l1-Optimal Robust Controller Design for Discrete Repetitive Processes

Abstract

We consider controller design to minimize the impact of unknown, bounded input disturbances acting on the class of unit-memory discrete repetitive processes. This class of systems includes the well-known iterative learning control systems as a special case. Focusing, with no loss of generality, on stable systems, we adopt the supervector formulation of ILC to develop a matrix fraction model of the discrete repetitive process. We then give a Youla parametrization of all stabilizing controllers for the plant, which in turn is used to define a model-matching problem. To minimize the effect of l(infinity) input disturbances, we pose and solve a multiple-input, multiple-output l(1)-optimal control problem. We consider controller designs for: (1) the case of arbitrary discrete repetitive process controllers and (2) the case of discrete repetitive process controllers with explicit integrating action in iteration to ensure constant reference tracking. Analysis shows that the best discrete repetitive process controller for both cases is first order in iteration and can achieve arbitrarily small disturbance gain, at the expense of high-gain feedback in the controller. Further, the solutions in each case produce a finite impulse response system between the disturbance and the output, with the disturbance attenuation gain appearing in the current cycle feedback terms and not in past cycle feedback terms. Results are seen to reduce to previously established results for the iterative learning control case when repetition-to-repetition output coupling is removed. An example illustrates the concepts in the paper.