Mathematical Modeling and Simulation of Open-Loop and Closed-Loop Second-Order DC Rotary Motor Type S-50-5
Keywords:
DC Motor; Mathematical Modeling; Open-Loop Control; Close-Loop Control; Ziegler-Nichols Tuning; Simulation; Transient Response;Abstract
This study thoroughly discusses the mathematical modeling of DC motors in both open-loop and closed-loop systems, each of which has distinct characteristics and performance. The DC motor itself is one of the most crucial components in various industrial applications, such as production machinery, robotics, and automation systems, due to its ability to provide precise control over the shaft’s speed and position. In an open-loop system, the DC motor is controlled by applying a certain input voltage without any feedback mechanism from the resulting output. This makes the system response less accurate, slower, and more vulnerable to external disturbances or load variations because the system cannot automatically adjust to changes in environmental conditions or workload.
The mathematical model of the open-loop system is based on relatively simple differential equations, which directly describe the relationship between input voltage, current, and motor output speed, without accounting for any correction of output errors. In contrast, the closed-loop system employs a feedback mechanism to continuously monitor the motor output and correct it so that it always matches the desired reference value or setpoint. The mathematical model of the closed-loop system is typically more complex because it involves additional control elements, such as PID (Proportional-Integral-Derivative) controllers, which function to minimize steady-state errors, reduce overshoot, and enhance the system’s stability and response speed to changes.
Through simulations and performance analysis, this study demonstrates that the closed-loop system significantly outperforms the open-loop system, particularly in terms of transient response, disturbance tolerance, and overall system stability. These findings further underscore the importance of implementing feedback in DC motors to improve the effectiveness, efficiency, and reliability of the system in practical applications within the modern industrial world.
