Optimal Control and Sub-Optimal Control for Single-Input Single-Output Deadbeat Repetitive Systems

Abstract

This paper discusses the repetitive control problem for a single-input, single-output linear digital system. The servo problem with periodic references signal and periodic disturbances is transformed into a regulator problem by using the deviation system of the augmented system. Then, the fixed-endpoint approach is applied, and the optimal control is obtained. Furthermore, the sub-optimal control which is more simple and practical than the optimal control is proposed. In both controls, the output follows the periodic reference signal without error within finite steps.