A discrete-time design of robust iterative learning controllers

A simple discrete-time design of robust iterative learning controllers taking account of the transient behavior as well as the uncertainty of a plant is proposed. Using the impulse response sequence of a plant, a simple finite-dimensional formulation of the problem is given. Assuming that a nominal impulse response sequence is given, a design based on the minimization of a quadratic performance index that can be regarded as a measure for the transient performance is proposed. The effect of the error in the impulse response data is analyzed. It is shown that an excessively high-order controller is not robust in the sense that the error severely deteriorates the transient performance. To obtain a robust controller with a reasonable order, a design based on a probabilistic modeling of the error in the impulse response data is proposed. The controller is obtained by minimizing an averaged quadratic performance index. Simulation examples are presented to illustrate the effectiveness of the proposed methods