Abstract

Reducing the order of higher order systems by mixed approach is Improved Pade-Pole clustering based method to derive a reduced order approximation for a stable continuous time system is presented. In this method, the denominator polynomial of the reduced order model is derive by improved pole-clustering approach and the numerator polynomial are obtain through Padé approximation technique and by parameter optimization by minimizing the mean square error between the time responses of the original and reduced system element through genetic algorithm. The reduced order model so obtained by improved clustering algorithm guaranteed the stability in the reduced model.

References

• R. Komarasamy, N. Albhonso & G. Gurusamy "Order reduction of linear systems with an improved pole clustering," Journal of Vibration and Control18 (12) 1876–1885, 2011.
• Gupta DK, Bhagat SK & Tewari JP (2002). "A mixed method for the simplification of linear dynamic systems". In Proceedings of International Conference on Computer Applications in Electrical Engineering, Roorkee, India, Feb. 21–23, pp. 455–459.
• Y. Shamash, "Linear system reduction using Padé approximations to allow retention of dominant poles," Int. J. control, vol. 21, no. 2, pp 257-272, 1975.
• Y. Shamash, "Viability of methods for generating stable reduced order models," IEEE trans. Automatic control, vol. 26, no. 6, pp 1285-1286, 1981.
• B. Vishwakarma, & R. Prasad, "Clustering method for reducing order of linear system using Padé approximation," IETE Journal of Research, vol. 54, no. 5, pp. 326-330, 2008.
• Vishwakarma C. B. , Prasad R. , "System reduction using modified pole clustering and Padé approximation," xxxii national systems conference, NSC-2008.
• S. Takahasi, K Yamanka, M Yamada, 1987, "Detection of dominant poles of systems with time delay by using Padé approximation," Int. J. control, vol. 45, no. 1, pp 251-254, 1987.
• A. kumar D. Chandra, "Improved Padé-pole clustering approximant," International Conference on Computer Science and Electronics Engineering.
• Shieh LS and Wei YJ (1975), "A mixed method for multivariate system reduction". IEEE Transactions on Automatic Control 20: 429–432.
• Parmar G, Prasad R and Mukherjee S (2007). "Order reduction of linear dynamic systems using stability equation method and GA. " International Journal of Computer, Information, and Systems Science, and Engineering 1(1): 26–32.
• Parmar G, Mukherjee S & Prasad R. "Reduced order system of linear MIMO system using Genetic Algorithm". Int j simul model 6(2007)3, pp 173-184, ISSN 1726-4529.
• C. B. Vishwakarma & R. Prasad, "MIMO System Reduction Using Modi?ed Pole Clustering and Genetic Algorithm," Modelling and Simulation in Engineering Volume 2009, Article ID 540895 doi:10. 1155/2009/540895.
• Mukherjee S and Mishra RN (1987) "Order reduction of linear systems using an error minimization technique". Journal of Franklin Institute 323(1): 23–32.
• Puri NN and Lan DP (1988), "Stable model reduction by impulse response error minimization using Mihailov criterion and Pade's approximation". ASME Journal of Dynamic Systems, Measurement, and Control 110: 389–394.
• A. K. Mittal, P. Prasad, and S. P. Sharma, "Reduction of linear dynamic systems using an error minimization technique," J. Inst. Eng. India, IE (I) J. EL 84, pp. 201–206, 2004.
• Zaer S Abo-Hammour, Othman MK Alsmadi, and Adnan M. Al-Smadi(2011). "Frequency-based model order reduction via genetic algorithm approach". IEEE 7th International Workshop on Systems, Signal Processing and their Applications (WOSSPA) 978-1-4577-0690-5.
• V. Singh, D Chandra, & H. Kar, "Improved Routh-Padé approximants: a computer-aided approach," IEEE, Trans. on automat. Contr. , Vol. 49, pp. 292-296, 2004.
• W. T. Beyene, "Pole-clustering and rational-interpolation techniques for simplifying distributed systems," IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Applications, vol. 46, no. 12, pp. 1468-1472, 1999.
• M. F. Hutton, & B. Friedland, "Routh approximation for reducing order of linear time invariant system", IEEE Trans. Auto. Cont. , AC-20, pp. 329-337, 1975.