H2 Design of Decoupled Control Systems Based on Directional Interpolations

Title & Authors
H2 Design of Decoupled Control Systems Based on Directional Interpolations
Park, Kiheon; Kim, Jin-Geol;

Abstract
$\small{H_2}$ design of decoupled control systems is treated in the generalized plant model. The existence condition of a decoupling controller is stated and a parameterized form of all achievable decoupled closed loop transfer matrices is presented by using the directional interpolation approaches under the assumption of simple transmission zeros. The class of all decoupling controllers that yield finite cost function is obtained as a parameterized form and an illustrative example to find the optimal controller is provided.
Keywords
Linear multivariable control;Decoupling design;Interpolation condition;$\small{H_2}$ design;
Language
English
Cited by
References
1.
C. A. Doseor and G. A. Gundes, "Decoupling linear multiinput multioutput plants by dynamic output feedback: An algebraic theory," IEEE Trans. on Automat. Contr., Vol. AC-31, No. 8, pp. 744-750, 1986.

2.
H. P. Lee and J. J. Bongiorno, Jr., "Wiener-Hopf design of optimal decoupled multivariable feedback control systems", IEEE Trans. on Automat. Contr., Vol. AC-38, pp. 1838-1843, 1993.

3.
H. P. Lee and J. J. Bongiorno, Jr., "Wiener-Hopf design of optimal decoupling controllers for plants with non-square transfer matrices," Int. Journal of Control, Vol. 58, No. 6, pp. 1227-1246, 1993.

4.
C. A. Lin, "Necessary and sufficient conditions for existence of decoupling controllers," IEEE Trans. on Automat. Contr., Vol. AC- 42, No. 8, pp. 1157-1161, Aug. 1997.

5.
D. C. Youla and J. J. Bongiorno, Jr., "Wiener-Hopf design of optimal decoupling one-degree-of-freedom controllers," Int. Journal of Control, Vol. 73, No. 18, pp. 1657-1670, 2000.

6.
G. I. Gomez and G. C. Goodwin, "An algebraic approach to decoupling in linear multivariable systems," Int. Journal of Control, Vol. 73, No. 7, pp. 582-599, 2000.

7.
M. G. Safonov and B. S. Chen, "Multivariable stability-margin optimization with decoupling and output regulation," IEE Proceedings (Part D), Vol. 129, pp. 276-282, 1982.

8.
T.S. Brinsmead and G.C. Goodwin, "Cheap decoupled control", Automatica, Vol. 37, pp. 1465-1471, 2001.

9.
J. J. Bongiorno, Jr. and D. C. Youla, "Wiener-Hopf design of optimal decoupling one-degree-of-freedom controllers for plants with rectangular matrices", Int. Journal of Control, Vol. 74, pp. 1393-1411, 2001

10.
K. Park, "Existence conditions of decoupling controllers in the generalized plant model," in Proc. of 47th Conf. on Decision and Control, Cancun, Mexico, pp. 5158- 5163, Dec. 2008.

11.
K. Park, "Parameterization of decoupling controllers in the generalized plant," IEEE Trans. on Automat. Contr., Vol. AC-57, pp. 1067-1070, April 2012.

12.
K. Park, " \$H_2\$ design of one-degree-of-freedom decoupling controllers for square plants," Int. Journal of Control, Vol. 81, No. 9, pp. 1343-1351, 2008.

13.
V. Kuccera , "Decoupling Optimal Controllers," 18th International Conference on Process Control, pp. 400-407, P1-Th-1, Tatranska Lomnica, Slovakia, June 14-17, 2011.

14.
K. Park, "\$H_2\$ design of decoupling controllers based on directional interpolations," in Proc. of Joint 48th IEEE Conf. on Decision and Control and 28th Chinese Control Conference, Shanghai, P.R. China, pp. 5333- 5338, Dec. 2009.

15.
J. W. Brewer, "Kronecker products and matrix calculus in system theory," IEEE Trans. on Circuits and systems, Vol. 25, pp. 772-781, Sep. 1978.

16.
K. Park and J. J. Bongiorno, Jr., "A general theory for the Wiener-Hopf design of multivariable control systems," IEEE Trans. on Automat. Contr., Vol. AC-34, pp. 619-626, June 1989.

17.
D. C. Youla, H. Jabr, and J. J. Bongiorno, Jr., "Modern Wiener-Hopf design of optimal controllers-Part II: The multivariable case," IEEE Trans. on Automat. Contr., Vol. AC-21, pp. 319-338, June 1976.

18.
C. N. Nett, "Algebraic aspects of linear control systems stability," IEEE Trans. on Automat. Contr., Vol. AC-31, pp. 941-949, 1986.

19.
K. Zhou, J. C. Doyle, and K. Glover, Robust and optimal control, Upper Saddle River, New Jersey: Prentice-Hall, 1996.

20.
J. L. Walsh, Interpolation and approximation. New York City, NY: American Mathematical Society, 1935.

21.
K. Park and J. J. Bongiorno, Jr., "Persistent inputs and the standard \$H_2\$ multivariable control problem," Int. Journal of Control, Vol. 82, No. 11, pp. 2002-2012, 2009.

22.
U. Shaked, "The structure of inner matrices that satisfy multiple directional interpolation requirements," IEEE Trans. on Automat. Contr., Vol. AC-34, pp. 1293-1296, December 1989.

23.
D. Henrion and M. Sebek, "An algorithm for polynomial matrix factor extraction," Int. Journal of Control, Vol. 73, No. 8, pp. 686-695, 2000.

24.
M. A. Dahler and I. J. Diaz-Bobillo, Control of uncertain systems-A linear programming approach, Englewood Cliffs, N. J.: Prentice-Hall, 1995.