Robust performance repetitive control systems

This paper addresses analysis and synthesis of robust stability and robust performance repetitive control systems. The repetitive control design probl em is formulated as a standard feedback form in the lin ear fractional tran sformation form such that the standard numerical optimization software can be used to obtain the solution. The main idea of the robust repetitive cont rol system design lies in introducing a fictitious complex uncertainty to r eplace the long delay chain in the internal model of the repetitive control system. This drastically reduces the order of the augmented plant for cont roller synthesis and hence generates a low order compensator, which in conj unction with the pure delay renders a repetitive controller that can be imp lemented efficiently in real time. The proposed approach can be applied to both the continuous and discrete-time domain repetitive control design for unstable open-loop plant. Sufficient conditions for the robust stability an d robust performance repetitive control systems are presented. Conservatism analysis shows that the sufficient conditions become necessary when the pu re delay approaches infinity. The robust repetitive control is applied to a n electrohydraulic actuator for tracking periodic trajectories. Experimenta l results are presented to illustrate the design procedure and control syst em performance.