A programme of vibration control to variable thickness plates with piezoelectric sensors and actuators based on wavelet theory

摘要

This paper is to present a numerical program of dynamic control for suppressing external disturbance to variable thickness beam-plates with sensors and actuators of piezoelectric layers on/in the structures using the scaling function transform of the Daubechies wavelet theory for approximation of functions. After the generalized Gaussian integral is applied to the scaling function transform, an explicit expression of identification of deflection configuration of the structures is expressed by the electric charge/current signals measured from the piezoelectric sensors. When a control law of negative feedback of the identified deflection and velocity signals is employed, the wavelet Galerkin method or wavelet weighted residual method is used to determine control voltage applied of the piezoelectric actuators. Due to that the scaling function transform is like a low-pass filter which can automatically filter out high-order signals of vibration or disturbance from the measurement and the controller employed here, this coontrol approach does not lead to the undesired phenomenon of control instability that is often generated in a control system and caused by the spilling over of high-order signals from measurement and controller if no special technique is used in the control system. Some numerical simulations are carried out to show the efficiency of the proposed approach.