System Reduction Using Modified Pole Clustering and Modified Cauer Continued Fraction
A mixed method by combining modified pole
clustering technique and modified cauer continued fraction is
proposed for reducing the order of the large-scale dynamic systems.
The denominator polynomial of the reduced order model is obtained
by using modified pole clustering technique while the coefficients of
the numerator are obtained by modified cauer continued fraction.
This method generated 'k' number of reduced order models for kth
order reduction. The superiority of the proposed method has been
elaborated through numerical example taken from the literature and
compared with few existing order reduction methods.
[1] V. Singh, D. Chandra and H. Kar, “Improved Routh Pade approximants:
A Computer aided approach”, IEEE Trans. Autom. Control, 49(2), 2004,
pp.292-296.
[2] S.Mukherjee and R.N. Mishra, “Reduced order modeling of linear
multivariable systems using an error minimization technique”, Journal
of Franklin Inst., 325 (2), 1988., pp.235-245.
[3] Sastry G.V.K.R Raja Rao G. and Mallikarjuna Rao P., “Large scale
interval system modeling using Routh approximants”, Electronic Letters,
36(8), 2000, pp.768-769.
[4] R. Prasad, “Pade type model order reduction for multivariable systems
using Routh approximation”, Computers and Electrical Engineering, 26,
2000, pp.445-459.
[5] G. Parmar, S. Mukherjee and R. Prasad, “ division algorithm and eigen
spectrum analysis”, Applied Mathematical Modelling, Elsevier, 31, 2007,
pp.2542-2552.
[6] C.B. Vishwakarma and R. Prasad, “Clustering method for reducing
order of linear system using Pade approximation” IETE Journal of
Research, Vol.54, No. 5, Oct. 2008, pp. 323-327.
[7] C.B. Vishwakarma and R. Prasad, “Order reduction using the
advantages of differentiation method and factor division”, Indian
Journal of Engineering & Materials Sciences, Niscair, New Delhi, Vol.
15, No. 6, December 2008, pp. 447-451.
[8] A.K. Sinha, J. Pal, Simulation based reduced order modeling using a
clustering technique, Computer and Electrical Engg., 16(3), 1990,
pp.159-169.
[9] CB Vishwakarma, “Order reduction using Modified pole clustering and
pade approximans”, world academy of science, engineering and
Technology 80 2011.
[10] Chen, C. F., and Shieh, L. S 'A novel approach to linear model
simplification', Intt. J. Control, 1968,8, pp. 561-570.
[11] Chaung, S. G. 'Application of continued fraction methods for modeling
transfer function to give more accurate initial transient response',
Electron . Lett., 1970,6, pp. 861-863
[12] R. Parthasarathy and S. John, “Cauer continued fraction method for
model reduction,” Electron. Lett., vol. 17, 1981, pp. 792-793. [13] R. Parthasarathy and S. John, “State space models using modified Cauer
continued fraction”, Proceedings IEEE (lett.), Vol. 70, No. 3, 1982, pp.
300-301.
[14] R. Parthasarathy and S. John, “System reduction by Routh
approximation and modified Cauer continued fraction”, Electronic
Letters, Vol. 15, 1979, pp. 691-692.
[15] A.K. Mittal, R. Prasad, and S.P. Sharma, “Reduction of linear dynamic
systems using an error minimization technique”, Journal of Institution
of Engineers IE(I) Journal – EL, Vol. 84, 2004, pp. 201-206.
[16] J. Pal, “Stable reduced order Pade approximants using the Routh urwitz
array”, Electronic Letters , Vol. 15, No.8, 1979, pp. 225-226.
[17] M. R. Chidambara, “On a method for simplifying linear dynamic
system”, IEEE Trans. Automat Control, Vol. AC-12, 1967, pp. 119-120.
[18] L. S. Shieh and Y. J. Wei, “A mixed method for multivariable system
reduction”, IEEE Trans. Automat. Control, Vol. AC-20, 1975, pp. 429-
432
[19] Bistritz Y. and Shaked U., “Stable linear systems simplification via pade
approximation to Hurwitz polynomial”, Transaction ASME, Journal of
Dynamic System Measurement and Control, Vol. 103, 1981, pp. 279-
284.
[20] Girish Parmar and Manisha Bhandari, “Reduced order modelling of
linear dynamic systems using eigen spectrum analysis and modified
cauer continued fraction” XXXII National Systems Conference, NSC
2008, December 17-19, 2008.
[21] R. Prasad and J. Pal, “Use of continued fraction expansion for stable
reduction of linear multivariable systems”, Journal of Institution of
Engineers, India, IE(I) Journal – EL, Vol. 72, 1991, pp. 43-47.
[1] V. Singh, D. Chandra and H. Kar, “Improved Routh Pade approximants:
A Computer aided approach”, IEEE Trans. Autom. Control, 49(2), 2004,
pp.292-296.
