Two-step design method for robust repetitive control systems

We propose a design method for robust modified repetitive control systems without solving the mu synthesis problem using a two-step design method. The basic idea of the two-step design method is that if the modified repetitive control system is robustly stable, then the modified repetitive controller must satisfy the robust stability condition. The parameterization form of all robustly stabilizing controllers for the plant are obtained using an H-infinity problem based on either the Riccati equation or on a Linear Matrix Inequality. Using the free parameter of the parameterization, we can design robust modified repetitive control systems. The necessary condition for the existence of robust modified repetitive controllers is given. Using the proposed method, the limitation on the low pass filter in the repetitive controller that exists in the robust repetitive controller is clarified. A numerical example is used to illustrate the effectiveness of the proposed method.