A Survey of Simple Transfer-Function from High-Order Transfer-Function
Keywords:
Realization, control, Design, analysis, implementation.Abstract
many engineering applications. It is often
desirable to represent a higher-order system by a lower-order
model. In most instances, such lower-order models provide
reasonable accuracy for realization, control, and/or
computational purposes. The fast development and use of smaller
processors, such as personal and minicomputers, in the design,
analysis, and/or implementation of dynamic systems enhance the
importance and increased interest in effective model reduction
schemes.
References
Electron. Lett., vol. 27, pp. 2260-2262, 1991.
L.A. Aguirre, “Open loop model matching in frequency domain,”
Electron. Lett., vol. 28, pp. 484-485, 1992.
L.A. Aguirre, “Validation of reduced order models for closed loop
applications,” in Proc. IEEE Conf. on Contr. Applications,
Vancouver, BC, 1993, pp. 605-610.
L.A. Aguirre, “Designing controller by means of model reduction
techniques,” Electron. Lett., vol. 29, pp. 389-390, 1993.
L.A. Aguirre, “Matrix formulae for open and closed-loop
approximate model matching in frequency domain,” Int. J. Syst.
Sci., vol. 26, pp. 2069-2089, 1995.
L.A. Aguirre, “Algorithm for approximate model matching for
loops with non-negligible feedback dynamics,” Trans. ASME, J.
Dyn. Syst. Meas. Contr., vol. 120, pp. 394-398, 1998.
B.D.O. Anderson and Y. Liu, “Controller reduction: concepts and
approaches,” IEEE Trans. Automat. Contr., vol. 34, pp. 802-812,
R.K. Appiah, “Linear model reduction using Hurwitz polynomial
approximation,” Int. J. Contr., vol. 28, pp. 476-488, 1978.
R.K. Appiah, “Padé methods of Hurwitz polynomial
approximation with application to linear system reduction,” Int. J.
Contr., vol. 29, pp. 39-48, 1979.
G.A. Baker, and P.R. Graves-Morris, Padé approximants, Part II:
Extension and Application. Addison-Wesley, London, 1981.
B. Bandyopadhyay, O. Ismail, and R. Gorez “Routh-Padé
approximation for interval systems,” IEEE Trans. Automat. Contr.,
vol. 39, pp. 2454-2456, 1994.
B. Bandyopadhyay, T.M. Kande, and M.C. Srisalam “Routh type
approximation for discrete system,” IEEE, Int. Symp. on circuits
and syst., vol. 3, pp. 2899-2902, 1988.
B. Bandyopadhyay, A. Upadhye, and O. Ismail, “g -d Routh
approximation for interval systems,” IEEE Trans. Automat. Contr.,
vol. 42, pp. 1127-1130, 1997.
Y. Bistritz, “Comments on mixed time/frequency domain
approach to model reduction,” Electron. Lett., vol. 16, pp. 189-
, 1980.
Y. Bistritz, “A discrete stability equation theorem and method of
stable model reduction,” Syst. Contr. Lett., vol. 1, pp. 373-381,
Y. Bistritz, “A direct Routh stability method for discrete system
modeling,” Syst. Contr. Lett., vol. 2, pp. 83-87, 1983.
Y. Bistritz and G. Langholz, “Model reduction by Chebyshev
polynomial techniques,” IEEE Trans. Automat. Contr., vol. AC-
, pp. 741-747, 1979.
Y. Bistritz and U. Shaked, “Stable linear systems simplification
via Padé approximations to Hurwitz polynomials,” Trans. ASME
J. Dyn. Syst. Meas. Contr., vol. 103, pp. 279-284, 1981.
T.C. Chen, C.Y. Chang, and K.W. Han, “Reduction of transfer
functions by the stability equation method,” J. Franklin Inst., vol.
, pp. 389-404, 1979.
T.C. Chen, C.Y. Chang, and K.W. Han, “Model reduction using
the stability-equation method and the Padé approximation
method,” J. Franklin Inst., vol. 309, pp. 473-490, 1980.
T.C. Chen, C.Y. Chang, and K.W. Han, “Stable reduced-order
Padé approximants using stability equation method,” Electron.
Lett., vol. 16, pp. 345-346, 1980.
C.T. Chen and B. Seo, “The inward approach in the design of
control systems,” IEEE Trans. Education, vol. 33, pp. 270-278,
C.F. Chen and L.S. Shieh, “A novel approach to linear model
simplification,” Int. J. Contr., vol. 8, pp. 561-570, 1968.
