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Model reduction using Harris hawk algorithm and moment matching

Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
Physical machine systems are represented in the form of differential equations. These differential equations may be of the higher order and difficult to analyses. Therefore, it is necessary to convert the higher-order to lower order which replicates approximately similar properties of the higher-order system (HOS). This article presents a novel approach to reducing the higher-order model. The approach is based on the hunting demeanor of the hawk and escaping of the prey. The proposed method unifies the Harris hawk algorithm and the moment matching technique. The method is applied on single input single output (SISO), multi-input multi-output (MIMO) linear time–invariant (LTI) systems. The proposed method is justified by examining the result. The results are compared using the step response characteristics and response error indices. The response indices are integral square error, integral absolute error, integral time absolute error. The step response characteristics such as rise time, peak, peak time, settling time of the proposed reduced order follows 97%–100% of the original system characteristics.
Rocznik
Strony
959--978
Opis fizyczny
Bibliogr. 50 poz., rys., tab., wz.
Twórcy
  • Department of Electrical Engineering, Rajasthan Technical University Rawath Bhata Road 324010, Kota, India
  • Department of Electrical Engineering, Rajasthan Technical University Rawath Bhata Road 324010, Kota, India
Bibliografia
  • [1] Lal M., Mitra R., Simplification of Large System Dynamics Using a Moment Evaluation Algorithm, IEEE Transactions on Automatic Control, vol. 19, no. 5, pp. 602–603 (1975), DOI: 10.1109/TAC.1974.1100671.
  • [2] Sambariya D.K., Sharma A.K., An efficient approach for stability preservation in model order reduction using moment matching technique, International Conference on Computer, Communications and Electronics (Comptelix), Jaipur, pp. 478–483 (2017), DOI: 10.1109/COMPTELIX.2017.8004017.
  • [3] Shamash Y., Stable reduced-order models using Padé-type approximations, IEEE Transactions on Automatic Control, vol. 19, no. 5, pp. 615–616 (1974), DOI: 10.1109/TAC.1974.1100661.
  • [4] Chen T.C., Chang C.Y., Han K.W., Reduction of Transfer Functions by the Stability-Equation Method, Journal of the Franklin Institute, vol. 308, no. 4, pp. 389–404 (1979), DOI: 10.1016/0016-0032(79)90066-8.
  • [5] Langholz G., Feinmesser D., Model reduction by Routh approximations, International Journal of Systems Science, vol. 9, no. 5, pp. 493–496 (1978), DOI: 10.1080/00207727808941714.
  • [6] Chen C.F., Model reduction of multivariable control systems by means of matrix continued fractions, International Journal of Control, vol. 5, no. 1, pp. 145–152 (1974), DOI: 10.1016/S1474-6670(17)68326-5.
  • [7] Davidson A.M., Lucas T.N., Linear-system reduction by continued-fraction expansion about a general point, Electronics Letters, vol. 10, no. 14, pp. 271–273 (1974), DOI: 10.1049/el:19740216.
  • [8] Marshall S.A., Calfe M.R., Healey M., Continued-fraction model-reduction technique for multivariable systems, Proceedings of the Institution of Electrical Engineers, vol. 121, pp. 1032-1033 (1974), DOI: 10.1049/piee.1974.0091.
  • [9] Shieh L.S., Goldman M.J., A Mixed Cauer Form for Linear System Reduction, IEEE Transactions on Systems, Man, and Cybernetics, SMC, vol. 4, no. 6, pp. 584–588 (1974), DOI: 10.1109/TSMC.1974.4309369.
  • [10] Pal J., Stable reduced-order Pade approximants using the Routh-Hurwitz array, Electronics Letters, vol. 15, no. 8, pp. 225–226 (1979), DOI: 10.1049/el:19790159.
  • [11] Chen T.C., Chang C.Y., Han K.W., Model reduction using the stability-equation method and the Padé approximation method, Journal of the Franklin Institute, vol. 309, no. 6, pp. 473–90 (1980), DOI: 10.1016/0016-0032(80)90096-4.
  • [12] Pal J., Ray L.M., Stable padé approximants to multivariable systems using a mixed method, Proceedings of the IEEE, vol. 68, no. 1, pp. 176–178 (1980), DOI: 10.1109/PROC.1980.11603.
  • [13] Parthasarathy R., Jayasimha K.N., System reduction using stability-equation method and modified Cauer continued fraction, Proceedings of the IEEE, vol. 70, no. 10, pp. 1234–1236 (1982), DOI: 10.1109/PROC.1982.12453.
  • [14] Parmar G., Mukherjee S., Prasad R., System reduction using eigen spectrum analysis and Padé approximation technique, International Journal of Computer Mathematics, vol. 84, no. 12, pp. 1871-1880 (2007), DOI: 10.1080/00207160701345566.
