A Static Anti-windup Synthesis for Internal Model Control

There are several controller factorization heuristics for applying the internal model control (IMC) to saturated linear systems. In this paper, we develop a static anti-windup synthesis strategy that efficiently factorizes the IMC controller for input-constrained multivariable systems. By parameterizing the linear control in terms of a static gain-matrix, we reduce the search for an optimal factorization to a convex search over a set of linear matrix inequality (LMI) constraints. The ensuing structure offers insights into the operation of the widely adopted modified IMC anti-windup scheme, and provides a unified framework for several existing anti-windup designs.