Fractional model and analytically determined response of DC motor with separate excitation

In recent years, the use of DC motors has been constantly increasing, both in different home appliances and industrial drives. Some specific applications, such as robots and medical devices, require more advanced mathematical model of electrical machine that incorporates the physical effects that the standard model cannot take into account. Additionally, such models provide a more detailed dynamic analysis. In this paper, the fractional mathematical model, which is suitable for analysis of DC motor with separate and constant excitation, is derived. The model is formulated in the form of a system of fractional different equations. Furthermore, the transfer functions of the electrical and mechanical subsystems, as well as the transfer functions that describe dependence between the rotation speed and supply voltage and the load torque, are specified. Moreover, analytical solutions of certain subsystems and for complete DC machine are derived.