Active Vibration Control of Plate Partly Treated with ACLD Using Hybrid Control

Abstract

A finite element model of plate partly treated with ACLD treatments is developed based on the constitutive equations of elastic, piezoelectric, viscoelastic materials and Hamilton’s principle. The Golla-Hughes-Mctavish (GHM) method is employed to describe the frequency-dependent characteristics of viscoelastic material (VEM). A model reduction is completed by using iterative dynamic condensation and balance model reduction method to design an effective control system. The emphasis is concerned on hybrid (combined feedback/feedforward) control system to attenuate the vibration of plates with ACLD treatments. The optimal linear quadratic Gaussian (LQG) controller is considered as a feedback channel and the adaptive filtered-reference LMS (FxLMS) controller is used as a feedforward channel. They can be utilized individually or in a hybrid way to suppress the vibration of plate/ACLD system. The results show that the hybrid controller which combines feedback/feedforward together can reduce the displacement amplitude of plate/ACLD system subjected to a complicated disturbance substantially without requiring more control effort. Furthermore, the hybrid controller has more rapid and stable convergence rate than the adaptive feedforward FxLMS controller. Meanwhile, perfect robustness to phase error of the cancellation path in feedforward controller and the weight matrices in feedback LQG controller is demonstrated in proposed hybrid controller. Therefore, its application in structural engineering can be highly appreciated.