Modeling, Parameter Identification And Active Vibration Control For Piezoelectric Flexible Structures

The research is concentrated on the modeling analysis and active vibration control for piezoelectric flexible structures in this dissertation. The new methods are developed for model reduction and modal parameters identification in Chapters 2 and 3. Robust vibration control laws are designed for flexible structures with either model uncertainties or non-linearity in Chapters 4 to 7. The dissertation consists of the following six parts.1. For flexible structures with multi-input and spatially distributed output, the contribution of modes to the dynamic response of systems may change with the location of piezoelectric actuator patches and the ability of actuators to control vibration modes has to be taken into account in developing a relatively low-order dynamic modal equation. Mode spatial norms, serving as a measure of the intensity of modes to system response, are used to pick relatively important modes for piezoelectric flexible structures. The simulation result shows that the low-order model obtained by using mode norms, which keeps relatively important modes, is the better approximation of the original system than that of direct mode truncation, and is helpful to suppress the vibration of structures better.2. The method of modal analysis for piezoelectric flexible structures using wavelet transform is introduced. The reasons why Morlet wavelet is attractive for analyzing signals that are generated by dynamical vibration systems are given, although there are a multitude of wavelets that could be used. Based on the characteristics of transient responses of vibration system and Morlet wavelet, a family of wavelet functions are introduced and used in the parameter identification of modal frequencies and mode shapes for piezoelectric flexible structures. The simulation results are straightforward and satisfactory.3. The linear fractional representation is developed for flexible structures with piezoelectric material as actuators and sensors, taking into account uncertainties due to modal parameters variation and un-modeled residual modes. Based on Linear matrix inequality, the vibration control problem with conflicting performance specifications, such as robust stability, damping ratio and decay rate requirement, disturbance rejection, actuator saturation constraints and so on, is converted into an linear convex optimization problem. The results show that the modal-based multi-objective vibration control law can suppress the low-frequency modes without exciting the high-frequency...