An anti-windup design problem is posed and it is shown that all "observer-based" anti-windup modifications solve this problem at least locally. Sufficient conditions for an observer-based anti-windup modification to solve the global version of this problem are presented. A novel observer-based anti-windup design is then proposed such that the anti-windup problem can be interpreted in terms of a reduced-order system. In particular, the proposed anti-windup design induces an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed-loops. The dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin, stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function. The second part of the paper shows how the original dynamic compensator can be modified, while retaining those dynamic features that produce a desirable closed-loop steady-state response, to ensure that the requisite invariant subspace exists and it is reasonably tuned for input saturation. Two case studies are carried out on systems that have been investigated in the literature.
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* Received 12 December 1995; revised 5 May 1997; received in final form 17 October 1997. Some results from this paper were presented at the IFAC World Congress, San Francisco, CA, 1996. This paper was recommended for publication in revised form by Associate Editor Hassan Khalil under the direction of Editor Tamer Bas,ar. Corresponding author Navneet Kapoor. Tel. (518)-387-4072; Fax (518)-387-5164; E-mail kapoor@ crd.ge.com. -GE Corporate Research and Development, P.O. Box 8, Schenectady, NY 12301, U.S.A. Work carried out as a graduate student in the Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455. Funded in part by the Shell Foundation. ‡ Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, U.S.A. Work carried out while with the Electrical Engineering Department, University of Minnesota. Funded in part by the NSF under grants ECS-9309523 and ECS-9502034 and by the AFOSR under grant F49620-96-1-0144. °Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, U.S.A. Funded in part by the Shell Foundation.
- Global stability
- Multivariable systems