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Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states

  • Intelligent and Information Systems
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Abstract

It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H ∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A&M University, Doha, 23874, Qatar

    Tzu-Sung Wu, Mansour Karkoub & Chien-Ting Chen

  2. Department of Electrical Engineering, Tatung University, Taipei, 104, Taiwan

    Wen-Shyong Yu

  3. Department of Mechanical Engineering, Tatung University, Taipei, 104, Taiwan

    Ming-Guo Her

  4. Mechanical and Systems Research Laboratories, Industrial Technology Research Institute (ITRI), Hsinchu, 310, Taiwan

    Jui-Yiao Su

Authors
  1. Tzu-Sung Wu
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  2. Mansour Karkoub
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  3. Chien-Ting Chen
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  4. Wen-Shyong Yu
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  5. Ming-Guo Her
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  6. Jui-Yiao Su
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Corresponding author

Correspondence to Tzu-Sung Wu.

Additional information

Recommended by Editorial Board member Juhoon Back under the direction of Editor Ju Hyun Park.

The authors would like to thank the anonymous reviewers for their helpful suggestions and valuable comments. This work has been supported by Qatar National Research Fund under NPRP Grant 4-537-2-200 and 4-536-2-199.

Tzu-Sung Wu was born in Taiwan, Republic of China in 1979. He received his B.S. degree in Electronic Engineering from Lunghwa University of Science and Technology, Taoyuan, Taiwan, in 2003, an M.S. degree in Electrical Engineering from Tatung University, Taipei, Taiwan in 2005 and a Ph.D. degree in Electrical Engineering from Tatung University, Taipei, Taiwan in 2011. He is currently a postdoctoral researcher in the Department of Mechanical Engineering at the University of Texas A & M, Doha, Qatar. His research interests include fuzzy logic, intelligent systems, and learning algorithms.

Mansour Karkoub received his B.S. degree in Mechanical Engineering with Highest Distinction in 1984, an M.S.M.E. in 1990, and a Ph.D. in 1994 all from the University of Minnesota, Minneapolis, Minnesota. He held a faculty position at Kuwait University from 1994–2005 and INRIA, France from 2002–2003. Also, he held faculty position at the Petroleum Institute in Abu Dhabi, UAE from 2005–2009. Currently, he is with the Mechanical Engineering Department, Texas A & M University, Qatar. His research interests are robust control, robotics, mechatronics, and vibration engineering.

Chien-Ting Chen was born in Taiwan, R.O.C., in 1986. He received his B.S. and M.S. degrees in Mechanical Engineering from Tatung University, Taipei, Taiwan, R.O.C., in 2010 and 2013, respectively. He was a research associate in Texas A & M University at Qatar in 2012. His research interests include fuzzy control, adaptive control and nonlinear control.

Wen-Shyong Yu was born in Taiwan, Republic of China in 1961. He received his B.S. degree in Electronic Engineering from Tamkang University, Taipei, Taiwan, in 1984, an M.S. degree in Electrical Engineering from Tatung Institute of Technology, Taipei, Taiwan, in 1986, and a Ph.D. degree in Electrical Engineering from National Taiwan University, Taipei, Taiwan, in 1995. From 1986 to 1989, he was a Lecturer of Electrical Engineering Department at the Tatung Institute of Technology and an Associate Professor from 1989 to 1990. Since August 1994, he has been with the Department of Electrical Engineering at the Tatung University, where he is currently a Professor. His research interests are in application of adaptive control and neural fuzzy control to power systems and robotics.

Ming-Guo Her received his B.S. degree in Mechanical Engineering in 1983 from Tatung Institute of Technology, Taipei, Taiwan, and both the M.S. and Ph.D. degrees in Mechanical Engineering from the University of Minnesota, Minneapolis, Minnesota, U.S.A. in 1988 and 1991, respectively. From 1991 to 1992, he was with the Department of Mechanical Engineering of the University of Minnesota as an Instructor. In 1992, he jointed Tatung Group. He is currently the Secretary General of Tatung Group and Professor in the Department of Mechanical Engineering at Tatung University. Dr. Her is on the board of directors of the Chinese Institute of Electrical Engineering. His research interests include design and control of robotic systems.

Jui-Yiao Su received his B.S. degree in Control Engineering from National Chiao Tung University, Hsinchu, Taiwan, in 1997, an M.S. degree in Electrical Engineering from Tatung Institute of Technology, Taipei, Taiwan, in 1999, and a Ph.D. degree in Electrical Engineering from Tatung University, Taipei, Taiwan, in 2007. He is currently a researcher in Mechanical and Systems Research Laboratories at Industrial Technology Research Institute, Hsinchu, Taiwan. His research interests include fuzzy logic, intelligent systems, and robotic control.

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Wu, TS., Karkoub, M., Chen, CT. et al. Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states. Int. J. Control Autom. Syst. 11, 1300–1313 (2013). https://doi.org/10.1007/s12555-012-0543-x

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