Research On Variable Gain Iterative Learning Control Of Nonlinear System

Iterative learning control is widely used in the trajectory tracking problem of controlled objects with repetitive motion characteristics.It uses the input and error information of previous batches to continuously modify the input signal of current batch.After enough batches,it can achieve accurate tracking.In practice,the controlled systems are generally nonlinear systems.Therefore,it is of great value to apply iterative learning control theory to tracking control of nonlinear systems.In the traditional iterative learning control research,the gain of learning law is mostly fixed and immutable constant,and the convergence speed of gain fixed system is also fixed.The initial parameters determine the operation of the system.The proposed variable gain learning law can make up for the shortcomings of traditional fixed gain and improve the dynamic regulation performance of the system.Therefore,for the object with nonlinear and time-delay characteristics,the variable gain iterative learning control can effectively solve the tracking problem of this kind of complex system,and further strengthen and improve the research on this aspect is very meaningful.This paper studies the variable gain iterative learning control of a class of nonlinear systems,and discusses the problems of state time delay and control time delay.The specific research content includes the following:(1)For a class of nonlinear systems that satisfy Lipschitz condition,based on the traditional fixed-gain iterative learning control law,using the advantages of PID control,a learning method in which the gain coefficient changes with time and batch is proposed.algorithm.First,the conditions for the system to meet the convergence are given.Secondly,the actual output of the system can effectively track the given curve after multiple iterations of learning using the operator lemma,and a rigorous theoretical proof is carried out.Able to ensure system convergence.The injection speed of the injection molding machine is modeled and simulated,and compared with the traditional fixed-gain algorithm,the advantages and effectiveness of the proposed control strategy are verified.(2)For a class of nonlinear systems that satisfy the Lipschitz condition,the learning law with variable gain coefficients is studied when there is a state delay problem.Using the expected output,expected control input and error information during system operation,a variable gain controller is designed.With the help of the operator lemma and inequality lemma,the convergence of the state delay system is proved,and the simulation experiment of the CSTR reaction temperature model with state delay is performed.The simulation results show that the algorithm is effective for the state delay system.(3)In this paper,the problem of a class of nonlinear systems with state delay and control delay is studied,and a variable gain PID type iterative learning control strategy with given lead is proposed.Firstly,the variable gain learning controller is designed by using the expected setting,expected control input and error of the system in the iterative learning process.Secondly,the convergence of the system is proved mathematically by using inequality lemma and operator lemma.Finally,the CSTR model is modeled and simulated to verify the feasibility of the proposed method,and the comparison with the fixed gain algorithm shows that the variable gain learning law has better dynamic regulation performance and faster convergence speed.