Analysis of the Transfer Function of a DC Motor HC785LP-012 as a Learning Medium for Fundamentals Basic Control Systems

Abstract

A key obstacle in teaching introductory control systems is the challenge students encounter in connecting abstract mathematical concepts to tangible real-world applications. Transfer function analysis, while foundational, is often viewed as excessively theoretical and detached from practical engineering contexts. Without accessible and relatable examples, students may struggle to understand critical control system behaviors, including stability, damping, and dynamic response. This study seeks to evaluate the transfer function of a DC motor and illustrate its efficacy as a practical and engaging educational tool in foundational control systems courses. The DC motor is selected due to its simplicity, cost-effectiveness, and widespread use in both academic and industrial settings. The primary contribution of this research lies in the development and simulation-based evaluation of a second-order transfer function for a standard DC motor. This model serves as an educational framework, enabling students to explore time-domain and frequency-domain responses while solidifying their understanding of fundamental control principles. The transfer function is derived by applying the Laplace transform to the motor’s electrical and mechanical dynamics. Python-based simulations are employed to analyze the system, including step response evaluation and Bode plot analysis. Key system parameters, such as steady-state gain, damping ratio, natural frequency, rise time, and settling time, are calculated to assess system performance. The analysis reveals a steady-state gain of 0.408, a damping ratio (ζ) of approximately 0.7, and a natural frequency (ωₙ) of 14.7 rad/s. The step response achieves 95% of its steady-state value within 0.25 seconds, exhibiting minimal overshoot and confirming the system’s stable, well-damped characteristics. The findings affirm that the DC motor’s transfer function is an effective pedagogical tool for bridging theoretical concepts and practical applications. This approach fosters enhanced student engagement and a deeper understanding of control systems fundamentals