Iterative Learning Control For Distributed Parameter Systems With Moving Boundaries

Distributed parameter systems with moving boundaries refer to the systems in which the boundary of the space domain depends on time changes.The models of such systems have a wide range of application backgrounds in fluid mechanics,chemical reaction processes,wave equations,industrial processes,etc.,which are different from the traditional distributed parameter system of fixed space domain.This class of system usually has time-varying characteristics,which will increase the difficulty of the control problem of moving boundary distributed parameter systems.And it is important to design a controller with high control accuracy and better observation performance for this type of system.Research questions.Iterative Learning Control(ILC)is an intelligent control method that repeatedly corrects unsatisfactory input signals according to the tracking error of the system,so that the system input is continuously updated along the iterative axis,and finally the actual trajectory of the system completely tracks the desired trajectory of the system.,And has the advantages of high tracking accuracy,easy design of the algorithm and simpler controller structure.This paper researched the output tracking problems of three different types of distributed parameter systems with moving boundaries,and designs different iterative learning control algorithms.And the convergence of the system is analyzed through rigorous mathematical theories,and the designed algorithms are verified by corresponding numerical simulations.The main research content includes the following three parts:(1)A class of linear parabolic distributed parameter systems with moving boundaries are researched.Then,an open-loop P-type iterative learning control algorithm is designed for the output tracking problem,and the convergent conditions for tracking error are obtained by using the principle of compressed mapping and Bellman-Gronwall inequality.,And the effectiveness of the algorithm is verified by numerical simulation.(2)The output tracking problem for a class of nonlinear parabolic distributed parameter systems with time-varying boundaries in space domain is discussed.Then,considering the large error of initial value reset,a closed-loop variable gain accelerated iterative learning control algorithm is designed.Through strict theoretical analysis,the condition of tracking error convergence is given,and at the same time,it is proved that the defined tracking error converges in the positive direction of the iteration axis in the sense of the~2norm,and when the number of iterations k??,the tracking error converges to zero.Finally,the effectiveness of the closed-loop variable gain accelerated iterative learning control algorithm is verified by numerical simulation.(3)Considering a class of second-order hyperbolic distributed parameter systems with moving boundary characteristics,research is carried out for the output tracking problem of the system,and a high-order iterative learning control algorithm is designed.Through rigorous theoretical analysis,sufficient conditions for the convergence of the system output tracking error are given,and the effectiveness of the high-order iterative learning control algorithm is verified by numerical simulation.