Dynamic Characterization of a DC Motor Through Open-Loop Transfer Function Testing

Abstract

This paper presents a simulation-based analysis of the dynamic behavior of a DC motor modeled
as a first-order system using MATLAB Simulink. The main objective is to characterize the motor’s open
loop response under step input conditions and to extract its corresponding transfer function parameters.
The simulation relies on simplified motor data obtained from standard datasheet references, explicitly
excluding second-order effects such as armature inductance and damping oscillations to maintain a linear
first-order approximation. The DC motor is defined by essential parameters, including an armature
resistance of 1.2 ohms, a torque constant of 0.06 Newton-meters per ampere, and a rotor inertia of 6.2 ×
10⁻⁴ kilogram-meter squared. Under the assumption that inductance is negligible, the system dynamics are
determined solely by mechanical inertia and electrical resistance. A unit step voltage is applied to the
Simulink model, and the resulting angular velocity response is recorded and evaluated. The simulation
results indicate that the motor displays a stable and consistent first-order behavior, with a rise time of
approximately 0.45 seconds and a settling time of around 0.82 seconds. The steady-state gain is observed
to be 0.05 radians per second per volt of input, while the time constant of the system is approximately 0.206
seconds. Based on this analysis, the open-loop transfer function of the motor can be expressed as a first
order system with a gain of 0.05 and a time constant of 0.206 seconds. These findings confirm that the
simplified model effectively captures the fundamental dynamics of the motor under open-loop conditions.
Moreover, the use of Simulink enables safe and flexible simulation, making it highly suitable for early-stage
control system development, particularly in educational and prototyping contexts. This validated model
lays the groundwork for the implementation of more advanced.