Vibration control of a smart piezo beam via gain scheduling H? controller based on LPV model

Abstract

In this study, a gain scheduling H-infinity controller based on Linear Parameter Varying (LPV) model was designed and applied to suppress the first out of plane bending vibration of a variable parameter smart beam equipped with Lead-Zirconium-Titanium (PZT) patches. This paper also introduces a novel LPV modelling technique which defalcates the zeros of the system. The controller design was carried out in three successive steps. In the first step, the variable parameter model of the beam with an added mass at its free end can rotate through a micro servo motor was experimentally obtained. In the second step, an original LPV model including the variable parameter model was obtained. Finally, H-infinity controller with gain scheduling was designed on LPV model. The obtained controller was then used both for simulations and experimental verifications. It was shown that in response to parameter changes in the system, the proposed controller is capable of suppressing the beam bending vibrations by also exhibiting a robust performance. In practice, the proposed LPV controller design strategy can be transacted for vibration control of aircraft wings, the parameters of which vary according to various load conditions changing in time and therefore deeply affects the passive characteristics of the system of interest.