Boundary control of a thin rectangular plate with clamped-clamped-clamped-free boundary conditions

Abstract

This paper investigates a boundary control aiming at vibration suppression for a Kirchhoff plate with clamped-clamped-clamped-free boundary conditions. We use the deflection, deflection rate, slope, and slope rate at the free edge as feedback signals and show that the closed-loop system is marginally stable by using the Lyapunov's direct method. Numerical simulations are carried out to demonstrate the performance of vibration suppression of the proposed controller. The simulation results illustrate that the boundary controller with relatively small feedback gains can suppress the vibration including high order vibration modes. In contrast, the boundary controller with extremely high gains changes the mode shapes of the closed-loop system and deteriorate the controller performance.