Coprime factor anti-windup for systems with sensor saturation

This paper considers the design of anti-windup compensators for linear systems with saturated sensor measurements. The architecture used for the anti-windup (AW) compensators resembles that commonly used in fault-detection and high performance control, rather than the traditional anti-windup approach. Stability of the system is examined and it transpires that the design problem reduces to choosing appropriately a coprime factorisation of the plant, and its associated Bezout complement. In turn, this new problem has a state-space interpretation which requires the choice of appropriate state-feedback and observer gains such that a certain nonlinear matrix inequality (NLMI) is feasible. Although this NLMI is not easily linearised, it is shown that, providing the plant under consideration is detectable and controllable, there always exists a choice of parameters such that this inequality is satisfied and therefore, there always exists an anti-windup compensator (of this particular form) such that the overall closed-loop system with sensor saturation is asymptotically stable.