A multiple Lyapunov function-based switching anti-windup design for linear systems under asymmetric input constraints and its application to aero-engines

This paper proposes a switching anti-windup design for linear, time-invariant (LTI) systems with asymmetric input constraint. Firstly, the input space of the LTI plant is divided into several regions based on the sign of each control input. In each of these regions, the original asymmetric saturation function can be equivalently written as a symmetric one. Then, we design a separate anti-windup gain for each region and implement it when the value of the input signal falls into this region. The online switching between different anti-windup gains enables the full utilisation of the available range of control action on both sides of the saturation limits, which is something that the classical single gain anti-windup design cannot achieve. By incorporating the special properties of asymmetric saturation constraints, a multiple Lyapunov function is constructed for closed-loop stability and performance analysis. This can significantly reduce the conservatism of the resulting stability and performance synthesis conditions. Finally, numerical simulation and aero-engine hardware-in-loop testing demonstrate that, the proposed design has the ability to obtain a significantly larger domain of attraction and an improved control performance than the existing methods.