Preview Repetitive Control Of Linear Uncertain Discrete Time-Delay Systems

The essence of repetitive control is internal model control.The time delay link can be integrated into the augmented system through state space description and promotion techniques,which can effectively solve the problem of periodic external excitation signal control,which means that periodic signals can be accurately tracked or suppressed.Preview control can use the future information of the desired target to reduce system disturbances caused by external interference without changing the dynamic structure of the closed-loop system,and then the tracking stability of the system can be improved.For high-performance servo systems,the existence of time lag cannot be ignored.Based on the existing research results of preview control and repetitive control,this paper combines the two control methods for several types of uncertain linear discrete time-delay systems,and studies the design of preview repetitive controller(PRC)and its stability analysis.The specific research content is as follows:(1)The guaranteed performance preview repetitive control of uncertain linear discrete-state time-delay systems.Aiming at a class of polynomial uncertain discrete systems with state time delays,a guaranteed performance repetitive controller including preview information modules is designed.First,the positive feedback delay link is introduced into the forward channel to form a high-precision feedback control system.The L-order difference operator and discrete boosting operation are used to build an augmented error system that has no state delay but incorporates preview future information.,The design problem of guaranteed performance PRC can be transformed into the problem of output feedback adjustment of the research system.The stability conditions of the system and the specific equations of the controller can be determined by the parameter-related Lyapunov second method and the linear matrix inequality(LMI)processing method,and a new PRC system structure block diagram is designed.(2)Preview repetitive control of uncertain linear discrete input time-delay systems.For a type of discrete-time system with input delay,first use the state translation method to integrate the state quantity in the augmented error system with the preview target value information,and replace the input delay term with a variable to obtain a formally no time delay Augmented system.The rank criterion is used to obtain the conditions for the existence of the preview repetitive controller,and based on the idea of preview feedback,a repetitive controller with both preview compensation and time delay compensation functions is obtained.(3)Preview repetitive control of time-varying uncertain linear discrete-state time-delay systems.For a class of time-varying uncertain discrete systems with state delays,PRC based on LMI is designed.The properties of the difference operator are used to fuse the future information of the target value and the output error information into the augmented system.On this basis,a discrete repetitive controller is introduced to improve the tracking accuracy of the system.The Lyapunov stability theory and the flexible use of the LMI method are used to provide a feasible strategy for solving the controller parameters,and then the PRC of the original time-delay system is obtained.