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03-04-2017 | Methodologies and Application

Reduced order modelling of linear time-invariant system using modified cuckoo search algorithm

Authors: Afzal Sikander, Padmanabh Thakur

Published in: Soft Computing | Issue 10/2018

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Abstract

In this paper modified cuckoo search (MCS) algorithm is considered to develop reduced order model (ROM) of higher-order linear time-invariant systems. Firstly, the MCS algorithm has been employed to minimize the integral square error (ISE) between original and proposed ROM to obtain its unknown coefficients. Five systems of different order are considered to obtain their reduced order model. Finally, various performance indices, such as ISE, integral of absolute and integral of time multiplied by absolute error, have been estimated to reveal the efficacy of the proposed model. Also, time and frequency response characteristics of original higher-order model are compared with the proposed MCS-based and some of other existing techniques-based ROM available in the literature. Furthermore, the results are compared in terms of time response specifications such as rise time (\(t_\mathrm{r} \)) in second, settling time (\( t_\mathrm{s}\)) in second and maximum peak overshoot (\( M_\mathrm{p}\)) in percentage. It is revealed that the response of the proposed MCS-based ROM is much closer to the response of the original higher-order system.

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Abu-Al-Nadi DI, Alsmadi OMK, Abo-Hammour ZS (2011) Reduced order modeling of linear MIMO systems using particle swarm optimization. In: 7th international conference on autonomic and autonomous systems, Venice, Italy, pp 62–66

Alsmadi OMK, Abo-Hammour ZS, Al-Smadi AM, Abu-Al-Nadi DI (2011) Genetic algorithm approach with frequency selectivity for model order reduction of MIMO systems. Math Comput Model Dyn Syst 17(2):163–181. doi:10.1080/13873954.2010.540806 MathSciNetCrossRefMATH

Biradar S, Hote YV, Saxena S (2016) Reduced-order modelling of linear time invariant systems using big bang big crunch optimization and time moment matching method. Appl Math Model 40(15–16):7225–7244MathSciNetCrossRef

Brown CT, Liebovitch LS, Glendon R (2007) Lévy flights in Dobe Ju/hoansi foraging patterns. Hum Ecol 35(1):129–138CrossRef

Desai SR, Prasad R (2013a) A novel order diminution of LTI systems using big bang big crunch optimization and routh approximation. Appl Math Model 37(16–17):8016–8028. doi:10.1016/j.apm.2013.02.052

Desai SR, Prasad R (2013b) A new approach to order reduction using stability equation and big bang big crunch optimization. Syst Sci Control Eng Open Access J 1:20–27CrossRef

Edgar TF (1975) Least squares model reduction using step response. Int J Control 22:261–270CrossRefMATH

Eitelberg E (1981) Model reduction by minimizing the weighted equation error. Int J Control 34(6):1113–1123MathSciNetCrossRefMATH

El-Attar RA, Vidyasagar M (1978) Order reduction by \({L_1}\) and \({L_\infty }\) norm minimization. IEEE Trans Autom Control 23(4):731–734CrossRefMATH

Erol OK, Eksin I (2006) A new optimization method: big bang-big crunch. Adv Eng Softw 37:106–111. doi:10.1016/j.advengsoft.2005.04.005 CrossRef

Ghosh S, Senroy N (2013) Balanced truncation approach to power system model order reduction. Electr Power Compon Syst 41:747–764. doi:10.1080/15325008.2013.769031 CrossRef

Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Boston 10.1007/s10589-009-9261-6MATH

Humphries NE, Weimerskirch H, Queiroz N, Southall EJ, Sims DW (2012) Foraging success of biological Lévy flights recorded in situ. Proc Natl Acad Sci 109(19):7169–7174CrossRef

Hutton MF, Friedland B (1975) Routh approximations for reducing order of linear, time-invariant systems. IEEE Trans Autom Control 20:329–337. doi:10.1109/TAC.1975.1100953 MathSciNetCrossRefMATH

Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE International Conference on Neural Networks, Perth, WA, vol 4, pp 1942–1948. doi:10.1109/ICNN.1995.488968

