (23), when compensation is performed in the acceleration dimension, the denominator of the inverse transfer function is 0th order and the numerator is 1st order, whereas when compensation is performed in the velocity dimension, the denominator is 1st order and the numerator is 3rd order. Therefore, performing compensation in the acceleration dimension reduces the amount of computation compared to performing compensation in the velocity dimension.

[0092] By performing simulations on the compensation of angular transmission errors, we investigated the difference in compensation performance between compensation in the velocity dimension and compensation in the acceleration dimension. Figure 8 is a block diagram showing the system used in the simulation. The system shown in Figure 8 has a configuration in which the encoder 17, acceleration sensor 31, and differentiator 61 have been removed from the system shown in Figure 7 for the simulation. Furthermore, instead of giving a position command, a velocity command ω m ref This provides the belt disturbance torque τ in the motor-side disturbance observer 52. belt The two components τ are explicitly b1 , τ b2 We decided to estimate it by dividing it into two parts. The angle transmission error ω is determined by the on / off state of switches 71 and 72 in the system. err Whether or not compensation is performed and the motor-side disturbance torque τ m dis The system allows switching between having compensation or not. In the reverse transfer function calculation unit 64, the compensation current i cmps The inverse transfer function T used in the calculation ml (s) is the inverse transfer function T' shown in equation (11) when compensation is performed in the velocity dimension. m (s) is given by the inverse transfer function T shown in equation (23) when compensation is performed in the acceleration dimension. m αl1 This is a proper version of (s). In the simulation, the angular transmission error ω err and motor-side disturbance torque τ m dis Load-side acceleration α when and lThe fluctuations were determined, and the frequency spectra of the oscillation components included in the fluctuations were obtained by performing a Fourier transform on them. The results are shown in Figures 9 and 10. Figure 9 shows the spectra with and without compensation for the velocity dimension, and Figure 10 shows the spectra with and without compensation for the acceleration dimension.

[0093] In Figures 9 and 10, among the peaks that appear when no compensation is performed, the peaks near 6 Hz and near 9 Hz are due to belt disturbance torque, and the peak near 14 Hz is due to angular transmission error. Belt disturbance torque was compensated well both when velocity-dimension was performed and when acceleration-dimension was performed. Regarding angular transmission error, as shown in Figure d, when velocity-dimension was performed, it could be reduced to 90% of the original value, and compensation was further improved by performing acceleration-dimension.

[0094] Embodiments of the present invention have been described above. In the above embodiments, when compensating for angular transmission errors, an inverse transfer function is used to calculate a compensation current for compensating for angular transmission errors from the angular transmission error. In the first embodiment, the inverse transfer function is set to compensate for the velocity dimension, and in the third embodiment, the inverse transfer function is set to compensate for the acceleration dimension. However, the inverse transfer function used to calculate the compensation current for compensating for angular transmission errors is not limited to these. For example, the torsional torque τ between the load side and the motor side. s , the twist angle θ between the load side and the motor side s , motor speed ω m It is also possible to use the inverse transfer function based on the torsional torque τ between the load side and the motor side. s This is, for example, the torsional torque in the reduction gear 20, and the torsional angle θ between the load side and the motor side. s This is, for example, the torsion angle in the reduction gear 20. In this invention, it is possible to first determine at which operating point in the plant the angular transmission error will be canceled out, then set the inverse transfer function, and design the control system.

[0095] Although the above explanation has used a transfer function based on the Laplace transform, the method described in the present invention can also be directly applied when using a discretized transfer function, i.e., a pulse transfer function. There are no restrictions on the discretization method, and known discretization methods can be used. In the appended claims, the term "transfer function" includes both a transfer function based on the Laplace transform or a transfer function in a continuous-time system, and a pulse transfer function. Furthermore, when discretized, the inverse transfer function can be obtained by methods such as phase error tracking control. Phase error tracking control methods are described in Non-Patent Literature 6, etc.

[0096] The above describes an example of a configuration for carrying out the present invention, but the above technology can take the following configuration.

