An anti-windup scheme with embedded internal model control anti-windup for improved performance

This paper considers the synthesis of an anti-windup(AW) compensator which comprises an internal model control(IMC) antiwindup compensator and a linear anti-windup compensator, for stable linear plants subject to input saturation. Built on the conventional internal model control antiwindup scheme which preserves the stability and stability robustness of the unconstrained linear closed-loop system, the proposed antiwindup scheme aims to improve the performance of the constrained closed-loop system by including another anti-windup compensator. The ℒ₂ gain of the constrained system from the exogenous input to the performance output is used as the performance objective for the the synthesis of the extra antiwindup compensator, resulting in nonconvex matrix conditions. For certain orders of the extra antiwindup compensator, the nonconvex matrix conditions are reduced into convex linear matrix inequalities(LMIs). Especially when the order the extra anti-windup compensator is zero, it is proven that there always exists such an anti-windup compensator guaranteeing a finite ℒ₂ gain for the antiwindup compensated constrained closed-loop system. This important result leads to the design of an overall plant order antiwindup compensator which improves system performance compared to the IMC anti-windup, as demonstrated by the simulation results.