The rapid advancement of telecommunications has significantly influenced various engineering applications, including control systems for electrical and mechanical systems. One crucial aspect of control system design is ensuring signal integrity and stability, particularly in Single-Input Single-Output (SISO) circuits. In this study, we analyze the performance of a DC motor within a SISO circuit using Linear Quadratic Regulator (LQR) and Linear Quadratic Tracking (LQT) control methods. The research employs a simulation-based approach, evaluating first-order and second-order system responses under different conditions, including scenarios with and without external noise interference. Experimental results indicate that each control approach exhibits distinct dynamic characteristics, influencing system stability, response time, and noise suppression capability. The presence of noise significantly affects system behavior, leading to deviations from the desired set point. An optimal control circuit is defined by minimal ripple, rapid convergence to the set point, and robustness against disturbances. Comparative analysis highlights that LQR and LQT methods offer significant improvements in trajectory tracking and system optimization, with LQT providing enhanced adaptability in the presence of external perturbations. This study contributes to the field of control engineering and automation by offering insights into the optimization of DC motor control in SISO circuits, with potential applications in robotics, industrial automation, and power electronics.