[0097] (1) An estimation method for estimating the angular transmission error of a reduction gear in a plant having a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, wherein the plant is assumed to consist of a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant which consists of the reduction gear and the load, and an estimation value of the angular transmission error is calculated using a first observer corresponding to the load-side plant based on the acceleration obtained with respect to the load and the angular velocity of the motor's rotation.

[0098] (2) The estimation method of (1), wherein, using the first observer, an estimated value of the torsional torque in the reduction gear is calculated in addition to the estimated value of the angular transmission error.

[0099] (3) The estimation method of (2), wherein a belt is provided between the motor and the input shaft of the reduction gear in the plant to transmit the driving force of the motor to the reduction gear.

[0100] (4) The estimation method of (2) or (3), which involves calculating an estimated value of disturbances input to the motor at the motor-side plant using a second observer corresponding to the motor-side plant, based on the current to the motor, the estimated angular velocity of the motor, and the estimated torsional torque of the motor.

[0101] (5) The estimation method of (4), wherein the periodic disturbance torque and step disturbance torque in the motor-side plant are estimated using the second observer.

[0102] (6) A control method for controlling the position or speed of a load in a plant comprising a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, based on a command input from an external source, comprising: generating a current command value for the motor by feeding back at least one of the rotational position and angular velocity of the motor; assuming that the plant is composed of a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant which comprises the reduction gear and the load, calculating an estimated value of the angular transmission error of the reduction gear using a first observer corresponding to the load-side plant based on the acceleration obtained with respect to the load and the angular velocity of the motor's rotation; using an inverse transfer function which calculates a first compensation current to compensate for the angular transmission error from the angular transmission error; applying the estimated value of the angular transmission error to the inverse transfer function to calculate the first compensation current; and compensating for the angular transmission error in the current command value using the calculated first compensation current.

[0103] (7) The control method of (6), wherein an estimated value of the torsional torque in the reduction gear is calculated using the first observer based on the acceleration obtained with respect to the load and the angular velocity of the motor's rotation; an estimated value of the disturbance to be input to the motor in the motor-side plant is calculated using the second observer corresponding to the motor-side plant based on the current to the motor, the angular velocity of the motor, and the estimated value of the torsional torque; a second compensation current is calculated based on the estimated value of the disturbance; and the disturbance is compensated for in the current command value using the calculated second compensation current.

[0104] (8) The control method of (6) or (7), wherein a belt is provided between the motor and the input shaft of the reduction gear in the plant to transmit the driving force of the motor to the reduction gear.

[0105] (9) The control method according to any of (6) to (8), wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to a predetermined operating point of the load by the transfer function from the first compensation current to the operating point.

[0106] (10) A control method according to any of (6) to (8), wherein the inverse transfer function is obtained by dividing the transfer function from the angular transfer error to the target quantity by the transfer function from the first compensation current to the target quantity, with the velocity and acceleration of the load as the target quantity.

[0107] (11) A control method according to any of (6) to (8), wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to the target quantity by the transfer function from the first compensation current to the target quantity, with respect to one of the torsional torque between the load side and the motor side, the torsional angle between the load side and the motor side, and the speed of the motor.

[0108] (12) Estimation device for estimating the angular transmission error of a reduction gear in a plant having a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, wherein the plant is composed of a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant which consists of the reduction gear and the load, and comprises: acceleration detection means for detecting the acceleration of the load; angular velocity detection means for detecting the angular velocity of the rotation of the motor; and a first observer represented by a state variable which includes at least the angular transmission error and a state equation corresponding to the load-side plant, wherein the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means are input to the first observer to calculate an estimated value of the angular transmission error.

[0109] (13) The estimation device of (12), wherein the state variable includes the torsional torque of the reduction gear, and the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means are input to the first observer to calculate an estimated value of the torsional torque.

[0110] (14) The estimation device of (13), further comprising a second observer represented by a state variable that includes at least a disturbance input to the motor and a state equation corresponding to the motor-side plant, wherein the current to the motor, the estimated values ​​of the angular velocity of the motor and the torsional torque are input to the second observer to calculate an estimated value of the disturbance.

