H ∞ Optimal Repetitive Controller Design for Stable Plants

Abstract

The repetitive controller design problem is studied for stable plants in the framework of the H∞ optimal control. For a given nominal repetitive controller, first stability robustness is optimized by solving a finite dimensional H∞ control problem. Then the nominal design is modified in an optimal way so that the performance is improved while keeping the robustness level approximately the same. This problem is formulated as a two block H∞ problem involving a delay system and two weighting functions. The resulting controller can be implemented by adding a few blocks to the existing nominal design. An example is given to illustrate the numerical aspects of this approach.