A robust anti-windup design procedure for SISO systems

A model-based anti-windup (AW) controller design approach for constrained uncertain linear single-input–single-output (SISO) systems is proposed based on quantitative feedback theory (QFT) loopshaping. The design approach explicitly incorporates uncertainty, is suitable for the solution of both the magnitude and rate saturation problems, and provides for the design of low-order AW controllers satisfying robust stability and robust performance objectives. Robust stability is enforced using absolute stability theory and generic multipliers (i.e. circle, Popov, Zames–Falb), and robust performance is enforced using linear lower-bounds on the input–output maps capturing the effects of saturation as a metric. Two detailed design examples are presented. These show that even for simple systems, certain popular AW techniques lead to compensators that may fail to ensure robust stability and performance when saturation is encountered, but that the proposed QFT design approach is able to handle both saturation and uncertainty effectively.