<![CDATA[Control systems are critical for managing, commanding, and regulating the behavior of dynamic systems. A DC motor converts direct current electrical energy into kinetic energy, requiring positive and negative voltage terminals for operation. Due to their ease of control across wide speed ranges, DC motors are widely applied in various industrial sectors. Speed regulation is typically achieved using control devices tailored to specific system requirements. To optimize DC motor performance, this study employs mathematical modeling and control strategies using MATLAB software. The 42D29Y401 DC motor is modeled and simulated using the Linear Quadratic Regulator (LQR) and Linear Quadratic Tracking (LQT) methods. Simulation results show that the first-order DC motor achieved a stable step response with an amplitude of 3.40, a rise time of 3.11 seconds, and minor overshoot and undershoot values of 0.501% and 1.98%, respectively. The LQR-optimized system improved performance with an amplitude close to 1, a faster rise time of 1.1 seconds, and reduced overshoot and undershoot at 0.505%. Comparatively, the LQR-based system demonstrated better overall performance than the unoptimized model, while the LQT-based system yielded the highest level of performance among all configurations.]]>
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