[2] S.Mukherjee and R.N. Mishra, “Reduced order modeling of linear
multivariable systems using an error minimization technique”, Journal
of Franklin Inst., 325 (2), 1988., pp.235-245.
[3] Sastry G.V.K.R Raja Rao G. and Mallikarjuna Rao P., “Large scale
interval system modeling using Routh approximants”, Electronic Letters,
36(8), 2000, pp.768-769.
[4] R. Prasad, “Pade type model order reduction for multivariable systems
using Routh approximation”, Computers and Electrical Engineering, 26,
2000, pp.445-459.
[5] G. Parmar, S. Mukherjee and R. Prasad, “ division algorithm and eigen
spectrum analysis”, Applied Mathematical Modelling, Elsevier, 31, 2007,
pp.2542-2552.
[6] C.B. Vishwakarma and R. Prasad, “Clustering method for reducing
order of linear system using Pade approximation” IETE Journal of
Research, Vol.54, No. 5, Oct. 2008, pp. 323-327.
[7] C.B. Vishwakarma and R. Prasad, “Order reduction using the
advantages of differentiation method and factor division”, Indian
Journal of Engineering & Materials Sciences, Niscair, New Delhi, Vol.
15, No. 6, December 2008, pp. 447-451.
[8] A.K. Sinha, J. Pal, Simulation based reduced order modeling using a
clustering technique, Computer and Electrical Engg., 16(3), 1990,
pp.159-169.
[9] CB Vishwakarma, “Order reduction using Modified pole clustering and
pade approximans”, world academy of science, engineering and
Technology 80 2011.
[10] Chen, C. F., and Shieh, L. S 'A novel approach to linear model
simplification', Intt. J. Control, 1968,8, pp. 561-570.
[11] Chaung, S. G. 'Application of continued fraction methods for modeling
transfer function to give more accurate initial transient response',
Electron . Lett., 1970,6, pp. 861-863
[12] R. Parthasarathy and S. John, “Cauer continued fraction method for
model reduction,” Electron. Lett., vol. 17, 1981, pp. 792-793. [13] R. Parthasarathy and S. John, “State space models using modified Cauer
continued fraction”, Proceedings IEEE (lett.), Vol. 70, No. 3, 1982, pp.
300-301.
[14] R. Parthasarathy and S. John, “System reduction by Routh
approximation and modified Cauer continued fraction”, Electronic
Letters, Vol. 15, 1979, pp. 691-692.
[15] A.K. Mittal, R. Prasad, and S.P. Sharma, “Reduction of linear dynamic
systems using an error minimization technique”, Journal of Institution
of Engineers IE(I) Journal – EL, Vol. 84, 2004, pp. 201-206.
[16] J. Pal, “Stable reduced order Pade approximants using the Routh urwitz
array”, Electronic Letters , Vol. 15, No.8, 1979, pp. 225-226.
[17] M. R. Chidambara, “On a method for simplifying linear dynamic
system”, IEEE Trans. Automat Control, Vol. AC-12, 1967, pp. 119-120.
[18] L. S. Shieh and Y. J. Wei, “A mixed method for multivariable system
reduction”, IEEE Trans. Automat. Control, Vol. AC-20, 1975, pp. 429-
432
[19] Bistritz Y. and Shaked U., “Stable linear systems simplification via pade
approximation to Hurwitz polynomial”, Transaction ASME, Journal of
Dynamic System Measurement and Control, Vol. 103, 1981, pp. 279-
284.
[20] Girish Parmar and Manisha Bhandari, “Reduced order modelling of
linear dynamic systems using eigen spectrum analysis and modified
cauer continued fraction” XXXII National Systems Conference, NSC
2008, December 17-19, 2008.
[21] R. Prasad and J. Pal, “Use of continued fraction expansion for stable
reduction of linear multivariable systems”, Journal of Institution of
Engineers, India, IE(I) Journal – EL, Vol. 72, 1991, pp. 43-47.
@article{"International Journal of Electrical, Electronic and Communication Sciences:68947", author = "Jay Singh and C. B. Vishwakarma and Kalyan Chatterjee", title = "System Reduction Using Modified Pole Clustering and Modified Cauer Continued Fraction", abstract = "A mixed method by combining modified pole
clustering technique and modified cauer continued fraction is
proposed for reducing the order of the large-scale dynamic systems.
The denominator polynomial of the reduced order model is obtained
by using modified pole clustering technique while the coefficients of
the numerator are obtained by modified cauer continued fraction.
This method generated 'k' number of reduced order models for kth
order reduction. The superiority of the proposed method has been
elaborated through numerical example taken from the literature and
compared with few existing order reduction methods.
", keywords = "Modified Pole Clustering, Modified Cauer
Continued Fraction, Order Reduction, Stability, Transfer Function.", volume = "8", number = "9", pages = "1526-5", }
