A Hybrid Method for Determination of Effective Poles Using Clustering Dominant Pole Algorithm

In this paper, an analysis of some model order
reduction techniques is presented. A new hybrid algorithm for model
order reduction of linear time invariant systems is compared with the
conventional techniques namely Balanced Truncation, Hankel Norm
reduction and Dominant Pole Algorithm (DPA). The proposed hybrid
algorithm is known as Clustering Dominant Pole Algorithm (CDPA),
is able to compute the full set of dominant poles and its cluster center
efficiently. The dominant poles of a transfer function are specific
eigenvalues of the state space matrix of the corresponding dynamical
system. The effectiveness of this novel technique is shown through
the simulation results.

• Anuj Abraham
• N. Pappa
• Daniel Honc
• Rahul Sharma

• Balanced truncation
• Clustering
• Dominant pole
• Hankel norm
• Model reduction.

[1] Huijun Gao, et al., “Hankel norm approximation of linear systems with
time-varying delay: continuous and discrete cases,” Int. J. Control,
2004, Vol. 77, No. 17, 1503–1520.
[2] Safonov, M.G., and R.Y. Chiang, “A Schur Method for Balanced Model
Reduction”, IEEE Trans. on Automat. Contr., Vol. 34, No. 7, July 1989,
pp. 729-733.
[3] A.C. Antoulas, D.C. Sorensen. “Approximation of large-scale dynamical
systems: An overview,” Int. J. Appl. Math. Comp. Sci.,
11(5):1093{1121, 2001.
[4] Aguirre, L. A. “Quantitative Measure of Modal Dominance for
Continuous Systems,” In Proc. of the 32nd Conf. on Decision and
Control 1993, pp. 2405–2410.
[5] Martins, N., Pinto, H. J. C. P., and Lima, L. T. G. “Efficient methods for
finding transfer function zeros of power systems,” IEEE Trans. Power
Syst. Vol.7, 3 in 1992, 1350–1361.
[6] Martins, N., Lima, L. T. G., and Pinto, H. J. C. P. “Computing dominant
poles of power system transfer functions,” IEEE Trans. Power Sys., Vol.
11, 1 in 1996, 162–170.
[7] S. K. Nagar, and S. K. Singh, “An algorithmic approach for system
decomposition and balanced realized model reduction,” J. Franklin Inst.,
Vol. 341, pp. 615-630, 2004.
[8] A.K. Mittal, R. Prasad, and S.P. Sharma, “Reduction of linear dynamic
systems using an error minimization technique,” J. Inst. Eng. India IE(I)
J. EL, Vol. 84, pp. 201-206, 2004.
[9] G. Parmar, S. Mukherjee, and R. Prasad, “System reduction using factor
division algorithm and eigen spectrum analysis,” Int. J. Applied Math.
Modeling, Vol. 31, pp. 2542-2552, 2007.
[10] J. Rommes and N. Martins, “Efficient computation of transfer function
dominant poles using subspace acceleration,” IEEE Trans. Power
System., Vol. 21, no. 3, pp. 1218–1226, 2006.
[11] Vinod Kumar, J. P. Tiwari, “Order Reducing of Linear System using
Clustering Method Factor Division Algorithm,” Int. J. of Applied
Information Systems (IJAIS) – ISSN : 2249-0868, Volume 3–No.5 ,
2012.
[12] Mihály Petreczky, et al., “Balanced truncation for linear switched
systems,” Elsevier, Nonlinear Analysis: Hybrid Vol. 10, 2013, pp. 4–20.
[13] Rommes, J., Martins, N., “Computing transfer function dominant poles
of large second-order dynamical systems,” SIAM Journal on Scientific
Computing, Vol. 30, Issue 4, 2008, pp. 2137-2157.