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Research Papers

A Gain-Scheduling Control Approach for Takagi–Sugeno Fuzzy Systems Based on Linear Parameter-Varying Control Theory

[+] Author and Article Information
Yang Liu

Center for Control Theory and
Guidance Technology,
Harbin Institute of Technology,
Harbin, Heilongjiang 150001, China
e-mail: liuyang5264@163.com

Xiaojun Ban

Center for Control Theory and
Guidance Technology,
Harbin Institute of Technology,
Harbin, Heilongjiang 150001, China
e-mail: banxiaojun@hit.edu.cn

Fen Wu

Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695
e-mail: fwu@ncsu.edu

H. K. Lam

Department of Informatics,
King's College London,
Strand, London WC2R 2LS, UK
e-mail: hak-keung.lam@kcl.ac.uk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 27, 2015; final manuscript received October 14, 2015; published online November 16, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 138(1), 011008 (Nov 16, 2015) (9 pages) Paper No: DS-15-1194; doi: 10.1115/1.4031914 History: Received April 27, 2015; Revised October 14, 2015

Due to the universal approximation capability of Takagi–Sugeno (T–S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T–S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T–S fuzzy models and LPV models provides a new perspective of the control problems for T–S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gain-scheduling control design approach for T–S fuzzy systems is presented to ensure globally asymptotical stability and optimize H performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.

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Figures

Grahic Jump Location
Fig. 1

Disturbance attenuation of Example 1: (a) measurement output, (b) control input, and (c) L2 gain

Grahic Jump Location
Fig. 2

Response to the initial condition x(0) = [85 deg 5.73 deg/s]T of Example 1: (a) measurement output and (b) control input

Grahic Jump Location
Fig. 3

Simulation results of Example 2: (a) plant states, (b) output, and (c) control input

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