A LQR Controller Design for Active Vibration Control of Flexible Structures

This paper demonstrates an active vibration control system of flexible structures by using piezoelectric sensors and actuators. A set of vibration control equations, sensing equations and actuating equations are derived through using the modal theory for piezoelectric flexible structures, then the model is converted into the state space form. With recent developments in sensors/actuators technologies, many researchers have concentrated on control methods for suppressing vibration of the structures using smart materials such as piezoelectric transducers (PZT). In this paper, two piezoelectric patches are collocated on both sides of the same position of the structure which used as modal sensors and actuators, and the optimal location of them is ascertained by the function of displacement deflection, a LQR controller is designed based on the independent mode space control techniques to suppress the vibration of the system. Finally, the paper takes a piezoelectric cantilever beam as an example, and gives the control simulation results which demonstrate the effectiveness of the method in this paper.