Authors

Afef Hfaiedh, Ahmed Chemori

Abstract

This chapter presents a comprehensive case study on the inertia wheel inverted pendulum. It an interesting example of an underactuated mechanical system (UMS) that is widely used in control theory research. The chapter begins with an introduction that highlights the importance of this system in both theoretical and practical applications. A detailed description of the system follows, emphasizing its key components and configurations. Real-life applications of the inertia wheel inverted pendulum, such as in robotics and balancing mechanisms, are also discussed. The core of the chapter focuses on the mathematical modeling of the system, starting with the derivation of the dynamic model. The open-loop behavior of the system is then analyzed, followed by the formulation of the port-Hamiltonian model. To facilitate control design, the system is linearized around its equilibrium point, providing insights into its controllability. Finally, the chapter presents the experimental setup and addresses the implementation issues, covering the mechanical and electrical components, the software used, and a detailed description of the evaluation scenarios conducted in real-time experiments.

Keywords

dynamic model, experimental setup, implementation issues, inertia wheel, mechanical systems

Citation

BibTeX

@inbook{Hfaiedh_2025,
  title={{The inertia wheel inverted pendulum case study}},
  ISBN={9780443240201},
  DOI={10.1016/b978-0-44-324020-1.00009-9},
  booktitle={{Control of Underactuated Mechanical Systems}},
  publisher={Elsevier},
  author={Hfaiedh, Afef and Chemori, Ahmed},
  year={2025},
  pages={39--58}
}

