Optimal Wiener-Hopf Decoupling Controller Formula for State-space Algorithms

  • Park, Ki-Heon (School of Information and Communication Engineering, Sungkyunkwan University) ;
  • Kim, Jin-Geol (School of Electrical Engineering, Inha University)
  • Published : 2007.08.31

Abstract

In this paper, an optimal Wiener-Hopf decoupling controller formula is obtained which is expressed in terms of rational matrices, thereby readily allowing the use of state-space algorithms. To this end, the characterization formula for the class of all realizable decoupling controller is formulated in terms of rational functions. The class of all stabilizing and decoupling controllers is parametrized via the free diagonal matrices and the optimal decoupling controller is determined from these free matrices.

Keywords

References

  1. C. A. Desoer and A. N. Gundes, 'Decoupling linear multiinput-multioutput plants by dynamic output feedback: An algebraic theory,' IEEE Trans. on Automatic Control, vol. 31, no. 8, pp. 744-750, 1986 https://doi.org/10.1109/TAC.1986.1104391
  2. H. P. Lee and J. J. Bongiorno, Jr., 'Wiener-Hopf design of optimal decoupled multivariable feedback control systems,' IEEE Trans. on Automatic Control, vol. 38, no. 12, pp. 1838-1843, 1993 https://doi.org/10.1109/9.250562
  3. G. I. Gomez and G. C. Goodwin, 'An algebraic approach to decoupling in linear multivariable systems,' International Journal of Control, vol. 73, no. 7, pp. 582-599, 2000 https://doi.org/10.1080/002071700219434
  4. D. C. Youla and J. J. Bongiorno, Jr., 'Wiener-Hopf design of optimal decoupling one-degree-of-freedom controllers,' International Journal of Control, vol. 73, no. 18, pp. 1657-1670, 2000 https://doi.org/10.1080/00207170050201744
  5. J. J. Bongiorno, Jr. 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, no. 14, pp. 1393-1411, 2001 https://doi.org/10.1080/00207170110067080
  6. K. Park, G. Choi, and T. Kuc, 'Wiener-Hopf design of the optimal decoupling control system with state-space formulas,' Automatica, vol. 38, no. 2, pp. 319-326, 2002 https://doi.org/10.1016/S0005-1098(01)00206-0
  7. K. Park and D. C. Youla, 'Numerical calculation of the optimal three-degree-of-freedom Wiener-Hopf controller,' International Journal of Control, vol. 56, no. 1, pp. 227-244, 1992 https://doi.org/10.1080/00207179208934311
  8. J. W. Brewer, 'Kronecker products and matrix calculus in system theory,' IEEE Trans. on Circuits and Systems, vol. 25, no. 9, pp. 772-781, 1978 https://doi.org/10.1109/TCS.1978.1084534
  9. K. Park, Y. S. Cho, J. S. Lee, and K. Kang, 'Wiener-Hopf approach to derivation of rational doubly coprime factorizations,' Automatica, vol. 35, no. 4, pp. 725-728, 1999 https://doi.org/10.1016/S0005-1098(98)00197-6
  10. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1994
  11. J. C. Doyle, K. Glover, P. P. Khargonkar, and B. A. Frnacis, 'State-space solutions to standard $H_2$ and $H_{\infty}$, control problems,' IEEE Trans. on Automatic Control, vol. 34, no. 8, pp. 831-847, 1989 https://doi.org/10.1109/9.29425
  12. A. Grace, A. J. Laub, J. N. Little, and C. M. Thompson, Control System Toolbox: User's Guide, The Math Works, Inc., 1992
  13. K. Park and J. J. Bongiorno, Jr., 'A general theory for the Wiener-Hopf design of multivariable control systems,' IEEE Trans. on Automatic Control, vol. 34, no. 6, pp. 619-626, 1989 https://doi.org/10.1109/9.24230