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Volume 6 Issue 6
Nov.  2019

IEEE/CAA Journal of Automatica Sinica

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Mohammad Javad Mahmoodabadi and Saideh Arabani Mostaghim, "Stability of Nonlinear Systems Using Optimal Fuzzy Controllers and Its Simulation by Java Programming," IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1519-1527, Nov. 2019. doi: 10.1109/JAS.2017.7510388
Citation: Mohammad Javad Mahmoodabadi and Saideh Arabani Mostaghim, "Stability of Nonlinear Systems Using Optimal Fuzzy Controllers and Its Simulation by Java Programming," IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1519-1527, Nov. 2019. doi: 10.1109/JAS.2017.7510388

Stability of Nonlinear Systems Using Optimal Fuzzy Controllers and Its Simulation by Java Programming

doi: 10.1109/JAS.2017.7510388
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  • In this paper, at first, the single input rule modules (SIRMs) dynamically connected fuzzy inference model is used to stabilize a double inverted pendulum system. Then, a multi-objective particle swarm optimization (MOPSO) is implemented to optimize the fuzzy controller parameters in order to decrease the distance error of the cart and summation of the angle errors of the pendulums, simultaneously. The feasibility and efficiency of the proposed Pareto front is assessed in comparison with results reported in literature and obtained from other algorithms. Finally, the Java programming with applets is utilized to simulate the stability of the nonlinear system and explain the internet-based control.


