First and Second Order Mathematical Modeling of the JY-3A-4 AC Motor Based on Step Response

Abstract

Accurate mathematical modeling plays a vital role in the analysis and design of control systems, especially for applications that demand precision, such as industrial automation and robotics. This study focuses on developing and comparing first-order and second-order mathematical models of the JY-3A-4 single-phase AC motor, based on its step response behavior. A step input voltage was applied to the motor, and the resulting rotational speed was recorded using an optical sensor connected to a microcontroller-based data acquisition system.

The first-order model provides a basic approximation of the motor’s response and is commonly used for simplified analysis. Meanwhile, the second-order model offers a more detailed representation, capturing dynamic behaviors such as oscillations, overshoot, and settling characteristics. Both models were derived from experimental data using time-domain analysis methods.

The results show that the second-order model more accurately reflects the real behavior of the motor, particularly in its transient response. It demonstrates faster rise time, shorter settling time, and a closer fit to the experimental data, with significantly lower error compared to the first-order model. The presence of overshoot and damped oscillation observed in the actual motor response is better captured using the second-order approach.

This study emphasizes the importance of choosing the appropriate model order for motor control applications. While a first-order model may suffice for systems that do not require high precision, a second-order model is more suitable for designing advanced control systems where accuracy and stability are critical. The findings contribute to the improvement of modeling practices for AC motors and support the development of more efficient and reliable control systems in practical applications.