STABILITY OF ACTIVELY CONTROLLED STRUCTURES WITH ACTUATOR SATURATION

Because of the stochastic nature of earthquakes and limited capacities of actuators, it is conceivable that the actuators used for the contr ol of civil engineering structures may be saturated during strong eart hquakes. In this paper, the stability of actively controlled linear st ructures under a variety of popular control methods during actuator sa turation is investigated. Sufficient conditions to guarantee the asymp totic stability of the structure during actuator saturation are examin ed and discussed. These conditions involve the solution of a system of simultaneous linear matrix inequalities (LMI). A simple and efficient computer code to solve a system of LMI, based on the MATLAB LMI toolb ox, is presented for use by the readers. Based on sufficient condition s, a method for designing general controllers, that guarantee asymptot ic stability during actuator saturation, is presented. It is shown ana lytically that Lyapunov controllers, H-infinity-type controllers, and sliding-mode controllers are asymptotically stable during actuator sat uration. For multi-degrees-of-freedom (MDOF) systems using pole assign ment and linear quadratic regulator (LQR) controllers, it has been sho wn through extensive simulations results that: (1) asymptotic stabilit y of structures is more likely to be guaranteed for low-gain controlle rs than for high-gain controllers; (2) adding active damping to the st ructure is much more beneficial than adding active stiffness, in terms of asymptotic stability; and (3) asymptotic stability can be guarante ed for quite high levels of added active damping to various modes of t he structure. Further extensive simulation results demonstrate that st atic output feedback controllers using only velocity feedback are alwa ys asymptotically stable in the range of practical applications. Likew ise, for static output controllers using collocated sensors, the regio n of asymptotic stability is quite large.