Active Vibration Control of Structures Subject to Parameter Uncertainties and Actuator Delay

Abstract

This article presents a robust H∞ controller design approach for active vibration attenuation of structures considering parameter uncertainties and time delay in control input. The parameter uncertainties dealt with belong to the polytopic type, and are assumed to be variations of the structural stiffnesses and damping coefficients. The time delay is an uncertain time-invariant with known constant bound. In terms of the feasibility of certain delay-dependent matrix inequalities, both state feedback and static output feedback controllers can be designed. To overcome the bilinear matrix inequality problems involved in the delay-dependent conditions, a genetic algorithm is used to find feasible solutions, after which use is made of the solvability of linear matrix inequalities. The performance of the presented approach is demonstrated by numerical simulations on the vibration control of a building structure subjected to seismic excitation. It is confirmed that the controllers designed by this method can effectively attenuate the structural vibration and ensure system stability even when there are parameter uncertainties and actuator delay.