A Practical Robust Direct Model Anti-windup Design

This paper considers the synthesis of robust anti-windup compensators using direct models for stable multivariable linear time invariant uncertain plants. An internal model control antiwindup compensator as a special case of the direct model, preserves the robust stability of the unconstrained linear closed-loop system. The proposed direct model antiwindup aims to improve the performance of the constrained closed-loop system while guaranteeing robust stability. Robust stability and performance are achieved by shaping two closed-loop transfer functions based on a decoupled representation of the constrained closed-loop. Trade offs between robust stability and robust performance are provided by adjusting performance and stability weights. The direct model synthesis is cast into a H∞ optimization or a μ synthesis problem, where the anti-windup objectives are robust stability and rapid recovery of the linear response. Two simulation examples, one single input single output(SISO), one multi-input multi-output(MIMO), demonstrate the design process and effectiveness of the proposed scheme.