Seismic Vibration Attenuation of a Structural System Having Actuator Saturation with a Delay-Dependent H∞ Controller

Abstract

This paper deals with the design of state-feedback delay-dependent H-infinity controller for active vibration control problem of seismic-excited structures having actuator delay, L-2 disturbances and actuator saturation. First sufficient delay-dependent criteria are developed by choosing a Lyapunov-Krasovskii functional candidate for a stabilizing H-infinity synthesis involving a matrix inequality conditions. Then actuator saturation phenomenon is added to the controller design using LMI constraints. The sufficient conditions for designing such controller are obtained in terms of delay-dependent bilinear matrix inequalities (BMIs). To overcome nonlinear optimization problem involved in the delay-dependent conditions, a cone complementary linearization method is used to find a feasible solution set. Using proposed method, a suboptimal controller with maximum allowable delay bound, minimum allowable disturbance attenuation level under actuator saturation constraints can be obtained simultaneously by a convex optimization technique. A four-degree-of-freedom structural system subject to Kobe Earthquake excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay bound under actuator saturation constraints.