Disturbance Rejection Design For Repetitive Control System With State Delay Based On Equivalent Input Disturbance Compensation

Repetitive control systems are systems with internal time delays that enable accurate tracking of periodic inputs or suppression of periodic disturbance signals by constructing an internal mode 1/（0）-1)within the closed-loop system for signals of arbitrary period.As a result,repetitive control systems are increasingly used in areas such as power systems,robotic systems,automotive systems,and motor systems.In addition,the presence of unknown disturbances external to the system degrades the tracking performance of the measurement output of the repetitive control system to the periodic reference input and generates large tracking errors,which can sometimes have a catastrophic impact on the system.Therefore,it is of great theoretical value and practical significance to carry out an in-depth study on the problem of suppressing unknown disturbances from external sources for repetitive control systems with time delays.In this paper,the system stability and disturbance suppression of a repetitive control system with time delays are investigated under the influence of periodic and non-periodic disturbances.The Equivalent Input Disturbance（EID）method is used to estimate an equivalent disturbance for updating the control input signal and compensating the impact of external disturbances on the system;the repetition controller is designed to ensure the high accuracy tracking of the measurement output to the periodic reference signal;the event-triggered time-lag repetition control system disturbance suppression strategy is proposed to ensure the stability of the system and reduce the communication resource loss.The research of this paper is as follows:Firstly,the problem of tracking the periodic reference input and suppressing the unknown perturbation is investigated for a time-delay repetitive control system with unknown perturbations.In the presence of unknown disturbance effects in the external environment,an EID is estimated and compensated at the input channel to offset the effects of the unknown disturbance on the system,so as to achieve the effect of suppressing the unknown disturbance.To improve the accuracy of disturbance estimation,a sliding film observer is used to observe the state of the system and estimate the equivalent disturbance.The sufficient conditions to guarantee the finite-time stability of the system are derived using linear matrix inequalities,and the controller gain and observer gain are designed.Numerical simulations verify the effectiveness of the proposed scheme.Then,the event-triggered problem for time-delay repetitive control systems based on EID is investigated.To reduce the communication resource loss,an event triggering device is added to the state feedback channel,and the signal transmission is updated by determining whether the condition is violated by the designed triggering condition.If no criterion is violated,the last triggered signal will be kept constant through zero-order holder.An event-triggered device is added at the state feedback in order to effectively save the communication resources of the system.A sufficient condition to guarantee the asymptotic stability of the system is obtained by modeling the system as an extended closed-loop system with time delay through the defined estimation error.Numerical simulations verify the validity of the proposed scheme.Finally,the main work done in this paper is summarized,and the problems of the current research on repetitive control systems based on EID and the future development trend are pointed out,and the future research work is also prospected.