Modeling, Optimization And Vibration Control Of Piezoelectric Structures

The piezoelectric structures are extensively used and have promising prospects. This dissertation is concentrated on active vibration control(AVC) of flexible beam- and plate-type structures with piezoelectric actuators and sensors. And general theory involving three main aspects of AVC are represented, namely modeling, optimization and control methods.Firstly, a higher order model of electrical potential filed is proposed to accurately describe the nonuniform distribution of electric filed through the thickness of piezoelectric layers. And also a higher order plate theory is adopted to model the displacement filed of composite beams and plates. Subsequently, the equations of coupled piezoelectric-mechanical dynamics are developed using finite element method. And then freedoms of electric field intensity are accurately condensed to make for more efficient equations. Numerical examples validate the accuracy of the proposed model.Then, three kinds of optimization problems are investigated. The first concerns the optimal thickness and embedding position of a piezoelectric actuator in the host beam or plate. And a constrained optimization problem is established aiming at maximizing the bending curvatures. The second concerns the optimal placement of actuators and sensors along a beam or over a plate for coupling-mode control applications. A criterion based on controllability and observability is presented which takes into account the distribution information of disturbances and performance objectives. The third problem is to design optimal modal actuators and sensors for independent modal control applications. And the objective functions are formulated taking aid at maximizing robustness and minimizing the spillover caused by residual modes.Subsequently, robustμcontrol theory is implemented in vibration control. An approach for modeling multiple uncertainties is presented, including modal parameter uncertainties, unmodeled dynamics and model errors of sensors and actuators. A generalized framework is then built for the synthesis of robust vibration controllers. Numerical simulations of vibration control of a clamped beam demonstrate the robust stability and performance of resultant controller.And finally, the independent modal space control method is combined with the variable structure control method. In respect that the main difficulty in actualization of independent modal control is the destabilization caused by the residual modes, two strategies, namely linearly-delayed switching and adaptive amplitude of control inputs, are proposed to avoiding destabilization of the residual modes while suppressing vibration of the controlled modes. Applications to the vibration control of a simply supported plate show the effectiveness of the proposed strategies.