Lee KS, Geem ZW (2004) A new structural optimization method based on the Harmony search algorithm. J Comput Struct 82:781–798CrossRef

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

Obinata G, Inooka H (1983) Authors reply to comments on model reduction by minimizing the equation error. IEEE Trans Autom Control 28:124–125CrossRef

Panda S, Yadav JS, Padidar NP, Ardil C (2009) Evolutionary techniques for model order reduction of large scale linear systems. Int J Appl Sci Eng Technol 5:22–28

Parmar G, Mukherjee S, Prasad R (2007a) Reduced order modeling of linear dynamic systems using particle swarm optimized eigen spectrum analysis. Int J Comput Math Sci 1(31):45–52

Parmar G, Mukherjee S, Prasad R (2007b) System reduction using eigen spectrum analysis and pade approximation technique. Int J Comput Math 84(12):1871–1880MathSciNetCrossRefMATH

Parmar G, Mukherjee S, Prasad R (2007c) System reduction using factor division algorithm and eigen spectrum analysis. Appl Math Model 31(11):2542–2552. doi:10.1016/j.apm.2006.10.004 CrossRefMATH

Parmar G, Prasad R, Mukherjee S (2007d) Order reduction of linear dynamic systems using stability equation method and GA. Int J Comput Inf Eng 1(1):26–32

Parmar G, Pandey MK, Kumar V (2009) System order reduction using GA for unit impulse input and a comparative study using ISE and IRE. In: International conference on advances in computing, communications and control, Mumbai, India, pp 23–24

Salim R, Bettayeb M (2011) \({H_2}\) and \({H_\infty }\) optimal model reduction using genetic algorithms. J Frankl Inst 348:1177–1191. doi:10.1016/j.jfranklin.2009.10.016 MathSciNetCrossRefMATH

Sambariya DK, Arvind G (2016) High order diminution of LTI system using stability equation method. Br J Math Comput Sci 13(5):1–15. doi:10.9734/BJMCS/2016/23243

Sikander A, Prasad R (2015a) Soft computing approach for model order reduction of linear time invariant systems. Circuit Syst Signal Process. doi:10.1007/s00034-015-0018-4

Sikander A, Prasad R (2015b) Time domain order reduction method using improved Hermite Normal Form. In: National conference on emerging trends in electrical and electronics engineering, JMI, New Delhi, India, pp 224–229

Sikander A, Prasad R (2015c) Linear time-invariant system reduction using a mixed methods approach. Appl Math Model 39(16):4848–4858MathSciNetCrossRef

Sikander A, Prasad R (2017) A new technique for reduced-order modelling of linear time-invariant system. IETE J Res 1–9. doi:10.1080/03772063.2016.1272436

Sikander A, Uniyal I, Thakur P (2016) Hybrid method of reduced order modelling for LTI system using evolutionary algorithm. In: IEEE international conference on next generation computing technologies, Dehradun, India

Viswanathan GM (2010) Fish in levy-flight foraging. Nature 465:1018–1019CrossRef

Vishwakarma CB, Prasad R (2008) System reduction using modified pole clustering and pade approximation. In: XXXII national systems conference, NSC 2008, pp 592–596

Vishwakarma CB, Prasad R (2009) MIMO system reduction using modified pole clustering and genetic algorithm. Model Simul Eng 2009:1–5CrossRef

Walton S, Hassan O, Morgan K, Brown MR (2011) Modified cuckoo search: a new gradient free optimisation algorithm. Chaos Solitons Fractals 44:710–718. doi:10.1016/j.chaos.2011.06.004 CrossRef

Wilson DA (1970) Optimal solution of model reduction problem. Proc Inst Electr Eng 117(06):1161–1165

Yang XS, Deb S (2008) Nature-inspired metaheuristic algorithms. Luniver Press, London

Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1:330–343MATH

Title: Reduced order modelling of linear time-invariant system using modified cuckoo search algorithm
Authors: Afzal Sikander
Padmanabh Thakur
Publication date: 03-04-2017
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 10/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-017-2589-4

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