The objective of the research was to design and simulate the lateral/directional dynamics control of an aircraft’s autopilot system to automate the landing approach execution, complying with the requirements of the Instrument Landing System (CAT III C). The design methodology involved integrating a Linear Quadratic Regulator (LQR) with Affine Parameterization techniques to create a robust control system. The prototype was developed using Matlab and simulated in Simulink. Through various simulations, adjustments were made to the Q and R matrices of the LQR controller based on Bryson’s rule, allowing the system to adapt to the nonlinearities and dynamic constraints of the aircraft model. These adjustments included modifying the lateral attitude control parameters to achieve the desired damping factors and time constants, ensuring flight quality standards according to MIL-8785C. Validation under real conditions through a flight simulator confirmed the control system’s effectiveness under various operational conditions. The controllers are able to maintain the aircraft’s alignment with the runway centerline, even in the presence of external disturbances, thus demonstrating the system’s robustness and reliability. The methodologies and results provide a solid foundation for future improvements and comparative analyses of autopilot systems within CAT III C requirements.