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Journal of Optimization
Volume 2013, Article ID 142390, 11 pages
Research Article

Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts

Advanced Electronics Lab, Department of ECE, Netaji Subhas Institute of Technology, Dwarka, New Delhi 110078, India

Received 28 February 2013; Revised 21 May 2013; Accepted 30 May 2013

Academic Editor: Manuel Lozano

Copyright © 2013 Maneesha Gupta and Richa Yadav. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Second and third order digital integrators (DIs) have been optimized first using Particle Swarm Optimization (PSO) with minimized error fitness function obtained by registering mean, median, and standard deviation values in different random iterations. Later indirect discretization using Continued Fraction Expansion (CFE) has been used to ascertain a better fitting of proposed integer order optimized DIs into their corresponding fractional counterparts by utilizing their refined properties, now restored in them due to PSO algorithm. Simulation results for the comparisons of the frequency responses of proposed 2nd and 3rd order optimized DIs and proposed discretized mathematical models of half integrators based on them, with their respective existing operators, have been presented. Proposed integer order PSO optimized integrators as well as fractional order integrators (FOIs) have been observed to outperform the existing recently published operators in their respective domains reasonably well in complete range of Nyquist frequency.