Optimal Control of Vibration Suppression in Flexible Systems via Dislocated Sensor~Actuator Positioning

In this study, we present a new controller design method that not only effectively suppresses vibration in fexible systems, but also has the ability to save control energy. The proposed method allows integrated determination of sensor/actuator locations and feedback gain by minimizing the sum of the integral flexible system energy and the integral control energy. Also, the cost function is characterized by an effective representation of control systems, and is determined via an efficient solution of the Lyapunov equation. The optimization problem is solved by a recursive quadratic programming algorithm. The feasibility of applying this method to a simple and flexible structure confirms the direct relationship between our optimization criterion and effectiveness in vibration suppression. Copyright © 1996 Published by Elsevier Science Ltd L Introduction The positioning of sensors/actuators has recently become a challenging task in controlling vibration in flexible systems, particularly since large, lightweight, lightlydamped structures are frequently used in current aerospace applications. Owing to the property of space distribution for flexible systems, determining the number and placement of control devices as well as feedback gain is inherently an integral part of controller design. Moreover, additional freedom offered by adjusting the placement of control devices can affect the control effect in addition to the feedback controller. Therefore, in this study, we develop an optimal controller that allows integrated determination of the placement of control devices and feedback gain to achieve the ultimate optimum desired performance in controlling flexible systems. Much research has centered on the problem of selecting optimal locations for sensors