The Transactions of the Korean Institute of Electrical Engineers D (대한전기학회논문지:시스템및제어부문D)

The Korean Institute of Electrical Engineers (대한전기학회)
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A New Improved Integral Variable Structure Controller for Uncertain Linear Systems

불확실 선형 시스템을 위한 새로운 개선된 적분 가변구조 제어기

  • 이정훈 (경상대 공대 전기전자공학부 제어계측전공, 항공기부품기술연구센터)
  • Published : 2001.04.01
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Abstract

In this paper, a new variable structure controller is designed for the tracker control of uncertain general plants so that the output of plants can controlled to a given arbitrary point in state space. By using the error between the steady state value of the output and the given reference, the sliding surface is defined, in advance, the surface from an initial state to the given reference without any reaching phase. A corresponding control input to satisfy the existence condition of the sliding mode is suggested to control the output on the predefined surface. Therefore the output controlled by the proposed controller is completely robust and identical to that of the sliding surface. Through an example, the usefulness is verified.

Keywords

References

  1. Utkin, V.I., Sliding Modes and Their Application in Variable Structure Systems. Moscow, 1978
  2. Itkis, U., Control Systems of Variable Structure. New York: John Wiley & Sons, 1976
  3. Utkin, V.I., 'Variable Structure Systems with Sliding Mode,' IEEE Trans. Automat. Control, 1977, AC-22, no.2, pp.212-222, 1977
  4. R. A. DeCarlo, S. H. Zak, and G. P. Matthews, 'Variable structure control of nonlinear multivariable systems: A Tutorial', Proceedings of IEEE, vol. 76, no. 3, pp. 212-232, 1988 https://doi.org/10.1109/5.4400
  5. J. Y. Hung, W. Gao, and J. C. Hung, 'Variable structure control: a survey', IEEE Trans. Industrial Electronics, vol. 40, no. 1, pp. 1- 21,1993 https://doi.org/10.1109/41.184817
  6. Utkin, V.I. and Yang, K.D., 'Methods for Constructing Discontinuity Planes in Multidemensional Variable Structure Systems,' Automat. Remote Control, 1978, 39, no. 10, pp.1466-1470
  7. T. L. Chern and Y. C. Wu, 'An Optimal Variable Structure Control with Integral Compensation for Electrohydraulic Position Servo Control System', IEEE, Trans., Vol. 39, No.5, pp. 460-463, 1992 https://doi.org/10.1109/41.161478
  8. El-Ghezawi, D.M.E., Zinober, A.S.I., Owens,D.H., and Bilings, S.A., 'Computation of the zeros and Directions of Linear Multivariable Systems,' Int. J. Control, 1982, vol. 36, no.5, pp.833-843 https://doi.org/10.1080/00207178208932933
  9. Dorling, C.M. and Zinober, A.S.I., 'Two Approaches to Hyperplane Design in Multivariable Variable Structure Control Systems,' Int. J. Control, 1986, 44, o.1, pp.65-82 https://doi.org/10.1080/00207178608933583
  10. EI-Ghezawi, D.M.E., Zinober, A.S.I., and Bilings, S.A, 'Analysis and Design of Variable Structure Systems Using a Geometric Approach,' Int. J. Control, 1983, 38, no.3, pp.657-671 https://doi.org/10.1080/00207178308933100
  11. Hebertt, S.R., 'Differential Geometric Methods in Variable Structure Control,' Int. J. Control, 1988, 48 https://doi.org/10.1080/00207178808906256
  12. Lee, D.S. and Youn, M. J., 'Controller Design of Variable Structure Systems with Nonlinear Sliding Surface,' Electroncs Letters 7Th. Dec., 1989, 25, no. 25, pp.1715-11717 https://doi.org/10.1049/el:19891147
  13. Chern, T.L. and Wu., Y.C., 'Design of Integral Variable Structure Controller and Application to Electrohydraulic Velocity Servosysterns,' lEE Proceedings-D, 1991, 138, No.5, pp.439-444
  14. Chang, L.W., 'A MIMO Sliding Control with a First-order plus Integral Sliding Condition,' Autometica, , 27, No. 5, pp.853-858 https://doi.org/10.1016/0005-1098(91)90040-9
  15. E. Y. Y. Ho and P. C. Sen, 'Control Dynamics of Speed Drive Systems using Sliding Mode Controllers with Integral Compensation', IEEE Trans. Ind. Appl. vol. 27, no. 5, pp. 883-892, 1991 https://doi.org/10.1109/28.90343
