A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search
Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2020  >  7(3): 822-832
Jia-Jun Wang and Tufan Kumbasar, "Optimal PID Control of Spatial Inverted Pendulum With Big Bang – Big Crunch Optimization," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 822-832, May 2020. doi: 10.1109/JAS.2018.7511267
Citation: Jia-Jun Wang and Tufan Kumbasar, "Optimal PID Control of Spatial Inverted Pendulum With Big Bang – Big Crunch Optimization," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 822-832, May 2020. doi: 10.1109/JAS.2018.7511267
shu

Optimal PID Control of Spatial Inverted Pendulum With Big Bang – Big Crunch Optimization

doi: 10.1109/JAS.2018.7511267
  • 1.

    School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China

  • 2.

    Control and Automation Engineering Department, Faculty of Electrical and Electronics Engineering, Istanbul Technical University, Istanbul TR-34469, Turkey

Funds:

the National Natural Science Foundation of China 61873079

More Information
    Abstract
  • As the extension of the linear inverted pendulum (LIP) and planar inverted pendulum (PIP), this paper proposes a novel spatial inverted pendulum (SIP). The SIP is the most general inverted pendulum (IP) than any existing IP. The model of the SIP is presented for the first time. The SIP inherits all the characteristics of the LIP and the PIP, which is a nonlinear, unstable and underactuated system. The SIP has five degrees of motion freedom and three control forces. Thus, it is a multiple-input and multiple-output (MIMO) system with nonlinear dynamics. To realize the spatial trajectory tracking of the SIP, the control structure with five PID controllers will be designed. The parameter tuning of the multiple PIDs is a challenging work for the proposed SIP model. To alleviate the difficulties of the parameter tuning for the multiple PID controllers, optimal PIDs can be achieved with the help of Big Bang-Big Crunch (BBBC) optimization. The BBBC algorithm can successfully optimize the parameters of the multiple PID controllers with high convergence speed. The optimization performance index of the BBBC algorithm is compared with that of the particle swarm optimization (PSO). Simulation results certify the rightness and effectiveness of the proposed control and optimization methods.

     

