Nonlinear Control Law Design for Inverted Pendulum Systems via RBF Neural Networks

Authors

  • Huynh Van Khuong Le Quy Don Technical University
  • Nguyen Xuan Chiem Le Quy Don Technical University
  • Alexander Obukhov Don State Technical University

DOI:

https://doi.org/10.59247/jfsc.v3i2.314

Keywords:

Backstepping, RBF Neural Networks, Adaptive Control, Inverted Pendulum System

Abstract

This paper presents the design of a nonlinear control law based on the Backstepping method combined with Radial Basis Function (RBF) neural networks to ensure the stability of an inverted pendulum system with unknown model parameters. The control design is developed using a general form of the system’s mathematical model, in which the unknown nonlinear functions are approximated by RBF neural networks. Experimental results conducted on the STM32F4 embedded platform demonstrate that the proposed approach not only guarantees system stability but also verifies the effectiveness and practical applicability of the control law.

References

L. B. Prasad, B. Tyagi, and H. O. Gupta, "Optimal control of nonlinear inverted pendulum system using PID controller and LQR: performance analysis without and with disturbance input," International Journal of Automation and Computing, vol. 11, no. 6, pp. 661-670, 2014, https://doi.org/10.1007/s11633-014-0818-1.

T.-B. Dang et al., “PID Control for Cart and Pole system: Simulation and Experiment,” Journal of Fuzzy Systems and Control, vol. 2, no. 1, pp. 29-35, 2024, https://doi.org/10.59247/jfsc.v2i1.165.

N. X. Chiem and L. T. Thang, “Synthesis of LQR Controller Based on BAT Algorithm for Furuta Pendulum Stabilization,” Journal of Robotics and Control (JRC), vol. 4, no. 5, pp. 662-669, 2023, https://doi.org/10.18196/jrc.v4i5.19661.

Fahmizal, Geonoky, and H. Maghfiroh, “Rotary Inverted Pendulum Control with Pole Placement,” Journal of Fuzzy Systems and Control, vol. 1, no. 3, pp. 90-96, 2023, https://doi.org/10.59247/jfsc.v1i3.152.

C. X. Nguyen, T. D. Pham, A. D. Lukynov, P. C. Tran, and Q. D. Truong, "Design embedded control system based controller of the quasi time optimization approach for a magnetic levitation system," IOP Conference Series: Materials Science and Engineering, vol. 1029, no. 1, p. 012020, 2021, https://doi.org/10.1088/1757-899X/1029/1/012020.

D.-P. Hoang, “A Survey of Experimental LQR for Cart and Pole,” Journal of Fuzzy Systems and Control, vol. 2, no. 2, pp. 97-103, 2024, https://doi.org/10.59247/jfsc.v2i2.211.

C. N. Xuan and T. Le Tran, "Design of State Feedback Controller with Optimal Parameters Using Bat Algorithm for Reaction Wheel Pendulum," 2021 International Conference on Advanced Technologies for Communications (ATC), pp. 172-177, 2021, https://doi.org/10.1109/ATC52653.2021.9598306.

N. X. Chiem and H. N. Phan, "Design controler of the quasi-time optimization approach for stabilizing and trajectory tracking of inverted pendulum," MATEC Web of Conferences, vol. 226, p. 02007, 2018, https://doi.org/10.1051/matecconf/201822602007.

H. N. Phan and C. X. Nguyen, "Building embedded quasi-time-optimal controller for two-wheeled self-balancing robot," MATEC Web of Conferences, vol. 132, p. 02005, 2017, https://doi.org/10.1051/matecconf/201713202005.

S. Irfan, A. Mehmood, M. T. Razzaq, and J. Iqbal, "Advanced sliding mode control techniques for inverted pendulum: Modelling and simulation," Engineering science and technology, an international journal, vol. 21, no. 4, pp. 753-759, 2018, https://doi.org/10.1016/j.jestch.2018.06.010.

