Global stability of systems with amplitude and rate saturation compensation

Abstract

Rate and amplitude saturation of the actuator is common in practical control systems. When the actuator is rate and amplitude saturated, the control performance can deteriorate rapidly, and in the worse case, the closed-loop system can become unstable. It is therefore important that both types of saturations are properly compensated. Following the approach for compensating amplitude constraints, a scheme for compensating systems with both rate and amplitude saturation is proposed in this paper. The conditions for the compensated system to be globally stable are derived, and from this result, a procedure for designing the rate and amplitude saturation compensators is devised. As it is difficult to design both the rate and the amplitude saturation compensators simultaneously, a two-step approach is adopted. In the proposed compensator design procedure, the amplitude saturation compensator is designed first, followed by the rate saturation compensator. As the compensators designed using the proposed procedure satisfy the conditions for global stability, the compensated system is therefore globally stable. It is also shown that these compensators can be designed using the LMI technique. The implementation of the design procedure is demonstrated by a simulation example. Copyright © 2004 John Wiley & Sons, Ltd.