Abstract
The hybrid method which combines the evolutionary programming technique, i.e., based on the swarm optimization algorithm and fuzzy c-means clustering method is used for reducing the model order of high-order linear time-invariant systems in the presented work. The process of clustering is used for finding the group of objects with similar nature that can be differentiated from the other dissimilar objects. The reduction of the numerator of original high-order model is done using the particle swarm optimization algorithm, and fuzzy c-means clustering technique is used for reducing the denominator of the higher-order model. The stability of the model is also verified using the pole zero stability analysis, and it was found that the obtained reduced-order model is stable. Further, the transient and steady state response of the obtained lower-order model as compared to the other existing techniques are better. The output of the obtained lower-order model is also compared with the other existing techniques in the literature in terms of ISE, ITSE, IAE, and ITAE.
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References
B. Bandyopadhyay and S. Lamba, “Time-domain Pade approximation and modal-Pade method for multivariable systems,” IEEE Transactions on Circuits and Systems, vol. 34, no. 1, pp. 91–94, Jan. 1987.
W. Enright and M. Kamel, “On selecting a low-order model using the dominant mode concept,” IEEE Transactions on Automatic Control, vol. 25, no. 5, pp. 976–978, Oct. 1980.
M. Hutton and B. Friedland, “Routh approximations for reducing order of linear, time-invariant systems,” IEEE Transactions on Automatic Control, vol. 20, no. 3, pp. 329–337, Jun. 1975.
V. Krishnamurthy and V. Seshadri, “Model reduction using the Routh stability criterion,” IEEE Transactions on Automatic Control, vol. 23, no. 4, pp. 729–731, Aug. 1978.
T. N. Lucas, “Some further observations on the differentiation method of modal reduction,” IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1389–1391, Sep. 1992.
V. Singh, D. Chandra, and H. Kar, “Improved Routh–PadÉ Approximants: A Computer-Aided Approach,” IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 292–296, Feb. 2004.
T. N. Lucas, “Scaled impulse energy approximation for model reduction,” IEEE Transactions on Automatic Control, vol. 33, no. 8, pp. 791–793, Aug. 1988.
N. Saxena, A. Tripathi, K. K. Mishra, and A. K. Misra, “Dynamic-PSO: An improved particle swarm optimizer,” 2015, pp. 212–219.
S. Mukherjee, Satakshi, and R. C. Mittal, “Model order reduction using response-matching technique,” Journal of the Franklin Institute, vol. 342, no. 5, pp. 503–519, Aug. 2005.
K. Hammouda and F. Karray, “A comparative study of data clustering techniques,” University of Waterloo, Ontario, Canada, 2000.
D. Napoleon and S. Pavalakodi, “A new method for dimensionality reduction using K-means clustering algorithm for high dimensional data set,” International Journal of Computer Applications, vol. 13, no. 7, pp. 41–46, 2011.
J. Kennedy, J. F. Kennedy, R. C. Eberhart, and Y. Shi, Swarm intelligence. Morgan Kaufmann, 2001.
T. Zeugmann et al., “Particle Swarm Optimization,” in Encyclopedia of Machine Learning, C. Sammut and G. I. Webb, Eds. Boston, MA: Springer US, 2011, pp. 760–766.
Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” 1998, pp. 69–73.
B. Alatas, E. Akin, and A. B. Ozer, “Chaos embedded particle swarm optimization algorithms,” Chaos, Solitons & Fractals, vol. 40, no. 4, pp. 1715–1734, May 2009.
C. B. Vishwakarma and R. Prasad, “System reduction using modified pole clustering and Pade approximation,” in XXXII National systems conference, NSC, 2008, pp. 592–596.
M. G. Safonov and R. Y. Chiang, “Model reduction for robust control: A schur relative error method,” International Journal of Adaptive Control and Signal Processing, vol. 2, no. 4, pp. 259–272, Dec. 1988.
J. Pal, “Stable reduced-order Padé approximants using the Routh-Hurwitz array,” Electronics Letters, vol. 15, no. 8, p. 225, 1979.
R. Prasad and J. Pal, “Stable reduction of linear systems by continued fractions,” Journal-Institution of Engineers India Part El Electrical Engineering Division, vol. 72, pp. 113–113, 1991.
P. Gutman, C. Mannerfelt, and P. Molander, “Contributions to the model reduction problem,” IEEE Transactions on Automatic Control, vol. 27, no. 2, pp. 454–455, Apr. 1982.
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Singh, N., Choudhary, N.K., Gautam, R.K., Tiwari, S. (2019). Model Order Reduction Using Fuzzy C-Means Clustering and Particle Swarm Optimization. In: Panigrahi, B., Trivedi, M., Mishra, K., Tiwari, S., Singh, P. (eds) Smart Innovations in Communication and Computational Sciences. Advances in Intelligent Systems and Computing, vol 670. Springer, Singapore. https://doi.org/10.1007/978-981-10-8971-8_8
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DOI: https://doi.org/10.1007/978-981-10-8971-8_8
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