Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Control Method for State Constrained Control Systems: Dynamic Anti-Widup Based Approach

동적 와인드엎 방지법에 기초한 상태 제한이 존재하는 시스템의 제어 방법

  • Park, Jong-Koo (Dept.of Electric Electronics Computer Engineering, Sungkyunkwan University)
  • 박종구 (성균관대학교 전기전자 및 컴퓨터공학부)
  • Published : 2000.08.01
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Abstract

Based on the dynamic anti-windup strategy a novel control methodology for state constrained control systems is presented. First a linear controller is designed for an open-loop stable plant to show a desirable nominal performance by ignoring state constraints. And then an additional dynamic compensator is introduced to preserve the nominal performance as closely as possible int he face of state constraints. This paper focuses on the second step under the assumption that a linear controller has already been designed appropriately by using an effective controller design method. By minimizing a reasonable performance index the dynamic compensator is derived explicitly which is expressed int he plant and controller parameters. the proposed method not only guarantees the total stability of the overall resulting systems but also provides desirable output performance because it solves the state-positioning problem completely.

Keywords

References

  1. K. J. Astrom and B. Wittenmark, Computer controlled systems: Theory and design, Prentice Hall, Englewood Cliffs, NJ, 1984
  2. S. Boyd and C. Barratt, Linear controller design: Limits of performance, Prentice Hall, Englewood Cliffs, NJ, 1991
  3. B. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, in Studies in Applied Mathematics, SIAM, Philadelphia, PA, vol. 15, 1994
  4. P. J. Campo and M. Morari, 'Robust control of processes subject to saturation nonlinearities,' Computers Chem. Engin., vol. 14, no. 4/5, pp. 343-358, 1990 https://doi.org/10.1016/0098-1354(90)87011-D
  5. C. T. Chen, Linear system theory and design, Holt, Rinehart and Winston, 1984
  6. C. -Y. Chen and M. -H. Perng, 'Optimal antiwindup control of saturating discrete-time MIMO systems,' Int. J. Contr., vol. 67, no. 6, pp. 933-959, 1997 https://doi.org/10.1080/002071797223875
  7. P. -O. Gutman and M. Cwikel, 'Admissible set and feedback control for discrete-time linear dynamical systems with bounded controls and states,' IEEE Trans. Automat. Contr., vol. 31, pp. 373-376, 1986 https://doi.org/10.1109/TAC.1986.1104270
  8. R. Hanus, M. Kinnaert, and J. L. Henrotte, 'Conditioning technique, a general anti-windup and bumpless transfer method,' Automatica, vol. 23, no. 6, pp. 729-739, 1987 https://doi.org/10.1016/0005-1098(87)90029-X
  9. T. Kailath, Linear systems, Prentice Hall, Englewood Cliffs, NJ, 1980
  10. P. V. Kokotovic, H. K. Khalil, and J. O'Reilly, Singular perturbation methods in control: Analysis and design, Academic Press, London, 1986
  11. P.V. Kokotovic, H. K. Khalil, and J. O'Reilly, Singular perturbation methods in control: Analysis and design, Academic Press, London, 1986
  12. M. V. Kothare, P. J. Campo, M. Morari, and C.N. Nett, 'A unified framework for the study of anti-windup designs,' Automatica, vol. 30, no. 12, pp. 1869-1883, 1994 https://doi.org/10.1016/0005-1098(94)90048-5
  13. Z. Lin, A. Saberi, and A. A. Stoorvogel, 'Semiglobal stabilization of linear discrete-time systems subject to input saturation via linear feedback - an ARE-based approach,' IEEE Trans. Automat. Contr., Vol. 41, No. 8, pp. 1203-1207, 1996 https://doi.org/10.1109/9.533685
  14. D. G. Luenberger, Introduction to linear and nonlinear programming, 2nd ed., Addison Wesley, Reading, Massachusetts, 1984
  15. M. Morari and E. Zafiriou, 'Robust process control,' Prentice Hall, Englewood Cliffs, NJ, 1989
  16. J. -K. Park and C. -H. Choi, 'Dynamic compensation method for multivariable control systems with saturating actuators,' IEEE Trans. Automat. Contr., vol. 40, no. 9, pp. 1635-1640, 1995 https://doi.org/10.1109/9.412636
  17. J. -K. Park and C. -H. Choi, 'Dynamical anti-reset windup method for discrete-time saturating systems,' Automatica, vol. 33, no. 6, pp. 1055-1072, 1997 https://doi.org/10.1016/S0005-1098(96)00208-7
  18. 박종구, '리셋 와인드엎 방지법에 기초한 상태 제한이 존재하는 제어 시스템의 보상 방법,' 제어.자동화.시스템공학 논문지, vol. 5, no. 5, pp. 511-520, 1999
  19. A. Saberi, Z. Lin, and A. R. Teel, 'Control of linear systems with saturating actuators,' IEEE Trans. Automat. Contr., vol. 41, no. 3, pp. 368-378, 1996 https://doi.org/10.1109/9.486638
  20. V. R. Saksena, J. O'Reilly, and P. V. Kokotovic, 'Singular perturbations and time-scale methods in control theory: Survey 1976-1983,' Automatica, vol. 20, no. 5, pp. 273-293, 1984 https://doi.org/10.1016/0005-1098(84)90044-X
  21. H. J. Sussmann, E. D. Sontag, and Y. Yang, 'A general result on the stabilization of linear systems using bounded controls,' IEEE Trans. Automat. Contr., vol. 39, pp. 2411-2425, 1994 https://doi.org/10.1109/9.362853
  22. A. Trofino-Neto and V. Kucera, 'Stabilization via output feedback,' IEEE Trans. Automat. Contr., vol. 38, no. 5, pp. 764-765, 1993 https://doi.org/10.1109/9.277243
  23. K. S. Walgama and J. Sternby, 'Inherent observer property in a class of anti-windup compensators,' Int. J. Contr., vol. 52, no. 3, pp. 705-724, 1990 https://doi.org/10.1080/00207179008953562
  24. K. S. Walgama and J. Sternby, 'On the convergence properties of adaptive pole-placement conrtollers with antiwindup compensators,' IEEE Trans. Automat. Contr., vol. 38, no. 1, pp. 128-132, 1993 https://doi.org/10.1109/9.186323
  25. K. S. Walgama, S. Ronnback, and J. Sternby, 'Generalisation of conditioning technique for anti-windup compensators,' Proc. IEE, Part D, vol. 139, pp. 109-118, 1992