Comparative Analysis of Open-Loop Response of the Brushless DC Motor DF45M024053-A2 Using First-Order and Second-Order Models

Abstract

In the design and analysis of motor control systems, accurate modeling is essential to ensure effective implementation. One of the challenges lies in selecting the appropriate system order to balance simulation accuracy and computational efficiency. This study addresses the problem of dynamic behavior representation of the Brushless DC (BLDC) motor DF45M024053-A2 under open-loop conditions by comparing first-order and second-order transfer function models.The primary aim of this research is to investigate the effects of model order on the motor’s transient and steady-state performance and to provide a suitable mathematical basis for control development. The main contribution of this work lies in presenting a comparative analysis of two modeling approaches using a real-world BLDC motor and showing how simplified models can still yield meaningful results for initial design stages.The modeling method involves the derivation of electrical and mechanical equations based on Kirchhoff’s and Newton’s laws, followed by Laplace transformation to obtain the transfer functions. Motor parameters such as resistance (R = 8 Ω), inductance (L = 0.025 H), back-EMF constant (Ke = 0.408), damping coefficient (B = 0.0034 Nm·s/rad), and inertia (J = 0.005 kg·m²) were obtained from datasheet and empirical estimation.Simulation results in MATLAB/Simulink showed that the first-order model achieved a rise time of 0.52 s and a steady-state error of 6.1%, whereas the second-order model improved accuracy with a reduced steady-state error of ≈1.5% and better transient response. However, the first-order model required less computational effort.In conclusion, both models can represent the motor’s behavior with acceptable accuracy, but the second-order model provides better fidelity for capturing inertia-related dynamics. These findings suggest the second-order model is more suitable for advanced control design, while the first-order model may suffice for early-stage analysis or embedded implementation. Overall, this work contributes to the selection of appropriate motor modeling strategies for control design and provides a foundation for further exploration into closed-loop control and intelligent algorithm integration.