Combined Feedback/Feedforward Active Control of Vibration of Plates with Active Constrained Layer Damping Treatments

In this paper, a finite element model of plates treated with ACLD treatments is developed based on the constitutive equations of elastic, piezoelectric, visco-elastic materials and energy approach. The damping behavior of visco-elastic layer is modeled by the complex modulus approach (CMA). The emphasis is concerned the simulation of feedback, adaptive feedforward and hybrid (combined feedback/feedforward) control systems on the vibration control of plates with ACLD treatments. The state space form of the dynamic system is derived and the modal reduction of state space model is performed to design an effective control system. After that, the optimal Linear Quadratic Gaussian (LQG) is considered as a feedback channel and the adaptive filtered-reference LMS is used as a feedforward channel. They can be utilized individually or in a hybrid way to suppress the vibration of plates/ACLD system. A case study regarding the disturbance rejection of a plates/ACLD system is researched. A broadband stochastic and a hybrid disturbance are considered and the feedback controller is used to control the vibration of the plates/ACLD system. The adaptive feedforward controller is also employed to cancel the effects of the periodic disturbance and hybrid disturbance on the control system at the output location. Finally, both controllers are joined together and result in a unified hybrid controller. The simulation results from individual and hybrid control strategies are demonstrated and evaluated. The results show that the hybrid controller improves the feedback performance and leads to an improved performance and convergence of the adaptive feedforward controller.