Parametrization and reliable extraction of proper compensators

characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function

N_{r} D_{r}^{- 1}

such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by

D_{k}

. The subclass is navigated and extracted through a conventional parametrization whose denominators are affine to row echelon form and the centre is in a compensator whose numerator has minimum column degrees. Applications include stabilization of linear multivariable systems.

How to cite

top

MLA
BibTeX
RIS

Kraffer, Ferdinand, and Zagalak, Petr. "Parametrization and reliable extraction of proper compensators." Kybernetika 38.5 (2002): [521]-540. <http://eudml.org/doc/33601>.

@article{Kraffer2002,
abstract = {The polynomial matrix equation $X_lD_r$$+$$Y_lN_r$$=$$D_k$ is solved for those $X_l$ and $Y_l$ that give proper transfer functions $X_l^\{-1\}Y_l$ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function $N_rD_r^\{-1\}$ such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by $D_k$. The subclass is navigated and extracted through a conventional parametrization whose denominators are affine to row echelon form and the centre is in a compensator whose numerator has minimum column degrees. Applications include stabilization of linear multivariable systems.},
author = {Kraffer, Ferdinand, Zagalak, Petr},
journal = {Kybernetika},
keywords = {compensator; stabilization; compensator; stabilization},
language = {eng},
number = {5},
pages = {[521]-540},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Parametrization and reliable extraction of proper compensators},
url = {http://eudml.org/doc/33601},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Kraffer, Ferdinand
AU - Zagalak, Petr
TI - Parametrization and reliable extraction of proper compensators
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 5
SP - [521]
EP - 540
AB - The polynomial matrix equation $X_lD_r$$+$$Y_lN_r$$=$$D_k$ is solved for those $X_l$ and $Y_l$ that give proper transfer functions $X_l^{-1}Y_l$ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function $N_rD_r^{-1}$ such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by $D_k$. The subclass is navigated and extracted through a conventional parametrization whose denominators are affine to row echelon form and the centre is in a compensator whose numerator has minimum column degrees. Applications include stabilization of linear multivariable systems.
LA - eng
KW - compensator; stabilization; compensator; stabilization
UR - http://eudml.org/doc/33601
ER -

References

top

Callier F. M., Proper feedback compensators for a strictly proper plant by solving polynomial equations, In: Proc. MMAR 2000. Miedzyzdroje 2000, pp. 55–59
Callier F. M., Polynomial equations giving a proper feedback compensator for a strictly proper plant, In: Proc. 1st IFAC Symposium on System Structure and Control, Prague 2001
Callier F. M., Desoer C. A., Multivariable Feedback Systems, Springer, New York 1982
Forney G. D., 10.1137/0313029, SIAM J. Control 13 (1975), 493–520 (1975) Zbl0269.93011 MR0378886 DOI10.1137/0313029
Golub G. H., Loan C. F. Van, Matrix Computations, North Oxford Academic, Oxford 1989
Kailath T., Linear Systems, Prentice Hall, Englewood Cliffs, N. J. 1980 Zbl0870.93013 MR0569473
Kučera V., Zagalak P., Proper solutions of polynomial equations, In: Proc. IFAC World Congress, Pergamon, Oxford 1999, pp. 357–362 (1999)
MacDuffee C. C., The Theory of Matrices, Springer, Berlin 1933 Zbl0007.19507
Popov V. M., 10.1007/BFb0059934, (Lecture Notes in Mathematics 144.) Springer, Berlin 1969, pp. 169–180 (1969) MR0395958 DOI10.1007/BFb0059934
Rosenbrock H. H., State-space and Multivariable Theory, Nelson, London 1970 Zbl0246.93010 MR0325201
Rosenbrock H. H., Hayton G. E., 10.1080/00207177808922416, Internat. J. Control 27 (1978), 837–852 (1978) Zbl0403.93017 MR0497005 DOI10.1080/00207177808922416
Dooren P. M. Van, 10.1109/TAC.1981.1102559, IEEE Trans. Automat. Control AC-26 (1981), 111–129 (1981) MR0609253 DOI10.1109/TAC.1981.1102559
Vidyasagar M., Control System Synthesis, MIT Press, Cambridge, MA 1985 Zbl0655.93001 MR0787045
Wang S. H., Davison E. J., 10.1109/TAC.1973.1100283, IEEE Trans. Automat. Control AC-18 (1973), 220–225 (1973) Zbl0261.93010 MR0441434 DOI10.1109/TAC.1973.1100283
Wedderburn J., Lectures on Matrices, American Mathematical Society, Providence, R.I. 1934 Zbl0176.30501
Wolovich W. A., Linear Multivariable Systems, Springer, New York 1974 Zbl0534.93026 MR0359881
Zagalak P., Kučera V., 10.1109/TAC.1985.1103920, IEEE Trans. Automat. Control AC-30 (1985), 286–289 (1985) MR0778436 DOI10.1109/TAC.1985.1103920

Citations in EuDML Documents

top

Frank Callier, Ferdinand Kraffer, Proper feedback compensators for a strictly proper plant by polynomial equations

NotesEmbed ?

top

You must be logged in to post comments.

Nice post, Thanks for sharing. https://www.blissshine.com/meaning/reliable/

page 1

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.