Hybrid Adaptive Anti-Windup PID Control for UAV Altitude Regulation Under Actuator Saturation: A Monte Carlo and Statistical Performance Evaluation

Abstract

This study develops a Hybrid Adaptive Anti-Windup PID controller for altitude regulation of a three-degree-of-freedom (3-DOF) Uncrewed Aerial Vehicle (UAV) operating under actuator saturation constraints. The proposed architecture continuously adjusts the anti-windup compensation based on the instantaneous severity of actuator limiting via a saturation-dependent adaptive weighting mechanism. The controller is evaluated against No Anti-Windup, Back-Calculation, and Conditional Integration strategies using Monte Carlo simulations comprising 50 independent runs for each of six challenging operating scenarios, including wind disturbances, payload variations, increased aerodynamic drag, large reference commands, and combined disturbances. Performance is assessed using Integral Absolute Error (IAE), overshoot, settling time, actuator saturation, and statistical measures. Across the evaluated scenarios, the Hybrid Adaptive strategy achieves IAE reductions of 58–65%, overshoot reductions of 80–88%, actuator-saturation reductions of 50–60%, and settling-time reductions of 28–35% relative to the No Anti-Windup baseline. The corresponding average reductions are 61.5%, 83.8%, 55.2%, and 30.7%, respectively. Analysis of variance (ANOVA) indicates statistically significant differences among the evaluated control strategies for all scenarios ((p<0.001)). At the same time, eta-squared effect sizes range from 0.58 to 0.75, with an overall mean of 0.68, indicating substantial practical effects. A Lyapunov-based convergence analysis is also formulated to provide a theoretical assessment of the closed-loop behavior under actuator constraints. The results further demonstrate effective altitude regulation under wind disturbances and positive actuator margins across the tested operating conditions. However, performance becomes more demanding under increased payload and reduced control authority. Overall, the findings indicate that saturation-dependent anti-windup compensation can improve tracking accuracy, transient recovery, disturbance rejection, and actuator utilization while retaining a relatively simple PID-based control structure. Future work will address experimental validation, parameter-sensitivity analysis, comparison with modern constrained-control approaches, and extension to a full 6-DOF UAV model.