Time-Delay Margin Analysis for an Adaptive Controller

Adaptive control has the potential to improve the performance and reliability of aircraft systems. Implementation of adaptive control on commercial and military aircraft requires the flight control system to be verified and validated with respect 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. Newly proposed nonlinear robustness analysis tools are applied to adaptive flight control in this paper. A standard model reference adaptive controller with sigma modification is designed for a linear short-period aircraft model. The resulting nonlinear closed-loop system is governed by polynomial dynamics. The nonlinear analysis algorithms rely on sum-of-squares polynomial optimization to assess the robustness of the adaptive closed-loop system with respect to a time delay. Time-delay margins are computed for various combinations of design parameters in the adaptive control law, as well as in the presence of parametric model uncertainty. Advantages and limitations of the proposed sum-of-squares-based robustness analysis are presented. Analysis results show a significant promise in the context of recent development in nonlinear robustness analysis.