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Robust H ∞ control for uncertain nonlinear active magnetic bearing systems via Takagi-Sugeno fuzzy models

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Abstract

In this paper, a systematic procedure to design the robust H ∞ fuzzy controller for a nonlinear active magnetic bearing (AMB) system affected by time-varying parametric uncertainties is presented. First, the continuous-time Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear AMB system. Next, based on the obtained fuzzy model, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for robust stability and H ∞ performance of the control system. The main feature of this paper is that some drawbacks existing in the previous approaches such as truncation errors and nonconvex bilinear matrix inequality (BMI) problem are eliminated by utilizing the homogeneous fuzzy model which includes no bias terms in the local state space models rather than the affine one which includes bias terms. Hence, the design method presented here will prove to be more tractable and accessible than the previous ones. Finally, numerical simulations demonstrate the effectiveness of the proposed approach.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Yonsei University, Seodaemun-gu, Seoul, 120-749, Korea

    Dong Hwan Lee & Jin Bae Park

  2. Department of Control, Robot, and Systems Engineering, Kunsan National University, Kunsan, Chonbuk, 573-701, Korea

    Young Hoon Joo

  3. Department of Mechanical, Material, and Aerospace Engineering, University of Central Florida Orlando, Orlando, Florida, USA

    Kuo Chi Lin

  4. Florida Space Institute, University of Central Florida Orlando, Orlando, Florida, USA

    Chan Ho Ham

Authors
  1. Dong Hwan Lee
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Corresponding author

Correspondence to Young Hoon Joo.

Additional information

Recommended by Editorial Board member Yangmin Li under the direction of Editor Jae Weon Choi. This work was partially supported by the National Research Foundation of Korea Grant funded by the Korean Government (MEST) (KRF-2009-220-D00034).

Dong Hwan Lee received his B.S. degree in Electronic Engineering from Konkuk University, Seoul, Korea, in 2008. He is currently working toward a M.S. degree in the Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea. His current research interests include stability analysis in fuzzy systems, fuzzy-model-based control, and robust control of uncertain linear systems.

Jin Bae Park received his B.E. degree in Electrical Engineering from Yonsei University, Seoul, Korea, and his M.S. and Ph.D. degrees in Electrical Engineering from Kansas State University, Manhattan, in 1977, 1985, and 1990, respectively. Since 1992, he has been with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea, where he is currently a Professor. His research interests include robust control and filtering, nonlinear control, mobile robot, fuzzy logic control, neural networks, genetic algorithms, and Hadamard transform spectroscopy. He serves as the Vice-President for the Institute of Control, Robot, and Systems Engineers (ICROS) (2009–2010) and Editor-in-Chief for the International Journal of Control, Automation, and Systems (IJCAS) (2006–2010).

Young Hoon Joo received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Yonsei University, Seoul, Korea, in 1982, 1984, and 1995, respectively. He worked with Samsung Electronics Company, Seoul, Korea, from 1986 to 1995, as a project manager. He was with the University of Houston, Houston, TX, from 1998 to 1999, as a visiting professor in the Department of Electrical and Computer Engineering. He is currently a Professor in the Department of Control, Robot, and Systems Engineering, Kunsan National University, Korea. His major interest is mainly in the field of intelligent robot, intelligent control, and human-robot interaction. He serves as President for Korea Institute of Intelligent Systems (KIIS) (2008–2009) and Editor for the International Journal of Control, Automation, and Systems (IJCAS) (2008–2010).

Kuo-Chi Lin received his M.S. and Ph.D. degrees in Aerospace Engineering from University of Michigan, Ann Arbor, Michigan, USA, in 1986, 1990, respectively. He has been a joint faculty between Institute for Simulation and Training (IST) and Department of Mechanical, Materials and Aerospace Engineering (MMAE) since joining University of Central Florida (UCF) in 1990. He is currently the Associate Chair of MMAE and an Associate Faculty in Florida Space Institute (FSI) at UCF. His major interest is mainly in the fields of renewable energy, rotating machinery, modeling and simulation, and small satellite.

Chan Ho Ham received his M.S. and Ph.D. degrees in Electrical Engineering from University of Central Florida (UCF), Orlando, Florida, USA, in 1991, 1995, respectively. He is an Assistant Professor in Florida Space Institute and School of Electrical Engineering and Computer Science at UCF. He has served as the Director of Maglev Program with the Kennedy Space Center and the Space Program Director in NASA Florida Space Grant Consortium. His major interest is in the fields of Maglev, space systems, and mechatronics.

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Lee, D.H., Park, J.B., Joo, Y.H. et al. Robust H ∞ control for uncertain nonlinear active magnetic bearing systems via Takagi-Sugeno fuzzy models. Int. J. Control Autom. Syst. 8, 636–646 (2010). https://doi.org/10.1007/s12555-010-0317-2

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