Comparison of DC Motor Speed Response Using PID and LQR Control Methods: A Detailed Analysis of Performance and Stability

Abstract

DC motors are widely used in various applications, such as industry, robotics, and home appliances, due to their ease of use and broad speed control range. Among different types of DC motors, series DC motors are known for their high starting torque, which often leads to significant overshoot during startup. Additionally, series DC motors tend to be less stable, with speed variations influenced by torque fluctuations; they slow down under high torque and speed up during idle conditions. To achieve stable speed control and minimize overshoot, the use of an appropriate controller is essential. This paper presents a detailed comparative analysis of two control strategies—PID (Proportional-Integral-Derivative) and LQR (Linear-Quadratic Regulator)—for controlling the speed of a series DC motor. A simulation was conducted using MATLAB, with the motor speed controlled across four different speed setpoints. The results demonstrate that both controllers lead to minimal speed errors, with the PID controller offering faster rotor speed response times compared to LQR. However, while the PID controller exhibits some overshoot, the LQR controller effectively eliminates this issue. Additionally, the PID controller results in higher starting current compared to the LQR controller.