CN-116203895-B - Online iterative compensation system and method for servo errors

CN116203895BCN 116203895 BCN116203895 BCN 116203895BCN-116203895-B

Abstract

The invention provides an online iteration compensation system and method for servo errors, wherein the online iteration compensation system comprises a disturbance observer module, a dual-loop high-bandwidth control module, an online iteration compensation module and an integral control scheme implementation module, wherein the disturbance observer module regards nonlinearity and external disturbance in a system in the process of compensating slow-knife servo errors by fast-knife servo as integral lumped disturbance to estimate and compensate, the dual-loop high-bandwidth control module is used for designing a positive acceleration-speed-position feedback damping controller to inhibit a light damping resonance mode in an inner loop, the online iteration compensation module predicts tracking errors of the robust high-bandwidth controller and carries out iterative compensation in an online reference track correction mode, and the integral control scheme implementation module comprises a disturbance observer, a high-bandwidth dual-loop controller and an online iteration compensation module, predicts states of the system in a prediction interval based on a linear model of a discrete system differential equation, and modifies a reference track in an online iteration mode to carry out error compensation. The invention can iterate compensation in real time, and improves the tracking precision and the anti-interference capability of the fast knife servo system in the process of compensating the slow knife servo error.

Inventors

ZHU LIMIN
MENG YIXUAN
ZHU ZHIWEI

Assignees

上海交通大学
南京理工大学

Dates

Publication Date: 20260505
Application Date: 20230209

Claims (7)

