Finite-Time Vibration Control of Earthquake Excited Linear Structures with Input Time-Delay and Saturation

Abstract

The problem of finite-time vibration control of earthquake excited linear structures with input time-delay and saturation is concerned in this paper. The objective of designing controllers is to guarantee the finite-time stability of closed-loop systems while attenuating earthquake-induced vibration of the structures. First, based on matrix transformation, the structural system is described as a state-space model, which contains actuator saturation and input time-delay. Then, based on a Lyapunov functional and finite-time stability analysis method, some sufficient conditions for the existence of saturationtolerant finite-time vibration-attenuation controllers are obtained. By solving these conditions, the desired controllers can be obtained for the closed-loop system to be finite-time stable with a prescribed level of disturbance attenuation. It is shown by the simulation results that compared with some Lyapunov asymptotic stability results, finite-time stability control can result in better state responses. Furthermore, saturation-tolerant controller can result in a much lower controller gain than the ones without considering actuator saturations.

Vibration-Attenuation Controller Design for Uncertain Mechanical Systems with Input Time Delay

“…It is worthy to point out that the input time delay ( ) considered in this paper is not a constant. Thus, the results obtained in this paper should be less conservatism and more fit for using in practical systems than those achievements obtained by the systems with constant time delay (some results about constant time delay can be found in [12,[15][16][17][18] and those references therein).…”

“…The mechanical systems with time-varying input delay are described as [3,12,15] ( ) +̇( ) + ( ) = ( − ( )) .…”

“…On the other hand, time delay or transportation lag is inevitable in many practical systems, such as chemical processes, long transmission lines, and pneumatic and hydraulic systems [10][11][12]. For mechanical systems, unavoidable time delays always appear in the controlled channel, particularly in the digital controller as it carries out the calculations associated with complex sophisticated control law and in sensors and actuators hardware such as large hydraulic actuators.…”

“…Based on LMI technique, the delayed ∞ control for an offshore steel jacket platforms subject to external wave force was presented in [17]. Based on Lyapunov theory, the problem of finite-time vibration control of earthquake excited linear structures with input time-delay and saturation was investigated in [12]. Moreover, uncertainty is another problem that need to be considered [18,19].…”

μ-Synthesis Controller Design for Seismic Alleviation of Structures with Parametric Uncertainties

“…As buildings become higher, structural stability and strength are challenged and cannot be guaranteed only by high quality materials. Therefore, the need for structural vibration control (SVC) techniques for seismic-excited or wind-excited structures becomes further important [1][2][3].…”