샘플치 시스템의 루프정형 2자유도 H_{\infty}디지털 제어기 설계

The Design of Loop-shaping Two-degree-of-freedom H_{\infty} Digital Controller for Sampled-data System

  • 발행 : 2000.09.01

초록

In this paper we propose a design procedure of loop-shaping two-degree-of-freedom H$\infty$ digital controller for sampled-data system. We extend the continuous time loop-shaping two-degree-of-freedom H$\infty$ control problem to sampled-data system. The configuration of generalized plant is modified for sampled-data system. And then using continuous lifting we obtain the digital controller. In the final stage of loop-shaping procedure the problem of absorbing weighting functions is discussed. We summarize this study to the design procedure and illustrate the application for an inverted pendulum on the cart.

키워드

참고문헌

  1. W.A. Wolovich, Automatic control systems : Basic analysis and design, Philadelphia, PA: Saunders, 1995
  2. G. Zames, 'Feedback and Optimal sensitivity : model reference transformations, multiplicative seminorms, and approximate inverses', IEEE Trans. Auto. Control, vol. AC-26, pp. 301-320, 1981 https://doi.org/10.1109/TAC.1981.1102603
  3. J.C. Doyle, K. Glover, P.P. Khargonekar, B.A. Francis, 'State-space solutions to standard $H_2$ and $H_{\infty}$ control problems', IEEE Trans. Auto. Control, vol. AC-34, pp. 831-847, 1989 https://doi.org/10.1109/9.29425
  4. K. Zhou, Robust and optimal control, Prentice-Hall, 1996
  5. J.C. Doyle, G. Stein, 'Multivariable Feedback Design : Concepts for a Classical/Modern Synthesis', IEEE Trans. Auto. Control, Vol. AC-26, No. 1, pp.4-16, 1981
  6. D. McFarlane, K. Glover, 'A loop-shaping Design Procedure Using H∞ Synthesis', IEEE Trans. Auto. Control, Vol. 37, No. 6, pp. 759-769, 1992 https://doi.org/10.1109/9.256330
  7. D.C. McFarlane, K. Glover, Lecture notes in control information sciences 138 : Robust controller design using normalized coprime factor plant descriptions, Springer-Verlag, 1990
  8. D.J.N. Limeber, E.M. Kasenally, J.D. Perkins, 'On the Design of Robust two-degree-of-freedom Controllers', Automatica, Vol. 29, No. 1, pp. 157-168, 1993 https://doi.org/10.1016/0005-1098(93)90179-W
  9. D.J. Walker, 'On the structure of a two-degree-freedom $H_{\infty}$ loop-shaping controller', INT. J. Control, Vol. 63, No. 6, pp. 1105-1127, 1996 https://doi.org/10.1080/00207179608921885
  10. B. Bamieh, J.B. Pearson, B.A. Francis, and A. Tannenbaum, 'A lifting technique for linear periodic systems with applications to sampled-data control', Systems & Control Letters, vol. 17, pp. 79-88, 1991 https://doi.org/10.1016/0167-6911(91)90033-B
  11. B. Bamieh, J.B. Pearson, 'A general framework for linear periodic systems with application to $H_{\infty}$ sampled-data control', IEEE Trans. Auto. Control, vol. AC-37, pp. 418-435, 1992 https://doi.org/10.1109/9.126576
  12. W. Sun, K.M. Nagpal, and P.P. Khargonekar, '$H_{\infty}$ control and filtering for sampled-data systems', IEEE Trans. Auto. Control, vol. AC-38, pp. 1162-1175, 1993 https://doi.org/10.1109/9.233150
  13. T. Chen, B.A. Francis, Optimal sampled-data control systems, Springer, 1995
  14. T. Chen, B.A. Francis, 'Input-output Stability of sampled-data systems', IEEE Trans. Auto. Control, vol. 36, pp. 50-58, 1991 https://doi.org/10.1109/9.62267
  15. R. M. Redheffer, 'On a certain linear fractional transformation', J. Maths. Phys., Vol. 39, pp. 269-286, 1960
  16. P. A. Iglesias, K. Glover, 'State space approach to discrete time $H_{\infty}$ control', Int. J. Control, Vol. 54, No.5 pp. 1031-1073, 1991 https://doi.org/10.1080/00207179108934198
  17. G. J. Balas, J.C. Doyle, K. Glover, A. Packard, R. Smith, ${\mu}$-analysis and synthesis toolbox, The MathWorks Inc, 1995
  18. 황영민, 이상철, 이석배, 이상효, 'LMI 기법에 의한 도립전자 시스템의 ${H_\infty}$ 제어기 설계
  19. Lee, Sang Hyo, Lee, Sang-Chuel, Park, Jong-Woo, Cho, Do-Hyeoun, Lee, Jong-Yong, 'The robust $H_{\infty}$ controller design via linear matrix inequalities (LMIs) for an inverted pendulum on the cart', The International Conference on Electrical Engineering, pp.288-290, 1998
  20. 조창호, 이상철, 조도현, 박종우, 이종용, 이상효, '샘플드 데이터 시스템에 대한 $H_{\infty}$ 제어기 설계 : 도립진자 예제
  21. THE MATHWORKS, SIMULINK - dynamic system simulation software, The MATHWORKS Inc., mass., U.S.A., 1995