Research On Iterative Learning Control Algorithm Based On Two-Dimensional Model

Iterative learning control,as an important part of intelligent control field,is widely used in industrial processes.It improves system control performances through repeated learning and error correction,and completes the task of trajectory tracking.Traditional iterative learning control methods usually only consider the relative performances of static iterative learning controller in time domain,which leads to some shortcomings in algorithm design.System internal signals is considered to construct and update controller based on the two-dimensional model in this paper.According to the actual situation that the controlled object has obvious frequency-domain characteristics in engineering,the iterative learning controller is designed in frequency domain,and the convergence performances are studied,which can improve overall system performances.The convergence sufficient conditions of the control system are derived by linear matrix inequality.Finally,the effectiveness of the control algorithms is verified by a series of simulation tests,and the superiority of the proposed algorithms is verified by comparative tests.The main research work of this paper includes the following aspects:1 For linear discrete systems with different relative degrees,the control problem of dynamic iterative learning controller is studied in the time domain.Based on the two-dimensional system theory,a two-dimensional discrete Roesser model was established,using the theory of linear repetitive process stability to analyze the monotone convergence conditions of the control system with different relative degrees,the sufficient conditions for the existence of iterative learning controller are given in the form of linear matrix inequalities,and the results are extended to the norm uncertainty model.Finally,the numerical simulation and the simulation of the injection velocity in injection molding model are compared with the static controller respectively to verify the feasibility and superiority of the design scheme.2 For discrete linear systems with different relative degrees,the control problem of dynamic iterative learning controllers in the finite frequency domain is studied.For the control objects with zero relative degree and high relative degree,the dynamic iterative learning controllers in the finite frequency domain are designed,using the generalized Kalman-Yakubovich-Popov(KYP)lemma,the sufficient conditions for the existence of the controller and the gain matrix of the controller are given in the form of linear matrix inequalities,and the results are extended to the norm uncertainty model.Finally,the superiority and feasibility of such a control law are tested on a spring damping system and a gantry robot,including a comparative performance against a static law applied to the same robot,the feasibility and superiority of the proposed algorithm are verified.3 For linear continuous systems with zero relative degree,the P-type iterative learning control problem with pole constraints in the frequency domain is studied.Firstly,the two-dimensional continuous Roesser model is proposed in the time domain.Then,based on the generalized KYP lemma,the tracking performance of iterative learning control systems and regional pole constraints problems are analyzed.The sufficient conditions of existence for the P-type controller are derived in terms of linear matrix inequalities,which can guarantee the control performance of the system along the trial direction and the time direction,and the results are extended to the norm uncertainty model.Finally,the simulations for a typical actuator of tracking servo system prove that the design is effective and feasible.4 For linear continuous systems with high relative degree,the D-type iterative learning control problem with additional performance requirements in the finite frequency domain is studied.Within the scope of the limited frequency domain by using linear matrix inequalities are given in the form of a sufficient condition for the existence of the D-type iterative learning controller,a new iterative learning control algorithm is designed to meet specific additional performance requirements,added additional decision variables,at the same time reduce the conservatism of the algorithm,and with the existing several additional performance requirements of iterative learning control algorithm are compared.Finally,the superiority of the proposed algorithm is verified in the model simulation and numerical simulation of permanent magnet DC motor.5 For linear discrete systems,the PD-type iterative learning control problem in finite frequency domain is studied.Firstly,an integrated state feedback PD-type iterative learning control strategy is proposed in the frequency domain,and the state space model of the iterative learning process is derived.Combined with the stability theory of discrete linear repeated processes,the dynamic performance conditions of the control system in the frequency domain are obtained.Secondly,the robust control problem with norm-bounded uncertainty and convex polyhedral uncertainty are also considered.Finally,the simulation of the injection velocity in injection molding verified that the proposed methods in this paper are more effective than the P-type state feedback iterative learning control algorithm.