Abstract
LSDP (Loop Shaping Design Procedure) is one of the most promising design procedures in H∞ control theory. It has many special features except a problem that its central controller tends to have higher order. In this paper, we investigate some possibility on the existence of lower order controllers in the set of LSDP controllers. If our proposed conditions are satisfied, the order of controller is same as the total order of weighting transfer matricies. Confirming the validity of our result, we apply it to the robust vibration control of a flexible beam with an electromagnet as actuator and gyro sensor which can detects angular velocity of beam. In this case, our proposed conditions are satisfied and a second order controller is obtained. As the controller is in the set of LSDP controller, it has the almost same characteristics as the central controller which has 10th order. Using the Balanced truncation method, the lower limit is 6th order.
