On a performance-robustness trade-off intrinsic to the natural anti-windup problem

Any natural definition of the anti-windup (AW) control problem requires the design of an add-on compensator which, connected to a saturating closed loop system (which would be well-behaved in the absence of saturation), guarantees stability and, as long as the saturation limits are never exceeded, preservation of the original linear behaviour. Three main contributions are given in this paper. First, it is shown that the “model-matching” requirement implied by the preservation of the linear response can be incompatible with the achievement of robust stability in the presence of large uncertainties, even if the controlled plant is robustly open loop stable. Then, a reasonable “weakened” AW problem is introduced, in which the “model-matching” requirement is considered just as a performance requirement (instead of a hard constraint) whose relaxation can be traded off with robustness to larger uncertainties. Finally, the approach proposed in Teel and Kapoor [(1997a). In Proceedings of the fourth European control conference] is extended to deal with the new problem, leading to a family of state feedback compensators parameterized in terms of a state feedback gain (already present in the original approach) and a stable linear time invariant filter. A detailed design procedure for determining suitable values of the parameters is also described.