Download the bib file

References

  • Boubaker, The inverted pendulum in control theory and robotics: from theory to new innovations. The Inverted Pendulum in Control Theory and Robotics (2017)
  • Lukowska, Simple human walking modelling. (2018)
  • Kajita S, Kanehiro F, Kaneko K, Fujiwara K, Yokoi K, Hirukawa H (2003) Biped walking pattern generation by a simple three-dimensional inverted pendulum model. Advanced Robotics 17(2):131–147. https://doi.org/10.1163/15685530332116509 – 10.1163/156855303321165097
  • Hazem ZB, Bingül Z (2023) Comprehensive Review of Different Pendulum Structures in Engineering Applications. IEEE Access 11:42862–42880. https://doi.org/10.1109/access.2023.326958 – 10.1109/access.2023.3269580
  • Garabédian, A futuristic monorail tramway stabilized by an inertia wheel. (2007)
  • Khraief Haddad N, Belghith S, Gritli H, Chemori A (2017) From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems. Int J Bifurcation Chaos 27(07):1750104. https://doi.org/10.1142/s021812741750104 – 10.1142/s0218127417501048
  • Gritli H, Belghith S (2018) Robust feedback control of the underactuated Inertia Wheel Inverted Pendulum under parametric uncertainties and subject to external disturbances: LMI formulation. Journal of the Franklin Institute 355(18):9150–9191. https://doi.org/10.1016/j.jfranklin.2017.01.03 – 10.1016/j.jfranklin.2017.01.035
  • Gritli H, Khraief N, Chemori A, Belghith S (2017) Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC. Nonlinear Dyn 89(3):2195–2226. https://doi.org/10.1007/s11071-017-3578- – 10.1007/s11071-017-3578-y
  • Hfaiedh, Rise controller for class I of underactuated mechanical systems: design and real-time experiments. (2018)
  • Hfaiedh, Disturbance observer-based super-twisting control for the inertia wheel inverted pendulum. (2020)
  • Hfaiedh, Stabilization of the inertia wheel inverted pendulum by advanced IDA-PBC based controllers: comparative study and real-time experiments. (2020)
  • Hfaiedh, Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: theory and real-time experiments. Transactions of the Institute of Measurement and Control (2021)
  • Hfaiedh A, Abdelkrim A (2021) Revisited adaptive sliding mode control of underactuated mechanical systems with real-time experiments. IJMIC 37(3/4):344. https://doi.org/10.1504/ijmic.2021.12184 – 10.1504/ijmic.2021.121848
  • Ho, Study on inertia wheel pendulum applied to self-balancing electric motorcycle. (2018)
  • Kanjanawanishkul, LQR and MPC controller design and comparison for a stationary self-balancing bicycle robot. Kybernetika (2015)
  • Vadlamudi, Self balancing motorcycle using reinforcement learning. (2024)
  • Burger, The gyroscope. (1966)
  • Zhang P, Wu Z, Dong H, Tan M, Yu J (2020) Reaction-Wheel-Based Roll Stabilization for a Robotic Fish Using Neural Network Sliding Mode Control. IEEE/ASME Trans Mechatron 25(4):1904–1911. https://doi.org/10.1109/tmech.2020.299203 – 10.1109/tmech.2020.2992038
  • Mayr J, Spanlang F, Gattringer H (2015) Mechatronic design of a self-balancing three-dimensional inertia wheel pendulum. Mechatronics 30:1–10. https://doi.org/10.1016/j.mechatronics.2015.04.01 – 10.1016/j.mechatronics.2015.04.019
  • Gajamohan, The Cubli: a cube that can jump up and balance. (2012)
  • Muehlebach, Nonlinear analysis and control of a reaction wheel-based 3D inverted pendulum. (2013)
  • Hofer M, Muehlebach M, D’Andrea R (2023) The One-Wheel Cubli: A 3D inverted pendulum that can balance with a single reaction wheel. Mechatronics 91:102965. https://doi.org/10.1016/j.mechatronics.2023.10296 – 10.1016/j.mechatronics.2023.102965
  • Townsend NC, Shenoi RA (2011) Gyrostabilizer Vehicular Technology. Applied Mechanics Reviews 64(1). https://doi.org/10.1115/1.400483 – 10.1115/1.4004837
  • Kim S-A (2020) A Study on the Control for Increasing Output Power Section of Gyro Generation System. KIEE 69(4):576–580. https://doi.org/10.5370/kiee.2020.69.4.57 – 10.5370/kiee.2020.69.4.576
  • Spry SC, Girard AR (2008) Gyroscopic stabilisation of unstable vehicles: configurations, dynamics, and control. Vehicle System Dynamics 46(sup1):247–260. https://doi.org/10.1080/0042311080193586 – 10.1080/00423110801935863
  • Sterke BT, Poggensee KL, Ribbers GM, Lemus D, Vallery H (2023) Light-Weight Wearable Gyroscopic Actuators Can Modulate Balance Performance and Gait Characteristics: A Proof-of-Concept Study. Healthcare 11(21):2841. https://doi.org/10.3390/healthcare1121284 – 10.3390/healthcare11212841
  • Townsend NC, Murphy AJ, Shenoi RA (2007) A new active gyrostabiliser system for ride control of marine vehicles. Ocean Engineering 34(11–12):1607–1617. https://doi.org/10.1016/j.oceaneng.2006.11.00 – 10.1016/j.oceaneng.2006.11.004
  • Mahvan, Gyrostabilized two wheeled inverted pendulum robot. (2015)
  • Romtrairat P, Virulsri C, Wattanasiri P, Tangpornprasert P (2020) A performance study of a wearable balance assistance device consisting of scissored-pair control moment gyroscopes and a two-axis inclination sensor. Journal of Biomechanics 109:109957. https://doi.org/10.1016/j.jbiomech.2020.10995 – 10.1016/j.jbiomech.2020.109957
  • Lemus D, Berry A, Jabeen S, Jayaraman C, Hohl K, van der Helm FCT, Jayaraman A, Vallery H (2020) Controller synthesis and clinical exploration of wearable gyroscopic actuators to support human balance. Sci Rep 10(1). https://doi.org/10.1038/s41598-020-66760- – 10.1038/s41598-020-66760-w
  • Chiu, Design of a wearable scissored-pair control moment gyroscope (SP-CMG) for human balance assist. (2014)
  • Oya, Preliminary experiments for postural control using wearable-CMG. (2017)
  • Olfati-Saber, Global stabilization of a flat underactuated system: the inertia wheel pendulum. (2001)
  • Çolak, First reaction wheel qualified in Türkiye. (2023)
  • Ratheesh, Field-oriented control for performance improvement in reaction wheels and implementation of algorithm in FPGA. (2023)
  • Mehrjardi, Developing a proposed satellite reaction wheel model with current mode control. (2015)
  • Cheon, Satellite actuator balancing based on the disturbance measurement table data. Renewable Energy and Power Quality Journal (2012)
  • Mattioni A, Wu Y, Ramirez H, Gorrec YL, Macchelli A (2018) Modelling and control of a class of lumped beam with distributed control. IFAC-PapersOnLine 51(3):217–222. https://doi.org/10.1016/j.ifacol.2018.06.05 – 10.1016/j.ifacol.2018.06.057
  • Harandi, Robust IDA-PBC for a spatial underactuated cable driven robot with bounded inputs. (2021)
  • Zhou, Energy-based trajectory tracking control of under-actuated unmanned surface vessels. Ocean Engineering (2023)
  • Ortega R, Spong MW, Gomez-Estern F, Blankenstein G (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Automat Contr 47(8):1218–1233. https://doi.org/10.1109/tac.2002.80077 – 10.1109/tac.2002.800770
  • Haddad, Stabilization of inertia wheel inverted pendulum by model reference adaptive IDA-PBC: from simulation to real-time experiments. (2015)
  • Haddad NK, Chemori A, Belghith S (2017) Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments. International Journal of Control 91(12):2657–2672. https://doi.org/10.1080/00207179.2017.133137 – 10.1080/00207179.2017.1331378
  • Ryalat M, Laila DS (2018) A Robust IDA-PBC Approach for Handling Uncertainties in Underactuated Mechanical Systems. IEEE Trans Automat Contr 63(10):3495–3502. https://doi.org/10.1109/tac.2018.279719 – 10.1109/tac.2018.2797191
  • Suresh, Vibration analysis of gearbox fault diagnosis using DWT and statistical features. Journal of Engineering Research (Kuwait) (2022)