An adaptive PID‐type iterative learning controller for nonlinear systems with non‐repeatable control tasks

Abstract

To deal with iterative learning control of nonlinear systems with non‐repeatable control tasks, an adaptive PID‐type iterative learning controller is presented in this paper. The control structure is constructed based on a time‐varying boundary layer so that the initial state error problem can be solved and possible undesirable chattering behavior can be removed. The PID‐type iterative learning controller is designed by using the fact that a PID controller can be used as an approximator for an optimal controller in a compact set. An error equation is derived to represent the relation between the control input and system tracking error. Since the optimal PID gains for the best approximation are in general unavailable, the control parameters are tuned between successive iterations to ensure internal stability and error convergence. Under this adaptive PID‐type iterative learning controller, the referenced trajectory is allowed to be iteration‐varying which means that it is not required to be the same at each iteration. It is shown that all the adjustable parameters and the internal signals remain bounded for all iterations. Furthermore, the norm of tracking error vector at each time instant will asymptotically converge to a tunable residual set.