[0111] (15) The estimation device of (14), which uses the second observer to estimate the periodic disturbance torque and the step disturbance torque in the motor-side plant, respectively.

[0112] (16) A control device for controlling the position or speed of a load in a plant comprising a motor, a load, and a reduction gear whose input shaft is driven by the motor and to which the load is connected as an output shaft, based on a command input from an external source, wherein the plant comprises a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant comprising the reduction gear and the load, a controller which generates a current command value for the motor by feeding back at least one of the rotational position and angular velocity of the motor, acceleration detection means for detecting the acceleration of the load, angular velocity detection means for detecting the rotational angular velocity of the motor, a first observer represented by a state variable which includes at least the angular transmission error of the reduction gear and a state equation corresponding to the load-side plant, and an inverse transfer function calculation unit which receives an estimated value of the angular transmission error obtained by inputting the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means to the first observer, The inverse transfer function calculation unit calculates the first compensation current from the estimated value of the angular transfer error using an inverse transfer function configured to calculate a first compensation current that compensates for the angular transfer error from the angular transfer error, and the control device performs compensation for the angular transfer error in the current command value using the calculated first compensation current.

[0113] (17) The control device of (16), further comprising a second observer represented by a state variable including at least a disturbance input to the motor and a state equation corresponding to the motor-side plant, wherein the acceleration measured by the acceleration detection means and the angular velocity detected by the angular velocity detection means are input to the first observer to calculate an estimated value of the torsional torque in the reduction gear, the current to the motor, the angular velocity of the motor and the estimated value of the torsional torque are input to the second observer to calculate an estimated value of the disturbance, a second compensation current is calculated based on the estimated value of the disturbance, and compensation for the disturbance is performed in the current command value using the calculated second compensation current.

[0114] (18) The control device according to (16) or (17), wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to a predetermined operating point of the load by the transfer function from the first compensation current to the operating point.

[0115] (19) A control device according to (16) or (17), wherein, with velocity and acceleration in the load as the target quantity, the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to the target quantity by the transfer function from the first compensation current to the target quantity.

[0116] (20) A control device according to (16) or (17), wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to the target quantity by the transfer function from the first compensation current to the target quantity, with respect to one of the following quantities: the torsional torque between the load side and the motor side, the torsional angle between the load side and the motor side, and the speed of the motor.

[0117] In the configurations shown in (1) and (12), the plant consisting of a motor, a load, and a gearbox whose input shaft is driven by the motor and to which the load is connected on the output shaft is divided into a load-side plant and a motor-side plant. An first observer corresponding to the load-side plant is used to estimate the angular transmission error. This allows the order of the first observer to be reduced to the fourth order, thereby reducing the computational load on the first observer and improving its resistance to sensor noise. Furthermore, since the motor-side plant does not need to be considered in the estimation of the angular transmission error, the number of parameters in the state equation of the first observer is reduced, making it less susceptible to the effects of parameter fluctuations and modeling errors.

[0118] In the configurations shown in (1) and (12), it is natural to include the torsional torque of the gearbox in the state variables of the first observer. Therefore, as shown in (2) and (13), an estimate of the torsional torque of the gearbox can be easily obtained. The estimated torsional torque is useful for analyzing the operation of the plant. Furthermore, as shown in (3), even if a belt is provided between the motor and the input shaft of the gearbox in the plant to transmit the driving force of the motor to the gearbox, the belt is included in the motor-side plant, so it becomes possible to ignore the influence of the belt on the estimation of the angular transmission error.

[0119] In the configurations shown in (4) and (14), a second observer corresponding to the motor-side plant is provided, and the estimated torsional torque obtained by the first observer is input to the second observer, making it easy to estimate disturbances input to the motor without the need for torque sensors or the like. In particular, as shown in (5) and (15), the periodic disturbance torque and step disturbance torque that constitute the motor-side disturbance torque can be estimated separately.

