Role of modern fractional derivatives in an armature-controlled DC servomotor

This paper deals with the comparative analysis of modern fractional techniques for an armature-controlled DC servomotor. The mathematical modeling of an armature-controlled DC servomotor is based on the angular displacement of the motor shaft and the armature current in ampere. The governing linear differential equations are fractionalized in terms of Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional differentiations in the ranges 0 ≤ ξ₁≤ 1 and 0 ≤ ξ₂≤ 1 , respectively. The fractional ordinary differential equations have been solved by implementing Laplace transform techniques. The transfer function of an armature-controlled DC servomotor is obtained by the coupling of fractional ordinary differential equations. The calculations of transfer functions have been traced out through the Mathcad 15 software while graphical simulation is based on MATLAB. In order to control the systems’ behavior, the transfer function is depicted graphically for fractional and non-fractional solutions along with embedded parameters. Our results suggest that the speed of rotation relies on the voltage which precisely controls the angular position of servomechanism through both types of fractional differentiation.