Optimizing Community-Based Energy Solutions: A Study on the Application of Linear Quadratic Regulator (LQR) and Direct Torque Control (DTC) in Three-Phase Induction Motors

Abstract

This study explores the development of a method for controlling the speed of three-phase induction motors using Linear Quadratic Regulator (LQR) and Direct Torque Control (DTC). By combining LQR and DTC, this method enables direct control of torque and stator flux, which plays a crucial role in optimizing energy systems for community-based applications. The rotor speed, torque, and flux are estimated using DTC, with input provided from stator voltage and current. The motor’s speed is compared to a reference speed, generating an error, which, along with the speed change rate (delta error), serves as input for the LQR controller. Simulation results demonstrate rapid speed response under startup conditions, load changes, and setpoint variations, highlighting the robustness of the control system in real-world applications, such as rural energy systems. During load change conditions, the speed response shows minimal deviation, ensuring stable operation even under disturbances. For a load torque of 30 N·m, the maximum overshoot is 4.6735%, with a peak time of 0.007 seconds and a settling time of 0.111 seconds. The motor speed errors for reference speeds of 1450 rpm, 725 rpm, 725 rpm, and 362.5 rpm are 0.03%, 0.03%, 0.08%, and 0.027%, respectively, compared to the actual motor speed. This research contributes to the development of efficient, low-cost energy solutions that could be adapted for community-based projects, particularly in rural and underserved areas, helping to optimize local power generation and distribution systems for sustainable development.