Abstract
An improved method is proposed to determine the reduced order model of large scale linear time invariant system. The dominant poles of the low order system are calculated by clustering method. The selection of pole to the cluster point is based on the contributions of each pole in redefining time moment and redefining Markov parameters. The coefficients of the numerator polynomial for reduced model are obtained using a factor division algorithm. This method is computationally efficient and keeps up the stability and input output characteristic of the original arrangement.
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References
Chen T C, Chang T Y and Han K W 1979 Reduction of transfer functions by the stability equation method. J. Franklin Inst. 308(4): 389–404
Parthasarathy R and Jayasimha K N 1982 System reduction using stability equation method and modified Cauer continued fraction. Proc. IEEE 70(10): 1234–1236
Gautam P O, Mannerfelt C F and Monlander 1992 Contribution to the model reduction problem. IEEE Trans. Autom. Control 27(2): 454–455
Lucas T N 1992 Some other observation on the differentiation method of model reduction. IEEE Trans. Autom. Control 37(9): 1389–1391
Prasad R, Pal J and Pant A K 1995 Multivariable system approximation using polynomial derivatives. J. Inst. Eng. 76: 186–188
Sinha A K and Pal J 1990 Simulation based reduced order modeling using a clustering technique. Comput. Electr. Eng. 16(3): 159–169
Pal J, Sinha A K and Sinha N K 1995 Reduced-order modelling using pole clustering and time-moments matching. J. Inst. Eng. (India), Electr. Eng. 76: 1–6
Vishwakarma C B and Prasad R 2008 Clustering methods for reducing order of linear system using Pade approximation. IETE J. Res. 54(5): 326–330
Vishwakarma C B and Prasad R 2009 MIMO system reduction using modified pole clustering and genetic algorithm. Hindawi Publishing Corporation Modeling and Simulation in Engineering DOI:10.1155/2009/540895
Saraswathi G 2011 An extended method for order reduction of large scale multivariable systems. Int. J. Comput. Sci. Eng. 2(6): 2109–2118
Parmar G, Mukherjee S and Prasad R 2007 System reduction using factor division algorithm and eigen spectrum analysis. Appl. Math. Modell. 31(11): 2542–2552
Lucas T N 1980 Factor division: A useful algorithm in model reduction. Proceeding IEE 130(6): 362–364
Vishwakarma C B 2011 Order reduction using modified pole clustering and Pade approximations. World Acad. Sci. Eng. Tech. 56: 787–791
Mukherjee S, Satakshi and Mittal R C 2005 Model order reduction using response matching. J. Franklin Inst. 342: 503–519
Mittal A K, Prasad R and Sharma S P 2004 Reduction of linear dynamic systems using an error minimization technique. J. Inst. Eng. IE(I) J. -EL 84: 201–206
Prasad R and Pal J 1991 Stable reduction of linear systems by continued fractions. J. Inst. Eng. IE(I) J. 72: 113–116
Safonoy M G and Chiang R Y 1988 Model reduction for robust control: A Schur relative error method. Proc. Int. J. Adapt. Control Signal 2(4): 259–272
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Tiwari, S.K., Kaur, G. An improved method using factor division algorithm for reducing the order of linear dynamical system. Sādhanā 41, 589–595 (2016). https://doi.org/10.1007/s12046-016-0499-2
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DOI: https://doi.org/10.1007/s12046-016-0499-2