Optimal DC Motor Speed Control Comparison

The study compares the Linear Quadratic Tracking (LQT) controller with other widely used control strategies, including Proportional-integral-derivative (PID) and Linear Quadratic Regulator (LQR) controllers for optimal speed control of DC motors, focusing on its effectiveness in maintaining precise motor shaft rotation. The DC motor and controllers are tested in the MATLAB software in terms of standard performance metrics such as Steady-state Error (SSE), Rise Time (Tr), Settling Time (Ts), Overshoot (OS), Control Input Saturation, Integral of Absolute Error (IAE), Integral of Squared Error (ISE), Integral of Time-weighted Absolute Error (ITAE), and Control Effort. The results indicate that the LQT controller provides comparable performance, achieving near zero SSE, minimal overshoot, moderate rise and settling times, and efficient control effort. Although the PID controller provides the fastest response time, it is less suitable for applications that require stability and efficiency due to its significant overshoot and high control effort. The LQR controller, while highly energy-efficient, offers slower response times and incurs a slightly higher $S S E$, making it ideal for energy-conservation-focused applications. In contrast, the LQT controller exhibits a well-balanced performance in multiple measures, excelling in processing step input signals with zero error.