Skip to main content
SpringerLink
Log in

Time Moments and Its Extension for Reduction of MIMO Discrete Interval Systems

  • Conference paper
  • First Online:
Social Networking and Computational Intelligence

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 100))

Abstract

This paper extends the reduction procedure available for reducing the order of single-input-single-output (SISO) discrete interval system (DIS) to the reduction of multi-input-multi-output (MIMO) DISs. The methodology utilizes the time moments (TMs) for deriving the numerator of model. The paper also provides the methods available for calculating the different expressions for TMs. For analyzing this technique, a two-input-two-output (TITO) DIS is considered for reducing the order of DIS. The whole study is performed in two phases. The denominator of discrete interval TITO model is obtained by clustering the poles of the given higher-order DIS at first. Then, the numerators of discrete interval TITO model are derived by matching the (TMs). The results are presented in the form of time-domain responses. Also, a comparative analysis is carried out using these responses.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Fortuna L, Nunnari G, Gallo A (2012) Model order reduction techniques with applications in electrical engineering. Springer Science & Business Media

    Google Scholar 

  2. Pan S, Pal J (1995) Reduced order modelling of discrete-time systems. Appl Math Model 19:133–138

    Article  Google Scholar 

  3. Deepa S, Sugumaran G (2011) Model order formulation of a multivariable discrete system using a modified particle swarm optimization approach. Swarm Evol Comput 1:204–212

    Article  Google Scholar 

  4. Bandyopadhyay B, Ismail O, Gorez R (1994) Routh-pade approximation for interval systems. IEEE Trans Autom Control 39:2454–2456

    Article  MathSciNet  Google Scholar 

  5. Shamash Y (1975) Model reduction using the routh stability criterion and the padé approximation technique. Int J Control 21:475–484

    Article  Google Scholar 

  6. Bandyopadhyay B, Upadhye A, Ismail O (1997) /spl gamma/-/spl delta/Routh approximation for interval systems. IEEE Trans Autom Control 42:1127–1130

    Article  Google Scholar 

  7. Hutton M, Friedland B (1975) Routh approximations for reducing order of linear, time-invariant systems. IEEE Trans Autom Control 20:329–337

    Article  MathSciNet  Google Scholar 

  8. Sastry G, Rao RR, Rao PM (2000) Large scale interval system modelling using routh approximants. Electron Lett 36:768–769

    Article  Google Scholar 

  9. Kumar Dk, Nagar S, Tiwari J (2011) Model order reduction of interval systems using modified Routh approximation and factor division method. In: 35th national system conference (NSC)

    Google Scholar 

  10. Potturu SR, Prasad R, (2017) Reduction of interval systems using Kharitonov’s polynomials and their derivatives. In: 2017 6th international conference on computer applications in electrical engineering-recent advances (CERA), pp 445–449

    Google Scholar 

  11. Sastry G, Rao PM (2003) A new method for modelling of large scale interval systems. IETE J Res 49:423–430

    Article  Google Scholar 

  12. Choudhary AK, Nagar SK (2017) Novel arrangement of routh array for order reduction of z-domain uncertain system. Syst Sci Control Eng 5:232–242

    Article  Google Scholar 

  13. Choudhary AK, Nagar SK (2018) Order reduction in z-domain for interval system using an arithmetic operator. Circuits Syst Signal Process, pp 1–16

    Google Scholar 

  14. Choudhary AK, Nagar SK (2018) Model order reduction of discrete-time interval system based on Mikhailov stability criterion. Int J Dyn Control, pp 1–9

    Google Scholar 

  15. Choudhary AK, Nagar SK (2018) Model order reduction of discrete-time interval systems by differentiation calculus. Autom Control Comput Sci 52:402–411

    Article  Google Scholar 

  16. Singh V, Chandra D (2012) Reduction of discrete interval system using clustering of poles with padé approximation: a computer-aided approach. Int J Eng, Sci Technol 4:97–105

    Google Scholar 

  17. Padhy AP, Singh VP, Pattnaik S (2018) Model reduction of multi-input-multi-output discrete interval systems using gain adjustment. Int J Pure Appl Math 119(12):12721–12739

    Google Scholar 

  18. Sastry G, Rao GR (2003) Simplified polynomial derivative technique for the reduction of large-scale interval systems. IETE J Res 49:405–409

    Article  Google Scholar 

  19. Singh VP, Chandra D (2010) Routh-approximation based model reduction using series expansion of interval systems. In: 2010 international conference on power, control and embedded systems (ICPCES), pp 1–4

    Google Scholar 

  20. Singh V, Chauhan DPS, Singh SP, Prakash T (2017) On time moments and markov parameters of continuous interval systems. J Circuits Syst Comput 26:1750038

    Article  Google Scholar 

  21. Singh VP, Chandra D (2011) Model reduction of discrete interval system using dominant poles retention and direct series expansion method. In: 2011 5th international power engineering and optimization conference (PEOCO), pp 27–30

    Google Scholar 

  22. Berge C (1971) Principles of combinatorics

    Google Scholar 

  23. Ismail O, Bandyopadhyay B, Gorez R (1997) Discrete interval system reduction using pade approximation to allow retention of dominant poles. IEEE Trans Circuits Syst I Fundam Theory Appl 44:1075–1078

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The work is supported by SERB, DST, GOI (ECR/2017/000212).

Author information

Authors and Affiliations

  1. National Institute Technology, Raipur, India

    A. P. Padhy & V. P. Singh

Authors
  1. A. P. Padhy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. P. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. P. Padhy .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Sagar Institute of Research and Technology, Bhopal, Madhya Pradesh, India

    Rajesh Kumar Shukla

  2. Department of Computer Science and Engineering, University Teaching Department, Rajiv Gandhi Technical University (State Technological University), Bhopal, Madhya Pradesh, India

    Jitendra Agrawal

  3. School of Information Technology, Rajiv Gandhi Technical University (State Technological University), Bhopal, Madhya Pradesh, India

    Sanjeev Sharma

  4. Department of Computer Science and Engineering, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India

    Narendra S. Chaudhari

  5. Department of Computer Science and Engineering, Indian Institute of Technology BHU, Varanasi, Uttar Pradesh, India

    K. K. Shukla

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Padhy, A.P., Singh, V.P. (2020). Time Moments and Its Extension for Reduction of MIMO Discrete Interval Systems. In: Shukla, R., Agrawal, J., Sharma, S., Chaudhari, N., Shukla, K. (eds) Social Networking and Computational Intelligence. Lecture Notes in Networks and Systems, vol 100. Springer, Singapore. https://doi.org/10.1007/978-981-15-2071-6_41

Download citation

Publish with us

Policies and ethics

Search

Navigation