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  • [1]
    Y. Becerikli and B. K. Celik, "Fuzzy control of inverted pendulum and concept of stability using Java application, " Math. Comput. Model., vol. 46, no. 1-2, pp. 24-37, Jul, 2007.
    M. J. Mahmoodabadi, A. Bagheri, S. Arabani Mostaghim, and M. Bisheban, "Simulation of stability using Java application for Pareto design of controllers based on a new multi-objective particle swarm optimization, " Math. Comput. Model., vol. 54, no. 5-6, pp. 1584-1607, Sep. 2011.
    Z. Liu, Y. Zhang, and Y. N. Wang, "A type-2 fuzzy switching control system for biped robots, " IEEE Trans. Syst. Man Cybern. Part C Appl. Rev., vol. 37, no. 6, pp. 1202-1213, Nov. 2007.
    C. S. Tseng and B. S. Chen, "Robust fuzzy observer-based fuzzy control design for nonlinear discrete-time systems with persistent bounded disturbances, " IEEE Trans. Fuzzy Syst., vol. 17, no. 3, pp. 711-723, Jun. 2009.
    C. H. Huang, W. J. Wang, and C. H. Chiu, "Design and implementation of fuzzy control on a two-wheel inverted pendulum, " IEEE Trans. Industr. Electron., vol. 58, no. 7, pp. 2988-3001, Jul. 2011.
    Y. G. Zhu, "Fuzzy optimal control for multistage fuzzy systems, " IEEE Trans. Syst. Man Cybern. Part B, vol. 41, no. 4, pp. 964-975, Aug. 2011.
    T. Wang, Y. F. Zhang, J. B. Qiu, and H. J. Gao, "Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements, " IEEE Trans. Fuzzy Syst., vol. 23, no. 2, pp. 302-312, Apr. 2015.
    J. Q. Yi, N. Yubazaki, and K. Hirota, "A new fuzzy controller for stabilization of parallel-type double inverted pendulum system, " Fuzzy Sets Syst., vol. 126, no. 1, pp. 105-119, Feb. 2002.
    D. A. Shook, P. N. Roschke, P. Y. Lin, and C. H. Loh, "GA-optimized fuzzy logic control of a large-scale building for seismic loads, "Eng. Struct., vol. 30, no. 2, pp. 436-449, Feb. 2008.
    H. Shayeghi, A. Jalili, and H. A. Shayanfar, " Multi-stage fuzzy load frequency control using PSO, "Energy Conver. Manage., vol. 49, no. 10, pp. 2570-2580, Oct. 2008.
    Z. Bingul and O. Karahan, " A fuzzy logic controller tuned with PSO ¨ for 2 DOF robot trajectory control, "Expert Syst. Appl., vol. 38, no. 1, pp. 1017-1031, Jan. 2011.
    B. Ahmadi, M. Ghamati, A. Jamali, and N. Nariman-Zadeh, " Pareto robust reliability-based controller design for probabilistic uncertain systems using fuzzy rules, "in Proc. IEEE Int. Symp. Innovations in Intelligent Systems and Applications (INISTA), Istanbul, Turkey, 2011, pp. 59-63.
    M. J. Mahmoodabadi, M. B. Salahshoor Mottaghi, and A. Mahmodinejad, " Optimum design of fuzzy controllers for nonlinear systems using multi-objective particle swarm optimization, "J. Vib. Control, vol. 22, no. 3, pp. 769-783, Feb. 2016. doi: 1077546314532116.
    J. Kennedy and R. Eberhart, " Particle swarm optimization, "in Proc. IEEE Int. Conf. Neural Networks, Perth, WA, Australia, 1995, pp. 1942- 1948.
    P. J. Angeline, " Using selection to improve particle swarm optimization, in Proc. IEEE Int. Conf. Evolutionary Computation Proc. IEEE World Congr. Computational Intelligence, Anchorage, AK, USA, 1998, pp. 84-89.
    H. Yoshida, K. Kawata, Y. Fukuyama, S. Fukuyama, and Y. Fukuyama, A particle swarm optimization for reactive power and voltage control considering voltage security assessment, "IEEE Trans. Power Syst., vol. 15, no. 4, pp. 1232-1239, Nov. 2000.
    X. Chen and Y. M. Li, " A modified PSO structure resulting in high exploration ability with convergence guaranteed, "IEEE Trans. Syst. Man Cybern. Part B, vol. 37, no. 5, pp. 1271-1289, Oct. 2007.
    Y. P. Chen, W. C. Peng, and M. C. Jian, " Particle swarm optimization with recombination and dynamic linkage discovery, "IEEE Trans. Syst. Man Cybern. Part B, vol. 37, no. 6, pp. 1460-1470, Dec. 2007.
    C. K. Monson and K. D. Seppi, " The Kalman swarm: A new approach to particle motion in swarm optimization, "in Proc. Genetic and Evolutionary Computation Conf., Seattle, WA, USA, 2004, pp. 140-150.
    S. Janson and M. Middendorf, " A hierarchical particle swarm optimizer and its adaptive variant, "IEEE Trans. Syst. Man Cybern. Part B, vol. 35, no. 6, pp. 1272-1282, Dec. 2005.
    R. A. Krohling and L. Dos Santos Coelho, " Coevolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems, "IEEE Trans. Syst. Man Cybern. Part B, vol. 36, no. 6, pp. 1407-1416, Dec. 2006.
    F. Van Den Bergh and A. P. Engelbrecht, " A new locally convergent particle swarm optimiser, "in Proc. IEEE Int. Conf. Systems, Man, and Cybernetics, Yasmine Hammamet, Tunisia, 2002, pp. 96-101.
    W. J. Zhang and X. F. Xie, " DEPSO: hybrid particle swarm with differential evolution operator, "in Proc. IEEE Int. Conf. Systems, Man, and Cybernetics, Washington, DC, USA, 2003, pp. 3816-3821.
