A Parameter Optimization for the Internal-Model Repetitive Controller based on Minimum-Variance Properties

Discrete-time repetitive controllers have traditionally been motivated with a purely deterministic problem formulation. Trade-offs for robustness, settling time and stochastic performance were at the cost of asymptotic regulation against a purely periodic disturbance. In this paper, we establish a connection between optimal prediction-based and repetitive control. We show that the simple modified repetitive control algorithm may be a good approximation of minimum variance control. Indeed, for stable plants, this control law is minimum-variance control for a particular stochastic disturbance model. This minimum-variance interpretation of repetitive control leads to a parameter optimization. Control law parameters are optimized to minimize, subject to stability and robustness constraints, the mean-squared output of a system driven by inputs with both deterministic and stochastic components. The result is a simple design procedure which is experimentally verified on a track curvature correction servo for a digital video production recorder.