Title: A mixed-method for order reduction of linear time invariant systems using big bang-big crunch and eigen spectrum algorithm

Authors: Akhilesh Kumar Gupta; Deepak Kumar; Paulson Samuel

Addresses: Electrical Engineering Department, MNNIT Allahabad, India ' Electrical Engineering Department, MNNIT Allahabad, India ' Electrical Engineering Department, MNNIT Allahabad, India

Abstract: In this article, a novel mixed approach is presented for order reduction of complex higher order linear time invariant systems by merging the attributes of big bang-big crunch (BB-BC) optimisation and eigen spectrum algorithm. The cosmological theory based BB-BC optimisation has the advantage of numerical simplicity with relatively fewer control parameters which makes this algorithm easier to implement. BB-BC optimisation technique is based on the generation of random points in first step and contraction of these to a typical point in following step by the centre of mass or minimal cost approach. Eigen spectrum is based on the preservation of centroid and stiffness of the original system into reduced model which guarantees the stability of resulting reduced order model for a stable original model. In the proposed approach, denominator polynomial of the reduced order model (ROM) is determined by the Eigen spectrum approach whereas the minimisation of fitness function, i.e., integral square error (ISE) by the BB-BC algorithm approach is adopted for the computation of numerator polynomial coefficients. The effectiveness of the proposed approach over well-known methods is validated with the help of numerical examples by the comparison of transient parameters and performance indices.

Keywords: big bang-big crunch; BB-BC; eigen spectrum; integral square error; ISE; ITSE; IAE; ITAE; model order reduction; MOR; reduced order model; ROM.

DOI: 10.1504/IJAAC.2019.098212

International Journal of Automation and Control, 2019 Vol.13 No.2, pp.158 - 175

Received: 14 Jul 2017
Accepted: 05 Sep 2017
Published online: 06 Mar 2019 *

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