B.S. Chen and T.Y. Yang, “Robust optimal model matching
control design for flexible manipulators,” Trans. ASME, J. Dyn.
Syst. Meas. Contr., vol. 115, pp. 173-178, 1993.
M.R. Chidambara and R.B. Schainker, “Lower order generalized
aggregated model and sub-optimal control,” IEEE Trans. Automat.
Contr., vol. AC-16, pp. 175-180, 1971.
Y. Choo, “Improvement to modified Routh approximation
method,” Electron. Lett., vol. 35, pp. 606-607, 1999.
Y. Choo, “Improvement to modified Routh approximation method
(correction),” Electron. Lett., vol. 35, pp. 1119, 1999.
Y. Choo, “Direct method for obtaining modified Routh
approximants,” Electron. Lett., vol. 35, pp. 1627-1628, 1999.
Y. Choo, “Improved bilinear Routh approximation method for
discrete time systems,” Trans. ASME J. Dyn. Syst. Meas. Contr.,
vol. 123, pp. 125-127, 2001.
S.C. Chuang, “Application of the continued-fraction method for
modeling transfer functions to give more accurate initial transient
response,” Electron. Lett., vol. 6, pp. 861-863, 1970.
Y. Dolgin and E. Zeheb, “On Routh-Padé model reduction of
interval systems,” IEEE Trans. Automat. Contr., vol. 48, pp. 1610-
, 2003.
M. Farsi, K. Warwick, and M. Guilandoust, “Stable reduced-order
models for discrete-time systems,” IEE Proc. D, vol. 133, pp. 137-
, 1986.
J.A. Frank, JR. “Stable partial Padé approximations for reducedorder
transfer functions,” IEEE Trans. Automat. Contr., vol. AC-
, pp. 159-162, 1984.
L.G. Gibarilo and F.P. Lees, “The reduction of complex transfer
function models to simple models using the method of moments,”
Chem. Eng. Sci., vol. 24, pp. 85-93, 1969.
P. Gutman, C.F. Mannerfelt, and P. Molander, “Contributions to
the model reduction problem,” IEEE Trans. Automat. Contr., vol.
AC-27, pp. 454-455, 1982.
J. Hickin, “Comment on mixed time/frequency domain approach
to model reduction,” Electron. Lett., vol. 16, pp. 338-339, 1980.
J. Hickin and N.K. Sinha, “Model reduction for linear
multivariable systems,” IEEE Trans. Automat. Contr., vol. AC-25,
pp. 1121-1127, 1980.
C.-S. Hsieh and C. Hwang, “Model reduction of continuous-time
systems using a modified Routh approximation method,” IEE
Proc. D., Contr. Theory & Appl., vol. 136, pp. 151-156, 1989.
C.-S. Hsieh and C. Hwang, “Order reduction of discrete-time
system via bilinear Routh approximants,” J. Chinese Inst. Engrs.,
vol. 12, pp. 529-538, 1989.
C.-S. Hsieh and C. Hwang, “Model reduction of linear discrete
time systems using bilinear Schwarz approximation,” Int. J. Syst.
Sci., vol. 21, pp. 33-49, 1990.
Y.T. Hsu, Y.T. Juang, and T.P. Tsai, “Lead-lag compensator
design by the Hough transform,” Syst. Contr. Lett., vol. 20, pp.
-372, 1993.
M.F. Hutton and B. Friedland, “Routh approximation for reducing
order of linear time invariant systems,” IEEE Trans. Automat.
Contr., vol. AC-20, pp. 329-337, 1975.
M.F. Hutton and M.J. Rabins, “Simplification of high-order
mechanical systems using the Routh approximation,” Trans.
ASME, J. Dyn. Syst. Meas. Contr., vol. 97, pp. 383-392, 1975.
C. Hwang and C.-S. Hsieh, “A new canonical expansion of ztransfer
function for reduced-order modeling of discrete-time
systems,” IEEE Trans. Circuits Syst., vol. 36, pp. 1497-1509,
C. Hwang and C.-S. Hsieh, “Reduced-order modeling of discretetime
systems via bilinear Routh approximation,” ASME, J. Dyn.
Syst. Meas. Contr., vol. 112, pp. 292-297, 1990.
C. Hwang, J.H. Hwang, and T.Y. Guo, “Multifrequency Routh
approximants for linear systems,” IEE Proc. Contr. Theory &
Appl., vol. 142, pp. 351-358, 1995.
