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A Sliding Mode Control Scheme for Inverted Pendulum System

슬라이딩 모드 제어기법을 이용한 도립진자 시스템 제어

  • Han, Sang-Wan (Electrical & Electronics Engineering, Chungnam Provincial Cheongyang College) ;
  • Park, Minho (Electrical & Electronics Engineering, Chungnam Provincial Cheongyang College)
  • 한상완 (충남도립청양대학 전기전자과) ;
  • 박민호 (충남도립청양대학 전기전자과)
  • Received : 2014.01.16
  • Accepted : 2014.02.05
  • Published : 2014.02.28

Abstract

A problem of sliding mode control is chattering because of controle input signal included unknown disturbance and nonlinear input parameters. This paper presents a sliding mode controller design to inverted pendulum system. In this paper, a sliding mode control algorithm to reduce a chattering is proposed. The reduction of chattering is accomplished by smoothing function for nonlinear control input. In this method, the dynamic equations of the inverted pendulum is decoupled by considering nonlinear parameters and external disturbances. Therefore, this study is applied to obtain switching control inputs for sliding mode controller. The proposed technique is tested to the control of inverted pendulum through computer simulations. The result shown reduced chattering in control input.

슬라이딩모드 제어의 문제는 제어입력에 포함된 알려지지 않은 외란 등 비선형 입력으로 인한 채터링의 발생이다. 본 연구는 채터링 발생의 문제를 해결하기 위한 제어 알고리듬에 대하여 고찰하고 채터링을 억제하는 슬라이딩모드 제어기를 설계하고자 한다. 슬라이딩모드 제어 시 발생하는 채터링을 억제하기 위해 알려지지 않은 외란을 포함한 비선형 입력에 대하여 평활함수를 적용한다. 이 방법에 의하여 도립진자 시스템의 동적 방정식에 포함된 비선형 요소와 외란에 의한 문제가 해결될 수 있음을 보인다. 또 슬라이딩모드 제어를 위한 제어 입력을 시스템에 적용하였고, 제안한 제어기의 제어성능을 검증하기 위하여 도립진자를 대상으로 컴퓨터 모의실험을 수행하였다. 모의실험 결과 제어입력에 포함된 큰 폭의 채터링이 제거되었음을 확인할 수 있다.

Keywords

References

  1. Utkin, V. I. "Variable Structure Systems with Sliding Modes", IEEE Transactions on Automatic Control, vol. 22, no. 2, pp. 212-222, 1977. DOI: http://dx.doi.org/10.1109/TAC.1977.1101446
  2. Young, K. K. D., "Controller Design for Manipulator Using Theory of Variable Structure Systems", IEEE Transactions on System, Man and Cybernetics, vol. 8, no. 2, pp. 101-109, 1978. DOI: http://dx.doi.org/10.1109/TSMC.1978.4309907
  3. Slotine, J. J. and Sastry, S. S., "Tracking Control of Non-linear Systems Using Sliding Surface with Application to Robot Manipulators", International Journal of Control, vol. 38, pp. 465-492. 1983 DOI: http://dx.doi.org/10.1080/00207178308933088
  4. Gert-Wim van der Linden and Paul F. Lambrechts, "$H_{\infty}$ Control of an Experimental Inverted Pendulum with Dry Friction", IEEE Control Systems, pp.44-50, August 1993. DOI: http://dx.doi.org/10.1109/37.229559
  5. John Nelson and L. Gordon Kraft, "Real Time Control of Inverted Pendulum System Using Complementary Neural Network and Optimal Techniques", Proceedings of the American Control Conference Baltimore, Maryland, pp. 2553-2554, June 1994.
  6. Choi, S. B., Park, D. W. and Jayasuriya, S., "A Time-Varying Sliding Surface for Fast and Robust Tracking Control of Second-Order Uncertain Systems", Automatica, vol. 30, no. 5, pp. 899-904, 1994. DOI: http://dx.doi.org/10.1016/0005-1098(94)90180-5
  7. Lee, M. C., Jin, S. Y. and Lee, M. H., "A Study on the Trajectory Control of a SCARA Robot Using Sliding Mode", Journal of Mechanical Science and Technology, vol. 19, no. 1, pp. 99-110, 1995.
  8. M. C. Lee, K. T. Shin, "Development of a Dynamic Simulator for SCARA Robot Using Sliding Mode Control", Journal of Mechanical Science and Technology, vol. 21, no. 4, pp. 535-548, 1997
  9. Bernhard Sprenger, Ladislav Kucera, and Safer Mourad,"Balancing of an Inverted Pendulum with a SCARA Robot", IEEE/ASME Transaction on Mechatronics, vol.3, no. 2, pp.91-97, June 1998. DOI: http://dx.doi.org/10.1109/3516.686676
  10. Young, K. D., Utkin, V. I. and Ozguner, U., "A Control Engineer's Guide to Sliding Mode Control", Control System Technology, IEEE Transactions, vol. 7, no. 2, pp. 328-342, 1999. DOI: http://dx.doi.org/10.1109/87.761053
  11. Park, D. W and Choi,, S. B., "Moving Sliding Surfaces for High-Order Variable Structure Systems", International Journal of Control, vol. 72, pp. 960-970, 1999. DOI: http://dx.doi.org/10.1080/002071799220506
  12. J. W. Cheon, S. B. Choi, H. J. Song, J. H. Ham, "Position Control of AC Servo Motor Using Sliding Mode Control", Journal of The Korean Society of Precision Engineering, Vol. 12, No. 3, pp. 44-50, March, 2004
  13. S. J. Lee, H. Park, K. S. Hong, "Sliding-Mode Control of Container Cranes", Journal of Korean Navigation and Port Research, vol. 29, no. 8, pp. 747-753, 2005 DOI: http://dx.doi.org/10.5394/KINPR.2005.29.8.747
  14. Lee, J. H., "Seismic Control of Tuned Mass Damper System with MDOF Sliding Mode Control Accounting for the Uncertainties", Journal of the Korea Institute for Structural Maintenance and Inspection, vol. 15, no. 1, pp. 235-242, 2011 https://doi.org/10.11112/jksmi.2011.15.1.235
  15. F. L. Lewis. "Applied Optimal Control & Estimation", Prentis Hall, 1992.