Stability of a Lyapunov Controller for a Semi-active Structural Control System with Nonlinear Actuator Dynamics

Abstract

We investigate semi-active control for a wide class of systems with scalar nonlinear semi-active actuator dynamics and consider the problem of designing control laws that guarantee stability and provide sufficient performance. Requiring the semi-active actuator to satisfy two general conditions, we present a method for designing quickest descent controllers generated from quadratic Lyapunov functions that guarantee asymptotic stability within the operating range of the semiactive device for the zero disturbance case. For the external excitation case, Ž bounded-input, bounded-output stability is achieved and a stable attractor ball of . ultimate boundedness of the system is computed based on the upper bound of the disturbances. We show that our wide class of systems covers, in particular, two nonlinear actuator models from the literature. Tuning the performance of the simple Lyapunov controllers is straightforward using either modal or state penalties. Simulation results are presented which indicate that the Lyapunov control laws can be selected to provide similar decay rates as a ''time-optimal'' controller for a semi-actively controlled single degree of freedom structure with no external excitation.

Semi-active friction tendons for vibration control of space structures

“…In order to control the semi-active devices, three control laws are developed. The first control law is developed from Lyapunov's stability-theory, yielding a quickest-descent controller which has already been studied in the literature [28]. The second control law introduces some assumptions on the former one, which are applicable due to the mechanical configuration of the considered system, resulting in a novel control law with interesting features.…”

A review of non-linear structural control techniques

“…MR dampers have been successfully used for applications such as seat and vehicle suspensions [61][62][63][64], helicopter dampers [65,66], buildings, and other large structures [67][68][69][70][71][72]. They have also been used to control non-linear structural systems [73,74] As a technical example, an MR damper is shown in Fig. 1(a), being tested in an experimental test rig.…”

“…Linear techniques such as optimal control [93][94][95], pole placement [96], and H-infinity [54] have been modified to be used in active structural control. Non-linear problems have also been considered using techniques such as sliding mode control [97][98][99], Lyapunov control design [73], particle filters [100], and adaptive approaches [101] (discussed in Section 6)see reference [102] for a review of techniques used for active aeroelastic control. Adaptive approaches have also been applied to vibration absorber applications using other actuation systems such as shape memory alloys, see, for example references [103] or magnetostrictive alloys [104].…”

Semi-active continuous control of base-excited structures: An exploratory study

“…Many authors have used the direct Lyapounov method in order to select active or SA control strategies; classical applications to SA control systems, often oriented to ON-OFF control laws, are reported in [24,25].…”