Optimal Gains of Iterative Learning Control with Forgetting Factor

In order to solve the optimization problems of convergence characteristics of a class of single-input single-output (SISO) discrete linear time-varying systems (LTI) with time-iteration-varying disturbances, an optimal control gain design method of PID type iterative learning control (ILC) algorithm with forgetting factor was presented. The necessary and sufficient condition for the ILC system convergence was obtained based on iterative matrix theory. The convergence of the learning algorithm was proved based on operator theory. According to optimization theory and Toeplitz matrix characteristics, the monotonic convergence condition of the system was established. The accurate solution of the optimal control gain and the relationship equation between the forgetting factor and the optimal control gains were obtained according to the optimal theory which ensures the fastest system convergence speed, thereby reaching the end of the system convergence improvement. The convergence condition is weaker than the known results. The proposed method overcomes the shortcomings of traditional optimal control gain in ILC algorithm with forgetting factor, effectively accelerates the system convergence speed, suppresses the system output track error fluctuation, and provides a better solution for LTI system with time-iteration-varying disturbances. Simulation verifies the effectiveness of the control algorithm