An Optimality-Based Repetitive Control Algorithm for Discrete-Time Systems

In this paper, we first demonstrate that the zeroth- order hold discretization of a class of well-known continuous- time repetitive control algorithms can result in instability. Having highlighted the potential problem that discretization can pose to controller structures of this form, a new optimality-based repetitive control algorithm is developed for discrete-time systems. Under mild technical conditions on the plant, the algorithm will result in asymptotic convergence for an arbitrary $T$-periodic reference signal and an arbitrary discrete-time linear time-invariant plant. The algorithm has been practically applied to a nonminimum phase spring-mass-damper system. It is shown that it is capable of producing near perfect tracking within a very small number of trials. The robustness of the controller is established for this plant in terms of the bounds on the uncertainty that will allow the system to satisfy the Nyquist stability criterion. A zero-phase filter is designed and implemented. Experimental results illustrate how long-term performance can be maintained using the proposed method.