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A comprehensive approach to double inverted pendulum modelling

Abstract

The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.

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Category:
Articles
Type:
artykuły w czasopismach
Published in:
Archives of Control Sciences no. 29, pages 459 - 483,
ISSN: 1230-2384
Language:
English
Publication year:
2019
Bibliographic description:
Andrzejewski K., Czyżniewski M., Zielonka M., Łangowski R., Zubowicz T.: A comprehensive approach to double inverted pendulum modelling// Archives of Control Sciences -Vol. 29,iss. 3 (2019), s.459-483
DOI:
Digital Object Identifier (open in new tab) 10.24425/acs.2019.130201
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  1. I. Ali and M. Hossen: A two-wheeled self-balancing robot with dynamics model. In Proceedings of the 4th International Conference on Advances in Electrical Engineering (ICAEE), Dhaka, Bangladesh, 271-275, 2017. open in new tab
  2. K. Andrzejewski, M. Czyżniewski, and M. Zielonka: Synthesis and im- plementation of control system for double inverted pendulum. BSc Thesis, Gdańsk University of Technology, (in Polish), 2017.
  3. R.P.M. Chan, K.A. Stol, and C.R. Halkyard: Review of modelling and control of two-wheeled robots. Annual Reviews in Control, 37(1), (2013), 89-103. open in new tab
  4. J. Chestnutt, M. Lau, G. Cheung, J. Kuffner, J. Hodgins, and T. Kanade: Footstep planning for the Honda ASIMO humanoid. In Pro- ceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, 629-634, 2005. open in new tab
  5. F. Dörfler and F. Bullo: Synchronization in complex networks of phase oscillators: A survey. Automatica, 50 (2014), 1539-1564. open in new tab
  6. C. Gonzalez, I. Alvarado, and D. Muñoz La Peña: Low cost two-wheels self-balancing robot for control education. In Proceedings of the 20th IFAC World Congress, Toulouse, France, 50 (2017), 9174-9179. open in new tab
  7. F. Grasser, A. D'Arrigo, S. Colombi, and A.C. Rufer: JOE: A mobile, inverted pendulum. IEEE Transactions on Industrial Electronics, 49(1), (2002), 107-114. open in new tab
  8. S. Jadlovská and J. Sarnovský: Classical double inverted pendulum -a complex overview of a system. In Proceedings of the IEEE 10th Jubilee In- ternational Symposium on Applied Machine Intelligence and Informatics, Herl'any, Slovakia, 103-108, 2012. open in new tab
  9. J. Kędzierski and K. Tchoń: Feedback control of a balancing robot. In Proceedings of the 14th IFAC Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, 42 (2009), 495-500. open in new tab
  10. H.E. Khalil: Nonlinear systems, 2nd edition. Prentice Hall, Upper Saddle River, New Jersey, US, 1996.
  11. Y. Kim, S H. Kim, and Y.K. Kwak: Dynamic analysis of a nonholonomic two-wheeled inverted pendulum robot. Journal of Intelligent and Robotic Systems: Theory and Applications, 44(1), (2005), 25-46. open in new tab
  12. U.E. Kocamaz, A. Göksu, H. Taşkın, and Y. Uyaroǧlu: Synchronization of chaos in nonlinear finance system by means of sliding mode and pas- sive control methods: A comparative study. Information Technology and Control, 44(2), (2015), 172-181. open in new tab
  13. I.D. Loram and M. Lakie: Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements. The Journal of Physiology, 540 (2002), 1111-1124. open in new tab
  14. M. Muhammad, S. Buyamin, M.N. Ahmad, and S.W. Nawawi: Dynamic modeling and analysis of a two-wheeled inverted pendulum robot. In Pro- ceedings of the 3rd International Conference on Computational Intelli- gence, Modelling and Simulation (CIMSim), Langkawi, Malaysia, 159- 164, 2011. open in new tab
  15. H.G. Nguyen, J. Morrell, K.D. Mullens, A.B. Burmeister, S. Miles, N. Farrington, K.M. Thomas, and D.W. Gage: Segway robotic mobility platform. In D.W. Gage, editor, Proceedings of SPIE Mobile Robots XVII, vol. 5609, 207-220, 2004. open in new tab
  16. M. Prasad and N.W. Nirwan: Design and fabrication of automatic balanc- ing bicycle. International Journal of Science, Engineering and Technology Research, 5 (2016), 532-536.
  17. M. Rosenblum and A. Pikovsky: Synchronization: from pendulum clocks to chaotic lasers and chemical oscillators. Contemporary Physics, 44(5), (2003), 401-416. open in new tab
  18. Y. Sakagami, R. Watanabe, C. Aoyama, S. Matsunaga, N. Higaki, and K. Fujimura: The intelligent ASIMO: system overview and integration. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, 2478-2483, 2002. open in new tab
  19. B. Sawatzky, I. Denison, S. Langrish, S. Richardson, K. Hiller, and B. Slobogean: The segway personal transporter as an alternative mobility device for people with disabilities: A pilot study. Archives of Physical Medicine and Rehabilitation, 88 (2007), 1423-1428. open in new tab
  20. J-J.E. Slotine and W. Li: Applied nonlinear control. Prentice Hall, Engle- wood Cliffs, New Jersey, US, 1991.
  21. N. Sozhamadevi and S. Sathiyamoorthy: Modeling and control of an unstable system using probabilistic fuzzy inference system. Archives of Control Sciences, 25(3), (2015), 377-396. open in new tab
  22. M.W. Spong: Underactuated mechanical systems. In B. Siciliano and K. P. Valavanis, editors, Control Problems in Robotics and Automation. Lecture Notes in Control and Information Sciences, vol. 230, Berlin, Heidelberg, 1998. Springer. open in new tab
  23. T. Takei, R. Imamura, and S. Yuta: Baggage transportation and naviga- tion by a wheeled inverted pendulum mobile robot. IEEE Transactions on Industrial Electronics, 56(10), (2009), 3985-3994. open in new tab
  24. M. Velazquez, D. Cruz, S. Garcia, and M. Bandala: Velocity and motion control of a self-balancing vehicle based on a cascade control strategy. International Journal of Advanced Robotic Systems, 13(3), (2016), 1-11. open in new tab
  25. S. Wenxia and C. Wei: Simulation and debugging of LQR control for two- wheeled self-balanced robot. In Proceedings of the Chinese Automation Congress (CAC), Jinan, China, 2391-2395, 2017. open in new tab
  26. W. Zhong and H. Röck: Energy and passivity based control of the double inverted pendulum on a cart. In Proceedings of the 2001 IEEE International Conference on Control Applications, Mexico City, Mexico, 896-901, 2001.
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