Analysis of Optimal Control Using the Linear Quadratic Regulator (LQR) Method in DC Motors: Relevance to Community Engagement Programs

Abstract

DC motors are indispensable across various industrial sectors due to their numerous advantages, including high torque output, absence of reactive power losses, non-disruptive impact on electrical supply harmonics, and superior control accuracy. In the realm of technological advancement, automatic control systems play a pivotal role in ensuring operational efficiency. A robust control system must adhere to predefined criteria, particularly those related to performance indices such as accuracy, stability, and response speed. Optimal control systems are designed based on the principle of performance index optimization, ensuring that system parameters are configured to achieve maximum or minimum values of desired operational metrics. In the context of DC motor speed regulation, the Linear Quadratic Regulator (LQR) optimal control technique offers a sophisticated approach by optimizing the performance index through precise calibration of the Q matrix. This process generates the K feedback amplifier matrix and the optimal L tracking matrix, which collectively enhance the motor's performance. This research emphasizes the integration of LQR in community engagement programs, demonstrating its potential for application in renewable energy systems, such as solar-powered water pumps or automated machinery for local industries. By bridging technical innovation with societal needs, the study highlights the role of advanced control techniques in fostering sustainable development and improving the quality of life in underserved communities.