Stability analysis of linear systems with actuator amplitude and rate saturations

In this paper a method for the stability analysis of a closed loop system, composed of a linear system and its controller with simultaneous acting amplitude and rate control commands limitations, is provided. This kind of nonlinearity is unavoidably encountered in many fields of control applications, because of physical constraints of the actuation devices. In particular, when the control input derivative exceeds the rate limit, the actuation system behaves as the series of a nonlinear element and a dynamic delay, i.e. with a behaviour that cannot be described by an input-output static relationship. The presence of a delay element may lead the whole closed loop system to instability; due to the presence of the saturation element such instability (if occurring) evolves into a limit cycle behaviour. It is proposed to analyse the nonlinear effects of amplitude and rate limited actuators in the frequency domain by using an optimal quasi-linearization approach. The main contribution of the paper is a methodology for the detection and the stability analysis of limit cycles; then the asymptotic stability of the equilibrium of the nonlinear closed loop system is investigated. The theory is applied to an aeronautical real world example to show the effectiveness of the proposed technique.