Comparing Linear Quadratic Regulator (LQR) with Proportional-Integral-Derivative (PID) Controllers for Increasing Stability in DC Motor Systems

Abstract

A DC motor is a versatile type of motor widely applied in industries, robotics, and household appliances due to its broad speed regulation range and ease of integration. Among the various types of DC motors, the series DC motor stands out for its high starting torque. However, this characteristic also leads to significant challenges, including overshooting during initial start-up and instability under varying load conditions. For instance, at high torque, the motor’s speed tends to decrease, while at low torque or no-load conditions, it often produces excessively high speeds. To address these issues and achieve accurate speed regulation with stable final results, a robust control strategy is required. Controllers play a pivotal role in minimizing overshoot and ensuring stability in motor performance. This research investigates the performance of two control methodologies—Proportional-Integral-Derivative (PID) and Linear Quadratic Regulator (LQR)—through MATLAB-based simulations for regulating the speed of a series DC motor. In this study, motor speed is analyzed to evaluate the effectiveness of the controllers. The simulation results reveal that both PID and LQR controllers achieve minimal error rates. However, there are notable differences in their dynamic response. The PID controller demonstrates a faster rotor speed response time compared to the LQR controller. Nonetheless, the PID controller exhibits a significant overshoot of approximately 20%, whereas the LQR controller effectively eliminates overshoot altogether. This study contributes to the growing body of knowledge in control systems engineering, particularly in evaluating advanced controllers for industrial applications.