Microsystem Technologies

, Volume 25, Issue 2, pp 641–649 | Cite as

Substructure preservation based approach for discrete time system approximation

  • Nafees Ahamad
  • Afzal SikanderEmail author
  • Gagan Singh
Technical Paper


In this study, a new technique for discrete time system reduction is suggested which preserves the substructure of the higher order system in the reduced system. Motivated by various system reduction and optimization techniques available in the literature, the proposed technique is based on Cuckoo search which is used to obtain unknown elements of the reduced system with an error criterion minimization. The efficacy of the proposed technique is justified by reducing few benchmark systems and the obtained results are compared with other well-known order reduction methods existing in the literature.



  1. Alsmadi OMK, Abo-Hammour ZS (2015) A robust computational technique for model order reduction of two-time-scale discrete systems via genetic algorithms. Comput Intell Neurosci 2015:1–9CrossRefGoogle Scholar
  2. Alsmadi OMK, Abo-Hammour ZS, Al-Smadi AM (2011) Artificial neural network for discrete model order reduction with substructure preservation. Appl Math Model 35:4620–4629MathSciNetCrossRefzbMATHGoogle Scholar
  3. Aoki M (1968) Control of large-scale dynamic systems by aggregation. IEEE Trans Autom Control 13(3):246–253CrossRefGoogle Scholar
  4. Bistritz Y (1982) A direct Routh stability method for discrete system modelling. Syst Control Lett 2(2):83–87MathSciNetCrossRefzbMATHGoogle Scholar
  5. Brown CT, Liebovitch LS, Glendon R (2007) Lévy Flights in Dobe Ju/hoansi Foraging Patterns. Hum Ecol 35(1):129–138CrossRefGoogle Scholar
  6. Chu YC, Glover K (1999) Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities. IEEE Trans Autom Control 44(3):471–483MathSciNetCrossRefzbMATHGoogle Scholar
  7. Desai SR (2013) Reduced order modelling in control system. Unpublished doctoral dissertation, Indian Institute of Technology Roorkee, Roorkee, IndiaGoogle Scholar
  8. El-Attar RA, Vidyasagar M (1978) Order reduction by \(L_1\) and \(L_\infty \) Norm minimization. IEEE Trans Autom Control 23(4):731–734CrossRefzbMATHGoogle Scholar
  9. Hutton MF, Friedland B (1975) Routh approximations for reducing order of linear, time-invariant systems. IEEE Trans Autom Control 20:329–337MathSciNetCrossRefzbMATHGoogle Scholar
  10. Hwang RY, Hwang C, Shih YP (1983) A stable residue method for model reduction of discrete systems. Comput Electr Eng 10(4):259–267CrossRefzbMATHGoogle Scholar
  11. Karimaghaee P, Noroozi N (2011) Frequency weighted discrete-time controller order reduction using bilinear transformation. J Electr Eng 62(1):44–48Google Scholar
  12. Moore BC (1981) Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans Autom Control 26(1):17–32MathSciNetCrossRefzbMATHGoogle Scholar
  13. Mukherjee S, Kumar V, Mitra R (2007) Order reduction of discrete systems using step response matching. Int J Model Simul 27(2):107–114CrossRefGoogle Scholar
  14. Namratha JN, Latha YH (2015) Order reduction of linear dynamic systems using improved generalise least-squares method and differential evolution algorithm. Int J Eng Res Appl 3(5):95.99Google Scholar
  15. Obinata G, Inooka H (1983) Authors reply to comments on model reduction by minimizing the equation error. IEEE Trans Autom Control 28:124–125CrossRefGoogle Scholar
  16. Pal J, Pan S (1992) Controller reduction for discrete time systems. In: Proceedings of international conference on systems science, Wroclaw, Poland, sept. 22-25, pp. 220–224Google Scholar
  17. Pan S, Pal J (1995) Reduced order modelling of discrete-time systems. Appl Math Model 19(3):133–138CrossRefzbMATHGoogle Scholar
  18. Reis T, Stykel T (2008) Balanced truncation model reduction of second-order systems. Math Comput Model Dyn Syst 14(5):391–406MathSciNetCrossRefzbMATHGoogle Scholar
  19. Shamash Y (1974) Stable reduced-order models using Padé-type approximations. IEEE Trans Autom Control 19(5):615–616CrossRefzbMATHGoogle Scholar
  20. Shih YP (1973) Simplification of \(z\)-transfer functions by continued fractions. Int J Control 17(5):1089–1094CrossRefzbMATHGoogle Scholar
  21. Sikander A, Prasad R (2015) Linear time-invariant system reduction using a mixed methods approach. Appl Math Model 39(16):4848–4858MathSciNetCrossRefGoogle Scholar
  22. Sikander A, Prasad R (2015) Soft computing approach for model order reduction of linear time invariant systems. Circuits Syst Signal Process 34(11):3471–3487CrossRefGoogle Scholar
  23. Sikander A (2016) Reduced order modelling for linear systems and controller design, Ph.D. Thesis. Indian Institute of Technology Roorkee, RoorkeeGoogle Scholar
  24. Singh VP, Chandra D (2012) Reduction of discrete interval systems based on pole clustering and improved Padé approximation: a computer-aided approach. Adv Model Optim 14(1):45–56MathSciNetzbMATHGoogle Scholar
  25. Telescu M, Iassamen N, Cloastre P, Tanguy N (2013) A simple algorithm for stable order reduction of z-domain Laguerre models. Signal Process 93(1):332–337CrossRefGoogle Scholar
  26. Vasu G, Sandeep G (2012) Design of PID controller for higher order discrete systems based on order reduction employing ABC algorithm. Control Theory Inform 2(4):4–16Google Scholar
  27. Viswanathan GM (2010) Fish in Levy-flight foraging. Nature 465:1018–1019CrossRefGoogle Scholar
  28. Yadav JS, Patidar NP, Singhai J (2010) Controller design of discrete systems by order reduction technique employing differential evolution optimization algorithm. Int J Electr Comput Energ Electron Commun Eng 4(1):39–45Google Scholar
  29. Yadav JS, Patidar NP, Singhai J (2010) Model order reduction and controller design of discrete system employing real coded genetic algorithm. Int J Adv Eng Technol I(III):134–144Google Scholar
  30. Yang XS, Deb S (2008) Nature-inspired metaheuristic algorithms. Luniver Press, BristolGoogle Scholar
  31. Yang XS, Deb S (2009) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1:330–343zbMATHGoogle Scholar
  32. Yang X-S, Deb S (2009) Cuckoo search via Levy flights. In: World congress on nature & biologically inspired computing, pp 210–214Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringDIT UniversityDehradunIndia
  2. 2.Department of Instrumentation and Control EngineeringDr. B. R. Ambedkar National Institute of Technology JalandharJalandharIndia

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