Mathematical Modeling and System Response Analysis of FABL3640-12-V1 DC Motor Using First and Second Order Approaches

Abstract

Mathematical modeling of DC motors plays a crucial role in designing accurate and efficient control systems. This study aims to analyze and compare first-order and second-order mathematical models of a DC motor, specifically the FABL3640-12-V1 type, to evaluate their performance and suitability for control system applications. The modeling process involves identifying motor parameters, including input voltage, nominal current, torque constant, armature resistance, inductance, and moment of inertia. These parameters are then used to derive the transfer functions in the Laplace domain.

Simulation and validation are conducted using MATLAB/Simulink to observe each model's response to a unit step input. The first-order model, due to its simplicity, produces a faster response with a rise time of approximately 0.0015 seconds and a settling time of 0.0042 seconds. However, it lacks the ability to reflect the physical dynamics of the motor, especially inertia and damping effects, resulting in an idealized but less realistic performance profile. In contrast, the second-order model includes mechanical dynamics, such as inertia and viscous friction, leading to a slightly slower response (rise time of 0.0022 seconds and settling time of 0.0056 seconds), but a significantly more accurate and stable representation of the motor’s behavior.

The findings confirm that while the first-order model is beneficial for basic or embedded control applications requiring fast computation, the second-order model is more appropriate for precision control systems where dynamic accuracy and stability are essential. The study highlights the importance of selecting the appropriate model order to balance computational efficiency and physical realism in control system design.