Vibration control of a smart piezo beam by using the gain scheduling h∞ controller based on LPV model

In this study, the effectiveness of a PID controller designed by weighted geometric center (WGC) method has been investigated to suppress the first out of plane bending vibration of a variable parameter smart beam equipped with Lead-Zirconium-Titanium (PZT) patches. Besides, a gain scheduling H∞ controller based on Linear Parameter Varying (LPV) model has been designed and applied. This study also introduces a novel LPV modelling technique which defalcates the zeros of the system. The mentioned robust controller design has been 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 has been experimentally obtained. In the second step, an original LPV model including the variable parameter model has been obtained. In the last step, H∞ controller with gain scheduling has been designed on LPV model. The obtained controller has been then used both for simulations and experimental verifications. It has been 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. Finally, the controller and the sensor output data obtained by applying the designed controller to the system have been taught to the artificial neural network in Matlab / Toolbox and the angle estimation of the servo arm mechanism integrated at the end of the beam has been performed both simulatively and experimentally. 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.