Design of a hierarchical fuzzy model predictive controller

  • Authors

    • Zeinab Fallah Department of Control Engineering Islamic Azad University, South Tehran Branch, Tehran, Iran
    • Mojtaba Ahmadieh Khanesar Department of Electrical & Control Engineering, Semnan University, Semnan, Iran
    • Mohammad Teshnehlab Department of Control Engineering, K. N. Toosi University of Tech. Tehran, Iran
    2015-04-15
    https://doi.org/10.14419/ijet.v4i2.2854
  • Control, Neuro-Fuzzy Network, Hierarchical Fuzzy System, Gradient Descent, Recursive Least Square, Continuous Stirred Tank Reactor.

  • Abstract

    In order to control a nonlinear system using Nonlinear Model Predictive Control (NMPC), a nonlinear model from system is required. In this paper, a hierarchical neuro-fuzzy model is used for nonlinear identification of the plant. The use of hierarchical neuro-fuzzy systems makes it possible to overcome the curse of dimensionality. In neuro-fuzzy systems, if the input number increases, then the number of rules increases exponentially. One solution to this problem is making use of Hierarchical Fuzzy System Mamdani (HFS) in which the number of the rules increases linearly. Gradient descent and recursive least square algorithm are used simultaneously to train the parameters of the HFS. Gradient Descent Algorithm is utilized to train the parameters, which appear nonlinearly in the output of HFS, and RLS is used to train the parameters of consequent the part, which appears linearly in the output of HFS. Finally, a model predictive fuzzy controller based on a predictive cost function is proposed. Using Gradient Descent Algorithm, the parameters of the controller are optimized. The proposed controller is simulated on the control of continuous stirred tank reactor. It is shown that the proposed method can control the system with high performance.

  • References

    1. [1] E. F. Camacho and C. Bordons, "Model predictive control", 2nd Edition, Springer, 2005.

      [2] F. Allgower and A. Z. Zheng, "Nonlinear model predictive control: Assessment and future directions for research", Birkhäuser Basel, Germany, 2000. http://dx.doi.org/10.1007/978-3-0348-8407-5.

      [3] Zhang, T., G. Feng, and X.-J. Zeng, "Output tracking of constrained nonlinear processes with oset-free input-to-state stable fuzzy predictive control", Automatica 45 (4): 900–909. 2009. http://dx.doi.org/10.1016/j.automatica.2008.11.016.

      [4] Lendek, Z., R. Babuska, and B. De Schutter, "Stability of cascaded fuzzy systems and observers", IEEE Transactions on Fuzzy Systems 17 (3): 641–653. 2009. http://dx.doi.org/10.1109/TFUZZ.2008.924353.

      [5] Khanesar, Mojtaba Ahmadieh, Mohammad Teshnehlab, and Okyay Kaynak, "Control and synchronization of chaotic systems using a novel indirect model reference fuzzy controller", Soft Computing 16 (7): 1253-1265, 2012. http://dx.doi.org/10.1007/s00500-012-0810-z.

      [6] Cheong, F. and R. Lai, "Designing a hierarchical fuzzy logic controller using the differential evolution approach", Applied Soft Computing 7 (2): 481–491. 2007. http://dx.doi.org/10.1016/j.asoc.2006.12.001.

      [7] Jahromi, M. Z. and M. Taheri, "A proposed method for learning rule weights in fuzzy rule-based classification systems", Fuzzy Sets and Systems 159 (4): 449–459. 2008. http://dx.doi.org/10.1016/j.fss.2007.08.007.

      [8] Lee, M. and W. Pedrycz, “Adaptive learning of ordinal-numerical mappings through fuzzy clustering for the objects of mixed features", Fuzzy Sets and Systems 161 (4): 564–577. 2010. http://dx.doi.org/10.1016/j.fss.2009.05.011.

      [9] Zeng XJ, Keane JA, “Approximation capabilities of hierarchical fuzzy systems", IEEE Trans Fuzzy Syst 13(5):659–672. 2005. http://dx.doi.org/10.1109/TFUZZ.2005.856559.

      [10] Khanesar, M. A., M. A. Shoorehdeli, and M. Teshnehlab, “Hybrid training of recurrent fuzzy neural network modelâ€, In Mechatronics and Automation, 2007. ICMA 2007. International Conference on, pp. 2598-2603, 2007.

      [11] Raju, G.V.S., Zhou, J., Kisner R.A, “Hierarchical Fuzzy Controlâ€, International Journal of Control 54(1991)1201-1216. 1991.

      [12] Fallah, Z., Khanesar, M.A., Teshnehlab, M., “Hierarchical fuzzy identification using gradient descent and recursive least square methodâ€, computer, control & communication (ic4), 2013 3rd international conference on, 25-26 sept. 2013.

      [13] Espinosa, Jairo J., and Joos Vandewalle, “ Predictive control using fuzzy modelsâ€, In Advances in Soft Computing, pp. 187-200, 1999.

      [14] Y. Chen, J. Dong, and B. Yang, “ Automatic design of hierarchical TS-FS model using ant programming and pso algorithmâ€, Proceedings 12th International Conference on Artificial Intelligence, Methodology, Systems and Applications, Lecture Notes on Artificial Inteligence, LNAI 3192, pages 285–294.2004.

      [15] Xiangyan Zhang and Naiyao Zhang, “Universal Approximation of Binary-Tree Hierarchical Fuzzy Systems with Typical FLUsâ€, Springer- Verlag Berlin Heidelberg. 2006.

      [16] D. Soloway and P. J Haley, “Neural Generalized Predictive Control; A Newton Raphson Implementationâ€, Proceeding of IEEE International Symposium on Intelligent Control, PP.2777-282, 1996.

      [17] P. Gil, J. Henriques, A. Dourado and H. Duarte-Ramos, “Extended Neural Model Predictive Control of Non-linear Systemsâ€, Proceeding of IASTED-ASC2000, PP. 94-100, 2000.

      [18] .C. Zhu: “Multivariable system identification for process controlâ€, Elsevier Science, Oxford, 2001.

      [19] M. Leskens, J.L.F Kessel. Van M. J. van den and O. H. Bosgra, “ Nonlinear Model Predictive Control with Moving Horizon State and Disturbance Estimation – with Application to MSW Combustion â€, Proceeding of 16th IFAC World Congress, PP.1-6,2005.

  • Downloads

  • How to Cite

    Fallah, Z., Ahmadieh Khanesar, M., & Teshnehlab, M. (2015). Design of a hierarchical fuzzy model predictive controller. International Journal of Engineering & Technology, 4(2), 342-349. https://doi.org/10.14419/ijet.v4i2.2854

    Received date: 2014-05-20

    Accepted date: 2014-06-21

    Published date: 2015-04-15