An anti-windup design for linear systems with input saturation

An anti-windup design problem is posed and it is shown that all "observer-based" anti-windup modifications solve this problem at least locally. Sufficient conditions for an observer-based anti-windup modification to solve the global version of this problem are presented. A novel observer-based anti-windup design is then proposed such that the anti-windup problem can be interpreted in terms of a reduced-order system. In particular, the proposed anti-windup design induces an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed-loops. The dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin, stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function. The second part of the paper shows how the original dynamic compensator can be modified, while retaining those dynamic features that produce a desirable closed-loop steady-state response, to ensure that the requisite invariant subspace exists and it is reasonably tuned for input saturation. Two case studies are carried out on systems that have been investigated in the literature.