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
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):7225–7244
Brown CT, Liebovitch LS, Glendon R (2007) Lévy flights in Dobe Ju/hoansi foraging patterns. Hum Ecol 35(1):129–138
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 1:20–27
Edgar TF (1975) Least squares model reduction using step response. Int J Control 22:261–270
Eitelberg E (1981) Model reduction by minimizing the weighted equation error. Int J Control 34(6):1113–1123
El-Attar RA, Vidyasagar M (1978) Order reduction by \({L_1}\) and \({L_\infty }\) norm minimization. IEEE Trans Autom Control 23(4):731–734
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
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
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Boston 10.1007/s10589-009-9261-6
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):7169–7174
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
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 82:781–798
Mukherjee S, Satakshi R, Mittal C (2005) Model order reduction using response-matching technique. J Frankl Inst 342:503–519
Obinata G, Inooka H (1983) Authors reply to comments on model reduction by minimizing the equation error. IEEE Trans Autom Control 28:124–125
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):1871–1880
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
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
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):4848–4858
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 465:1018–1019
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 2009:1–5
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
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 1:330–343
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Sikander, A., Thakur, P. Reduced order modelling of linear time-invariant system using modified cuckoo search algorithm. Soft Comput 22, 3449–3459 (2018). https://doi.org/10.1007/s00500-017-2589-4
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DOI: https://doi.org/10.1007/s00500-017-2589-4