Bond Graph Modelling of a Rotary Inverted Pendulum on a Wheeled Cart

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Jessica A. Onwuzuruike 1,* Suleiman U. Hussein 1

1. Department of Electric and Electronics Engineering, Nile University of Nigeria, Abuja, 900108, Nigeria

* Corresponding author.


Received: 1 Jul. 2020 / Revised: 12 Aug. 2020 / Accepted: 26 Sep. 2020 / Published: 8 Dec. 2021

Index Terms

Bond graph, wheeled rotary inverted pendulum, state space


There are some systems that are yet to be modelled using certain methods. One of them is Rotary Inverted Pendulum (RIP) on a wheeled cart which is yet to be modeled using the bond graph technique. Therefore, this work explored the bond graph technique for this system. Using this technique, which uses the concept of energy (power) transfer between elements in a system, the system was modeled. Then, the state space equations of the system, which give the first-order differential equations, were derived. It was observed that the system has five state variables because of the five integrally causal storage elements.

Cite This Paper

Jessica A. Onwuzuruike, Suleiman U. Hussein, " Bond Graph Modelling of a Rotary Inverted Pendulum on a Wheeled Cart", International Journal of Modern Education and Computer Science(IJMECS), Vol.13, No.6, pp. 25-29, 2021.DOI: 10.5815/ijmecs.2021.06.03


[1] Agarana, M. C., and Ajayi, O. O. “Dynamic Modeling and Analysis of Inverted Pendulum Using Lagrangian-Differential Transform Method.” 2017.

[2] Dai, F., Gao, X., Jiang, S., Guo, W., and Liu, Y. “A Two-Wheeled Inverted Pendulum Robot with Friction Compensation.” Mechatronics, Vol. 30, 2015, pp. 116–125.

[3] Cui, R., Guo, J., and Mao, Z. “Adaptive Backstepping Control of Wheeled Inverted Pendulums Models.” Nonlinear Dynamics, Vol. 79, No. 1, 2015, pp. 501–511.

[4] Huang, J., Ri, S., Liu, L., Wang, Y., Kim, J., and Pak, G. “Nonlinear Disturbance Observer-Based Dynamic Surface Control of Mobile Wheeled Inverted Pendulum.” IEEE Transactions on Control Systems Technology, Vol. 23, No. 6, 2015, pp. 2400–2407.

[5] Sultan, K., and Mirza, A. “Inverted Pendulum, Analysis, Design and Implementation.” Visionaries Document, 2003.

[6] Muehlebach, M., and D’Andrea, R. “Nonlinear Analysis and Control of a Reaction-Wheel-Based 3-D Inverted Pendulum.” IEEE Transactions on Control Systems Technology, Vol. 25, No. 1, 2016, pp. 235–246.

[7] Yang, X., and Zheng, X. “Swing-up and Stabilization Control Design for an Underactuated Rotary Inverted Pendulum System: Theory and Experiments.” IEEE Transactions on Industrial Electronics, Vol. 65, No. 9, 2018, pp. 7229–7238.

[8] Hamza, M. F., Yap, H. J., Choudhury, I. A., Isa, A. I., Zimit, A. Y., and Kumbasar, T. “Current Development on Using Rotary Inverted Pendulum as a Benchmark for Testing Linear and Nonlinear Control Algorithms.” Mechanical Systems and Signal Processing, Vol. 116, 2019, pp. 347–369.

[9] Kelly, M., and Ruina, A. Non-Linear Robust Control for Inverted-Pendulum 2D Walking. Presented at the 2015 IEEE International Conference on Robotics and Automation (ICRA), 2015.

[10] Shahbazi, M., Babuška, R., and Lopes, G. A. “Unified Modeling and Control of Walking and Running on the Spring-Loaded Inverted Pendulum.” IEEE Transactions on Robotics, Vol. 32, No. 5, 2016, pp. 1178–1195.

[11] Roman, M., Bobasu, E., and Sendrescu, D. Modelling of the Rotary Inverted Pendulum System. In 2008 IEEE International Conference on Automation, Quality and Testing, Robotics, No. 2, 2008, pp. 141–146.

[12] Ragusila, V., and Emami, M. R. “Modelling of a Robotic Leg Using Bond Graphs.” Simulation Modelling Practice and Theory, Vol. 40, 2014, pp. 132–143.

[13] Pacheco, F. E. An Inverted Pendulum Cart Modeled Using the Bond Graph Approach. Presented at the 2017 IEEE Second Ecuador Technical Chapters Meeting (ETCM), 2017.

[14] Khaouch, Z., Zekraoui, M., Kouider, N., and Mabrouki, M. “Mechatronic Control Model of an Inverted Pendulum.” IOSR Journal of Electrical and Electronics Engineering, Vol. 12, pp 24-30, 2017

[15] Banerjee, S. Dynamics for Engineers. John Wiley & Sons, 2005.