Optimal placement of the sensors for Static Output Feedback of fluttering plates in the supersonic flow

Abstract

The widespread use of lightweight and flexible structures in industries such as aerospace and the increasing use of thin plates in these structures, which are easily fluttered and unstable in rapid air currents, make the use of active and inactive flutter control methods inevitable. In the present study, by examining the governing equations and employing SOF (Static Output Feedback) method, we have tried to position the vibration sensors to get the closest performance to the LQR controller. To do this, a rectangular plate exposed to supersonic current is considered. A piezoelectric patch is used to control the vibrations. A rectangular plate exposed to supersonic current is considered. A piezoelectric patch is used to control the vibrations. Von Karman thin plate theory and Mindlin moderately thick plate theory are used for simulating the plate. The first-order piston theory is used to model the airflow. The equations of motion are obtained using the Lagrange method and the displacement field approximation by finite power series. Then, a criterion for finding the points whose displacement feedback combination can provide the closest control performance to the LQR controller is presented. Finally, the performance of the obtained criterion has been evaluated and confirmed by numerical simulation. The results show that the plate's flutter can be effectively suppressed at speeds beyond twice the critical velocity, feeding back a specific combination of certain points' displacements. The results show this method presents a performance comparable to the LQR controller, despite removing the state estimator.