Active vibration control of smart structures using piezoelements.

摘要

Active vibration control of flexible structures using piezoelectric sensors and actuators is addressed in this thesis. The objective of this thesis is to find a simple and efficient active controller for vibration suppression of flexible structures, which is to be demonstrated experimentally.; The work begins with a modal method being used to derive the dynamic equations of flexural vibration of a flexible beam. The passive and active influences of the piezoactuators and piezosensors on the flexible beam are also derived in modal form. A state space modal model of the integrated flexible structure with bonded piezotransducers, i.e., smart structure, is then used to design the control system. A linear quadratic optimal regulator (LQR) is designed and implemented successfully in both simulation and experiment. Since piezoelements are very sensitive to noises, a linear quadratic Gaussian LQG compensator is introduced for noise rejection which performed very well. In order to observe and control each dynamic mode individually, an active modal controller is designed which can control individual low frequency modes separately using only rectangular piezotransducers. To find the optimum shape and location of the piezoactuators in the active control system, an optimization procedure is employed which provides simultaneous optimal shape and location of the distributed piezoactuators.; Although the modal modeling and control of the smart structure demonstrated satisfactory performance, this method is very dependent on a good dynamic model and simulation program to obtain the control gains. As an alternative to the modal method, the wave method is used in the second part of the thesis to obtain a distributed dynamic model of the system. A novel wave based model of the integrated smart structure is obtained which is then used in the control design. Using the local parameters of the system such as the length of piezotransducers, a local wave absorbing controller (LWAC) is designed in the frequency domain to suppress the flexural vibration. Since the expression of the controller in the frequency domain is nonlinear and very difficult to realize in practice, a time domain approximation of the controller is introduced which results in a parameter based controller, i.e., the control gains are obtained from a parametric formula without the need for any dynamic model or simulation program. To improve the performance of the wave controller, the global parameters of the system such as the length of structure and the positions of the piezoelements with respect to the boundaries are also taken into account, and a novel global wave absorbing controller (GWAC) is derived. The performance of the controller is substantially better than that of the LWAC. This performance is also compared with that based on the conventional optimal approach, and demonstrates performance similar to that of optimal controllers while being much simpler to design. Experimental results match quite well with simulation and the objective of this research: "design and implementation of a simple and efficient active control system for vibration suppression of flexible structures" is well met.