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 flexible systems, but also has the ability to save control energy. The proposed method allows integrated determination of sensor/actuator location 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.