1. An online iterative compensation system for servo errors, comprising: the disturbance observer module regards the nonlinearity and external disturbance in the system in the process of compensating the slow-knife servo error by the fast-knife servo as integral lumped disturbance to estimate and compensate; The double-loop high-bandwidth control module is used for designing a positive acceleration-speed-position feedback damping controller to inhibit a light damping resonance mode in an inner loop of the system; the online iteration compensation module predicts the tracking error of the robust high-bandwidth controller through a differential equation of a discrete system and carries out online reference track correction; the system comprises a whole control scheme implementation module, a system state prediction module, a system error compensation module and a system error compensation module, wherein the whole control scheme implementation module comprises a disturbance observer, a high-bandwidth double-loop controller and an online iteration compensation module; The disturbance observer module includes: the driving mode of the fast knife servo system is piezoelectric driving or normal stress electromagnetic driving, and the whole system is described by the following third-order model in the Laplace continuous domain: 1) Wherein, the , , , , , , As a parameter of the system model, Is a Laplacian operator; the third-order model is a non-minimum phase system, and in order to ensure the stability of the disturbance observer, the third-order model needs to be corrected to be the minimum phase system: 2) to meet minimum phase system inversion The order constraint condition of (2) requires designing a corresponding low-pass filter So that The method can be realized in practical application, and a second-order low-pass filter is adopted: 3) Wherein, the To determine the parameters of the bandwidth of the low-pass filter, tuning the parameters to maximize the bandwidth, the lumped disturbance of the system is estimated as And compensating by using a control method; the dual-loop high-bandwidth control module comprises: The positive acceleration-speed-position feedback damping controller has an inner loop damping controller expression of: 4) The inner loop damping controller has a total of 5 parameters that can be used for adjustment: , , , , the desired positions of the 5 system poles can thus be arbitrarily configured to achieve the desired system damping ratio, and therefore the transfer function of the inner loop damping portion is: 5) for the input of middle and low frequency segments, the inner ring damping part is integrally regarded as a second-order rigid system, and the expression is as follows: 6) Wherein, the , , , In the outer loop, a high gain proportional-integral tracking controller is applied to reduce residual tracking error and realize accurate track tracking, and the expression of the outer loop tracking controller is as follows: 7) Wherein, the And High bandwidth control is realized by adjusting parameters of the inner ring damping controller and the outer ring tracking controller; the disturbance observer module and the high-bandwidth double-loop control module jointly form a robust high-bandwidth controller.
2. The on-line iterative compensation system of servo errors of claim 1, wherein the on-line iterative compensation module comprises: Linear error prediction sub-module according to equation 6) and equation 7), the fast knife servo system is derived from the input To output to Transfer function writing between: 8) the transfer function is a third order transfer function expressed in the form of a differential equation in the discrete domain: + + 9) Wherein, the , , , , , Is a constant related to the sampling frequency and coefficients in the overall closed loop transfer function; in the state space, equation 9) writes: 10) Wherein, the Representing the sampling points of a discrete system. For the above-described spatial state equation, Is a state vector in which , , , , , State matrix Input matrix Output matrix ; Representing the lumped disturbance of the system, estimated by a designed disturbance observer and fed back into the control loop for compensation, and therefore, for a linear error prediction model, Non-linear influence of (a) is ignored at the current sampling instant All parameters can be obtained, so that the state prediction at the next moment is realized as follows: 11) I.e. 12) Assume that For the prediction interval, all states in the prediction interval can be predicted, and the predicted system output is deduced as follows: 13) Implementation of this prediction requires a reference trajectory at a future time Compensating slow knife servo error for the fast knife servo system, wherein the reference track of the fast knife servo system is generated in real time according to the servo error measured by the slow knife servo system, thereby And the method cannot be directly obtained and needs to be obtained by a future moment reference track prediction module.
3. The on-line iterative compensation system of servo error of claim 2, wherein the on-line iterative compensation module further comprises: the future time reference track prediction sub-module uses a quadratic polynomial to interpolate, fits coefficients of the quadratic polynomial used for interpolation through the reference tracks of the ten sampling points at the current sampling time and the previous nine sampling times, namely slow knife servo errors of the ten sampling points, and then, The output of the fast knife servo system in the prediction interval can be predicted by interpolation of the quadratic polynomial.
4. The online iterative compensation system of servo errors of claim 3, wherein the online iterative compensation module further comprises: Error iteration compensation submodule Defined as the difference between the reference track and the actual tracking track and without compensation, The tracking error of the time instant is predicted as: 14) Assume that Is a compensation interval, and When compensating term Added to the reference track Tracking error during the middle period Changes due to system output Changes occur, and the changes of the system output are: 15) Wherein, the Is a constant, and therefore, after compensation, the error of the system is derived as: 16) The error is compensated gradually in an iterative manner due to the fact that in the prediction interval The system state in the model is accurately predicted, and the iterative process is realized on line in the model prediction process; the compensation term in the first iteration is set as Then there is 17) Wherein, the Compensation gain; substituting equation 17) into equation 15), deriving the tracking error after the first iteration as: 18) During the course of the second iteration, Is also integrated in the compensation term and is designed to: 19) Thus, the tracking error after the second iteration is: 20) The compensation term and the tracking error after the nth iteration are obtained by deducting in the same way, and the expression is as follows: 21) 22) therefore, when the compensation gain satisfies the following condition: 23) If n approaches infinity, the tracking error of the system approaches 0.