M. Mahmoud, R. Saleh, and A. Ma’arif, "Stabilizing of inverted pendulum system using Robust sliding mode control," International Journal of Robotics and Control Systems, vol. 2, no. 2, pp. 230-239, 2022, https://doi.org/10.31763/ijrcs.v2i2.594.

H.-G.-B. Pham, “Trajectories Tracking Control for Rotary Inverted Pendulum using Backstepping Method,” Journal of Fuzzy Systems and Control, vol. 3, no. 1, pp. 57-63, 2025, https://doi.org/10.59247/jfsc.v3i1.276.

C. Nguyen, H. Phan, and H. Nguyen, “An energy saving method of stable control of inverted pendulum system when affected by external interference using auxiliary pendulum,” E3s web of conferences, vol. 104, p. 5, 2019, https://doi.org/10.1051/e3sconf/201910401015.

C. X. Nguyen, A. D. Lukianov, T. D. Pham, and A. D. Nguyen, "Synthesis of a nonlinear control law with efficiency energy for the self-balancing two wheeled vehicle," IOP Conference Series: Materials Science and Engineering, vol. 900, no. 1, p. 012002, 2020, https://doi.org/10.1088/1757-899X/900/1/012002.

C. X. Nguyen, T. T. Le, P. C. Tran, A. D. Lukianov, K. D. Truong, and T. D. Pham, "Synthesis of non-linear controller to energy efficiency for damped-elastic-jointed inverted pendulum," E3S Web of Conferences, vol. 279, p. 01020, 2021, https://doi.org/10.1051/e3sconf/202127901020.

A. Jain, D. Tayal, and N. Sehgal, "Control of non-linear inverted pendulum using fuzzy logic controller," International Journal of Computer Applications, vol. 69, no. 27, pp. 7-11, 2013, https://doi.org/10.5120/12141-8278.

J. Liu, “Radial Basis Function (RBF) Neural Network Control for Mechanical Systems,” Springer Nature Link, 2013, https://doi.org/10.1007/978-3-642-34816-7.

A. Bounemeur, M. Chemachema, and S. Bouzina, "Fuzzy Fault-Tolerant Control Applied on Two Inverted Pendulums with Nonaffine Nonlinear Actuator Failures," International Journal of Robotics and Control Systems, vol. 3, no. 2, pp. 144-160, 2023, https://doi.org/10.31763/ijrcs.v3i2.917.

C. Xia, I. Qaisar, and M. S. Aslam, "Design of Hybrid Controller using Qualitative Simulation Internal Modeling for Inverted Pendulum," International Journal of Robotics and Control Systems, vol. 2, no. 4, pp. 638-651, 2022, https://doi.org/10.31763/ijrcs.v2i4.777.

M. S. Mahmoud, R. A. Saleh, and A. Ma’arif, "Stabilizing of Inverted Pendulum System Using Robust Sliding Mode Control," International Journal of Robotics and Control Systems, vol. 2, no. 2, pp. 230-239, 2022, https://doi.org/10.31763/ijrcs.v2i2.594.

N.-C. Tran, “LQR Control for Experimental Double Rotary Inverted Pendulum,” Journal of Fuzzy Systems and Control, vol. 2, no. 2, pp. 104-108, 2024, https://doi.org/10.59247/jfsc.v2i2.212.

C.-H. Nguyen, “ANFIS-based LQR Control for Rotary Double Parallel Inverted Pendulum,” Journal of Fuzzy Systems and Control, vol. 2, no. 2, pp. 109-116, 2024, https://doi.org/10.59247/jfsc.v2i2.214.

64

Downloads

Published

2025-08-27

How to Cite

[1]
H. Van Khuong, N. X. Chiem, and A. Obukhov, “Nonlinear Control Law Design for Inverted Pendulum Systems via RBF Neural Networks”, J Fuzzy Syst Control, vol. 3, no. 2, pp. 164–169, Aug. 2025.