Reduced Order Modeling of Linear MIMO Systems Using Soft Computing Techniques

  • Umme Salma
  • K. Vaisakh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7077)


A method is proposed for model order reduction for a linear multivariable system by using the combined advantages of dominant pole reduction method and Particle Swarm Optimization (PSO). The PSO reduction algorithm is based on minimization of Integral Square Error (ISE) pertaining to a unit step input. Unlike the conventional method, ISE is circumvented by equality constraints after expressing it in frequency domain using Parseval’s theorem. In addition to this, many existing methods for MIMO model order reduction are also considered. The proposed method is applied to the transfer function matrix of a 10th order two-input two-output linear time invariant model of a power system. The performance of the algorithm is tested by comparing it with the other soft computing technique called Genetic Algorithm and also with the other existing techniques.


Reduced order model Integral Square Error Parseval’s theorem Particle Swarm Optimization Genetic Algorithm 


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  1. 1.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: IEEE Int. Conf. on Neural Networks, IV, pp. 1942–1948 (1995)Google Scholar
  2. 2.
    Pamar, G., Mukherjee, S., Prasad, R.: Relative mapping errors of linear time invariant systems caused by Particle swarm optimized reduced order model. World Academy of Science and Technology, 336–342 (2007)Google Scholar
  3. 3.
    Singh, V., Chandra, D., Kar, H.: Optimal Routh approximants through integral squared error minimization:Computer-aided approach. IEE Proc., Contr. Theory Appl. 151, 53–58 (2004)CrossRefGoogle Scholar
  4. 4.
    Parmar, G., Mukherjee, S., Prasad, R.: Reduced order modeling of Linear MIMO systems using Genetic algorithm. International Journal of Simulation Modeling 6(3), 173–184 (2007)CrossRefGoogle Scholar
  5. 5.
    Lakshmi, R.J., Mallikarjuna Rao, P., Vishnu Chakravarti, C.: A method for the reduction of MIMO systems using Interlacing property and Coefficients matching. International Journal of Computer Applications (0975 – 8887) 1(9), 14–17 (2010)Google Scholar
  6. 6.
    Bei-bei, W., Chaun-qing, G.U.: A matrix Pade type – Routh model reduction method for multivariable linear systems. Journal of Shanghai University, 377–380 (2006)Google Scholar
  7. 7.
    Vishwakarma, C.B., Prasad, R.: Order reduction using the advantages and differentiation method and factor division algorithm. Indian Journal of Engineering and Material Sciences 15, 447–451 (2008)Google Scholar
  8. 8.
    Prasad, R., Sharma, S.P., Mittal, A.K.: Improved Pade approximants for multivariable systems using Stability equation method. Institution of Engineers India IE (I) Journal-EL 84, 161–165 (2003)Google Scholar
  9. 9.
    Pal, J., Ray, L.M.: Stable Pade approximants to multivariable systems Using a mixed method. Proceedings of the IEEE 68(1) (1980)Google Scholar
  10. 10.
    Shieh, L.S., Wei, Y.J.: A mixed method for multivariable system reduction. IEEE Trans. Automatic Control AC-20, 429–432 (1975)CrossRefzbMATHGoogle Scholar
  11. 11.
    Shamash, Y.: Multivariable system reduction via modal methods and Pade approximation. IEEE Transactions on Automatic Control 20, 815–817 (1975)CrossRefzbMATHGoogle Scholar
  12. 12.
    Habib, N., Prasad, R.: An observation on the differentiation and modified Cauer continued fraction expansion approaches of model reduction technique. In: XXXII National Systems Conference (December 2008)Google Scholar
  13. 13.
    Agrawal, A.V., Mittal, A.: Reduction of large scale linear MIMO systems using Eigen Spectrum analysis and CFE form. In: XXXII National Systems Conference (December 2008)Google Scholar
  14. 14.
    Liaw, C.M.: Mixed method of model reduction for linear multivariable systems. International Journal of Systems Science 20(11), 2029–2041 (1989)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Umme Salma
    • 1
  • K. Vaisakh
    • 2
  1. 1.Department of Electrical and Electronics EngineeringGITAM Institute of Technology, GITAM UniversityVisakhapatnamIndia
  2. 2.Department of Electrical EngineeringAU College of Engineering, Andhra UniversityVisakhapatnamIndia

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