Optimal design of wideband fractional order digital integrator using symbiotic organisms search algorithm

Optimal design of digital rational approximations with -dependant coefficients to model the fractional order integrator of any arbitrary order , where epsilon (0, 1), is presented in this work. The analytical expressions of the coefficients for the proposed fractional order digital integrators (FODIs) are derived by a two-step method: (a) the coefficients of FODIs for varying from 0.01 to 0.99 in steps of 0.01 are determined by a meta-heuristic optimisation algorithm called symbiotic organisms search (SOS) and (b) curve fitting is applied on the SOS-optimised coefficients to obtain their generalised expressions. Previous works dealing with the design of FODI based on various meta-heuristic optimisers have considered only a few specific fractional orders; hence, the practical usability of such designs is restricted. This gap provides the motivation for conducting this research. Design quality robustness and convergence consistency of SOS are extensively compared with three other well-known meta-heuristic algorithms. The superior modelling accuracy of the proposed designs is justified by comparing with the recent literature. Simulation results validate the effectiveness of the proposed models as a fractional order proportional-integral controller.