Mathematical Modeling and Simulation of the Brushless DC Motor DF45M024053-A2 for Control Applications

Abstract

This paper presents the mathematical modeling and simulation of the Brushless DC (BLDC) motor DF45M024053-A2, aiming to support the development, analysis, and implementation of reliable and effective control systems. The modeling process begins with the systematic formulation of both the electrical and mechanical subsystems of the motor. For the electrical part, Kirchhoff’s voltage law is applied to represent the circuit dynamics, while for the mechanical subsystem, Newton’s second law of motion is used to describe the rotor’s rotational dynamics under the influence of torque and inertia.

These two subsystems are then integrated into a unified electromechanical model, which is subsequently transformed into the s-domain using the Laplace transform. This process results in a comprehensive transfer function that characterizes the relationship between the input voltage and the motor's angular velocity, providing a foundation for dynamic analysis and control design.

Key parameters  including armature resistance, phase inductance, back EMF constant, torque constant, friction coefficient, and rotor inertia  are obtained from the motor datasheet and validated through supporting calculations where necessary. Using this mathematical model, the motor’s behavior is simulated under both open-loop and closed-loop conditions in MATLAB/Simulink, allowing observation of its transient and steady-state performance.

Both first-order and second-order models are developed to compare dynamic responses and highlight the trade-offs between model simplicity and accuracy. The results demonstrate that the derived model accurately reflects the real-world dynamics of the motor and is suitable for control system development. This study also emphasizes the significance of parameter identification and model order reduction in optimizing system performance without compromising essential dynamic characteristics