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Swing-up Control of an Inverted Pendulum Subject to Input/Output Constraints

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  • Meta, Tum (Program in Robot Engineering, Inha University) ;
  • Gyeong, Gi-Young (Department of Electrical Engineering, Inha University) ;
  • Park, Jae-Heon (Department of Electrical Engineering, Inha University) ;
  • Lee, Young-Sam (Department of Electrical Engineering, Inha University)
  • ;
  • 경기영 (인하대학교 전기공학과) ;
  • 박재헌 (인하대학교 전기공학과) ;
  • 이영삼 (인하대학교 전기공학과)
  • Received : 2014.05.19
  • Accepted : 2014.06.02
  • Published : 2014.08.01

Abstract

In this paper we propose a swing-up strategy for a single inverted pendulum. The proposed method has a feature whereby can handle the input and output constraint of a pendulum in a systematic way. For the swing-up of a pendulum, we adopt a 2-DOF control structure that combines the feedforward and feedback control. In order to generate the swing-up feedforward trajectories that satisfy the input and output constraint, we formulate the problem of generating feedforward trajectories as a nonlinear optimal control problem subject to constraints. We illustrate that the proposed method is more flexible than the existing method and provides great freedom in choosing the actuator of the inverted pendulum. Through an experiment, we show that the proposed method can swing a pendulum upward effectively while satisfying all the imposed constraints.

Keywords

References

  1. K. Astrom and K. Fruta, "Swinging up a pendulum by energy control," Automatica, vol. 36, no. 2, pp. 287-295, 2000. https://doi.org/10.1016/S0005-1098(99)00140-5
  2. D. Chatterjee, A. Patra, and H. K. Joglekar, "Swing-up and stabilization of a cart-pendulum system under restricted cart track length," Systems & Control Letters, vol. 47, pp. 355-364, 2002. https://doi.org/10.1016/S0167-6911(02)00229-3
  3. K. Furuta, M. Yamakitan, and S. Kobayashi, "Swing-up control of inverted pendulum using pseudo-state feedback," Journal of System and Control Engineering, vol. 206, pp. 263-269, 1992.
  4. K. Graichen, M. Treuer, and M. Zeitz, "Swing up of the double pendulum on a cart by feedforward and feedback control with experimental validation," Automatica, vol. 43, pp. 63-71, 2007. https://doi.org/10.1016/j.automatica.2006.07.023
  5. D. E. Kirk. Optimal Control Theory : An Introduction, Prentice Hall, 1970.
  6. R. Lozano, I. Fantoni, and D. J. Block, "Stabilization of the inverted pendulum around its homoclinic orbit," System & Control Letters, vol. 40, pp. 197-204, 2000. https://doi.org/10.1016/S0167-6911(00)00025-6
  7. J. M. Maciehowski, Predictive Control with Constraints, Prentice Hall, 2002.
  8. N. Muskinja and B. Tovornik, "Swinging up and stabilization of real inverted pendulum," IEEE Transactions on Industrial Electronics, vol. 53, no. 2, pp. 631-639, 2006.
  9. Y. Otani, T. Kurokami, A. Inoue, and Y. Hirashima, "A swingup control of an inverted pendulum with cart position control," In Proc. of the IFAC Conference on New Technologies for Computer Control, pp. 13-22, Hongkong, China, 2001.
  10. M. A. Patterson and A. V. Rao, GPOPS - II Version 1.0:A General-purpose Matlab Toolbox for Solving Optimal Control Problems using Variable-order Gaussian Quadrature Collocation Methods, 2014.
  11. M. Wilklund, A. Kristenson, and K. Astrom, "A new strategy for swing up an inverted pendulum," In Proc. of IFAC 12th World Congress, vol. 9, pp. 151-154, Sydney, Australia, 1993.
  12. X. Xin, "Analysis of the energy-based swing-up control for the double pendulum on a cart," International Journal of Robust and Nonlinear Control, vol. 21, pp. 387-403, 2010.
  13. J. H. Yang, S. Y. Shim, J. H. Seo, and Y. S. Lee, "Swing up control for an inverted pendulum with restricted cart rail length," International Journal of Control, Automation, and Systems, vol. 70, no. 4, pp. 674-680. 2009. https://doi.org/10.1007/s12555-009-0419-x

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