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

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, bounded-input, bounded-output stability is achieved and a stable attractor Žball 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.