Approximation of PM DC Micromotor Transfer Function by Fractional Order Transfer Function

Transfer function of permanent magnets (PM) DC micromotor speed is quite complex, which in turn complicates the synthesis of automatic control systems. It is established that for this class of micromotors the electromechanical time constant becomes commensurate with the electric time constant of the armature, which leads to overshooting of the output coordinate, so simplification of transfer function of speed by discarding the s
²
component will result in aperiodic process and considerable accuracy loss. A series of experimental PM DC micromotor studies using a high-precision laser tachometer to obtain the necessary parameters for the high-accuracy micromotor model development have been carried out. The developed high-accuracy model made it possible to obtain the appropriate transition process of speed with overshooting. Approximation of complex transfer function of PM DC micromotor speed by a more compact fractional order transfer function using the intelligent particle swarm optimization method has been performed, and the approximation accuracy has been estimated on the basis of transition and frequency characteristics analysis.