Simultaneous Optimization of Low-pass Filter and Controller in Robust Repetitive Control Systems

One problem with existing methods of designing repetitive control systems is that they cannot simultaneously optimize the parameters of a low-pass filter and a repetitive controller. This paper presents a method of doing that for a repetitive control system containing a class of uncertain plants. First, linear matrix inequalities for calculating the parameter of a low-pass filter are derived under the condition that the robust stability of the system is guaranteed. Next, the problem of designing a state-feedback repetitive controller that guarantees the robust stability of the closed-loop system is converted into an H_infin state-feedback design problem. Then, iterative algorithms for calculating the largest cut-off angular frequency of a low-pass filter and the gain of an H_infin state-feedback controller are presented. The algorithms produce a combination of parameters that yields the highest control precision under the condition that the robust stability of the system is guaranteed. Finally, the validity of the method is verified by a numerical example.