[0120] In the configurations shown in (6) and (16), the plant consisting of a motor, a load, and a reduction gear whose input shaft is driven by the motor and to which the load is connected on the output shaft is divided into a load-side plant and a motor-side plant. An angle transmission error is estimated and a compensation current is calculated using a first observer corresponding to the load-side plant. This allows the order of the first observer to be reduced to the fourth order, reducing the computational load on the first observer, improving immunity to sensor noise, and enabling high-precision control. Furthermore, since the motor-side plant does not need to be considered in the estimation of the angle transmission error, the number of parameters in the state equation of the first observer is reduced, making it less susceptible to the effects of parameter fluctuations and modeling errors.

[0121] In the configurations shown in (7) and (17), a second observer corresponding to the motor-side plant is provided, and the estimated torsional torque obtained by the first observer is input to the second observer. This makes it easy to estimate disturbances input to the motor without the need for torque sensors, and thus makes it easy to compensate not only for angular transmission errors but also for motor-side disturbances. In particular, as shown in (8), when a belt that transmits the motor's driving force to the reduction gear is provided between the motor and the input shaft of the reduction gear in the plant, it becomes possible to accurately compensate for both periodic disturbances on the motor side caused by the belt and for angular transmission errors.

[0122] With the configurations shown in (9) and (18), the inverse transfer function for obtaining the first compensation current can be easily set. In particular, with the configurations shown in (10), (11), (19), and (20), the first compensation current for compensating for the angular transmission error can be easily calculated.

[0123] 10...Base; 15...Motor; 17...Encoder; 20...Gear reducer; 25...Belt; 30...Load; 31...Accelerometer; 35...Motor and belt section; 41...Load-side plant; 42...Motor-side plant; 51...Gear reducer ATE observer; 52...Motor-side disturbance observer; 61...Differentiator; 62...Position and velocity controller; 64...Inverse transfer function calculation unit.

Claims

1. An estimation method for estimating the angular transmission error of a reduction gear in a plant having a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, wherein the plant is assumed to consist of a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant which consists of the reduction gear and the load, and an estimation value of the angular transmission error is calculated using a first observer corresponding to the load-side plant based on the acceleration obtained with respect to the load and the angular velocity of the motor's rotation.

2. The estimation method according to claim 1, wherein, using the first observer, an estimated value of the torsional torque in the reduction gear is calculated in addition to the estimated value of the angular transmission error.

3. The estimation method according to claim 2, wherein a belt is provided between the motor and the input shaft of the reduction gear in the plant to transmit the driving force of the motor to the reduction gear.

4. The estimation method according to claim 2 or 3, wherein an estimated value of disturbances input to the motor in the motor-side plant is calculated using a second observer corresponding to the motor-side plant, based on the current to the motor, the estimated angular velocity of the motor, and the estimated torsional torque.

5. The estimation method according to claim 4, wherein the periodic disturbance torque and the step disturbance torque in the motor-side plant are estimated using the second observer.

6. A control method for controlling the position or speed of a load in a plant comprising a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, based on a command input from an external source, comprising: generating a current command value for the motor by feeding back at least one of the rotational position and angular velocity of the motor; assuming that the plant is composed of a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant which comprises the reduction gear and the load, calculating an estimated value of the angular transmission error of the reduction gear using a first observer corresponding to the load-side plant based on the acceleration obtained with respect to the load and the angular velocity of the motor's rotation; using an inverse transfer function which calculates a first compensation current to compensate for the angular transmission error from the angular transmission error; calculating the first compensation current by applying the estimated value of the angular transmission error to the inverse transfer function; and compensating for the angular transmission error in the current command value using the calculated first compensation current.

7. The control method according to claim 6, comprising: calculating an estimated value of torsional torque in the reduction gear using the first observer based on the acceleration obtained with respect to the load and the angular velocity of the motor's rotation; calculating an estimated value of disturbance input to the motor at the motor-side plant using a second observer corresponding to the motor-side plant based on the current to the motor, the angular velocity of the motor, and the estimated value of torsional torque; calculating a second compensation current based on the estimated value of the disturbance; and performing compensation for the disturbance in the current command value using the calculated second compensation current.

8. The control method according to claim 6 or 7, wherein a belt is provided between the motor and the input shaft of the reduction gear in the plant for transmitting the driving force of the motor to the reduction gear.

