Conference Paper

Sufficient conditions for dissipativity on Duhem hysteresis model

Dept. Discrete Technol. & Production Autom., Univ. of Groningen, Groningen, Netherlands
DOI: 10.1109/CDC.2009.5400790 Conference: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
Source: IEEE Xplore


This paper presents sufficient conditions for dissipativity on the Duhem hysteresis model. The result of this paper describes the dissipativity property of several standard hysteresis models, including the backlash and Prandtl operator. It also allows the curve in the hysteresis diagram (the phase plot between the input and the output) to have negative gradient.

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Available from: Bayu Jayawardhana, Jan 17, 2016
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    • "For the case y(t) < f an (u(t)), the non-negativity of H 1 can be checked using the same routine. If we have g an = 0, the non-negativity of H 1 can be checked directly (we refer also to [6]). △ C. Storage function using ν Φ Dual to the results from the previous subsection, we can also define storage functions based on ν Φ . "
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    ABSTRACT: In this paper, we discuss the dissipativity property of Duhem hysteresis models. Under some sufficient conditions on the functions which defines the Duhem model, an explicit construction of the storage functions is given which takes into account the data on the anhysteresis function. We present an example on the semi-linear Duhem model.
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    ABSTRACT: In this paper we investigate the dissipativity property of a certain class of Duhem hysteresis operator, which has clockwise (CW) input-output (I/O) behavior. In particular, we provide sufficient conditions on the Duhem operator such that it is CW and propose an explicit construction of the corresponding storage function satisfying dissipation inequality of CW systems. The result is used to analyze the stability of a second order system with hysteretic friction which is described by a Dahl model.
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    ABSTRACT: In this paper, we investigate the stability of a feedback interconnection between a linear system and a Duhem hysteresis operator, where the linear system and the Duhem hysteresis operator satisfy either the counter-clockwise (CCW) or clockwise (CW) input-output dynamics. More precisely, we present sufficient conditions for the stability of the interconnected system that depend on the CW or CCW properties of the linear system and the Duhem operator. Based on these results we introduce a control design methodology for stabilizing a linear plant with a hysteretic actuator or sensor without requiring precise information on the hysteresis operator.
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