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A new view of anti‐windup design for uncertain linear systems in the frequency domain
Author(s) -
Berger Ari,
Gutman PerOlof
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3397
Subject(s) - control theory (sociology) , describing function , limit cycle , frequency domain , benchmark (surveying) , actuator , transfer function , compensation (psychology) , controller (irrigation) , linear system , computer science , stability (learning theory) , limit (mathematics) , mathematics , control (management) , engineering , nonlinear system , artificial intelligence , psychoanalysis , mathematical analysis , biology , psychology , geodesy , quantum mechanics , machine learning , agronomy , computer vision , physics , electrical engineering , geography
Summary This paper presents a new perspective on the stability problem for uncertain LTI feedback systems with actuator input amplitude saturation. The solution is obtained using the quantitative feedback theory and a 3 DoF non‐interfering control structure. Describing function (DF) analysis is used as a criterion for closed loop stability and limit cycle avoidance, but the circle or Popov criteria could also be employed. The novelty is the combination of a controller parameterization from the literature and describing function‐based limit cycle avoidance with margins for uncertain plants. Two examples are given. The first is a benchmark problem and a comparison is made with other proposed solutions. The second is an example that was implemented and tested on an X‐Y linear stage used for nano‐positioning applications. Design and implementation considerations are given. An example is given on how the method can be extended to amplitude and rate saturation with the help of the generalized describing function, and a novel anti‐windup compensation structure inspired by previous contributions. Copyright © 2015 John Wiley & Sons, Ltd.