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Stability and robust position control of hysteretic systems
Author(s) -
Valadkhan Sina,
Morris Kirsten,
Khajepour Amir
Publication year - 2009
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.1457
Subject(s) - control theory (sociology) , bounded function , position (finance) , monotonic function , controller (irrigation) , constant (computer programming) , tracking error , stability (learning theory) , signal (programming language) , mathematics , hysteresis , computer science , control (management) , physics , mathematical analysis , finance , artificial intelligence , machine learning , agronomy , economics , biology , programming language , quantum mechanics
Position control of a wide class of hysteretic systems, which includes those described by a Preisach model, is considered. The main focus of this paper is stability, tracking and the trajectories of a hysteretic system controlled by a PI controller. The system output (not its derivative) is measured and controlled. It is shown that, for arbitrary reference signals, the closed‐loop system is bounded‐input–bounded‐output‐stable with a finite gain of one. Furthermore, the absolute value of the error decreases monotonically for a constant reference signal. In this case, provided that the desired output is within the limits of the system output, zero steady‐state error is guaranteed. A bound on the time required to achieve a specified error is obtained. Only a simple condition on the controller parameters is required. The results imply that stability and position control are guaranteed, even if large errors in the model exist. Copyright © 2009 John Wiley & Sons, Ltd.