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Stabilization of the quadruple inverted pendulum by variable universe adaptive fuzzy controller based on variable gain H ∞ regulator

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Abstract

In this paper, the variable universe adaptive fuzzy controller based on variable gain H∞ regulator (VGH∞R) is designed to stabilize a quadruple inverted pendulum. The VGH∞R is a novel robust gain-scheduling approach. By utilizing VGH∞R technique, a more precise real-time feedback gain matrix, which is changing with states, is obtained. Via the variable gain matrix 10 state variables of quadruple inverted pendulum are transformed into a kind of synthesis error (E) and synthesis rate of change of error (EC) at sampling time. Therefore, the dimension of the multivariable system is reduced and the variable universe adaptive fuzzy controller is built. Experiments illustrate the effectiveness of the proposed control scheme.

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Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Yongli Zhang & Hongxing Li

  2. School of Mathematical Sciences, Beijing Normal University, Key Laboratory of Mathematics and Complex System, Ministry of Education, Beijing, 100875, China

    Jiayin Wang

Authors
  1. Yongli Zhang
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  2. Jiayin Wang
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  3. Hongxing Li
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Corresponding author

Correspondence to Yongli Zhang.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 61074044, 61104038, and 60834004, Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20090041110003, and the National 973 Basic Research Program of China under Grant Nos. 2009CB320602 and 2002CB312200.

This paper was recommended for publication by Editor Yiguang HONG.

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Zhang, Y., Wang, J. & Li, H. Stabilization of the quadruple inverted pendulum by variable universe adaptive fuzzy controller based on variable gain H ∞ regulator. J Syst Sci Complex 25, 856–872 (2012). https://doi.org/10.1007/s11424-012-0011-y

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  • DOI: https://doi.org/10.1007/s11424-012-0011-y

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