Robust Design of Uncertain Repetitive Control System

This paper presents a coordinated design method for repetitive control systems with dynamic uncertainties. The equivalent-input-disturbance (EID) method is applied to improve the control performance of aperiodic disturbances or disturbances with different periods from repetitive control. By the two-degrees-of-freedom (2-DOF) characteristics of an EID-based control system, the reference tracking and disturbance rejection performance are mainly determined by the outer loop and inner loop, respectively. The separation theorem is used to simplify the system design. To be specific, the linear matrix inequality (LMI) technique and optimal control are used to find the gains of the state-feedback controller and state observer, respectively. Then, a necessary and sufficient condition is derived to ensure the robust stability of the closed-loop repetitive control system. Further, the design algorithm of the system is also given. Lastly, a simulation validates the developed method.