Robust higher order repetitive learning control algorithm for tracking control of delayed repetitive systems

A robust higher-order PID (proportional plus integral plus derivative)-type ILC (iterative learning control) algorithm is presented for tracking control of delayed nonlinear time-varying MIMO (multiple-input multiple-output) repetitive systems. A convergence proof is given in a more general case. When initial state bias exists, a repetitive ILC scheme (i.e. forward learning and backward learning) is proposed to make the algorithm more robust with respect to this bias. Simulation results indicate that the proposed method converges faster than previous methods. The effect of system delay (or even multidelays and time-varying delays) on the ILC convergence is very small. Examples are provided to demonstrate the efficiency of the proposed methods