C.Y. Hwang and Y.C. Lee, “A new family of Routh
approximants,” Circuits Syst. Signal Process., vol. 16, pp. 1-25,
C. Hwang and Y.P. Shih, “Routh approximation for reducing
order of discrete systems” ASME J. Dyn. Syst. Meas. Contr., vol.
, pp. 107-109, 1982.
R.Y. Hwang and Y.P. Shih, “Combined method for model
reduction via discrete laguerre polynomials,” Int. J. Contr., vol. 37,
pp. 615-622, 1984.
C. Hwang, Y.P. Shih, and R.Y. Hwang, “A combined time and
frequency domain method for model reduction of discrete
systems,” J. Franklin Inst., vol. 311, pp. 391, 1981.
C. Hwang and S.F. Yang, “Comments on the computation of
interval Routh approximants,” IEEE Trans. Automat. Contr., vol.
, pp. 1782-1787,1999.
C.C. Hyland and S. Richter, “On direct versus indirect methods
for reduced-order controller design,” IEEE Trans. Automat. Contr.,
vol. 35, pp. 377-379, 1990.
S. John and R. Parthasarathy, “System reduction by Routh
approximation and modified Cauer continued fraction,” Electron.
Lett., vol. 15, pp. 691-692, 1979.
E.A. Jonckheere and L.M. Silverman, “A new set of invariants for
linear systems: applications to reduced order compensator design,”
IEEE Trans. Automat. Contr., vol. AC-28, pp. 953-964, 1983.
E. Kahorado and J.L. Gutierrfz, “Inversion algorithm to
construction Routh approximants,” Electron. Lett., vol. 21, pp.
-425, 1975.
V. Krishnamurthy and V. Seshadri, “A simple and direct method
of reducing order of linear systems using Routh approximants in
frequency domain,” IEEE Trans. Automat. Contr., vol. AC-21, pp.
-799, 1976.
V. Krishnamurthy and V. Seshadri, “Model reduction using Routh
stability criterion,” IEEE Trans. Automat. Contr., vol. AC-23, pp.
-731, 1978.
M. Lal and R. Mitra, “Simplification of large systems dynamics
using a moment evaluation algorithm,” IEEE Trans. Automat.
Contr., vol. AC-19, pp. 602-603, 1974.
S.S. Lamba and B. Bandyopadhyay, “An improvement on Routh
approximation techniques,” IEEE Trans. Automat. Contr., vol.
AC-31, pp. 1047-1050, 1986.
S.S. Lamba and S.V. Rao, “On sub optimal control via the
simplified model of Davinson,” IEEE Trans. Automat. Contr., vol.
AC-19, pp. 448-450, 1974.
C.M. Liaw, “Mixed method of model reduction for linear
multivariable systems,” Int. J. Syst. Sci., vol. 20, pp. 2029-2041,
C.M. Liaw, and C.T. Pan, and M. Ouyang, “Model reduction of
discrete systems using the power decomposition method and the
system identification method,” IEE Proc. D, vol. 133, pp. 30-34,
Y. Liu and B.D.O. Anderson, “Controller reduction via stable
factorization and balancing,” Int. J. Contr., vol. 44, pp. 507-531,
T.N. Lucas, “Factor division: a useful algorithm in model
reduction,” IEE Proc. D., vol. 130, pp. 362-364, 1983.
T.N. Lucas, “Biased model reduction by Factor division,”
Electron. Lett., vol. 20, pp. 582-583, 1984.
T.N. Lucas, “ Linear system reduction by the modified factor
division method,” IEE Proc. D., vol. 133, pp. 293-296, 1986.
T.N. Lucas, “Differentiation reduction method as a multipoint
Padé approximant,” Electron. Lett., vol. 24, pp. 60-61, 1988.
T.N. Lucas, “Some further observation on the differentiation
method of model reduction,” IEEE Trans. Automat. Contr., vol.
, pp. 1389-1391, 1992.
T.N. Lucas, “The bilinear method: a new stability-preserving order
reduction approach,” Proc. Inst. Mech. Eng. I, J. Syst. Contr. Eng.,
vol. 216, pp. 429-436, 2002.
M.S. Mahmoud and M.G., Singh, Large Scale System Modeling,
Oxford: Pergamon, 1981.
Downloads
Published
Issue
Section
License
Copyright Notice
Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication.
Copyrights for articles published in World Scholars journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.