Research On Iterative Learning Control Of Uncertain Discrete Repeated Processes

For systems with repeated operations such as robotic arms,it is often necessary to complete the trajectory tracking problem within a limited time,and iterative learning control is one of the effective methods to solve such problems.In the process of studying iterative learning control,factors such as nonlinearity,time delay and uncertainty bring difficulty to the iterative learning control algorithm.Therefore,the influence of these factors needs to be considered in the system,especially considering the existence of uncertainty in the system.It can more realistically describe the changes of actual system parameters and the effects of various disturbances.This paper mainly discusses two kinds of uncertainties,one is the multi-cell uncertainty in the system,and the other is the norm uncertainty in the system.At the same time,since most of the actual systems work in the limited frequency domain,it is considered that the stability of the system can be well reduced by considering the stability of the system in a limited frequency domain.In this paper,based on the stability theory of repeated processes,the finite frequency domain and reliable stability problems of iterative learning control are discussed respectively for linear discrete uncertain systems and nonlinear uncertain systems.The research contents of the thesis are as follows:(1)For systems with polytopic uncertainty,consider the case of state delays in the system.By designing a static iterative learning controller,the system is converted into an equivalent repetitive process,discussing along the time axis and batch,and the stability criterion of the repeated process and Kalman-Yakubovich-Popov(KYP)lemma are given to the sufficient conditions for the stability of the system in the finite frequency domain.Finally,the finite frequency domain design algorithm is verified by the simulation.(2)Based on the research of static iterative learning control method,the dynamic iterative learning controller is further designed to transform the system into a polytopic uncertainty repetitive process with multiple time delays.The stability conditions of the system in the high frequency,intermediate frequency and low frequency range are given by the linear matrix inequality,and ensure the tracking performance of the system under multiple time delays,finally verify the effectiveness of the dynamic iterative learning control method and improve the convergence speed of the tracking error system.(3)A class of linear discrete iterative learning control problems with norm uncertainty and existence state time delay are studied.A Proportional Differential(PD)-type iterative learning controller is designed in a finite frequency domain to convert the studied system into two subsystems.The parallel form is then used to discuss the stability conditions of the system in the finite frequency domain by KYP lemma.Finally,the validity of the proposed PD-type iterative learning control law is verified by simulation,and the dynamic performance of the system is further improved.(4)The problem of iterative learning fault-tolerant control for a class of discrete nonlinear discrete processes with norm uncertainty in the presence of unknown faults in the actuator is studied.By designing iterative learning fault-tolerant control law and defining the mixed Lyapunov function based on batch axis and time axis,the stability of the system under normal and fault conditions is discussed respectively,and the existence of robust fault-tolerant controller is given in the form of linear matrix inequality.Finally,the method is applied to the single-rod manipulator system simulation to verify the effectiveness of the proposed faulttolerant control method.