An Approach to Fuzzy Modeling of Anti-lock Braking Systems

  • Radu-Codruţ DavidEmail author
  • Ramona-Bianca Grad
  • Radu-Emil Precup
  • Mircea-Bogdan Rădac
  • Claudia-Adina Dragoş
  • Emil M. Petriu
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 223)


This chapter proposes an approach to fuzzy modeling of Anti-lock Braking Systems (ABSs). The local state-space models are derived by the linearization of the nonlinear ABS process model at ten operating points. The Takagi-Sugeno (T-S) fuzzy models are obtained by the modal equivalence principle, where the local state-space models are the rule consequents. The optimization problems are defined in order to minimize the objective functions expressed as the squared modeling errors, and the variables of these functions are a part of the parameters of input membership functions. Simulated Annealing algorithms are implemented to solve the optimization problems and to obtain optimal T-S fuzzy models. Real-time experimental results are included to validate the new optimal T-S fuzzy models for ABS laboratory equipment.


Anti-lock braking systems Optimization Real-time experiments Simulated annealing Takagi-Sugeno fuzzy models 



This work was supported by a grant in the framework of the Partnerships in priority areas—PN II program of the Romanian National Authority for Scientific Research ANCS, CNDI—UEFISCDI, project number PN-II-PT-PCCA-2011-3.2-0732, and by a grant of the NSERC of Canada.


