Multi-loop control approach to designing iterative learning controllers

In this paper we consider convergence of iterative learning control (ILC) algorithms. We use a multiloop control interpretation of the signal flow in ILC to derive a necessary and sufficient condition for convergence of discrete-time, linear, time-invariant systems. We then use our multiloop approach to develop an iterative learning control algorithm that can converge in as few as four trials. The scheme uses an adaptive (in trial number) gain adjustment that does not have to be “tuned”. This is combined with the use of feedforward correction terms (in time) to produce the complete algorithm. A simulation illustrates the effectiveness of the strategy. The paper concludes with comments on how the multiloop approach can be used to address (i) higher-order ILC schemes for dealing with noise in the process and with initial state uncertainty (using a Kalman filter in trial number); (ii) ILC convergence for nonlinear and time-varying systems; and (iii) the adaptive gain adjustment rule