    • FullText(HTML)
  • loading
    • Recommended by Associate Editor Hongyi Li.
    References(20)
  • [1]
    K. J. Åström and K. Furuta, "Swinging up a pendulum by energy control, " Automatica, vol. 36, no. 2, pp. 287-295, Feb. 2000. http://www.sciencedirect.com/science/article/pii/S0005109899001405
    [2]
    N. A. Chaturvedi, N. H. McClamroch, and D. S. Bernstein, "Asymptotic smooth stabilization of the inverted 3-D pendulum, " IEEE Trans. Autom. Control, vol. 54, no. 6, pp. 1204-1215, May 2009. http://www.researchgate.net/publication/224471854_Asymptotic_Smooth_Stabilization_of_the_Inverted_3-D_Pendulum
    [3]
    J. Lee, R. Mukherjeea, and H. K. Khalil, "Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties, " Automatica, vol. 54, pp. 146-157, Apr. 2015. http://dl.acm.org/citation.cfm?id=2784152
    [4]
    G. Y. Liu, D. Nešić, and I. Mareels, "Non-linear stable inversion-based output tracking control for a spherical inverted pendulum, " Int. J. Control, vol. 81, no. 1, pp. 116-133, Jan. 2008. http://www.researchgate.net/publication/236210284_Non-linear_stable_inversion-based_output_tracking_control_for_a_spherical_inverted_pendulum
    [5]
    K. Furuta, M. Yamakita, and S. Kobayashi, "Swing-up control of inverted pendulum using pseudo-state feedback, " J. Syst. Control Eng., vol. 206, no. 6, pp. 263-269, Nov. 1992.
    [6]
    P. L. Kapitza, "Dynamic stability of the pendulum with vibrating suspension point, " Sov. Phys. JETP, vol. 21, no. 5, pp. 588-597, 1951.
    [7]
    S. Delgado and P. Kotyczka, "Energy shaping for position and speed control of a wheeled inverted pendulum in reduced space, " Automatica, vol. 74 pp. 222-229, Dec. 2016. http://www.sciencedirect.com/science/article/pii/S0005109816303132
    [8]
    J. Shen, A. K. Sanyal, N. A. Chaturvedi, D. S. Bernstein, and N. H. McClamroch, "Dynamics and control of a 3-D pendulum, " in Proc. IEEE Conf. Decision Control, 2004, pp. 323-328.
    [9]
    K. Furuta, "Control of pendulum: From super mechano-system to human adaptive mechatronics, " in Proc. 42nd IEEE Conf. Decision Control, Dec. 2003, pp. 1498-1507.
    [10]
    G. J. Silva, A. Datta, and S. P. Bhattacharyya, "New results on the synthesis of PID controllers, " IEEE Trans. Autom. Control, vol. 47, no. 2, pp. 241-252, Aug. 2002.
    [11]
    A. Ghosh, T. R. Krishnan, and B. Subudhi, "Robust proportional-integral-derivative compensation of an inverted cart-pendulum system: an experimental study, " IET Control Theory Appl., vol. 6, no. 8, pp. 1145-1152, Jul. 2012.
    [12]
    S. Jung, H.-T. Cho, and T. C. Hsia, "Neural network control for position tracking of a two-axis inverted pendulum system: experimental studies, " IEEE Trans. Neural Netw, vol. 18, no. 4, pp. 1042-1048, Jul. 2007.
    [13]
    J. J. Wang, "Simulation studies of inverted pendulum based on PID controllers, " Simul. Model Pract. Theory, vol. 19, pp. 440-449, Jan. 2011.
    [14]
    M. J. Neath, A. K. Swain, U. K. Madawala, and D. J. Thrimawithana, "An optimal PID controller for a bidirectional inductive power transfer system using multiobjective genetic algorithm, " IEEE Trans. Power Electron., vol. 29, no. 3, pp. 1523-1531, May 2014.
    [15]
    A. Z. Gaing, "A particle swarm optimization approach for optimum design of PID controller in AVR system, " IEEE Trans. Energy Convers., vol. 19, no. 2, pp. 384-391, May 2004.
    [16]
    A. Monaram, M. A. El-Hosseini, and H. A. Ahi, "Design of optimal PID controller using hybrid differential evolution and particle swarm optimization with an aging leader and challengers, " Appl. Soft Comput, vol. 38, pp. 727-737, Jan. 2016. http://www.sciencedirect.com/science/article/pii/S156849461500681X
    [17]
    O. K. Erol and I. Eksin, "A new optimization method: Big Bang-Big Crunch, " Adv. Eng. Softw., vol. 37, pp. 106-111, Feb. 2006.
    [18]
    T. Kumbasar and H. Hagras, "Big Bang-Big Crunch optimization based interval type-2 fuzzy PID cascade controller design strategy, " Inf. Sci., vol. 282, pp. 277-295, Oct. 2014.
    [19]
    T. Kumbasar and H. Hagras, "A self-tuning zSlices-based general type-2 fuzzy PI controller, " IEEE Trans. Fuzzy Syst., vol. 23, no. 4, pp. 991- 1013, Jul. 2015.
    [20]
    E. Yesil, "Interval type-2 fuzzy PID load frequency controller using Big Bang-Big Crunch optimization, " Appl. Soft Comput, vol. 15, pp. 100- 112, Feb. 2014. http://www.sciencedirect.com/science/article/pii/S1568494613003657
    • Related Articles
    • Supplements(0)

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(11)  / Tables(5)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1366) PDF downloads(73) Cited by()

    Highlights

    • A novel spatial inverted pendulum (SIP) is proposed for the first time.
    • Five PID controllers are designed for the SIP to realize the tracking control.
    • The parameters of the PID controllers are optimized with Big Bang-Big Crunch (BBBC).
    • The optimization performance of the BBBC is compared with that of the PSO.

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return