  16. Dubovitskii, V. A., 'Necessary and Sufficient Conditions of Minimum in Optimal /Control Problems with Sliding Modes and Generalized Controls,' Automat. Remote Control, 1984, 44, no. 2, pp.168-
  17. Ashchepkov, L. T., 'Optimization of Sliding Motions in a Discontinuous System,' Automat. Remote Controly, 1984, 44, no. 11, pp.1408-1415
  18. J.J. Slotine and S.S. Sastry, 'Tracking control of non-linear systems using sliding surface, with application to robot manipulators,' Int. J. Contr., vol. 38, no. 2, 1983, pp. 465-492 https://doi.org/10.1080/00207178308933088
  19. Young, K. K. D., Kokotovic, P.V., and Utkin, V.I., 'A Singlur Perturbation Analysis of High-Gain Feedback Systems,' IEEE Trans. Autom. Contr, 1977, AC-22, no. 6, pp.931-938
  20. S. B., Ceong, C. C., and Park, D. W., 'Moving Switching surfaces for Robust Ccontrol Second-Order Variable Structure System,' Int. J. Control, 1993, 58, no.1, pp.229-245 https://doi.org/10.1080/00207179308922999
  21. Harashima, F., Hashimoto, H., and Kondo, S., 'MOSFET Converter-Fed Position Servo System with Sliding Mode Control,' IEEE Trans. Ind. Electron., 1985, IE-32, no.3 https://doi.org/10.1109/TIE.1985.350165
  22. Kim, J. J., Lee, J. J., Park, K. B., and Youn, M. J., 'Design of New Time-Varying Sliding Surface for Robot Manipulator Using Variable Structure Controler,' Electronics Letters, 1993, Vol. 29, no.2, pp.195-196 https://doi.org/10.1049/el:19930131
  23. Chang, T. H. and Hurmuzlu, Y., 'Sliding Control Without Reaching Phase and its Application to Bipedal Locomotion' Trans of ASME, 1993, Vol. 115, pp.447-455
  24. Kwon, B. H., and Youn, M. J., 'Optimal Observer Using Time-Weighted Performance Index With Prespecfied Eigenvalues,' J. Dynamic Systems, Measurement, and Control(Trans. of ASME), 1986, 108, pp. 366-368
  25. Slotine, J. J. E., and Li, W., Applied Nonlinear Control. New Jersey: Prentice-Hall, 1991
  26. Kamman, R. E., 'When is a Linear Control System Optimal?,' J. Basic Eng.(Trans. of ASME),y_ 86, March, pp. 1-10, 1964
  27. Lee, J.H., et. al, Continuous variable structure controller for BLDDSM position control with prescribed tracking performance, IEEE Trans. Ind. Electron., 1994, IE-41, no.5., 483-491 https://doi.org/10.1109/41.315266
  28. Chang F.J., Twu, S.H., and Chang S., Adaptive Chattering Alleviation of Variable Structure System Control,' IEE Proceedings-D. 1990, 137, No.1, pp.31-39
  29. Su, W.C., Drakunov, S.V., and Ozguner, U. Constructing discontinuity Surfaces for Variable Structure Systems: A Lyapunov Approach, 1996, 32, No.6, pp.925-928 https://doi.org/10.1016/0005-1098(96)00017-9
  30. S. K. Park, H. G. Ahn, 'Robust controller design with novel sliding surface,' lEE Proceeding Control Theory Applications, vo1.146, no.3, pp.242-246, 1999 https://doi.org/10.1049/ip-cta:19990436
  31. Drazenovic, B.:The invariance conditions in variable structure systems, Automatica, 1969, (5), pp.287-295 https://doi.org/10.1016/0005-1098(69)90071-5
  32. F. Lewis and V. Syrmos, Optimal Control, New York, John Wiley & Sons, 1995
  33. J. H. Lee and W. B. Shin, Continuous variable structure systems for tracking control of BLDDSM, Proc. Of IEEE Int. Workshop on VSS, Tokyo, pp.84-89, 1996 https://doi.org/10.1109/VSS.1996.578564
  34. S. C. Chung and C. L. Lin,, A general class of sliding surface for sliding mode control, IEEE Trans. On Automatic Control, vol.43, no, 1. pp.115-119,1998 https://doi.org/10.1109/9.654911
  35. J. H. Lee and M. H. Lee, A new variables structure controller using integral-augmented sliding surface for BLDDSM position control with prescribed output dynamics, Proc. Of 3rd Asia-Pacific Conference on Control & Measurement, Dunhuang-China, pp.197-202, 1998
  36. J. H. Lee and M. J. Youn, A new integral variable structure regulation controller for robot manipulators with accurately predetermined output, Proc. Of IEEE Int. Symposium on Industrial Electronics, Bled-Slovenia, pp.336-341, 1999 https://doi.org/10.1109/ISIE.1999.801809
  37. J. H. Lee A new improved integral variables structure system for uncertain systems, Proc. Of 4th Asia-Pacific Conference on Control & Measurement, Guilin-China, pp.176-181, 2000