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Reduced Order Modeling of Linear Time-Invariant Systems Using Soft Computing Technique

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International Conference on Advanced Computing Networking and Informatics

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 870))

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Abstract

Nature has the key to solve every single problem that exists. This paper strives to propose a method which is based on flower pollination algorithm to acquire a stable reduced order model (ROM) of a higher order linear time-invariant (LTI) system. The suggested method utilizes Padé-based moment matching technique to deduce denominator approximants for the reduced order system, whereas the reduced order approximants of numerator polynomial are obtained using flower pollination (FP) algorithm. To prove the viability of the suggested method, numerical examples are solved considering single-input single-output (SISO) systems. A comparison has been drawn between suggested method and existing methods which are available in the current literature and is presented in this paper. This comparison is founded on a performance index which is known as integral square error (ISE).

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References

  1. E. Davison, A method for simplifying linear dynamic systems. IEEE Trans. Automat. Contr. 11(1), 93–101 (1966)

    Article  Google Scholar 

  2. M. Chidambara, Comments on the simplification of linear systems. IEEE Trans. Automat. Contr. 18(1), 76–77 (1973)

    Article  Google Scholar 

  3. G. Marchesini, S. Karni, N. Ahmed, On obtaining transfer functions from gain-function derivatives. IEEE Trans. Automat. Contr. 12(6), 800 (1967)

    Article  Google Scholar 

  4. A. Sikander, R. Prasad, A novel order reduction method using cuckoo search algorithm. IETE J. Res. 61(2), 83–90 (2015)

    Article  Google Scholar 

  5. B. Buttelmann, M. Lohmann, Model simplification and order reduction of non-linear systems with genetic algorithms, in IMACS Symposium on Mathematical Modelling, pp. 777–781 (2000)

    Google Scholar 

  6. S. Panda, S.K. Tomar, R. Prasad, C. Ardil, Reduction of linear time-invariant systems using Routh-approximation and PSO. Int. J. Electr. Comput. Energy Electron. Commun. Eng. 3(9), 1769–1776 (2009)

    Google Scholar 

  7. Z.S. Abo-Hammour, O.M.K. Alsmadi, A.M. Al-Smadi, Frequency-based model order reduction via genetic algorithm approach, in International Workshop on Systems, Signal Processing and their Applications, WOSSPA, pp. 91–94 (2011)

    Google Scholar 

  8. S. Mukherjee, R.C. Mittal, Order reduction of linear discrete systems using a genetic algorithm, Appl. Math. Model. 29(6), 565–578 (2005)

    Google Scholar 

  9. S. Lavania, D. Nagaria, Evolutionary approach for model order reduction. Perspect. Sci. 8, 361–363 (2016)

    Article  Google Scholar 

  10. O.P. Bharti, R.K. Saket, S.K. Nagar, Controller design of DFIG based wind turbine by using evolutionary soft computational techniques. Eng. Technol. Appl. Sci. Res. 7(3), 1732–1736 (2017)

    Google Scholar 

  11. S.R. Desai, R. Prasad, A new approach to order reduction using stability equation and big bang big crunch optimization. Syst. Sci. Control Eng. 1(1), 20–27 (2013)

    Article  Google Scholar 

  12. Y. Shamash, Stable reduced-order models using Padé-type approximations. IEEE Trans. Automat. Contr. 19(5), 615–616 (1974)

    Article  Google Scholar 

  13. Y. Shamash, Model reduction using the Routh stability criterion and the Padé approximation technique. Int. J. Control 21(3), 475–484 (1975)

    Article  Google Scholar 

  14. A. Pati, A. Kumar, D. Chandra, Suboptimal control using model order reduction, Chinese J. Eng. 1–5 (2014)

    Article  Google Scholar 

  15. S. Lavania, D. Nagaria, Pade approximation based moment matching technique for model order reduction, in 2015 International Conference on Computer, Communication and Control (IC4), pp. 1–4 (2015)

    Google Scholar 

  16. S. Lavania, D. Nagaria, Eigen spectrum based moment matching technique for model order reduction, in 2015 39th National Systems Conference (NSC), pp. 1–5 (2015)

    Google Scholar 

  17. X.-S. Yang, Flower pollination algorithm for global optimization, in Lecture Notes in Computer Science, pp. 240–249 (2012)

    Chapter  Google Scholar 

  18. X.-S. Yang, M. Karamanoglu, X. He, Multi-objective flower algorithm for optimization. Proc. Comput. Sci. 18, 861–868 (2013)

    Article  Google Scholar 

  19. N. Singh, Reduced Order Modelling and Controller Design, (Unpublished Thesis) (Indian Institute of Technology, Roorkee, 2008)

    Google Scholar 

  20. M.S. Mahmoud, M.G. Singh, Large Scale System Modeling (Pergamon Press International Series on System and Control, First, 1981)

    Google Scholar 

  21. G. Parmer, R. Prasad, S. Mukherjee, Order reduction of linear dynamic systems using stability equation method and GA. Int. J. Electr. Comput. Energ. Electron. Commun. Eng. 1(2), 236–242 (2007)

    Google Scholar 

  22. S.R. Desai, R. Prasad, A new approach to order reduction using stability equation and big bang big crunch optimization. Syst. Sci. Control Eng. 1(1), 20–27 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Dr. A.P.J. Abdul Kalam Technical University, Lucknow, India

    Shilpi Lavania

  2. Bundelkhand Institute of Engineering & Technology, Jhansi, India

    Deepak Nagaria

Authors
  1. Shilpi Lavania
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  2. Deepak Nagaria
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Corresponding author

Correspondence to Shilpi Lavania .

Editor information

Editors and Affiliations

  1. Medi-Caps University, Indore, Madhya Pradesh, India

    Raj Kamal

  2. Loughborough University, Loughborough, UK

    Michael Henshaw

  3. Medi-Caps Group of Institutions, Indore, Madhya Pradesh, India

    Pramod S. Nair

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Lavania, S., Nagaria, D. (2019). Reduced Order Modeling of Linear Time-Invariant Systems Using Soft Computing Technique. In: Kamal, R., Henshaw, M., Nair, P. (eds) International Conference on Advanced Computing Networking and Informatics. Advances in Intelligent Systems and Computing, vol 870. Springer, Singapore. https://doi.org/10.1007/978-981-13-2673-8_2

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  • DOI: https://doi.org/10.1007/978-981-13-2673-8_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-2672-1

  • Online ISBN: 978-981-13-2673-8

  • eBook Packages: EngineeringEngineering (R0)

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