Comparative Analysis of PID and LQR Controllers for Speed Regulation of Series DC Motors

Abstract

A DC motor is a widely used electromechanical device known for its ease of application and versatile speed regulation capabilities, making it essential in various industries, robotics, and household appliances. Among different types of DC motors, the series DC motor is noted for its high starting torque, which can cause significant overshoot at startup. Moreover, this motor exhibits inherent instability, with speed decreasing at higher torques and increasing under low loads, potentially reaching very high speeds in no-load conditions. In order to achieve precise speed control and mitigate overshoot, the implementation of an effective control system is crucial. This study presents a comparative simulation analysis, conducted using MATLAB, between two widely used controllers: PID (Proportional-Integral-Derivative) and LQR (Linear Quadratic Regulator), for regulating the speed of a series DC motor. The results demonstrate that both controllers achieve minimal errors, with the PID controller delivering a faster rotor speed response compared to the LQR controller. However, the PID controller exhibits a notable overshoot of approximately 20%, while the LQR controller successfully eliminates any overshoot. Additionally, the initial current surge observed with the PID controller is significantly higher than with the LQR controller, with the PID's starting current overshoot reaching about 460%, compared to only 188% for the LQR.