Incorporating Robustness Requirements Into Antiwindup Design

Abstract

Abstract-This paper treats the problem of synthesizing antiwindup compensators that are able to handle plant uncertainty in addition to controller saturation. The uncertainty considered is of the frequency-weighted additive type, often encountered in linear robust control theory, and representative of a wide variety of uncertainty encountered in practice. The main results show how existing linear matrix inequality based antiwindup synthesis algorithms can be modified to produce compensators that accommodate uncertainty better. Embedded within these results is the ever-present performance-robustness tradeoff. A remarkable feature is that the often criticized internal model control antiwindup solution emerges as an "optimally robust" solution. A simple example demonstrates the effectiveness of the modified algorithms.

Positiveμmodification as an anti-windup mechanism

“…Therefore, if A is known to not be Hurwitz, but is otherwise unknown, anti-windup design with a priori guarantees becomes extremely difficult. In this case, it would seem more sensible to use an estimate of a model and to design a robust anti-windup compensator to cope with the mismatch [28,6]. Note that some local conditions (size of initial state) have been given in [19] but they are extremely conservative and dependent on the (unknown) adaptive gains K * x and K * r -this is not a criticism of these results but a consequence of the difficulties of anti-windup when A is unknown and has unstable eigenvalues.…”

“…In addition, a recent paper reports the development of a so-called model-reference anti-windup (MRAW) scheme for MRAC controllers but the architecture of this scheme is complicated and the properties this scheme bestows upon the closed-loop is difficult to discern. In fact, for linear systems the development of a MRAW scheme requires one to have a reasonably good ( [28]) model of the plant; in MRAC this model is assumed to be unknown so the generalisation of this to MRAC schemes is not straightforward.…”

Gain-scheduled, model-based anti-windup for LPV systems

“…Assumption 1 (which is a necessary condition for robust anti-windup compensation; see Galeani and Teel (2006), Turner et al (2007)) implies global robust asymptotic stability of Σ U , but otherwise allows plant (1) to be both unstable and affected by large uncertainties. This is a novelty with respect to previously available literature on anti-windup, where the plant is only allowed to be either unstable or affected by large uncertainties, but not both.…”

“…the surveys (Åström & Rundqwist, 1989;Hanus, 1988) for background) and robust control to counteract plant uncertainty. However, as pointed out in Turner, Herrmann and Postlethwaite (2007), there is a surprising lack of literature about the study of robustness limitations specifically arising in anti-windup control systems, as well as about the problem of designing anti-windup compensators ensuring robust-in-the-large stability (i.e. for any uncertainty in an a priori assigned, possibly ''large'', set of uncertainties, so that small gain arguments cannot be easily invoked).…”

“…The main conceptual contribution of this paper is that the necessary condition of unsaturated closed-loop robust stability (Galeani & Teel, 2006;Turner et al, 2007) is also sufficient for LPV antiwindup, so that no performance-robustness trade-off in the sense of Galeani and Teel (2006) arises; and that gain scheduling has a key role in reducing the anti-windup problem to a constrained robust stabilization problem, but not in solving this last problem.…”