Infinite horizon optimal repetitive control of fractional-order linear systems

Abstract

This paper presents a linear quadratic regulator-based repetitive control algorithm for fractional-order linear systems. First, a new repetitive control configuration for fractional-order linear system is proposed that contains a dynamic compensator and a state-feedback controller. Next, using fractional variational principle, the analytical solution for optimal repetitive controller is presented and the parameters of both the feedback controller and dynamic compensator are designed simultaneously. For the case of infinite time horizon, and under assumption of being in the middle of the control process the algorithm has the same form as for integer order case. Furthermore, new tuning parameters are introduced to modify the algorithm when the system is not exactly at the middle of the control process. Finally, a numerical example demonstrates the validity of the proposed approach.