  • [15] Parmar G., Prasad R., Mukherjee S., A Mixed Method for Large–Scale Systems Modelling using Eigen Spectrum Analysis and Cauer Second Form, IETE Journal of Research, vol. 53, no. 0.2, pp. 93–102 (2007), DOI: 10.1080/03772063.2007.10876125.
  • [16] Hein R., Orlikowski C., Hybrid reduced model of rotor, Archives of Mechanical Engineering, vol. 60, no. 3, pp. 319-333 (2013), DOI: 10.2478/meceng-2013-0021.
  • [17] Horla D., Talar S., Giernacki W., Kozierski P., Influence of time delay on fractional-order PI-controlled system for a second-order oscillatory plant model with time delay, Archives of Electrical Engineering, vol. 66, no. 4, pp. 693–704 (2017), DOI: 10.1515/aee–2017-0052.
  • [18] Gupta A. K., Kumar D., Samuel P., A meta-heuristic cuckoo search and eigen permutation approach for model order reduction, Sadhana, vol. 43, no. 65, pp. 1–11 (2018), DOI: 10.1007/s12046-018-0810-5.
  • [19] Tiwari S. K., Kaur G., Model Reduction by New Clustering Method and Frequency Response Matching, Journal of Control, Automation and Electrical Systems, vol. 28, pp. 78–85 (2017), DOI: 10.1007/s40313-016-0282-y.
  • [20] Sikander A., Prasad R., A New Technique For Reduced-Order Modelling of Linear Time–Invariant System, IETE Journal of Research, vol. 63, no. 3, pp. 316–32 (2017), DOI: 10.1080/03772063.2016.1272436.
  • [21] Precup R., David R., Petriu E.M., Grey Wolf Optimizer Algorithm-Based Tuning of Fuzzy Control Systems With Reduced Parametric Sensitivity, IEEE Transactions on Industrial Electronics, vol. 64, no. 1, pp. 527–534 (2017), DOI: 10.1109/TIE.2016.2607698.
  • [22] Das S., Jha R., Model order reduction of high order LTI system using particle swarm optimisation, 2016 International Conference on Computer, Electrical and Communication Engineering (ICCECE), pp. 1–6 (2016), DOI: 10.1109/ICCECE.2016.8009543.
  • [23] Alsmadi O.M.K., Abo-Hammour Z.S., Al-Smadi A.M., Abu-Al-Nadi D.I., Genetic algorithm approach with frequency selectivity for model order reduction of MIMO systems, Mathematical and Computer Modelling of Dynamical Systems, vol. 17, no. 2, pp. 163–181 (2011), DOI: 10.1080/13873954.2010.540806.
  • [24] Sambariya D.K., Manohar H., Model order reduction by integral squared error minimization using bat algorithm, 2015 2nd International Conference on Recent Advances in Engineering and Computational Sciences (RAECS), pp. 1–7 (2015), DOI: 10.1109/RAECS.2015.7453413.
  • [25] Biradar S., Hote Y.V., Saxena S., Reduced-order modeling of linear time invariant systems using big bang big crunch optimization and time moment matching method, Applied Mathematical Modelling, vol. 40, no. 15–16, pp. 7225–7244 (2016), DOI: 10.1016/j.apm.2016.03.006.
  • [26] Lavania S., Nagaria D., Evolutionary approach for model order reduction, Perspectives in Science, vol. 8, pp. 361–363 (2016), DOI: 10.1016/j.pisc.2016.04.075.
  • [27] Ganguli S., Kaur G., Sarkar P., A hybrid intelligent technique for model order reduction in the delta domain: a unified approach, Soft Computing, vol. 23, pp. 4801–4814 (2019), DOI: 10.1007/S00500-018-3137-6.
  • [28] Gupta A.K., Kumar D., Samuel P., Order reduction of linear time–invariant systems using Eigen permutation and Jaya algorithm, Engineering Optimization, vol. 51, no. 9, pp. 1626–1643 (2019), DOI: 10.1080/0305215X.2018.1536751.
  • [29] Heidari A.A., Mirjalili S., Faris H., Aljarah I., Mafarja M., Chen H., Harris hawks optimization: Algorithm code: Algorithm and Applications, (aliasgharheidari.com): Future Generation Computer Systems, vol. 97, pp. 849–872 (2019), DOI: 10.1016/j.future.2019.02.028.
  • [30] Ekinci S., Hekimoğlu B., Demirören A., Kaya S., Harris Hawks Optimization Approach for Tuning FOPID Controller in DC-DC Buck Converter, 2019 International Artificial Intelligence and Data Processing Symposium (IDAP), pp. 1–9 (2019), DOI: 10.1109/IDAP.2019.8875992.
  • [31] Izci D., Ekinci S., Demirören A., Hedley J., HHO Algorithm based PID Controller Design for Aircraft Pitch Angle Control System, 2020 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA), pp. 1–6 (2020), DOI: 10.1109/HORA49412.2020.9152897.
