DOI QR코드

DOI QR Code

Decoupling Controller Design for H Performance Condition

  • Park, Tae-Dong (Dept of Applied Robot Convergent Technology R&D Division, Korea Institute of Industrial Technology) ;
  • Choi, Goon-Ho (IT Media Research Center, Korea University of Technology and Education) ;
  • Cho, Yong-Seok (Dept of Electronic and Information Engineering, Konyang University) ;
  • Park, Ki-Heon (Dept of Electrical Engineering, SungKyunKwan University)
  • Received : 2010.01.06
  • Accepted : 2011.08.31
  • Published : 2011.11.01

Abstract

The decoupling design for the one-degree-of-freedom controller system is treated within the $H_{\infty}$ framework. In the present study, we demonstrate that the $H_{\infty}$ performance problem in the decoupling design is reduced into interpolation problems on scalar functions. To guarantee the properness of decoupling controllers and the overall transfer matrix, the relative degree conditions on the interpolating scalar functions are derived. To find the interpolating functions with relative degree constraints, Nevanlinna-Pick algorithm with starting function constraint is utilized in the present study. An illustrative example is given to provide details regarding the solution.

Keywords

References

  1. A. I. G. Vardulakis, "Internal Stabilization and Decoupling in Linear Multivariable Systems by Unity Output Feedback Compensation," IEEE Transactions on Automatic Control, Vol 32. pp. 735-739, 1987. https://doi.org/10.1109/TAC.1987.1104701
  2. C. A. Lin, "Necessary and Sufficient Conditions for Existence of Decoupling Controllers," IEEE Transactions on Automatic Control, Vol. 42, pp. 1157-1161, 1997. https://doi.org/10.1109/9.618247
  3. D. C. Youla and J. J. Bongiorno, "Wiener-Hopf Design of Optimal Decoupling One-Degree-of-Freedom Controllers," International Journal of Control, Vol. 73, pp. 1657-1670, 2000. https://doi.org/10.1080/00207170050201744
  4. G. I. Gómez and G. C. Goodwin, "An Algebraic Approach Decoupling in Multivariable Systems," International Journal of Control, Vol. 73, pp. 582-599, 2000. https://doi.org/10.1080/002071700219434
  5. T. S. Brinsmed and G. C. Goodwin, "Cheap Decoupled Control", Automatica, Vol. 37, pp. 1465-1471, 2001. https://doi.org/10.1016/S0005-1098(01)00096-6
  6. J. J. Bongiorno and D. C. Youla, "Wiener-Hopf Design of Optimal Decoupling One-Degree-of-Freedom controllers for Plants with Rectangular Matrices," International Journal of Control, vol. 74, pp. 1393-1411, 2001 . https://doi.org/10.1080/00207170110067080
  7. K. Park, G. Choi and T. Kuc, "Wiener-Hopf Design of the Optimal Decoupling Control System with State-Space Formulas," Automatica, Vol. 38, pp. 319-326, 1994.
  8. K. Park," $H_2$ Design of Decoupling Controller based on Directional Interpolations," 48th IEEE Conference on Decision and Control, pp. 5333-5338, 2009.
  9. G. H. Choi, K. Park and J. H. Jung, "An Optimal H2 Decoupling Design for Non-Square Plant Systems based on the Two-Degree-of-Freedom Standard Model", IJCAS, Vol. 7, pp. 193-202, 2009.
  10. K. Park and G.H. Choi., "Necessary and Sufficient Conditions for the Existence of Decoupling Controllers in the Generalized Plant Model," Journal of Electrical Engineering & Technology, Vol. 6, pp. 706-712, 2011. https://doi.org/10.5370/JEET.2011.6.5.706
  11. C.A. Desoer and A.N. Gundes, "Decoupling linear multiinput-multioutput plant by dynamic output feedback: An algebraic theory," IEEE Transactions on Automatic Control, Vol. 31, No. 8, pp. 744-750, 1986. https://doi.org/10.1109/TAC.1986.1104391
  12. H.P. Lee and J.J. Bongiorno Jr., "Wiener-Hopf design of optimal decoupled multivariable feedback control systems," IEEE Transactions on Automatic Control, Vol. 38, No. 12, pp. 1838-1843, 1993. https://doi.org/10.1109/9.250562
  13. H.P. Lee and J.J. Bongiorno Jr., "Wiener-Hopf design of optimal decoupling controllers for plants with nonsquare transfer matrices," International Journal of Control, Vol. 58, No. 6, pp. 1227-1246, 1993. https://doi.org/10.1080/00207179308923052
  14. M. G. Safonov and B. S. Chen, "Multivariable Stability-Margin Optimization with Decoupling and Output Regulation," IEE Proceedings(PartD), Vol. 129, pp. 276-282, 1982.
  15. T. D. Park and K. Park., "Robust Stability Design of Decoupling Controllers using Nevanlinna-Pick Algorithm with Relative Degree Constrains," International Journal of Control, Vol. 84, pp. 1342-1349, 2011. https://doi.org/10.1080/00207179.2011.596282
  16. K. Zhou, J. C. Doyle and K. Glover, Robust and Optimal Control, Prentice-Hall, New Jersey, 1996.
  17. John C. Doyle, Bruce A. Francis and Allen R. Tannenbaum, Feedback Control Theory, Macmillan Publishing Company, New York, 1992.
  18. J. L. Walsh, Interpolation and Approximation, American Mathematical Society, New York, 1935.
  19. Hidenori Kimura, "Robust Stabilizability for a Class of Transfer Functions," 22nd IEEE Conference on Decision and Control, pp. 860-864, 1983.