Control of the Inverted Pendulum Using Quickly Adjustable, Discrete FOPID Controller

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


In the paper the control of inverted pendulum by discrete, Quickly Adjustable Fractional Order PID (QAFOPID) controllers is addressed. The fractional order parts of the both controllers are approximated using CFE approximation. The fractional orders can be easily switched using predefined CFE coefficients loaded from memory. The QAFOPIDs were tuned using GWO optimizer and simulations. Results of simulations and experiments show that the use of QAFOPID controllers allows one to obtain good control performance in the sense of the considered cost function.


Fractional order systems Fractional PID control Inverted pendulum Real time system GWO optimizer 



This paper was sponsored by AGH project no


  1. 1.
    Agarwal, H., Singh, A.P., Srivastava, P.: Fractional order controller design for inverted pendulum on a cart system (POAC). WSEAS Trans. Syst. Control 10, 172–178 (2015). E-ISSN 2224-2856Google Scholar
  2. 2.
    Caponetto, R., Dongola, G., Fortuna, l., Petras, I.: Fractional Order Systems. Modeling and Control Applications. World Scientific Series on Nonlinear Science, Series A, vol. 72. World Scientific Publishing Google Scholar
  3. 3.
    Chen, Y.Q., Moore, K.L.: Discretization schemes for fractional order differentiators and integrators. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 49(3), 263–269 (2002)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Dziedzic, K.: Identification of fractional order transfer function model using biologically inspired algorithms. In: Automation 2019 (2019).
  5. 5.
  6. 6.
    Jia-Jun, W.: Position and speed tracking control of inverted pendulum based on double PID controllers. In: 2015 34th Chinese Control Conference (CCC), Hangzhou, pp. 4197–4201 (2015).
  7. 7.
  8. 8.
    Maruki, Y., Kawano, K., Suemitsu, H., Matsuo, T.: Adaptive backstepping control of wheeled inverted pendulum with velocity estimator. Int. J. Control Autom. Syst. 12, 1040–1048 (2014)CrossRefGoogle Scholar
  9. 9.
    Mirjalili, S., Mohammad Mirjalili, S., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)CrossRefGoogle Scholar
  10. 10.
    Mishra, S.K., Chandra, D.: Stabilization and tracking control of inverted pendulum using fractional order PID controllers. J. Eng. (2014). Article ID 752918, 9 pagesGoogle Scholar
  11. 11.
    Oprzedkiewicz, K., Gawin, E., Gawin, T.: Real-time PLC implementations of fractional order operator. In: Szewczyk, R., Zielinski, C., Kaliczynska, M. (eds.) Automation 2018: Innovations in Automation, Robotics and Measurement Techniques. Advances in Intelligent Systems and Computing, vol. 743, pp. 36–51. Springer, Cham (2018). ISSN 2194-5357CrossRefGoogle Scholar
  12. 12.
    Ostalczyk, P.: Discrete Fractional Calculus. Applications in Control and Image Processing. Series in Computer Vision, vol. 4. World Scientific Publishing, Singapore (2016)CrossRefGoogle Scholar
  13. 13.
    Paliwal, S., Pathak, V.K.: Analysis & control of inverted pendulum system using PID controller. J. Eng. Res. Appl. 7(5), 01–04 (2018). ISSN 2248-9622.
  14. 14.
    Petráš, I.: Fractional - order feedback control of a DC motor. J. Electr. Eng. 60(3), 117–128 (2009)Google Scholar
  15. 15.
  16. 16.
    Stanislawski, R., Latawiec, K.J., Lukaniszyn, M.: A comparative analysis of Laguerre-based approximators to the Grunwald-Letnikov fractional-order difference. Math. Probl. Eng. (2015). Article ID 512104, 10 pages.
  17. 17.
    Vinagre, B.M., Podlubny, I., Hernandez, A., Feliu, V.: Some approximations of fractional order operators used in control theory and applications. Fract. Cal. Appl. Anal. 3(3), 231–248 (2000)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Wang, H., Dong, H., He, L., Shi, Y., Zhang, Y.: Design and simulation of LQR controller with the linear inverted pendulum. In: 2010 International Conference on Electrical and Control Engineering, Wuhan, pp. 699–702 (2010).
  19. 19.
    Yu, L.H., Jian, F.: An inverted pendulum fuzzy controller design and simulation. In: 2014 International Symposium on Computer, Consumer and Control, Taichung, pp. 557–559 (2014).
  20. 20.
    Żegleń, J.: Advanced control methods of an inverted pendulum on the card implemented in PLC (Zaawansowane metody sterowania modelem laboratoryjnym wahadła na wózku implementowane w sterowniku PLC). Master thesis at AGH University under supervision M. Rosół (2018)Google Scholar
  21. 21.
    Żegleń, J.: The application of an adaptive controller combined with the LQR controller for the inverted pendulum. Pomiary Automatyka Robotyka 4(2019), 47–54 (2019). Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Automatic Control and RoboticsAGH UniversityKrakowPoland

Personalised recommendations