5. The system of claim 4, wherein the overall control scheme implementation module is configured to compensate for tracking error at a next sampling instant by compensating for a compensation interval Must be 1 or more, so the prediction interval Must be greater than or equal to 2.
6. An online iterative compensation method for servo errors, comprising the steps of: a disturbance observer step of taking the nonlinearity and external disturbance in the system in the process of compensating the slow-knife servo error by the fast-knife servo as an integral lumped disturbance to estimate and compensate; The dual-loop high-bandwidth control step is that a positive acceleration-speed-position feedback damping controller is designed in an inner loop of the system to inhibit a light damping resonance mode; an online iterative compensation step, namely predicting the tracking error of the robust high-bandwidth controller through a differential equation of a discrete system, and carrying out iterative compensation in an online reference track correction mode; the method comprises the steps of predicting the state of a system in a prediction interval based on a linear model of a discrete system differential equation, and modifying a reference track in an online iteration mode to perform error compensation; the disturbance observer step comprises: the driving mode of the fast knife servo system is piezoelectric driving or normal stress electromagnetic driving, and the whole system is described by the following third-order model in the Laplace continuous domain: 1) Wherein, the , , , , , , As a parameter of the system model, Is a Laplacian operator; the third-order model is a non-minimum phase system, and in order to ensure the stability of the disturbance observer, the third-order model needs to be corrected to be the minimum phase system: 2) to minimize the phase system inversion The order constraint condition of (2) requires designing a corresponding low-pass filter So that The method can be realized in practical application, and a second-order low-pass filter is adopted: 3) Wherein, the To determine the parameters of the bandwidth of the low-pass filter, the parameters are optimized, and the lumped disturbance of the system is estimated as And compensating by using a control method; the step of dual-ring high-bandwidth control comprises the following steps: The positive acceleration-speed-position feedback damping controller has an inner loop damping controller expression of: 4) The inner loop damping controller has a total of 5 parameters that can be used for adjustment: , , , , the desired positions of the 5 system poles are arbitrarily configured to achieve the desired system damping ratio, and therefore the transfer function of the inner loop damping portion is: 5) for the input of middle and low frequency segments, the inner ring damping part is integrally regarded as a second-order rigid system, and the expression is as follows: 6) Wherein, the , , , In the outer loop, a high gain proportional-integral tracking controller is applied to reduce residual tracking error and realize accurate track tracking, and the expression of the outer loop tracking controller is as follows: 7) Wherein, the And High bandwidth control is realized by adjusting parameters of the inner ring damping controller and the outer ring tracking controller; The disturbance observer step and the high-bandwidth double-loop control step jointly form a robust high-bandwidth controller.
7. The method of on-line iterative compensation for servo errors according to claim 6, wherein said on-line iterative compensation step comprises: Linear error prediction substep, fast knife servo from input according to equations (6) and (7) To output to Transfer function writing between: 8) the transfer function is a third order transfer function expressed in the form of a differential equation in the discrete domain: + + 9) Wherein, the , , , , , Is a constant related to the sampling frequency and coefficients in the overall closed loop transfer function; in the state space, equation 9) writes: 10) for the above-described spatial state equation, Is a state vector in which , , , , , State matrix Input matrix Output matrix ; Representing the lumped disturbance of the system, estimated by a designed disturbance observer and fed back into the control loop for compensation, and therefore, for a linear error prediction model, Non-linear influence of (a) is ignored at the current sampling instant All parameters can be obtained, so that the state prediction at the next moment is realized as follows: 11) I.e. 12) Assume that For the prediction interval, all states in the prediction interval can be predicted, and the predicted system output is deduced as follows: 13) Implementation of this prediction requires a reference trajectory at a future time Compensating a slow cutter servo error for a fast cutter servo system, wherein a reference track of the fast cutter servo system is generated in real time according to the servo error measured by the slow cutter servo system; The online iterative compensation step further comprises: the future time reference track prediction sub-module uses a quadratic polynomial to interpolate, fits coefficients of the quadratic polynomial used for interpolation through the reference tracks of the ten sampling points at the current sampling time and the previous nine sampling times, namely slow knife servo errors of the ten sampling points, and then, The output of the fast cutter servo system in the prediction interval can be predicted by interpolation of the quadratic polynomial; The online iterative compensation step further comprises: error iterative Compensation substep Defined as the difference between the reference track and the actual tracking track and without compensation, The tracking error of the time instant is predicted as: 14) Assume that Is a compensation interval, and When compensating term Added to the reference track Tracking error during the middle period Changes due to system output Changes occur, and the changes of the system output are: 15) Wherein, the Is a constant, and therefore, after compensation, the error of the system is derived as: 16) The error is compensated gradually in an iterative manner due to the fact that in the prediction interval The system state in the model is accurately predicted, and the iterative process is realized on line in the model prediction process; the compensation term in the first iteration is set as Then there is 17) Wherein, the Compensation gain; substituting equation 17) into equation 15), deriving the tracking error after the first iteration as: 18) During the course of the second iteration, Is also integrated in the compensation term and is designed to: 19) Thus, the tracking error after the second iteration is: 20) The compensation term and the tracking error after the nth iteration are obtained by deducting in the same way, and the expression is as follows: 21) 22) therefore, when the compensation gain satisfies the following condition: 23) If n approaches infinity, the tracking error of the system approaches 0; the whole control scheme realizes the compensation of the tracking error at the next sampling moment in the module, and the compensation interval Must be 1 or more, so the prediction interval Must be greater than or equal to 2.

