Time-Delay Margin Analysis for an Adaptive Controller

Adaptive control has the potential to improve performance and reliability in aircraft systems. 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 article addresses the application of nonlinear robustness analysis tools to an adaptive flight control system. First, a model reference adaptive controller is derived for a linear aircraft short-period model. The resulting closed-loop system is nonlinear and governed by polynomial dynamics. Sum-of-squares polynomial optimization is applied to the closed-loop system 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 parametric model uncertainty.