Robustness Analysis Applied to Autopilot Design, Part 1: mu-Analysis of Design Entries to a Robust Flight Control Benchmark

mu-Analysis is a powerful tool for the assessment of the stability of uncertain parametric systems by means of the Structured Singular Value µ. The peak upper bound value of µ over a frequency range provides information on the stability margin of a system for given variations of uncertain parameters, while the computed lower bound on µ allows to obtain worst-case parameter combinations destabilizing the system. The applicability of µ-analysis is however conditioned by the availability of adequate uncertainty models based on Linear Fractional Transformations (LFTs). For complex systems, like aircraft models, LFT modeling is a very demanding and time-consuming task. In this paper we present the generation of an LFT-based uncertainty model for a civil aircraft, starting from a nonlinear dynamic model with explicit parametric dependencies. This nonlinear model was the basis for the design of twelve different flight controllers according to identical specifications. We applied µ-analysis for stability robustness assessment of the twelve control configurations to uncertainties in the aircraft mass, the center of gravity location, and the on-line computational time delay. We determined the corresponding stability margins and the worst-case destabilizing parameter combinations. We used nonlinear simulations to validate our results.