A Wavelet-Based Approach for Dynamic Control of Intelli-Gent Piezoelectric Plate Structures with Linear and Non-Linear Deformation

Abstract

Piezoelectric devices present an important new group of sensors and actuators for active vibration control systems [1, 2, 3, 4]. Indeed, this technology allows to developing spatially distributed devices, which requires special control techniques to improve the dynamical behavior of this kind of smart structure. Especially to geometrically nonlinear plates with piezoelectric sensing and actuating, there is a little of numerical results in the literature to quantitatively analyze the behavior of the vibration control of the structures [5, 6, 7]. This paper is concerned with the mathematical model of this kind of vibration control for a geometrically nonlinear plate with piezoelectric sensors and actuators by means of the scaling function transform of the wavelet theory [8, 9]. Based on the generalized Gaussian integral to the scaling function transform, an explicit formula or algorithm of identification for the deflection of plates from the measured electric signals, i.e., electric charges and currents, on piezoelectric sensors is established. When a control law of negative feedback of the identified signals is employed, the applied voltages on piezoelectric actuators are determined by the wavelet Galerkin method. Finally, some typical examples, e.g., beam-plates with either small deflection or geometrically nonlinear deformation, of simulation are taken to show the feasibility of this control approach. It is found that this control model may auto-avoid those undesired phenomena of control instability generated from the interaction between measurement and controller with spilling over of high-order signals since the scaling function transform is low-pass.