Performance Comparison of PID and ANFIS Controller for Stabilization of x and x-y Inverted Pendulums

  • Ishan Chawla
  • Vikram ChopraEmail author
  • Ashish Singla
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 940)


Inverted pendulum is a highly unstable, nonlinear and an under-actuated system. Its dynamics resembles many real-time systems such as segways, self-balancing robots, vertical take-off and landing aircraft (VTOL) and crane lifting containers etc. These real-time applications demand the need of a robust controller. In literature, many different control strategies have been discussed to stabilize an inverted pendulum, out of them, the most robust being fuzzy control and sliding mode control. The former is difficult to tune and has a problem of rule explosion for multivariable system, whereas the latter has a problem of discontinuity and chattering. To address the issues in fuzzy controller, a novel robust linear quadratic regulator (LQR) based adaptive-network fuzzy inference system (ANFIS) controller is proposed and implemented on the stabilization of x and x-y inverted pendulums. These pendulums differ from each other in degrees-of-freedom, complexity of the mathematical model and their respective degree of under-actuation. The proposed controller is able to solve the problem of robustness in the LQR controller as well as the difficulty in tuning along with rule explosion in fuzzy controller. Furthermore, the designed controller is tested for different pendulum masses and the results show that as compared with conventional PID controller, the proposed controller gives better performance in achieving lesser overshoot and settling time along with better robustness properties.


Inverted pendulum Stabilization ANFIS controller Robustness 



The authors are grateful to the Thapar Institute of Engineering and Technology (TIET), Patiala for providing the financial support under seed money grant project (TU/DORSP/57/426, 28-03-2017) to perform this research.


  1. 1.
    Astrom, K.J., Furuta, K.: Swinging up a pendulum by energy control. Automatica 36(2), 287–295 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Martin, P., Devasia, S., Paden, B.: A different look at output tracking: control of a VTOL aircraft. Automatica 32(1), 101–107 (1996)CrossRefGoogle Scholar
  3. 3.
    Younis, W., Abdelati, M.: Design and implementation of an experimental segway model. In: AIP Conference Proceedings Tunisia, pp. 1–7 (2009)Google Scholar
  4. 4.
    Tsai, C.C., Huang, H.C., Lin, S.C.: Adaptive neural network control of a self balancing two-wheeled scooter. IEEE Trans. Industr. Electron. 57(4), 1420–1428 (2010)CrossRefGoogle Scholar
  5. 5.
    Elhasairi, A., Pechev, A.: Humanoid robot balance control using the spherical inverted pendulum mode. Front. Rob. AI 2, 1–13 (2015)Google Scholar
  6. 6.
    Furuta, K., Yamakita, M., Kobayashi, S.: Swing-up control of inverted pendulum using pseudo-state feedback. In: Proceedings of the Institution of Mechanical Engineers, Part I: J. Syst. Control Eng. 206(4), 263–269 (1992)Google Scholar
  7. 7.
    Spong, M.W.: The swing up control problem for the acrobot. IEEE Control Syst. 15(1), 49–55 (1995)CrossRefGoogle Scholar
  8. 8.
    Fantoni, I., Lozano, R., Spong, M.W.: Energy based control of the pendubot. IEEE Trans. Autom. Control 45(4), 725–729 (2000)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Block, D.J., Åström, K.J., Spong, M.W.: The reaction wheel pendulum. In: Synthesis Lectures on Control and Mechatronics, vol. 1, no. 1, pp. 1–105 (2007)CrossRefGoogle Scholar
  10. 10.
    Acosta, J.: Furuta’s pendulum: a conservative nonlinear model for theory and practice. Math. Prob. Eng. (2010)Google Scholar
  11. 11.
    Muskinja, N., Tovornik, B.: Swinging up and stabilization of a real inverted pendulum. IEEE Trans. Industr. Electron. 53(2), 631–639 (2006)CrossRefGoogle Scholar
  12. 12.
    Wang, J.J.: Stabilization and tracking control of X–Z inverted pendulum with sliding-mode control. ISA Trans. 51(6), 763–770 (2012)CrossRefGoogle Scholar
  13. 13.
    Wang, J.J.: Simulation studies of inverted pendulum based on PID controllers. Simul. Model. Pract. Theory 19(1), 440–449 (2011)CrossRefGoogle Scholar
  14. 14.
    Kumar, E.V., Jerome, J.: Robust LQR controller design for stabilizing and trajectory tracking of inverted pendulum. Procedia Eng. 64, 169–178 (2013)CrossRefGoogle Scholar
  15. 15.
    Ghosh, A., Krishnan, T.R., Subudhi, B.: Robust PID compensation of an inverted cart-pendulum system: an experimental study. IET Control Theory Appl. 6, 1145–1152 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Bui, H.L., Tran, D.T., Vu, N.L.: Optimal fuzzy control of an inverted pendulum. J. Vib. Control 18(14), 2097–2110 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kharola, A.: A PID based ANFIS & fuzzy control of inverted pendulum on inclined plane (IPIP). Int. J. Smart Sens. Intell. Syst. 9(2), 616–636 (2016)Google Scholar
  18. 18.
    Castillo, O., Malin, P.: Intelligent adaptive model-based control of robotic dynamic systems with a hybrid fuzzy-neural approach. Appl. Soft Comput. 3(4), 363–378 (2003)CrossRefGoogle Scholar
  19. 19.
    Castillo, O., Malin, P.: Intelligent control of complex electrochemical systems with a neuro-fuzzy-genetic approach. IEEE Trans. Industr. Electron. 48(5), 951–955 (2001)CrossRefGoogle Scholar
  20. 20.
    Melin, P.: Intelligent control of a stepping motor drive using a hybrid neuro-fuzzy approach. Appl. Soft Comput. 8(8), 546–555 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThapar Institute of Engineering and TechnologyPatialaIndia
  2. 2.Department of Electrical and Instrumentation EngineeringThapar Institute of Engineering and TechnologyPatialaIndia

Personalised recommendations