새로운 저차 안정화기와 시간응답을 위한 1차 및 PID 제어기 설계

New Low-Order Stabilizers and Its Application to the First-Order and PID Controllers with Time Response Specifications

  • 발행 : 2006.01.01

초록

This paper presents the problems of designing low-order controller for a linear time-invariant(LTI) system in parameter space, wherein both transient response requirements and stability shall be considered in the same space. For a LTI system, we, (1) develop a method determining the existence of low-order stabilizers of the first-order and PID structures, (2) develop an algorithm of finding such a stabilizing region. (3) Both procedures are carried out by means of a parametric approach in the same frame work. This leads to easily obtain a subset of controller gains from the stabilizing set, that meet good time response requirements. It is illustrated by examples.

키워드

참고문헌

  1. Y. C. Kim, L. H. Keel, and S. P. Bhattacharyya, 'Transient Response Control via Characteristic Ratio Assignment,' IEEE Trans. on Automatic Control, vol. AC-48, no.12, pp.2238-2244, Dec. 2003 https://doi.org/10.1109/TAC.2003.820153
  2. A. V. Lipatov and N. I. Sokolov, 'Some sufficient conditions for stability and instability of continuous linear stationary Systems,' Automation and Remote Control, Vol. 39, pp. 1285-1291, 1979
  3. C. T. Chen, Analog and Digital Control System Design : Transfer- function, State space and Algebraic method, Saunders College Pub., 1993
  4. K Zhou, Essentials of Robust control, Prentice-Hall, NJ, 1998
  5. M. A. Dahleh and I. J. Diaz-Bobillo, Control of Uncertain Systems: A Linear Programming Approach, Prentice Hall Publishing, Upper Saddle River, NJ, 1995
  6. L. H. Keel and S. P. Bhattacharyya, 'Robust, Optimal, or Fragile?,' IEEE Trans. on Automatic Control, Vol. AC-42, pp. 1098-1105, 1997 https://doi.org/10.1109/9.618239
  7. L. H. Keel and S. P. Bhattacharyya, 'State-space Design of Low-order Stabilizers,' IEEE Trans. on Automatic Control, Vol. AC-35, pp. 182-186, 1990 https://doi.org/10.1109/9.45175
  8. D. W. Gu, B. W. Choi, and I. Postlewaite, 'Low-order Stabilizing Controllers,' IEEE Trans. on Automatic control, Vol. AC-38, pp. 1713-1717, 1993 https://doi.org/10.1109/9.262047
  9. A. Linnemann, 'A Class of Single-Input Single-Output Systems Stabilizable by Reduced-order Controllers,' System & Control Letter, Vol. 11, pp. 27-33, 1988 https://doi.org/10.1016/0167-6911(88)90107-7
  10. Q. G. Wang, T. H. Lee, and J. H. Lee, 'Low-order Stabilizers for Linear Systems,' Automatica, Vol. 33, pp. 651-654, 1997 https://doi.org/10.1016/S0005-1098(96)00192-6
  11. A. Datta, M. T. Ho, and S. P. Bhattacharyya, Structure and Synthesis of PID Controllers, London, U. K. : Springer-Verlag, 2000
  12. R. N. Tantaris, L. H. Keel, and S. P. Bhattacharyya, 'Stabilization of continuous time systems by first order controllers,' Proc of the 10th Mediterranean Conference on Control and Automation, Lisbon, Porutugal, July, 2002
  13. P. Naslin, Essentials of Optimal Control, Boston Technical Publishers, Inc., 1969
  14. K. S. Kim, Y. C. Kim, L. H. Keel, and S. P. Bhattacharyya, 'PID Controller Design with Response Specifications,' Proc. of the 2003 American Control Conference, Denver, Colorado, 2003 https://doi.org/10.1109/ACC.2003.1242519
  15. Youngchol Kim, Keunsik Kim and Shunji Manabe, Sensitivity of Time Response to Characteristic Ratios,' Proc of the 2004 American Control Conference, pp.2723-2728, Boston, USA, June, 2004
  16. 김근식, 조태신, 김영철, '시간응답 설계규격을 만족하는 PI, PD, PID제어기 설계,' 제어. 자동화.시스템공학회지 제9권 4호, pp.259-268, 2003 https://doi.org/10.5302/J.ICROS.2003.9.4.259
  17. Shunji Manabe, 'Coefficient Diagram Method,' Proc. of IFAC Symposium on Advanced Control in Aerospace, Seoul, Korea, 2002
  18. 한상용, 조태신, 김영철, '단조 스텝응답을 주는 연속계 전달함수의 합성 조건: 가설,' 2003정보및제어학술회의 논문집, 춘천, 2003