  • [32] Sahoo D.K., Sahu R. K., Panda S., Chaotic Harris Hawks Optimization based type–2 Fractional Order Fuzzy PID controller for frequency regulation of power systems, International Journal of Ambient Energy, pp. 1–13 (2020), DOI: 10.1080/01430750.2020.1860128.
  • [33] Qu C., He W., Peng X., Peng X., Harris Hawks optimization with information exchange, Applied Mathematical Modelling, vol. 84, pp. 52–75 (2020), DOI: 10.1016/j.apm.2020.03.024.
  • [34] Lefebvre L., Whittle P., Lascaris E., Finkelstein A., Feeding innovations and forebrain size in birds, Animal Behaviour, vol. 53, no. 3, pp. 549–560 (1997), DOI: 10.1006/anbe.1996.0330.
  • [35] Heidari A.A., Mirjalili S., Faris H., Aljarah I., Mafarja M., Chen H., Harris hawks optimization: Algorithm and applications, Future Generation Computer Systems, vol. 97, pp. 849–872 (2019), DOI: 10.1016/J.FUTURE.2019.02.028.
  • [36] Desai S., Prasad R., A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh Approximation, Applied Mathematical Modelling, vol. 37, no. 16–17, pp. 8016–8028 (2013), DOI: 10.1016/J.APM.2013.02.052.
  • [37] Mukherjee S., Mishra R.N., Order reduction of linear systems using an error minimization technique, Journal of the Franklin Institute, vol. 323, no. 1, pp. 23–32 (1987), DOI: 10.1016/0016-0032(87)90037-8.
  • [38] Sambariya D.K., Sharma O., Model Order Reduction Using Routh Approximation and Cuckoo Search Algorithm, Journal of Automation and Control, vol. 4, no. 1, pp. 1–9 (2016), DOI: 10.12691/AUTOMATION-4-1-1.
  • [39] Parmar G., Prasad R., Mukherjee S., Order reduction of linear dynamic systems using stability equation method and GA, International Journal of Computer, Information, and Systems Science, and Engineering, vol. 1, pp. 26–32 (2007), DOI: 10.1.1.308.4502.
  • [40] Parmar G., Mukherjee S., Prasad R., System reduction using factor division algorithm and eigen spectrum analysis, Applied Mathematical Modelling, vol. 31, no. 11, pp. 2542–2552 (2007), DOI: 10.1016/j.apm.2006.10.004.
  • [41] Sikander A., Prasad R., A Novel Order Reduction Method Using Cuckoo Search Algorithm, IETE Journal of Research, vol. 61, no. 2, pp. 83–90 (2015), DOI: 10.1080/03772063.2015.1009396.
  • [42] Sikander A., Prasad R., Soft Computing Approach for Model Order Reduction of Linear Time Invariant Systems, Circuits, Systems, and Signal Processing, vol. 34, pp. 3471–3487 (2015), DOI: 10.1007/s00034-015-0018-4.
  • [43] Sikander A., Prasad R., Linear time–invariant system reduction using a mixed methods approach, Applied Mathematical Modelling, vol. 39, no. 16, pp. 4848–4858 (2015), DOI: 10.1016/j.apm.2015.04.014.
  • [44] Sambariya D., Rajawat A., Model order reduction by routh stability array with stability equation method for siso and mimo systems, Universal Journal of Engineering Science, vol. 4, no. 1, pp. 1-13 (2016), DOI: 10.1109/CCAA.2016.7813843.
  • [45] Sambariya D.K., Manohar H., Model order reduction by differentiation equation method using with Routh array method, 2016 10th International Conference on Intelligent Systems and Control (ISCO), pp. 1–6, no. 2 (2016), DOI: 10.1109/ISCO.2016.7726996.
  • [46] Narwal A., Prasad R., Optimization of LTI Systems Using Modified Clustering Algorithm, IETE Technical Review, vol. 34, no. 2, pp. 201–213 (2017), DOI: 10.1080/02564602.2016.1165152.
  • [47] Narwal A., Prasad B.R., A Novel Order Reduction Approach for LTI Systems Using Cuckoo Search Optimization and Stability Equation, IETE Journal of Research, vol. 62, no. 2, pp. 154–163 (2016), DOI: 10.1080/03772063.2015.1075915.
  • [48] Narwal A., Prasad R., Order Reduction of LTI Systems and Their Qualitative Comparison, IETE Technical Review, vol. 34, no. 6, pp. 1–9 (2016), DOI: 10.1080/02564602.2016.1237859.
  • [49] Shamash Y., Model reduction using minimal realisation algorithms, Electronics Letters, vol. 11, no. 16, pp. 385–387 (1975), DOI: 10.1049/el:19750293.
  • [50] Shamash Y., Order Reduction of Linear Systems by Pade Approximation Methods, University of London (1973).
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8e761966-69f6-4118-a9a1-28cd85d82fdb
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