Wavelet control model of suppressing beam plate vibration with piezoelectric sensors and actuators

Abstract

A dynamic control model of suppressing external disturbance to beam-plates with piezoelectric sensors and actuators is developed by means of the scaling function transform of the Daubechies wavelet theory. By virtue of this new mathematical tool, an explicit formulation of identification of deflection configuration is expressed in terms of electric charge/current signals measured from piezoelectric sensors. After 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 a distribution of 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 model does not lead to those undesired phenomena of control instability which is often appeared in a control system and caused by the spilling over of high-order signals from measurement and controller if no special technique is taken in the control system. Finally, a numerical simulation is carried out to show the efficiency and ability of the control program proposed in this paper. It is found that this control model is more efficient than a control program of convection to the example.