Truong-Phuong-Nam Pham ¹, Huy-Minh-Quan Ha ¹, Truong-Nhat-Minh Bui ¹, Pha-Phim Nguyen ¹, Anh-Huy Nguyen ¹, Duc-Cuong Vu ¹, Van-Dat Nguyen ¹, Hai-Thanh Nguyen ²*

¹ Ho Chi Minh City University of Technology and Engineering (HCM-UTE)
Vo Van Ngan Street, No. 01, Ho Chi Minh City (HCMC), Vietnam
² Nguyen Huu Canh Technical and Economics Intermediate School
500-502, Huynh Tan Phat St., HCMC, Vietnam
* Corresponding author. E-mail: nguyenhaithanh@nhct.edu.vn

Robotica & Management, Vol. 30, No. 2, pp. 33-38
DOI: https://doi.org/10.24193/rm.2025.2.6

Abstract: Double inverted pendulum on cart (DIPC) is a high-order single input-multi output (SIMO) model. Due to its challenges in balancing control, there are less experimental results on this model. This paper extends our previous LQR experiments on the double inverted pendulum on cart (DIPC) by introducing an ANFIS-based LQR controller. Experimental results show enhanced stability and robustness under nonlinear dynamics, confirming the effectiveness of combining optimal control with intelligent learning methods.

Keywords: Double inverted pendulum, SIMO system, ANFIS, Underactuated System, Experimental Validation.

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References

[1] Lundberg K.H., Barton T.W.: “History of Inverted-Pendulum Systems”, IFAC Proceedings, Vol. 42, No. 24, pp. 131–135, 2010.

[2] Boubaker O.: “The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey”, Inverted Pendulum – New Trends, Applications and Control, InTechOpen, London, 2013.

[3] Irfan S., Zhao L., Ullah S., Mehmood A., Butt M.F.U.: “Control Strategies for Inverted Pendulum: A Comparative Analysis of Linear, Nonlinear, and AI Approaches”, PLoS ONE, Vol. 19, No. 3, 2024.

[4] Yadav S.K., Sharma S., Singh N.: “Optimal Control of Double Inverted Pendulum Using LQR Controller”, Int. J. Adv. Res. Comput. Sci. Softw. Eng., Vol. 2, No. 2, pp. 189–192, 2012.

[5] Yaren Y., Kizir S.: “Energy-Based Modeling and LQR Controller Design for Cart–Pole Double Inverted Pendulum”, Proc. Int. Conf. Systems and Control (ICSC), pp. 1–6, 2021.

[6] Vi-Do Tran et al: “Balancing control for double-linked inverted pendulum on cart: simulation and experiment”, Journal of Technical Education Science, Vol. 12, No. Special Issue 02, pp. 68–75, 2017.

[7] Jang J.-S.R.: “ANFIS: Adaptive-Network-Based Fuzzy Inference System”, IEEE Trans. Systems, Man, and Cybernetics, Vol. 23, No. 3, pp. 665–685, 1993.

[8] Qiang S., Zhou Q., Gao X.Z., Yu S.: “ANFIS Controller for Double Inverted Pendulum”, Proc. 6th IEEE Int. Conf. Industrial Informatics, pp. 475–480, Daejeon, 2008.

[9] Nguyen C.-H. et al: “ANFIS-Based LQR Control for Rotary Double Parallel Inverted Pendulum”, Journal of Fuzzy Systems and Control, Vol. 2, No. 2, pp. 109–116, 2024.

[10] Pham T.-P.-N. et al: “An LQR-Based ANFIS Control for Double-Linked Inverted Pendulum on Cart”, Journal of Fuzzy Systems and Control, Vol. 3, No. 2, pp. 135–141, 2025.

[11] Truong-Phuong-Nam Pham. et al: “Experimental LQR Control for a Double-Linked Inverted Pendulum on Cart”, Journal of Science and Transport Technology, In Progress.

[12] Tran T.-B. et al: “A Survey of Identification Experimental System Parameters Using Genetic Algorithm”, Robotica & Management, Vol. 29, No. 1, pp. 39–44, 2024.

[13] Craig J.J.: “Introduction to Robotics: Mechanics and Control”, Pearson Education Inc., Upper Saddle River, NJ, 2005.