Robust Nonlinear Forced Vibration Control of a Flexible Plate Based on Operator Theory

In this paper, robust nonlinear forced vibration control method based on operator theory for a flexible plate with piezoelectric actuators is proposed. In the interest of control effect from the piezoelectric actuators to a flexible plate determine the optimal position, the FEM(Finite Element Method) is used. The hysteresis nonlinearity of the piezoelectric actuators is expressed using P-I(Prandtl-Ishlinskii) model. The model of flexible plate is shown. In order to guarantee the stability of a nonlinear control system, the method of guarantee the stability based on the operator theory which is one of the nonlinear control system design approaches is shown. And an operator based method for removal of the disturbance is proposed. Finally, the validity of the designed control system by the simulation results is shown.