Minimum order-controller design via plant order reduction by using singular perturbation

Abstract

In this thesis is studied how to design the minimum order-controller. The order of plant is firts reduced by using the singular perturbation and then the minimum-order controller is deigned for the reduced-order plant.The procedure of the singular perturbation can be expressed as follows : first, the state space of the high-order plant is transformed to the balanced realization. And then, the balanced staet varisbles are devided into the slow and fast modes based on the Hankel singular values. The Small hankel Singular values are as ast mode, otherwise are as the slow mode. The reduced-order plant can be obtained by setting the velocity of the fast mode equal to zeros. furthermore, the necessary conditions for stability of the reduced-order plant and the upper bound of the reduction eror in the H infinite norm are derived. Finally, the necessary of sufficient conditions for the existence of admissible comtroller is discussed. to verify the performence of the minimum-order controller, it is applied to aflexible structure having 30th order. Inthis case, the order of the reduced plants is 11, so the orer controller is 11