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

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

DOI QR Code

Design of PI, PD and PID Controllers with Time Response Specifications

시간응답 설계규격을 만족하는 PI, PD, PID제어기 설계

  • 김근식 (대천대학 컴퓨터전자전계열) ;
  • 조태신 (충북대학교 전자공학과) ;
  • 김영철 (충북대학교 전기전자컴퓨터공학부)
  • Published : 2003.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers the problem of determining a set of PI, PD and PID controller gains, for a given linear time invariant plant, that meets or exceeds the closed loop step response specifications. The proposed method utilizes two recent results: for a given system, (1) finding a set of stabilizing PI, PD and PID gains and (2) the relationship between time response (overshoot and speed) and the coefficients of the characteristic polynomial. The method allows us to extract a subset of PI, PD and PID gains that meets stability as well as time domain performance requirements. The intersections of two dimensional sets described by linear and quadratic inequalities in the controller design space are need to be Identified through numerical computation. The procedure is illustrated by examples.

Keywords

References

  1. P. Naslin, The Dynamics of Linear and Non-Linear Systems, Gordon and Breach Science Publishers, New York, NY, 1965
  2. P. Naslin, Essentials of Optimal Control, Boston Technical Publishers, Inc., Cambridge, M.A, 1969
  3. S. Manabe, 'Coefficient diagram method', Proc. of the 14th IFAC Symposium on Automatic Control in Aerospace, pp. 199-210, Seoul, Korea, 1998
  4. 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
  5. Y. C. Kim, L. H. Keel, and S. P. Bhattacharyya, 'Transient Response Control via Characteristic Ratio Assignment,' Proc. of the 2002 American Control Conference, Anchorage, Alaska, 2002 https://doi.org/10.1109/ACC.2002.1023257
  6. Y. C. Kim, L. H. Keel, and S. Manabe, 'Controller design for time domain specifications,' Proc. of IFAC World Congress, Barcelona, Spain, July, 2002
  7. A. Datta, M. T. Ho, and S.P. Bhattacharyya, Structure and Synthesis of PID Controllers, London, U.K. : Springer-Verlag, 2000
  8. D. S. Bernstein and W. M. Haddad, 'LQG control with an $H_{infty} performance bound: a Riccati equation approach,' IEEE Trans. Automatic Control, vol. AC-34, pp. 293-305, March 1989 https://doi.org/10.1109/9.16419
  9. P. Dorato, Analytic Feedback System Design: An Interpolation Approach, Brooks Cole Publishing, Pacific Grove, CA, 2000
  10. H. Chestnut and R. W. Mayer, Servomechanisms and Regulating System Design, vol. 1, John Wiley & Sons, Inc., NY, 1959
  11. J. L. Goldberg, Matrix Theory with Applications, McGraw-Hill, Inc., 1992
  12. D. D. Siljak, Nonlinear Systems : The Parameter Analysis and Design, John Wiley and Sons, Inc., NY., 1969
  13. G. C. Goodwin, S. F. Graebe, M.E. Salgado, Control System Design, Prentice Hall, New Jersey, 2001