Periodic Signal Tracking Control And Performance Optimization Of Servo System Based On Equivalent Input Disturbance Compensation

In engineering practice,the system needs to complete periodic control tasks.Repetitive control provides an effective method for solving these periodic signal tracking/suppression problems.Its theoretical basis is the internal model principle.By implanting the internal model of the periodic signal into the stable closed-loop system,it can achieve steady-state tracking/suppression without bias for any target signal.Repetitive control is widely used due to its simple structure and high control precision.However,there are inevitably a variety of uncertainties in the actual control system,such as unmodeled dynamics,external disturbances,noise,etc.,which make the control accuracy of the repetitive control system difficult to meet the requirements sometimes,and even affect the stability of the system.This paper takes the servo system widely used in industrial production as the control plant,and introduces an active disturbance suppression method based on equivalent input disturbance compensation in the repetitive control system,aming to improve the disturbance suppression performance and robustness of the disturbed servo system,and ensure that the servo system can track the given periodic reference input with high precision in complex environment.This paper will carry out research work from the following three aspects:(1)An modified repetitive control system design method based on equivalent input disturbance compensation is proposed.For a class of servo systems with both periodic reference input and aperiodic disturbances,an improved repetitive control system parameter optimization design method based on equivalent input disturbance compensation is proposed.First,an equivalent input disturbance estimator is constructed by using the estimation error of the full-dimensional state observer,and a composite repetitive control law based on equivalent input disturbance compensation is established by inversely compensating the estimated value of the equivalent input disturbance to the control input.Then,based on the small gain theorem,the stability conditions of the system are derived,and a performance objective function for overall evaluation of the system’s antidisturbance performance,tracking performance and convergence speed is construct,and the system parameter optimization model is established.The particle swarm optimization algorithm is used to achieve the system Simultaneous optimization of repetitive controller parameters,equivalent input disturbance estimator parameters,and state feedback controller parameters.Finally,the validity and superiority of the proposed method are demonstrated by numerical simulation and comparative analysis.(2)An modified repetitive control system nonlinear compensation and parameter optimization method based on equivalent input disturbance is proposed.For a class of servo systems with non-integral chain and unknown nonlinear dynamics,an improved nonlinear compensation design method for repetitive control systems based on equivalent input disturbances is proposed.First,using the information of the control object model,an improved extended state observer is designed to estimate the equivalent input disturbance and the system state,and the estimated value of the equivalent input disturbance is incorporated into the repetitive control law to compensate the influence of the nonlinear disturbance.Then,the stability condition of the system is deduced by using the small gain theorem,a performance objective function is established for the overall evaluation of the system’s anti-disturbance performance,tracking performance and transient performance,and the system controller parameters are optimized by particle swarm optimization algorithm.Finally,the proposed method is applied to the speed control of brushless DC motor,and the effectiveness of the method is demonstrated by simulation comparison.(3)An command-filtered backstepping repetitive control for uncertain nonlinear systems based on equivalent input disturbance compensation is proposed.For uncertain nonlinear systems with multiple disturbances,a command-filtered backstepping repetitive control method based on additive state decomposition technique and equivalent input disturbance compensation method is proposed.First,the original nonlinear system is decomposed into a linear time-invariant primary system with periodic inputs and a nonlinear secondly system with multiple,aperiodic disturbances.Accordingly,the tracking control problem of the original nonlinear system is decomposed into two sub-problems: the repetitive control problem for linear time-invariant periodic system and the robust stabilization problem for nonlinear system.Then,using the known information of the model,a linear extended state observer is constructed to estimate the equivalent input disturbance and the system state,and then a command-filtered backstepping control law using the equivalent input disturbance estimate is designed for the secondly system that ensures robust stability and compensates for the effects of multiple disturbances and residual nonlinearity.According to the Lyapunov stability theory,the stability criterion of each subsystem is established.In addition,a particle swarm optimization algorithm is adopted to simultaneously optimize the controller parameters of the system.Finally,the effectiveness and superiority of this method are verified by simulation examples and motor control system experiments.