Adaptive PID control for stability enhancement of tilt-tri-rotor vertical take-off and landing of unmanned aerial vehicles

Abstract Tilt-tri-rotor (TTR) VTOL unmanned aerial vehicles demand precise, robust control across takeoff, hover, and transition phases regimes where conventional fixed-gain PID controllers critically fail under parametric variations and external disturbances. To overcome this fundamental limitation, this work proposes an Adaptive Fuzzy-Gain-Scheduled PID (AFGS-PID) controller employing a Mamdani fuzzy inference engine for real-time gain adaptation across roll, pitch, yaw, and altitude channels. Benchmarked against a genetic-algorithm-tuned PID in MATLAB/Simulink, the AFGS-PID delivers 34.7 % faster settling, 61.2 % lower overshoot, 88.9 % steady-state error reduction, and 67.6 % superior wind-gust rejection, with frequency margins improved by +3.3 dB and +16.2°. Closed-loop stability is rigorously established via Lyapunov analysis, elevating this beyond empirical tuning to a formally verified intelligent control framework. This study delivers the first four-channel AFGS-PID design with Lyapunov stability proof for TTR VTOL platforms, providing a formally verified intelligent control architecture for aerospace deployment.