Description

Online iterative compensation system and method for servo errors Technical Field The invention relates to the technical field of ultra-precise machining and motion control, in particular to an online iteration compensation system and method for servo errors. Background Slow-tool servo diamond turning has wide application in ultra-precision machining, however, its dynamic servo error seriously affects machining accuracy. The master-slave control strategy integrating the fast knife servo in the slow knife servo system can effectively realize the compensation of the dynamic servo error of the slow knife servo, and the reference track of the fast knife servo system is the slow knife servo error generated in real time. Because the reference track cannot be predicted in advance, the fast knife servo system can only be controlled by a simple feedback mode, and the tracking accuracy is inevitably affected by phase lag errors and the like. The invention patent with publication number of CN112947310A discloses a rotary servo motor track precompensation method and device based on a predictive model, the patent predicts the tracking error of the rotary servo motor accurately based on a linear error prediction model, and compensates the tracking error in an online iteration mode through a track pre-compensation method. The method does not combine high-bandwidth control and robust control, cannot realize high-frequency track tracking and interference suppression, and cannot be applied to scenes requiring high-speed movement such as fast knife servo processing. Meanwhile, the method can complete error prediction compensation only under the condition that the reference track at the future moment is known, and cannot be applied to a scene that the reference track such as a fast cutter compensation slow cutter servo error needs to be generated in real time according to a measurement result. The closest paper: (1) ,"Intell igent Tracking Error Prediction and Feedforward Compensat ion for Nanoposit ioning Stages with High-bandwidth Control,"IEEE Transactions on Industrial Informatics,2022,DOI:10.1109/TII.2022.3199263. of Shanghai university of traffic, meng Yixuan and the like proposes a high-bandwidth controller intelligent error prediction and feedforward compensation method based on a Gaussian process, which is applied to a nano positioning system, but the method only needs to realize offline prediction of errors, predicts tracking errors of each point on the whole reference track under the condition that all the reference tracks are known, then compensates, and needs to consume a large amount of time for error prediction and compensation when the data quantity is large, and has no robustness for coping with track change. Meanwhile, the method is not provided with a disturbance observer, so that the disturbance resistance is poor, and the method is not suitable for application scenes with large disturbance such as cutting force in fast cutter servo processing. (2) ,"Simultaneous damping and tracking control of a normal-stressed electromagnetic actuated nano-positioning stage",Sensors and Actuators A:Phys ical,2022. Of Shanghai university, wang Xiangyuan and the like provides a double-loop controller with synchronous optimization of inner loop and outer loop, which can effectively inhibit the hysteresis nonlinearity and light damping resonance characteristic of a system and improve the control bandwidth to be higher than the first-order resonance frequency of the system. However, the method is a simple feedback controller, phase lag inevitably exists, tracking errors caused by larger phase lag exist for tracks with higher frequency, and the controller has no interference resistance. Disclosure of Invention Aiming at the defects in the prior art, the invention provides an online iteration compensation system and method for servo errors. According to the on-line iterative compensation system and the method for servo errors provided by the invention, the scheme is as follows: in a first aspect, an online iterative compensation system for servo errors is provided, the system comprising: the disturbance observer module regards the nonlinearity and external disturbance in the system in the process of compensating the slow-knife servo error by the fast-knife servo as integral lumped disturbance to estimate and compensate; The double-loop high-bandwidth control module is used for designing a positive acceleration-speed-position feedback damping controller to inhibit a light damping resonance mode in an inner loop of the system; the online iteration compensation module predicts the tracking error of the robust high-bandwidth controller through a differential equation of a discrete system and carries out online reference track correction; The integral control scheme implementation module comprises a disturbance observer, a high-bandwidth double-loop controller and an online iteration compensation module, wherein the state of a system