Controller Reduction by the Block Balanced Realization with Frequency-Weightings for μ-Controllers

Abstract

The robust controller has good characteristic which can deal with disturbances and model errors. Especially μ-synthesis is a design method for the tradeoff between performance and robust stability, removing conservativeness due to unstructured singular values. We called the controller obtained by this method a μ-controller. However, it has the higher order generally. From a standpoint of cost and reliability, it is preferred that its order is reduced, which causes the degradation of the closed-loop performance. In order to decrease the degradation, it is necessary to take account the closed-loop configuration in the reduction process. For it, the authors developed the block balanced realization method in H_∞ control. In this paper, we use the scaling matrix D obtained by the D-K iteration as frequency weights for the block balanced realization method. A numerical example is given to illustrate the effectiveness of our method.