9. The control method according to claim 6 or 7, wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to a predetermined operating point of the load by the transfer function from the first compensation current to the operating point.

10. The control method according to claim 6 or 7, wherein, with velocity and acceleration in the load as the target quantity, the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to the target quantity by the transfer function from the first compensation current to the target quantity.

11. The control method according to claim 6 or 7, wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angle transfer error to the target quantity by the transfer function from the first compensation current to the target quantity, with respect to one of the following quantities: the torsional torque between the load side and the motor side, the torsional angle between the load side and the motor side, and the speed of the motor.

12. Estimation device for estimating the angular transmission error of a reduction gear in a plant having a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, wherein the plant is composed of a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant which consists of the reduction gear and the load, and comprises: acceleration detection means for detecting the acceleration of the load; angular velocity detection means for detecting the angular velocity of the motor's rotation; and a first observer represented by a state variable which includes at least the angular transmission error and a state equation corresponding to the load-side plant, wherein the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means are input to the first observer to calculate an estimated value of the angular transmission error.

13. The estimation device according to claim 12, wherein the state variable includes the torsional torque of the reduction gear, and the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means are input to the first observer to calculate an estimated value of the torsional torque.

14. The estimation device according to claim 13, further comprising a second observer represented by a state variable that includes at least a disturbance input to the motor and a state equation corresponding to the motor-side plant, wherein the current to the motor, the estimated angular velocity of the motor, and the estimated torsional torque are input to the second observer to calculate the estimated value of the disturbance.

15. The estimation device according to claim 14, wherein the second observer is used to estimate the periodic disturbance torque and the step disturbance torque in the motor-side plant, respectively.

16. A control device for controlling the position or speed of a load in a plant comprising a motor, a load, and a reduction gear whose input shaft is driven by the motor and whose output shaft is connected to the load, based on a command input from an external source, wherein the plant comprises a motor-side plant which includes the motor and extends from the motor to the input shaft of the reduction gear, and a load-side plant comprising the reduction gear and the load, a controller which generates a current command value for the motor by feeding back at least one of the rotational position and angular velocity of the motor, acceleration detection means for detecting the acceleration of the load, angular velocity detection means for detecting the rotational angular velocity of the motor, a first observer represented by a state variable which includes at least the angular transmission error of the reduction gear and a state equation corresponding to the load-side plant, and an inverse transfer function calculation unit which receives an estimated value of the angular transmission error obtained by inputting the acceleration detected by the acceleration detection means and the angular velocity detected by the angular velocity detection means to the first observer, The inverse transfer function calculation unit calculates the first compensation current from the estimated value of the angular transfer error using an inverse transfer function configured to calculate a first compensation current that compensates for the angular transfer error from the angular transfer error, and the control device performs compensation for the angular transfer error in the current command value using the calculated first compensation current.

17. The control device according to claim 16, further comprising a second observer represented by a state variable including at least a disturbance input to the motor and a state equation corresponding to the motor-side plant, wherein the acceleration measured by the acceleration detection means and the angular velocity detected by the angular velocity detection means are input to the first observer to calculate an estimated value of the torsional torque in the reduction gear, the current to the motor, the angular velocity of the motor and the estimated value of the torsional torque are input to the second observer to calculate an estimated value of the disturbance, a second compensation current is calculated based on the estimated value of the disturbance, and compensation for the disturbance is performed in the current command value using the calculated second compensation current.

18. The control device according to claim 16 or 17, wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to a predetermined operating point of the load by the transfer function from the first compensation current to the operating point.

19. The control device according to claim 16 or 17, wherein, with velocity and acceleration in the load as the target quantity, the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to the target quantity by the transfer function from the first compensation current to the target quantity.

20. The control device according to claim 16 or 17, wherein the inverse transfer function is a transfer function obtained by dividing the transfer function from the angular transfer error to the target quantity by the transfer function from the first compensation current to the target quantity, with respect to one of the following quantities: the torsional torque between the load side and the motor side, the torsional angle between the load side and the motor side, and the speed of the motor.

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