Vibration control of variable thickness plates with piezoelectric sensors and actuators based on wavelet theory

An approach of dynamic control for suppressing external disturbance to variable thickness beam plates with sensors and actuators of piezoelectric layers on/in the structures is proposed in this paper using the scaling function transform of the Daubechies wavelet theory for approximation of functions. By means of the generalized Gaussian integral to the scaling function transform, an expression of identification of deflection configuration of the structures is explicitly formulated by the electric charge/current signals measured from the piezoelectric sensors. After a control law of negative feedback of the identified deflection and velocity signals is chosen, the wavelet Galerkin method or wavelet weighted residual method is used to determine control voltage applied on 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 control 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 interaction between the measurement and the controller if no special techniques is used in the control system. Finally, a numerical simulation is carried out to show the efficiency of the proposed approach. (C) 2000 Academic Press.