Anti-windup design via nonsmooth multi-objective H∞ optimization

This paper investigates constrained control design problems involving mixed magnitude and rate saturations. We show that simultaneous design of structured feedback and anti windup gains can be recast as minimizing two H∞-norm objectives. One is associated with nominal system operation while the other also captures the saturations effects. Because of the two-block structure of the controller, the problem is inherently difficult. We use recently available tools in nonsmooth optimization to compute controller components in a single run thereby alleviating the conservatism of more conventional schemes. The proposed methodology is applied to an aircraft control problem for which a PID feedback controller and a second-order anti-windup compensator are optimized simultaneously.