  1. 1.
    Zhao, Z., Yu, Z., Sun, Z.: Research on fuzzy road surface identification and logic control for anti-lock braking system. In: Proceedings of IEEE International Conference on Vehicular Electronics and Safety, Shanghai, China, pp. 380–387 (2006)Google Scholar
  2. 2.
    Zheng, T., Ma, F., Zhang, K.: Estimation of reference vehicle speed based on T-S fuzzy model. In: Proceedings of international conference on advanced in control engineering and information science, Dali, China, vol. 15, pp. 188–193 (2011)Google Scholar
  3. 3.
    Wang, W.-Y., Chen, M.-C., Su, S.-F.: Hierarchical T-S fuzzy-neural control of anti-lock braking system and active suspension in a vehicle. Automatica 48, 1698–1706 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Precup, R.-E., Spătaru, S.V., Rădac, M.-B., Petriu, E.M., Preitl, S., Dragoş, C.-A., David, R.-C.: Experimental results of model-based fuzzy control solutions for a laboratory antilock braking system. In: Hippe, Z.S., Kulikowski, J.L., Mroczek, T., (eds.), Human-Computer Systems Interaction: Backgrounds and Applications 2, Part 2, AICS, vol. 99, pp. 223–234. Springer, New York (2012)Google Scholar
  5. 5.
    Naderi, P., Farhadi, A., Mirsalim, M., Mohammadi, T.: Anti-lock and Anti-slip braking system, using fuzzy logic and sliding mode controllers. In: Proceedings of IEEE Vehicle Power and Propulsion Conference, Lille, France, p. 6 (2010)Google Scholar
  6. 6.
    Topalov, A.V., Oniz, Y., Kayacan, E., Kaynak, O.: Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm. Neurocomputting 74, 1883–1893 (2011)CrossRefGoogle Scholar
  7. 7.
    Bhandari, R., Patil, S., Singh, R.K.: Surface prediction and control algorithms for anti-lock brake system. Trans. Res. Part C Emerg. Technol. 21, 181–195 (2012)CrossRefGoogle Scholar
  8. 8.
    Aleksendrić, D., Jakovljević, Ž., Ćirović, V.: Intelligent control of braking process. Expert Syst. Appl. 39, 11758–11765 (2012)CrossRefGoogle Scholar
  9. 9.
    Garibaldi, J.M., Ifeachor, E.C.: Application of simulated annealing fuzzy model tuning to umbilical cord acid-base interpretation. IEEE Trans. Fuzzy Syst. 7, 72–84 (1999)CrossRefGoogle Scholar
  10. 10.
    Liu, G., Yang, W.: Learning and Tuning of fuzzy membership functions by simulated annealing algorithm. In: Proceedings of 2000 IEEE Asia-Pacific Conference on Circuits and Systems, Tianjin, China, pp. 367–370 (2000)Google Scholar
  11. 11.
    Almaraashi, M., John, R., Coupland S., Hopgood A.: Time series forecasting using a TSK fuzzy system tuned with simulated annealing. In: Proceedings of 2010 IEEE International Conference on Fuzzy Systems, Barcelona, Spain, p. 6 (2010)Google Scholar
  12. 12.
    Yanara, T.A., Akyürek, Z.: Fuzzy model tuning using simulated annealing. Expert Syst. Appl. 38, 8159–8169 (2011)CrossRefGoogle Scholar
  13. 13.
    Precup, R.-E., David, R.-C., Petriu, E.M., Preitl, S., Rădac, M.-B.: Fuzzy control systems with reduced parametric sensitivity based on simulated annealing. IEEE Trans. Industr. Electron. 59, 3049–3061 (2012)CrossRefGoogle Scholar
  14. 14.
    David, R.-C., Dragoş, C.-A., Bulzan, R.-G., Precup, R.-E., Petriu, E.M., Rădac, M.-B.: An approach to fuzzy modeling of magnetic levitation systems. Int. J. Artif. Intell. 9, 1–18 (2012)Google Scholar
  15. 15.
    Inteco: ABS: The laboratory anti-lock braking system controlled from PC—user manual, Inteco Sp. z o. o., Krakow, Poland (2007)Google Scholar
  16. 16.
    Grad, R.-B.: Biologically inspired optimization algorithm for fuzzy modeling of an anti-lock braking system laboratory equipment. M.Sc. thesis, “Politehnica” University of Timisoara, Timisoara, Romania (2012)Google Scholar
  17. 17.
    Köppen, M.: Light-weight evolutionary computation for complex image-processing applications. In: Proceedings of 6th International Conference on Hybrid Intelligent Systems, Auckland, New Zealand, pp. 3–3 (2006)Google Scholar
  18. 18.
    Deb, K., Gupta, S., Daum, D., Branke, J., Mall, A.K., Padmanabhan, D.: Reliability-based optimization using evolutionary algorithms. IEEE Trans. Evol. Comput. 13, 1054–1074 (2009)CrossRefGoogle Scholar
  19. 19.
    Blažič, S., Matko, D., Škrjanc, I.: Adaptive law with a new leakage term. IET Control Theory Appl. 4, 1533–1542 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Carrano, E.G., Takahashi, R.H.C., Fonseca, C.M., Neto, O.M.: Non-linear network optimization—an embedding vector space approach. IEEE Trans. Evol. Comput. 14, 206–226 (2010)CrossRefGoogle Scholar
  21. 21.
    Ko, M., Tiwari, A., Mehnen, J.: A review of soft computing applications in supply chain management. Appl. Soft Comput. 10, 661–674 (2010)CrossRefGoogle Scholar
  22. 22.
    Kudelka, M., Horak, Z., Snásel, V., Krömer, P., Platos, J., Abraham, A.: Social and swarm aspects of co-authorship network. Logic J. IGPL 20, 634–643 (2012)CrossRefGoogle Scholar
  23. 23.
    Johanyák, Z.C.: Student evaluation based on fuzzy rule interpolation. Int. J. Artif. Intell. 5, 37–55 (2010)Google Scholar
  24. 24.
    Vaščák, J., Madarász, L.: Adaptation of fuzzy cognitive maps—a comparison study. Acta Polytech. Hung. 7, 109–122 (2010)Google Scholar
  25. 25.
    Castillo, O., Melin, P., Garza, A.A., Montiel, O., Sepúlveda, R.: Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms. Soft. Comput. 15, 1145–1160 (2011)CrossRefGoogle Scholar
  26. 26.
    Schaefer, G., Hu, Q., Zhou, H., Peters, J.F., Hassanien, A.E.: Rough C-means and fuzzy rough C-means for colour quantisation. Fundam. Inf. 119, 113–120 (2012)MathSciNetGoogle Scholar
  27. 27.
    Kirkpatrick, S., Gelatt Jr, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 20, 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Geman, S., Geman, D.: Stochastic relaxation, gibbs distribution and the bayesian restoration in images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984)CrossRefzbMATHGoogle Scholar
  29. 29.
    Precup, R.-E., David, R.-C., Petriu, E.M., Rădac, M.-B., Preitl, S., Fodor, J.: Evolutionary optimization-based tuning of low-cost fuzzy controllers for servo systems. Knowl. Based Syst. 38, 74–84 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Radu-Codruţ David
    • 1
    Email author
  • Ramona-Bianca Grad
    • 1
  • Radu-Emil Precup
    • 1
  • Mircea-Bogdan Rădac
    • 1
  • Claudia-Adina Dragoş
    • 1
  • Emil M. Petriu
    • 2
  1. 1.Department of Automation and Applied Informatics“Politehnica” University of TimisoaraTimisoaraRomania
  2. 2.School of Electrical Engineering and Computer ScienceUniversity of OttawaOttawaCanada

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