Quantifying the robustness of flight control systems using Nichols exclusion regions and the structured singular value

Abstract

This paper establishes some connections between classical stability metrics currently used in the aerospace industry for the certification of flight control laws and modern tools for the robustness analysis of uncertain multivariable systems. Multiloop simultaneous gain and phase margin robustness specifications are written as Nichols plane exclusion regions for the open-loop frequency response of each loop of the system. Satisfaction of these robustness specifications for uncertain multivariable systems is then shown to be exactly equivalent to satisfying a certain bound on the structured singular value μ of the closed-loop system. The proposed tools are applied to the problem of analysing the robustness of an integrated flight and propulsion control system for a future V/STOL aircraft concept subject to variations in aircraft mass and centre of gravity. In particular, the implications for the proposed method of difficulties in computing tight bounds on μ are considered.