Fixed order dynamic compensation for the h2/H∞ benchmark problem

Abstract

This paper presents a robust fixed order compensator design for the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem. The design uses an approximate Loop Transfer Recovery (LTR) method to achieve performance robustness to unstructured uncertainty at the plant output. To provide robustness to the real structured uncertainty, the performance index is modified to include a penalty on the closed loop sensitivity dynamics. The formulation avoids the explicit introduction of the sensitivity states into the performance index, and thus, the formulation does not increase the overall dimension of the problem. A brief outline of the design procedure is as follows. First, full state gains are designed for the dual system which is the equivalent of designing a full order observer. Next, the loop characteristics at the dual system input are approximated with an observer canonical compensator. After the loop transfer functions is sufficiently recovered, then the penalty on the sensitivity dynamics is introduced. Finally the optimal gains are implemented in the dual compensator, which is the controller form. The implemented compensator ensured tracking performance and robustness to unstructured uncertainty as well as robustness to the structured parameter variations resulting from the uncertain spring stiffness.