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Microsystem Technologies

, Volume 25, Issue 1, pp 105–114 | Cite as

Application of stochastic fractal search in approximation and control of LTI systems

  • Rajesh BhattEmail author
  • Girish Parmar
  • Rajeev Gupta
  • Afzal Sikander
Technical Paper
  • 64 Downloads

Abstract

The present work deals with the application of evolutionary computation in approximation and control of linear time invariant (LTI) systems. Stochastic fractal search algorithm (SFS) has been proposed to obtain low order system (LOS) from LTI higher order system (HOS) as well as in speed control of DC motor with PID controller. SFS is quite simple to use in control system and employs the diffusion property present in random fractals to discover the search space. In approximation of LTI systems, the integral square error (ISE) while in control of DC motor, the integral of time multiplied absolute error has been taken as an objective/fitness functions. In system’s approximation, the results show that the proposed SFS based LOS preserves both the transient and steady state properties of original HOS. The simulation results have also been compared in terms of; ISE, integral absolute error and impulse response energy with well known familiar and recently published works in the literature which shows the superiority of SFS algorithm. In control of DC motor, the obtained results are satisfactory having no overshoot and less rise and settling times in comparison to existing techniques.

Notes

Acknowledgements

The author would like to thank Rajasthan Technical University, Kota, Rajasthan for providing the lab and simulation facilities to complete this work.

References

  1. Ang KH, Chong G, Li Y (2005) PID control system analysis, design and technology. IEEE Trans Control Syst Technol 13:559–576CrossRefGoogle Scholar
  2. Biradar S, Hote YV, Saxena S (2016) Reduced-order modeling of linear time invariant systems using big bang big crunch optimization and time moment matching method. Appl Math Model 40(7225–7244):2016MathSciNetGoogle Scholar
  3. Clerc M, Kennedy J (2002) The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73CrossRefGoogle Scholar
  4. Desai SR, Prasad R (2013a) A new approach to order reduction using stability equation and big bang big crunch optimization. Syst Sci Control Eng 1(20–27):2013Google Scholar
  5. Desai SR, Prasad R (2013b) A novel order diminution of LTI systems using big bang big crunch optimization and Routh approximation. Appl Math Model 37:8016–8028MathSciNetCrossRefzbMATHGoogle Scholar
  6. Hoos HH, Stiitzle T (2005) Stochastic local search foundation and application. Elsevier, New YorkGoogle Scholar
  7. Khalilpuor M, Razmjooy N, Hosseini H, Moallem P (2011) Optimal control of DC motor using invasive weed optimization (IWO) algorithm. In: Majlesi conference on electrical engineering. IranGoogle Scholar
  8. Khanam I, Parmar G (2017) Application of stochastic fractal search in order reduction of large scale LTI systems. In: IEEE international conference on computer, communications and electronics (Comptelix 2017), Manipal University, Jaipur (India), pp 190–194Google Scholar
  9. Mittal AK, Prasad R, Sharma SP (2004) Reduction of linear dynamic systems using an error minimization technique. J Inst Eng (India) 84:201–206Google Scholar
  10. Mukherjee S, Satakshi M, Mittal RC (2005) Model order reduction using response matching technique. J Frankl Inst 342:503–519MathSciNetCrossRefzbMATHGoogle Scholar
  11. Narwal A, Prasad R (2015) A novel order reduction approach for LTI systems using cuckoo search optimization and stability equation. IETE J Res 62:154–163CrossRefGoogle Scholar
  12. Parmar G, Mukherjee S, Prasad R (2007a) System reduction using Eigen spectrum analysis and pade approximation technique. Int J Comput Math (Taylor & Francis) 84:1871–1880MathSciNetCrossRefzbMATHGoogle Scholar
  13. Parmar G, Mukherjee S, Prasad R (2007b) System reduction using factor division algorithm and Eigen spectrum analysis. Appl Math Model (Elsevier) 31:2542–2552CrossRefzbMATHGoogle Scholar
  14. Parmar G, Mukherjee S, Prasad R (2007c) Reduced order modelling of linear multivariable systems using particle swarm optimisation technique. Int J Innov Comput Appl (IJICA) Indersci 1:128–137CrossRefGoogle Scholar
  15. Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl Based Syst (Elsevier) 75:1–18CrossRefGoogle Scholar
  16. Sambariya DK, Arvind G (2016) High order diminution of LTI system using stability equation method. Br J Math Comput Sci 13:1–15Google Scholar
  17. Sambariya DK, Manohar H (2016) Preservation of stability for reduced order model of large scale systems using differentiation method. Br J Math Comput Sci 13:1–17Google Scholar
  18. Sambariya DK, Sharma O (2016a) Routh approximation: an approach of model order reduction in SISO and MIMO systems. Indones J Electr Eng Comput Sci 2:486–500CrossRefGoogle Scholar
  19. Sambariya DK, Sharma O (2016b) Model order reduction using Routh approximation and cuckoo search algorithm. J Autom Control 4:1–9Google Scholar
  20. Saraswat P, Parmar G (2015) A comparative study of differential evolution and simulation annealing for order reduction of large scale systems. In: IEEE conference on communication, control and intelligent systems (CCIS-2015), GLA Univ., Mathura (UP)Google Scholar
  21. Sikander A, Prasad R (2015a) Soft computing approach for model order reduction of linear time invariant system. Circuit Syst Signal Process (Springer Science, New York) 34:3471–3487CrossRefGoogle Scholar
  22. Sikander A, Prasad R (2015b) A novel order reduction method using cuckoo search algorithm. IETE J Res 61(83–90):2015Google Scholar
  23. Sikander A, Prasad R (2017a) A new technique for reduced-order modelling of linear time-invariant system. IETE J Res 1–9:2017Google Scholar
  24. Sikander A, Prasad R (2017b) New technique for system simplification using cuckoo search and ESA. Indian Acad Sci 1–6:2017zbMATHGoogle Scholar
  25. Sikander A, Thakur P (2017) Reduced order modelling of linear time invariant system using modified cuckoo search algorithm. Soft Computing. Springer, Berlin, pp 1–11Google Scholar
  26. Singh J, Chatterjee K, Vishwakarma CB (2014) System reduction by eigen permutation algorithm and improved padé approximations. IJMCPECE World Acad Sci Eng Technol 8:180–184Google Scholar
  27. Vishwakarma CB (2009) Model order reduction of linear dynamic systems for control system design. Ph.D. Thesis, IIT Roorkee, Roorkee IndiaGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Electronics EngineeringRajasthan Technical UniversityKotaIndia
  2. 2.Department of Instrumentation and Control EngineeringDr. B. R. Ambedkar National Institute of TechnologyJalandharIndia

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