    X. H. Hu and R. C. Eberhart, " Multiobjective optimization using dynamic neighborhood particle swarm optimization, "in Proc. Congr. Evolutionary Computation, Honolulu, HI, USA, 2002, pp. 1677-1681.
    J. E. Fieldsend and S. Singh, " A multi-objective algorithm based upon particle swarm optimisation, an efficient data structure and turbulence, in Proc. Workshop on Computational Intelligence, Birmingham, UK, 2002, pp. 34-44.
    S. Mostaghim and J. Teich, "Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO), " in Proc. IEEE Swarm Intelligence Symp., Indianapolis, IN, USA, 2003, pp. 26-33.
    K. E. Parsopoulos, D. K. Tasoulis, and M. N. Vrahatis, "Multiobjective optimization using parallel vector evaluated particle swarm optimization, " in Proc. IASTED Int. Conf. Artificial Intelligence and Applications, Innsbruck, Austria, 2004.
    G. G. Yen and W. F. Leong, "Dynamic multiple swarms in multiobjective particle swarm optimization, " IEEE Trans. Syst. Man Cybern. Part A Syst. Hum., vol. 39, no. 4, pp. 890-911, Jul. 2009.
    W. F. Leong and G. G. Yen, "PSO-based multiobjective optimization with dynamic population size and adaptive local archives, " IEEE Trans. Syst. Man Cybern. Part B, vol. 38, no. 5, pp. 1270-1293, Oct. 2008
    N. Yubazaki, J. Yi, M. Otani, and K. Hirota, "SIRMs connected fuzzy inference model and its applications to first-order lag systems and second-order lag systems, " in Proc. Asian Fuzzy Systems Symp. Soft Computing in Intelligent Systems and Information Processing, Kenting, China, 1996, pp. 545-550.
    R. C. Eberhart, R. Dobbins, and P. K. Simpson, Computational Intelligence PC Tools. British Columbia, Canada: Morgan Kaufmann Publishers, 1996.
    A. P. Engelbrecht, Computational Intelligence: An Introduction. West Sussex, England: John Wiley & Sons, 2002.
    A. P. Engelbrecht, Fundamentals of Computational Swarm Intelligence. Hoboken, NJ, USA: John Wiley & Sons, 2005.
    R. C. Eberhart and Y. H. Shi, "Comparison between genetic algorithms and particle swarm optimization, " in Proc. 7th Int. Conf. Evolutionary Programming Ⅶ, San Diego, California, USA, 1998, pp. 611-616.
    R. C. Eberhart and J. Kennedy, "A new optimizer using particle swarm theory, " in Proc. 6th Int. Symp. Micro Machine and Human Science, Nagoya, Japan, 1995, pp. 39-43.
    A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, "Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficient, " IEEE Trans. Evol. Comput., vol. 8, no. 3, pp. 240-255, Jun. 2004.
    S. J. Tsai, T. Y. Sun, C. C. Liu, S. T. Hsieh, W. C. Wu, and S. Y Chiu, "An improved multi-objective particle swarm optimizer for multiobjective problems, " Expert Syst. Appl., vol. 37, no. 8, 5872-5886, Aug. 2010.
    S. Mostaghim and J. Teich, " The role of ε-dominance in multi objective particle swarm optimization methods, " in Proc. Congr. Evolutionary Computation, Canberra, ACT, Australia, 2003, pp. 1764-1771.
    Y. J. Wang and Y. P. Yang, "Particle swarm optimization with preference order ranking for multi-objective optimization, " Inf. Sci., vol. 179, no. 2, pp. 1944-1959, May 2009.
    G. Hernández-Díaz, L. V. Santana-Quintero, C. A. Coello Coello, J. Molina, and R. Caballero, "Improving the efficiency of"-dominance based grids, "Inf. Sci., vol. 181, no. 15, pp. 3101-3129, Aug. 2011.
    M. J. Mahmoodabadi, S. Arabani Mostaghim, A. Bagheri, and N. Nariman-Zadeh, " Pareto optimal design of the decoupled sliding mode controller for an inverted pendulum system and its stability simulation via Java programming, " Math. Comput. Model., vol. 57, no. 5-6, pp. 1070-1082, Mar. 2013.
    K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, " A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ, "IEEE Trans. Evol. Comput., vol. 6, no. 2, pp. 182-197, Apr. 2002.
    H. Gould, J. Tobochnik, and W. Christian, An Introduction to Computer Simulation Methods: Applications to Physical Systems, 3rd ed. Reading, Mass., USA: Addison-Wesley Publishing, 2006.
    H. M. Deitel and P. J. Deitel, Java? How to Program, 6th ed. Upper Saddle River, NJ, USA: Prentice Hall Publishing, 2004.
    P. Chan and S. E. Ingram, Developing Professional Java Applets. Indianapolis, IN, USA: Macmillan Publishing Co., 1996.


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    • A novel multi-objective particle swarm optimization was introduced
    • The leader selection method was based on density measures, the personal best positions were determined via Sigma method, the dynamic elimination technique was applied to prune the archive, and the turbulence operator was utilized to escape from the local minima.
    • An optimal fuzzy controllers was designed for the double inverted pendulum system.
    • The modeling, control and stability simulation of the double inverted pendulum system were presented on the net using Java Applets with educational goals.


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