Optimal Control of a Ball and Beam Nonlinear Model Based on Takagi-Sugeno Fuzzy Model

  • José Miguel AdánezEmail author
  • Basil Mohammed Al-Hadithi
  • Agustín Jiménez
  • Fernando Matía
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


In this work, an improved approach for Takagi-Sugeno system identification is used. Linear Quadratic Regulator is applied for an optimal state feedback. Duality theorem and Linear Quadratic Regulator is applied for an optimal state estimation. Simulation results over the ball and beam nonlinear model show a stable closed loop in the full range and good transient response.


Ball and beam Takagi-Sugeno model State model Linear Quadratic Regulator Duality theorem 



This work is funded by Spanish Ministry of Economy and Competitiveness (Assisted Navigation through Natural Language (NAVEGASE) project 265 (DPI 2014-53525-C3-1-R)).


  1. 1.
    AMIRA GmbH: BW500 Laboratory Setup Ball and Beam. Deutschland, Germany (1999)Google Scholar
  2. 2.
    Ballesteros, J., Rodriguez, D., Sanchez, L., Castillo, F., Payo, I.: Teaching-learning model based on the design of didactic equipment for laboratory practices in engineering schools. In: Proceedings of EDULEARN16 Conference, Barcelona, Spain, 4–6 July 2016Google Scholar
  3. 3.
    Marton, A., Hodel, S., Lantos, B., Hung, J.Y.: Underactuated robot control: comparing LQR, subspace stabilization, and combined error metric approaches. IEEE Trans. Ind. Electron. 55(10), 3724–3730 (2008)CrossRefGoogle Scholar
  4. 4.
    Takagi, T., Sugeno, S.: Fuzzy identification of systems and its applications to modelling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)CrossRefzbMATHGoogle Scholar
  5. 5.
    Lewis, F.L., Xie, L., Popa, D.: Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, vol. 29. CRC Press, Boca Raton (2007)zbMATHGoogle Scholar
  6. 6.
    Ogata, K.: Modern Control Engineering, 5th edn. Upper Saddle River, New Jersey (2009)zbMATHGoogle Scholar
  7. 7.
    Al-Hadithi, B.M., Jiménez, A., Matía, F.: A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems. Appl. Soft Comput. 12(1), 280–290 (2012)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • José Miguel Adánez
    • 1
    Email author
  • Basil Mohammed Al-Hadithi
    • 1
    • 2
  • Agustín Jiménez
    • 1
  • Fernando Matía
    • 1
  1. 1.Intelligent Control GroupCentre for Automation and Robotics UPM - CSIC, Universidad Politécnica de MadridMadridSpain
  2. 2.Department of Electrical, Electronics, Control Engineering and Applied Physics, Higher Technical School of Industrial Design and EngineeringUniversidad Politécnica de MadridMadridSpain

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