2B15 Semi-active Vibration Control of Smart Structures with Sliding Mode Control

Abstract

In this study, a semi-active vibration suppression system comprising piezoelectric elements is developed for flexible structures. The vibration suppression system comprises a cantilevered beam with bimorph piezoelectric ceramic tiles shunted by an RL electrical circuit with a switch. A general design method for vibration suppression of the beam is theoretically analyzed using mode analysis, wherein it is assumed that the piezoelectric elements are sufficiently thin and do not change the mode shape of the beam. With this assumption, the vibration suppression system for the beam is designed by tuning the optimal resistance and inductance parameters of the shunted RL network. In this paper, we propose a semi-active vibration control law to improve the damping effect while maintaining the stability of the passive control system. The proposed control law is similar to a sliding-mode control that accelerates the convergence of the system by using switching functions. As an example, numerical simulations have been performed for a cantilevered beam. This study shows that the resonant circuit functions as a type of a dynamic damper for mechanical systems and that sliding-mode control is very effective in damping the multi-mode responses. The results of the numerical simulations show that the semi-active vibration control system is practically more effective in damping vibrations than the passive control system.