Frequency-domain characterization of a fractional-order armature DC motor via a modified integral transform: a comparative analysis with the Laplace transform

Integral transforms play an essential role in the transfer-function analysis of dynamical systems. In this work, a recently introduced integral transform is investigated for the analysis of fractional-order electromechanical systems. The formulation of this transform includes a parameterized kernel, which allows controlled modification of the associated transform domain and consequently, influences the pole distribution. To illustrate its applicability, a fractional-order model of an armature-controlled DC motor is considered. The transfer functions obtained using the Laplace transform and the proposed transform are compared through pole analysis and Bode frequency responses. The analysis demonstrates that the proposed transform preserves the stability and dynamic characteristics of the original system while providing additional flexibility in the transformed domain through systematic pole relocation and frequency-response adjustment. The fractional-order model exhibits improved phase margins and faster transient responses compared with the corresponding integer-order model. Furthermore, experimental validation confirms that the fractional-order model with $$\vartheta =0.8$$ provides the closest agreement with the measured motor response, demonstrating the capability of fractional-order modeling to capture the memory-dependent dynamics of the system. These results indicate that the proposed transform constitutes an effective framework for the transfer-function analysis of fractional-order dynamical systems without compromising their fundamental physical characteristics.