**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32937

##### System Reduction Using Modified Pole Clustering and Modified Cauer Continued Fraction

**Authors:**
Jay Singh,
C. B. Vishwakarma,
Kalyan Chatterjee

**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.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1099050

**References:**

[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.