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Design and control of real-time inverted pendulum system with force-voltage parameter correlation

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Abstract

The inverted pendulum is a non-linear system which requires a robust controller for its stabilization. The mathematical modelling of the system is done using Lagrangian mechanics, and the state-space feedback method is employed to derive the Proportional, Integral and Derivative (PID) values needed to control the system. In this paper, we propose a novel experiment to map the voltage supplied, to the dynamics of the system. The performance of the system in real-time for the proposed method as well as for the conventional method (which involves assuming V = F, where F is the force acting on the cart, V is the voltage across the motor) is measured in terms of settling time of the system, maximum pendulum angle offset after settling, and cart position displacement. The proposed method proves to improve the performance of the system significantly. Also, we have discussed solutions for some real-time issues with low-cost electronic components that help reduce the cost of implementation of the entire system.

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References

  1. Zheng Y, Luo S, Lv Z (2006) Control Double Inverted Pendulum by Reinforcement Learning with Double CMAC Network. In: 18th International on pattern recognition (ICPR’06), Hong Kong, pp 639-642, https://doi.org/10.1109/ICPR.2006.416

  2. Williams V, Matsuoka K (1991) Learning to balance the inverted pendulum using neural networks. In: [Proceedings] 1991 IEEE international joint conference on neural networks, Singapore, pp 214-219 vol 1, https://doi.org/10.1109/IJCNN.1991.170406

  3. Anderson CW (1989) Learning to control an inverted pendulum using neural networks. IEEE Control Syst Mag 9(3):31–37. https://doi.org/10.1109/37.24809

    Article  Google Scholar 

  4. Denai MA, Palis F, Zeghbib A (2007) Modeling and control of non-linear systems using soft computing techniques. Appl Soft Comput 7(3):728–738

    Article  Google Scholar 

  5. Varsek A, Urbancic T, Filipic B (1993) Genetic algorithms in controller design and tuning. IEEE Trans Syst Man Cybern 23:1330–1339. https://doi.org/10.1109/21.260663

    Article  Google Scholar 

  6. Magana ME, Holzapfel F (1998) Fuzzy-logic control of an inverted pendulum with vision feedback. IEEE Trans Educ 41(2):165–170. https://doi.org/10.1109/13.669727

    Article  Google Scholar 

  7. Liu Y, Chen Z, Xue D, Xu X (2009) Real-time controlling of inverted pendulum by fuzzy logic. In: 2009 IEEE international conference on automation and logistics, Shenyang, pp 1180-1183, https://doi.org/10.1109/ICAL.2009.5262618

  8. Ji CW, Lei F, Kin LK (1997) Fuzzy logic controller for an inverted pendulum system. In: 1997 IEEE international conference on intelligent processing systems (Cat. No.97TH8335), Beijing, China, pp. 185-189 vol.1, https://doi.org/10.1109/ICIPS.1997.672762

  9. Burov AA, Kosenko II (2014) Pendulum motions of extended lunar space elevator. Mech. Solids 49:506–517. https://doi.org/10.3103/S0025654414050033

    Article  Google Scholar 

  10. Stability and Control of an Inverted Pendulum Motion - Scientific Figure on ResearchGate.[Online] Available: https://www.researchgate.net/figure/3-Segway-is-one-of-inverted-pendulum-applications_fig3_330825329 [accessed 14 Sep, 2020]

  11. Vinodh Kumar E, Jerome J (2013) Robust LQR controller design for stabilizing and trajectory tracking of inverted pendulum. In: Int. Conf. Design Manuf., vol 64, pp 169-178

  12. Shehu M, Ahmad MR, Shehu A, Alhassan A (2015) LQR, double-PID and pole placement stabilization and tracking control of single link inverted pendulum. In: 2015 IEEE International conference on control system, computing and engineering (ICCSCE), George Town, 2015, pp 218-223, https://doi.org/10.1109/ICCSCE.2015.7482187

  13. Prasad LB, Tyagi B, Gupta HO (2014) Optimal control of nonlinear inverted pendulum system using PID controller and LQR: performance analysis without and with disturbance Input. Int. J. Autom. Comput. 11:661–670

    Article  Google Scholar 

  14. Mahapatra C, Chauhan S (2017) Tracking control of inverted pendulum on a cart with disturbance using pole placement and LQR. In: 2017 International conference on emerging trends in computing and communication technologies (ICETCCT), Dehradun, 2017, pp. 1-6, https://doi.org/10.1109/ICETCCT.2017.8280311

  15. (1997) “Modelling and control of inverted pendulum on a cart”,van Dijk, H. (Author). 30 Apr

  16. Taylor JR (2005) Classical Mechanics. University Science Books, Sausalito, Calif

    MATH  Google Scholar 

  17. Sastry S (1999) Nonlinear systems: analysis, stability, and control. Spring-Verlag, New York. https://doi.org/10.1007/978-1-4757-3108-8

  18. Lewis FL (1986) Optimal Control. John Wiley & Sons Inc., New York

    Google Scholar 

  19. Ogata K (2010) Modern Control Engineering, 5th edn. Prentice Hall, New Jersey

    MATH  Google Scholar 

  20. STM32F103 Datasheet [Online] Available: https://www.st.com/resource/en/datasheet/cd00237391.pdf

  21. Inverted Pendulum: System Modeling [Online] Available: http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SystemModeling

  22. Inverted Pendulum: Decay Rate [Online] Available: https://www.ucl.ac.uk/~zcapg66/work/Modelling%20Damping%20for%20a%20Pendula.pdf

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Funding

Funded by SSN Research Centre and supported by S4S Club (Department of Electrical and Electronics Engineering, Sri Sivasubramaniya Nadar College of Engineering)

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Sri Sivasubramaniya Nadar College of Engineering, Chennai, Tamil Nadu, India

    Sriram Shreedharan, Vignesh Ravikumar & Senthil Kumaran Mahadevan

Authors
  1. Sriram Shreedharan
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  2. Vignesh Ravikumar
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  3. Senthil Kumaran Mahadevan
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Contributions

Vignesh Ravikumar and Sriram Shreedharan contributed equally to this research.

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Correspondence to Sriram Shreedharan.

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There is no conflict of interest among the authors.

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Shreedharan, S., Ravikumar, V. & Mahadevan, S.K. Design and control of real-time inverted pendulum system with force-voltage parameter correlation. Int. J. Dynam. Control 9, 1672–1680 (2021). https://doi.org/10.1007/s40435-020-00753-5

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  • DOI: https://doi.org/10.1007/s40435-020-00753-5

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