Hoang-Linh Le 1, Phong-Luu Nguyen 1, Duc-Thu Nguyen 2*
1 Ho Chi Minh City University of Technology and Engineering (HCM-UTE)
Vo Van Ngan Str., No. 01, Ho Chi Minh City (HCMC), Vietnam
2 Ho Chi Minh City Power Corporation (EVNHCMPC)
Str. No 4, Di An ward, HCMC, Vietnam
* Corresponding author. E-mail: thund@hcmpc.com.vn
Robotica & Management, Vol. 31, No. 1, pp. 10-15
DOI: https://doi.org/10.24193/rm.2026.1.2
Abstract: This paper presents a nonlinear control strategy for trajectory tracking of a cart–pendulum system based on the backstepping approach. First, the nonlinear dynamic model of the system is formulated in a state-space representation. A systematic controller design procedure is then developed by introducing virtual control inputs. The stability of the closed-loop system is rigorously analyzed using Lyapunov theory, which guarantees the asymptotic convergence of the tracking errors. The proposed controller enables the cart position to accurately track a sinusoidal reference trajectory while maintaining the pendulum angle around the equilibrium point. Both simulation and experimental results demonstrate the effectiveness and stability of the proposed control method. The obtained results confirm that the controller provides satisfactory tracking performance for the nonlinear system.
Keywords: Backstepping control; Nonlinear control; Trajectory tracking; Inverted pendulum; Lyapunov stability.
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References
[1] Rudra S., Barai R.K.: “Robust Adaptive Backstepping Control of Inverted Pendulum on Cart System”, International Journal of Control and Automation, Vol. 5, No. 1, pp. 13-26, 2012.
[2] Ma’arif A., Heryanto M.A., Susanto E., Pramudita B.A.: “Backstepping Sliding Mode Control for Inverted Pendulum System with Disturbance and Parameter Uncertainty”, Journal of Robotics and Control, Vol. 3, No. 1, pp. 86-92, 2021.
[3] Gupta N., Dewan L.: “Adaptive Neural Network-Based Sliding Mode Control of Rotary Inverted Pendulum System”, Journal of Control and Decision, 2024.
[4] Leng X.: “Second-Order Sliding Mode Optimization Control of Inverted Pendulum System Based on Fuzzy Adaptive Technology”, Frontiers in Mechanical Engineering, Vol. 10, Article 1458852, 2024.
[5] Hou M., Zhang Y., Li J., Wang X.: “Hierarchical Sliding Mode Control Combined with Nonlinear Disturbance Observer for Wheeled Inverted Pendulum Robot Trajectory Tracking”, Applied Sciences, Vol. 13, No. 7, Article 4350, 2023.
[6] Mofid O., Rahmani A., Ghanbari M.: “Adaptive Finite-Time Command-Filtered Backstepping Sliding Mode Control for Stabilization of a Disturbed Rotary-Inverted-Pendulum with Experimental Validation”, Journal of Vibration and Control, Vol. 29, No. 5-6, pp. 1431-1446, 2023.
[7] Saco R..: “Subspace Identification of an Inverted Pendulum on a Cart using State Variables Transformation,” IFAC-PapersOnLine, vol. 52, no. 11, pp. 244-249, 2019.
[8] Hoang D.-P.: “A Survey of Experimental LQR for Cart and Pole ”, J Fuzzy Syst Control, vol. 2, no. 2, pp. 97–103, May 2024.