Second-Order PID Control of S-50-52 Rotary Servo Motor Based on the Ziegler-Nichols Method

Abstract

In various industrial and robotic applications, achieving high precision and stable control of DC servo motors is challenging due to parameter variations over time caused by aging and wear, which degrade performance. Existing controllers often suffer from high overshoot, long settling times, and inadequate steady-state accuracy. This study aims to develop and evaluate a second-order mathematical model and an optimized PID controller, tuned using the Ziegler-Nichols method, to improve the performance of an S-50-52 rotary DC servo motor in both open-loop and closed-loop configurations. The research presents a comprehensive comparison of proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controllers implemented on a second-order motor model, highlighting the advantages of PID control with Ziegler-Nichols tuning for precision motion control. The study begins with constructing a second-order dynamic model of the S-50-52 servo motor using its datasheet parameters. The PID parameters are tuned using both Ziegler-Nichols reaction curve and oscillation methods. The performance of P, PI, and PID controllers is evaluated via simulations in MATLAB/Simulink under open-loop and closed-loop conditions, analyzing key metrics like overshoot, rise time, settling time, and steady-state error. In the closed-loop system, the PID controller achieved an overshoot of 57.93%, undershoot of -2%, settling time of 2.33 ms, rise time of 6.73 µs, and steady-state output of 1.01 — demonstrating superior balance of speed, stability, and accuracy compared to P and PI controllers. The PID controller tuned by Ziegler-Nichols in a closed-loop system delivers optimal performance, combining fast response, lower overshoot, and high accuracy, making it the preferred choice for precision servo motor applications.