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

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Time Discretization of Nonlinear System with Variable Time-delay Input Using Taylor Series Expansion

Taylor series를 이용한 시변 지연 입력을 갖는 비선형 시스템의 이산화

  • 최형조 (전북대학교 메카트로닉스공학과) ;
  • 박지향 (삼성 SDI) ;
  • 이수영 (전북대학교 전자정보공학부) ;
  • 정길도 (전북대학교 전자정보공학부)
  • Published : 2005.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

A new discretization algorithm for nonlinear systems with delayed input is proposed. The algorithm is represented by Taylor series expansion and ZOH assumption. This method is applied to the sampled-data representation of a nonlinear system with the time-delay input. Additionally, the delay in input is time varying and its amplitude is bounded. The maximum time-delay in input is assumed to be two sampling periods. The mathematical expressions of the discretization method are presented and the ability of the algorithm is tested for some of the examples. The computer simulation proves the proposed algorithm discretizes the nonlinear system with the variable time-delay input accurately.

Keywords

References

  1. M. Boutayeb, 'Observer design for lienar time-delay systems', System & Control Letters, 2001 https://doi.org/10.1016/S0167-6911(01)00129-3
  2. R. C. Luo, L.-Y. Chung, 'Stabilization for linear uncertain systems with time latency', IEEE Transactions on Industrial electronics, 2002 https://doi.org/10.1109/TIE.2002.801243
  3. M. Nihtila, T. Damak, J. P. Babary, 'On-line estimation of the time delay via orthogonal collocation', Simulation Practice and Theory, 1997
  4. 노영훈, 오준호, '시간지연 시스템에서의 불확실성 추정을 갖는 슬라이딩 모드제어', 제어자동화시스템공학 논문지, 제6권, 제11호,pp. 963-967, 11, 2000
  5. 송성호, 박섭형, 이봉영, '시변 시간 지연을 갖는 불확실한 이산 시간 선형 시스템의 견실 안정성', 제어자동화시스템공학 논문지, 제5권, 제6호,pp. 641-646, 8,1999
  6. 임흥재, 정완균, 서일홍, '시간 지연이 있는 양방향 원격 제어 시스템의 예측 제어', 제어자동화시스템공학 논문지 제6권, 제4호, pp. 295-304, 4, 2000
  7. C. T. Chen, 'Linear system theory and design. holt', Rinhart and Winston, Orlando 1984
  8. S. Hohmann, A. Konrad, and Y. Krebs, 'Exact sampled-data representation of continuous-time nonlinear systems by finite polynomials with exactly determined coefficients', Proceedings of the 2001 American Control Conference, pp. 1628-1633, 2001 https://doi.org/10.1109/ACC.2001.945960
  9. Franklin, G. F., Powell, J. D. and Workman, M. L., 'Digital control of dynamic system.' Addison-Wesley, New York 1988
  10. R. J. Vaccaro, 'Digital control.' McGraw-Hill, New York 1995
  11. A. Isidori, 'Nonlinear control systems: an introduction', Springer-Verlag, Berlin, 1989
  12. M. Vidyasagar, 'Nonlinear systems analyses.' Prentice Hall, Englewood Cliffs, 1978
  13. N. Kazantzis, and C. Kravaris, 'System-theoretic properties of sampled-data representations of nonlinear systems obtained via taylor-lie series', Int. J. Control, pp. 997-1020, 1997 https://doi.org/10.1080/002071797223901
  14. N. Kazantzis, and C. Kravaris, 'Time-discretization of nonlinear control systems via taylor methods, Comp. Chem. Engn. pp. 763-784,1999 https://doi.org/10.1016/S0098-1354(99)00007-1
  15. N. Kazantzis, K. T. Chong, J. H. Park, A. G. Parlos, 'Control-relevant discretization of nonlinear systems with time-delay using taylor-lie series', Journal of ASME, 2003 https://doi.org/10.1109/ACC.2003.1238929
  16. B. R. Holt, and M. Morari, 'Design of resilient processing plants-V.: The effect of deadtime on dynamic resilience.' Chem. Eng. Sci., pp. 1229-1237, 1985 https://doi.org/10.1016/0009-2509(85)85081-8