Time Delay Margin Analysis Applied to Model Reference Adaptive Control

Adaptive control has the potential to improve performance and reliability in aircraft. Implementation of adaptive control on commercial and military aircraft requires verification and validation of the control system’s robustness to modeling error, uncertainty, and time delay. Currently, there is a lack of tools available to rigorously analyze the robustness of adaptive controllers due to their inherently nonlinear dynamics. This paper addresses the use of nonlinear robustness analysis for adaptive flight control systems. First, a model reference adaptive controller (MRAC) is derived for a linear aircraft short-period model. Sum-of-squares (SOS) polynomial optimization is applied to the closed-loop model to assess its robustness to time delay. Time delay margins are computed for various combinations of design parameters in the adaptive law, as well as in the presence of model uncertainty. This paper extends and refines previous work through the implementation of more advanced polynomial optimization algorithms and analysis conditions.