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Research Papers

Adaptive Control for Uncertain Hysteretic Systems

[+] Author and Article Information
Xiaotian Zou

Department of Biomedical Engineering,
University of Massachusetts,
Lowell, MA 01854
e-mail: Xiaotian_Zou@student.uml.edu

Jie Luo

e-mail: jie.luo@engr.uconn.edu

Chengyu Cao

Assistant Professor
Mem. ASME
e-mail: ccao@engr.uconn.edu
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 30, 2012; final manuscript received August 1, 2013; published online October 7, 2013. Assoc. Editor: Qingze Zou.

J. Dyn. Sys., Meas., Control 136(1), 011011 (Oct 07, 2013) (7 pages) Paper No: DS-12-1395; doi: 10.1115/1.4025241 History: Received November 30, 2012; Revised August 01, 2013

This paper presents an approach to use the L1 adaptive controller for a class of uncertain systems in the presence of unknown Preisach-type hysteresis in input, unknown time-varying parameters, and unknown time-varying disturbances. The hysteresis operator can be transformed into an equivalent linear time-varying (LTV) system with uncertainties, which means that the effect of the hysteresis can be considered as general uncertainties to the system. Without constructing the inverse hysteresis function, the L1 adaptive control is used to handle the uncertainties introduced by the hysteresis, as well as system dynamics. The adaptive controller presented in this paper ensures uniformly bounded transient and tracking performance for uncertain hysteretic systems. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results with Preisach-type hysteresis are provided to verify the theoretical findings.

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Figures

Grahic Jump Location
Fig. 1

Preisach hysteresis operator

Grahic Jump Location
Fig. 2

Relation between h(u,t) and ω(t)u(t)

Grahic Jump Location
Fig. 3

Hysteresis operator

Grahic Jump Location
Fig. 4

Performance of L1 adaptive controller, (a) y(t) (solid) and ydes(t) (dotted) and (b) the error between y(t) and ydes(t)

Grahic Jump Location
Fig. 5

Time-history of u(t)

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