The Parametrization of All Robust Stabilizing Modified Repetitive Controllers

Abstract

In this paper, we give the parametrization of all robust stabilizing modified repetitive controllers for single-input/single-output systems. The basic idea to obtain the parametrization of all robust stabilizing modified repetitive controllers is very simple. If the repetitive controller stabilizes the plant, then the repetitive controller must be included in the class of all robust stabilizing controllers for the plant. The parametrization of all robust stabilizing controllers for the plant, which is not necessarily modified repetitive controllers, are obtained by solving an H∞ control problem based on either the Riccati equation or on a Linear Matrix Inequality. The parametrization of all robust stabilizing controllers for the plant includes a free parameter, which is stable. That is, robust stabilizing modified repetitive controllers can be designed using the free parameter in the parametrization of all robust stabilizing controllers for the plant. Using this idea, we obtain the parametrization of all robust stabilizing modified repetitive controllers. The limitation on the low pass filter in the repetitive controller that exists in the robust repetitive controller is clarified explicitly. Finally, a numerical example is illustrated to show the effectiveness of the proposed parametrization.