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Research Papers

State Estimate-Based Robust Adaptive Control of a Linked Mass-Spring System With Nonlinear Friction

[+] Author and Article Information
Yong Fu Wang

Professor
School of Mechanical Engineering and Automation,
Northeastern University,
Shenyang, 110004, China
e-mail: yfwang@mail.neu.edu.cn

Dian Hui Wang

Associate Professor
Department of Computer Science and Computer Engineering,
La Trobe University,
Melbourne, VIC 3086, Australia
e-mail: dh.wang@latrobe.edu.au

Tian You Chai

Professor, Fellow IEEE
State Key Laboratory of Synthetical Automation for Process Industries,
Northeastern University, Shenyang, 110004, China
e-mail: tychai@mail.neu.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received November 14, 2010; final manuscript received May 1, 2012; published online November 7, 2012. Assoc. Editor: Luis Alvarez.

J. Dyn. Sys., Meas., Control 135(2), 021004 (Nov 07, 2012) (8 pages) Paper No: DS-10-1336; doi: 10.1115/1.4007239 History: Received November 14, 2010; Revised May 01, 2012

This paper aims to develop a state estimate-based friction fuzzy modeling and robust adaptive control techniques for controlling a class of multiple degrees of freedom (MDOF) mechanical systems. A fuzzy state estimator is proposed to estimate the state variables for friction modeling. Under some conditions, it is shown that such a state estimator guarantees the uniformly ultimate boundedness (UUB) of the estimate error. Based on system input–output data and our proposed state estimator, a robust adaptive fuzzy output-feedback control scheme is presented to control multiple degrees of freedom system with friction. The adaptive fuzzy output-feedback controller can guarantee the uniformly ultimate boundedness of the tracking error of the closed-loop system. A typical mass-spring system is employed in our simulation studies. The results demonstrate that our proposed techniques in this paper have good potential in controlling nonlinear systems with uncertain friction.

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Figures

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Fig. 1

Schematic view of multiple degrees of freedom system

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Fig. 2

Schematic view of two degrees of freedom system

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Fig. 3

Used friction characteristics

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Fig. 4

Actual state x and estimated state x∧ (friction model: m1—Coulomb; m2—Coulomb + viscous)

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Fig. 5

Actual state x and estimated state x∧ (friction model: m1—Stribeck; m2—Coulomb + viscous)

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Fig. 6

Tracking responses of state x and reference input yr for output-feedback controller

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Fig. 7

Tracking responses of state x and reference input yr for output-feedback controller

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