전기학회논문지 (The Transactions of The Korean Institute of Electrical Engineers)

  • 제57권6호
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  • Pages.1048-1057
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  • 2008
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  • 1975-8359(pISSN)
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  • 2287-4364(eISSN)
대한전기학회 (The Korean Institute of Electrical Engineers)
권호 표지

제어기 영점의 영향을 감소시키는 종속형 저차 제어기의 설계

Design of Low Order Cascade Controller to Reduce the Effects of Its Zeros

  • 발행 : 2008.06.01
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초록

This paper represents a design method for PID or low-order controllers cascaded with a linear plant in the unit feedback system where it is required to meet the given time response specifications such as overshoot and settling time. This problem is difficult to solve because the zeros of the controller appear in the numerator of the overall system and thus those zeros may make the time response design difficult. In this paper, we propose a new approach based on the partial model matching and the so called K-polynomial. The partial matching problem is formulated to an optimization problem in which a quadratic function of coefficient errors between a target model and the resulting closed loop system is minimized. For the sake of satisfying the closed loop stability, a set of quadratic constraints associated with the cost function is introduced. As a result, the controller designed meets both time response requirements and the closed loop stability, if any. It is shown through several examples that the present method can be easily applied to these problems.

키워드

참고문헌

  1. P. Dorato, "Quantified Multivariate Polynomial Inequalities: The Mathematics of Practical Control Design Problems." IEEE Control System Magazine, vol. 20, no.5, pp.48-58, 2000 https://doi.org/10.1109/37.872903
  2. T. Kitamori, "A Method of Control System Design Based upon Partial Knowledge about Controlled Process," SICE Trans. Japan, vol.15, no. 4, pp.549-555, 1979 https://doi.org/10.9746/sicetr1965.15.549
  3. E. Emre and L.M. Silverman, "Partial Model Matching of Linear Systems," IEEE Trans. Automatic Control, vol.25, no.2, pp.280-281, 1980 https://doi.org/10.1109/TAC.1980.1102321
  4. V. Kucera, J.C.Martinez Garcia and M. Malabre, "Partial Model Matching: Parametrization of Solutions,"Automatica, vol.33, no.5, pp.975-977, 1997 https://doi.org/10.1016/S0005-1098(96)00252-X
  5. 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
  6. D. Henrion and J.B. Lasserre, "Solving Nonconvex Optimization Problem,"IEEE Control System Magazine, vol. 24, no.3, pp.72-82, 2004 https://doi.org/10.1109/MCS.2004.1299534
  7. Y.C. Kim, L.H. Keel, and S.P. Bhattacharyya, "Transient Response Control via Characteristic Ratio Assignment", IEEE Trans. Automatic Control, vol.48, No.12, pp.2238-2244, 2003 https://doi.org/10.1109/TAC.2003.820153
  8. Y.T. Woo and Y.C. Kim, " Digital Control of a Single Phase UPS Inverter for Robust AC-Voltage Tracking," Journal of IJCAS, vol.3, no.4, pp.620-629, 2005
  9. S.Y. Han, T.S. Cho, Y.C. Kim, "A synthesis condition of continuous-time transfer function for monotonic step response : Hypothesis," Proc. CICS 03, pp.127-130, Chuncheon, Korea, Nov. 2003
  10. D. Henrion, J. B. Lasserre "GloptiPoly : Global Optimization over Polynomials with MATLAB and SeDuMi", ACM Trans. Math. Software, vol. 29, no. 2, pp.165-194, 2003 https://doi.org/10.1145/779359.779363
  11. D. Peaucelle, D. Henrion, Y. Labit, K. Taitz "User's Guide for SeDuMi Interface 1.04" LAAS-CNRS Research Report No. 02333, September 2002