Optimal Control of the 40 Volt EC MAX-40 DC Motor Using Linear Quadratic Regulator (LQR) and Linear Quadratic Tracking (LQT) Approaches

Abstract

Direct current (DC) motors have been an integral part of technological developments for more than a century. Although induction motors or AC Shunt Motors have dominated a wide range of modern applications, DC motors remain the top choice in systems that require high-precision control, such as servo motors. DC motors require direct current (DC) voltage to operate, and their wide use in daily life, both for industrial and household applications, demands efficient control of speed and angular position. In an effort to improve the stability and performance of DC motors, this study explores the application of the Linear Quadratic Regulator (LQR) and Linear Quadratic Tracking (LQT) methods. The LQR method is designed to optimize system response by minimizing overshoot, undershoot, and settling time, so as to efficiently approach the desired setpoint. Meanwhile, LQT provides dynamic tracking capabilities against variable references, making it ideal for systems with high adaptability needs. This approach leverages the optimal controller properties of LQR and LQT, offering resistance to external interference, reliability in a wide range of operating conditions, and optimal static gain. The LQR/LQT technique is applied by minimizing the predefined cost function using a linear squared performance index, which allows multi-output control to be carried out efficiently, economically, and accurately on large-scale systems. The results of this research are expected to make a significant contribution to the development of DC motor control technology, especially for applications that require high stability and precision.