Nonlinear vibration control of cable net structures with bounded uncertainties

Abstract

The active vibration control of cable net structures by piezoelectric stacked actuators is the subject of the present work. The focus of this paper lies on the proposal of a nonlinear method to address the vibration problem for such structures in the presence of uncertainties. To this end, a cable net structure with integrated piezoelectric stacked actuators is considered. For the structure, a nominal model is derived through the finite element method, and an uncertain model is constructed on the basis of the nominal model by taking into consideration the uncertainties. Based on the established uncertain model, a nonlinear state feedback control is deduced through the Lyapunov stability theory. This control guarantees that every uncertain system response enters and remains within a certain neighborhood of the zero state after a finite interval of time. To demonstrate the superiority of the proposed nonlinear control, a linear control based on the linear quadratic regulator is presented for comparison. Displacement responses and control voltages of the uncertain system under an impulse excitation are simulated for both the nonlinear and linear control cases. It is observed that the nonlinear method is feasible and robust as it stabilizes the uncertain system to a smaller size of the region of ultimate boundedness. Besides, the nonlinear approach improves the performance of the uncertain system by reducing the vibration to a lower amplitude within a shorter time.