Quadcopters are widely used in modern applications; however, maintaining a stable hover and accurate path following remains challenging owing to their nonlinear dynamics. In this study, an efficient simulation-based control framework was developed, in which a nonlinear model was derived using the Newton–Euler method and subsequently linearized via feedback linearization. In MATLAB/Simulink, two proportional–integral–derivative tuning methods—manual tuning and a genetic algorithm (GA) with a population size of 30 and up to 30 generations—were employed to design the controller. Manual tuning achieved an integral square error (ISE) value of 0.03316, whereas the GA-based approach generated an ISE of 0.030056, corresponding to an average improvement of 13.9%. Furthermore, the GA-based tuning produced a smoother system response with reduced overshoot, thereby enhancing the quadcopter stability and trajectory tracking and contributing to more reliable real-world flight performance.