System Reduction by Eigen Permutation Algorithm and Improved Pade Approximations
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System Reduction by Eigen Permutation Algorithm and Improved Pade Approximations

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

Abstract:

A mixed method by combining a Eigen algorithm and improved pade approximations is proposed for reducing the order of the large-scale dynamic systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the other well known existing order reduction methods. The superiority of the proposed method is shown through examples taken from the literature.

Keywords: Eigen algorithm, Order reduction, improved pade approximations, Stability, Transfer function.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091240

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References:


[1] M.S. Mahmoud and M.G. Singh, "Large Scale Systems Modeling”, Pergamon Press, International Series on Systems and Control 1st ed., (1981) 3.
[2] A.K. Mittal, R. Prasad, S.P. Sharma, "Reduction of Linear Dynamic Systems Using an Error Minimization Technique”, J. Inst. Eng. India, IE (I) J. EL 84 (March) (2004) 201–206.
[3] S. Mukherjee, Satakshi and R.C.Mittal, "Model Order Reduction Using Response-Matching Technique”, Journal of Franklin Inst., Vol. 342, 2005, 503-519.
[4] S. Mukherjee, R.N. Mishra, "Order Reduction of Linear Systems Using an Error Minimization Technique, J. Franklin Inst.”, 323 (1), (1987) 23–32.
[5] 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, 323-327.
[6] Y. Dolgin and E. Zeheb, "On Routh-Pade Model Reduction of Interval Systems”, IEEE Trans Automat Control, Vol. 48, No. 9, Sept. 2003, 1610-1612.
[7] V. Singh, D. Chandra and H. Kar, "Improved Routh Pade Approximants: A Computer Aided Approach”, IEEE Trans. Automat Control, Vol. 49,No.2, Feb. 2004, 292-296.
[8] J.Pal, A.K.Sinha and N.K.Sinha, "Reduced Order Modeling Using Pole Clustering and Time Moments Matching”, Journal of the Institution of engineers (India), Pt .EL, Vol, 1995, pp.1-6.
[9] C.B.Vishwakarma "Order Reduction Using Modified Pole Clustering and Pade Approximations” World Academy of Science, Engineering and Technology, (2011) 56.
[10] S.Mukherjee, "Order Reduction of Linear Systems Using Eigen Spectrum Analysis”, Journal of Electrical Engineering IE(I), Vol 77, (1996)76-79.
[11] G.Parmar, S.Mukherjee, R.Prasad, "System Reduction Using Factor Division Algorithm and Eigen Spectrum Analysis”, Applied Mathematical Modelling Science direct, (2007).2542-2552.
[12] J.Pal , "Improved Pade Approximamts Using Stability Equation Method” IEEE, Electronics letters 26 May 1983 vol. 19 No.11.
[13] C.B. Vishwakarma "Model Order Reduction of Linear Dynamic Systems for Control System Design” Ph.D Thesis, Indian Institute of Technology Roorkee, Roorkee India 2009.
[14] Shamash Y., "Linear System Reduction Using Pade Pade Approximation to Allow Retention of Dominant Modes”, International Journal of Control, Vol. 21, (1975) 257-272.
[15] Krishnamurthy V. and Seshadri V., "Model Reduction Using the Routh Stability Criterion”, IEEE Transactions on Automatic Control, Vol. AC-23, No. 4, 1978, 729-731.
[16] Prasad R., Sharma S.P. and Mittal A.K.., "Linear Model Reduction Using the Advantages of Mihailov Criterion and Factor Division”, Journal of Institution of Engineers India, IE(I) Journal-EL, Vol. 84, 2003, 7-10.
[17] Smith I.D. and Lucas T. N., "Least-Squares Moment Matching Reduction Methods”, Electronics Letters, Vol. 31, (1995) 929-930.