Optimal Approximation of Fractional-Order Systems with Model Validation using CFOA

Optimal integer-order transfer function approximation of linear time-invariant fractional-order systems (FOS) using a straight-forward approach is proposed here. The error between the rational approximant and the FOS (commensurate/non-commensurate/oscillatory types etc.) is minimised directly in the frequency domain, subject to design stability constraints, by using the colliding bodies optimisation (CBO) algorithm. Comparisons with other well-known metaheuristics regarding the computational time and the design effort expended in parameter tuning justify the efficiency of the proposed method. The CBO-optimised models achieve a superior solution quality regarding both the magnitude and phase responses in comparison to the reported literature. Analogue circuit implementations of the models using the current feedback operational amplifier are also presented. Simulations carried out in OrCAD PSPICE environment validate the practical efficacy of the proposed models.