Skip to main content

SISO Method Using Modified Pole Clustering and Simulated Annealing Algorithm

  • Conference paper
  • First Online:
Advances in System Optimization and Control

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 509))

Abstract

A mixed method by using the modified pole clustering technique and simulated annealing is proposed to reduce higher-order mathematical model into a smaller one. The denominator and numerator polynomials are obtained by using a modified pole clustering technique and simulated annealing algorithm, respectively. The proposed-biased method generates k number of reduced models from higher-order systems. The compatibility of the method has been checked via time responses of the original higher-order system and the reduced-order system, respectively. Also, the proposed method has been compared with few known model-order reduction techniques through performance indices.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. J. Singh, K. Chatterjee, C.B. Vishwakarma, MIMO system using eigen algorithm and improved Pade approximations. SOP Trans. Appl. Math. 1(1), 60–70 (2014)

    Article  Google Scholar 

  2. J. Singh, K. Chatterjee, C.B. Vishwakarma, System reduction by eigen permutation algorithm and improved Pade approximations. Int. J. Math. Comput. Sci. Eng. 8(1), 1–5 (2014)

    Google Scholar 

  3. J. Singh, C.B. Vishwakarma, K. Chatterjee, Biased reduction method by combining improved modified pole clustering and improved Pade approximations. Appl. Math. Model. Elsevier 40, 1418–1426 (2016)

    Article  MathSciNet  Google Scholar 

  4. J. Pal, Improved Pade approximants using stability equation methods. IEEE Electron. Lett. 19(11), 426–427 (1983)

    Article  Google Scholar 

  5. A.K. Sinha, J. Pal, Simulation based reduced order modeling using a clustering technique. Comput. Electr. Eng. 16(3), 159–169 (1990)

    Article  Google Scholar 

  6. C.B. Vishwakarma, R. Prasad, MIMO system reduction using modified pole clustering and genetic algorithm. Model. Simul. Eng. 2009, 1–6 (2009). Hindawi Publishing Corporation

    Article  Google Scholar 

  7. A.K. Sinha, J. Pal, Simulation based reduced order modelling using a clustering technique. Comput. Electr. Eng. 16(3), 159–169 (1990)

    Article  Google Scholar 

  8. C.B. Vishwakarma, R. Prasad, Time domain model order reduction using Hankel matrix approach. J. Franklin Inst. Elsevier 351, 3445–3456 (2014)

    Article  MathSciNet  Google Scholar 

  9. N.K. Sinha, G.T. Bereznai, Optimal approximation of high order systems by low order models. Int. J. Control 14, 951–959 (1971)

    Article  Google Scholar 

  10. S.A. Marshall, An approximation method for reducing the order of a large system. Control Eng. 10, 642–648 (1966)

    Google Scholar 

  11. C.P. Therapos, Internally balanced minimal realization of discrete SISO systems. IEEE Trans. Autom. Control 30(3), 297–299 (1985)

    Article  MathSciNet  Google Scholar 

  12. S.K. Nagar, S.K. Singh, An algorithmic approach for system decomposition and balanced realized model reduction. J. Franklin Inst. 341, 615–630 (2004)

    Article  MathSciNet  Google Scholar 

  13. A.K. Mittal, R. Prasad, S.P. Sharma, in Reduction of Multivariable Systems Using Stability Equation Method and Error Minimization Technique. Proceedings of the 27th National Systems Conference (NSC-2003), Indian Institute of Technology, Kharagpur, India, 17–19 December 2003, pp. 34–38

    Google Scholar 

  14. S. Mukherjee, R.N. Mishra, Reduced order modelling of linear multivariable systems using an error minimization technique. J. Franklin Inst. 325(2), 235–245 (1988)

    Article  Google Scholar 

  15. S. Mukherjee, R.N. Mishra, Order reduction of linear systems using an error minimization technique. J. Franklin Inst. 323(1), 23–32 (1987)

    Article  MathSciNet  Google Scholar 

  16. 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, 201–206 (2004)

    Google Scholar 

  17. G. Parmar, S. Mukherjee, R. Prasad, Division algorithm and eigen spectrum analysis. Appl. Math. Model. Elsevier 31, 2542–2552 (2007)

    Article  Google Scholar 

  18. S. Mukherjee, Satakshi, R.C. Mittal, Model order reduction using response matching technique. J. Franklin Inst. 342, 503–519 (2005)

    Article  MathSciNet  Google Scholar 

  19. 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, 201–206 (2004)

    Google Scholar 

  20. R. Prasad, J. Pal, Stable reduction of linear systems by continued fractions. J. Inst. Eng. India IE (I) J. EL 72, 113–116 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jay Singh .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Singh, J., Chatterjee, K., Vishwakarma, C.B. (2019). SISO Method Using Modified Pole Clustering and Simulated Annealing Algorithm. In: Singh, S., Wen, F., Jain, M. (eds) Advances in System Optimization and Control. Lecture Notes in Electrical Engineering, vol 509. Springer, Singapore. https://doi.org/10.1007/978-981-13-0665-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-0665-5_13

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0664-8

  • Online ISBN: 978-981-13-0665-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics