Finite-Horizon Robustness Analysis of an Automatic Landing System Under Probabilistic Uncertainty

Abstract

This paper demonstrates the utility of novel probabilistic robustness analysis tools on an industry-sized autolanding system of a civil transport aircraft. The closed-loop aircraft model is representative of an Airbus A330 during final approach and landing. It is modeled as a linear time-varying system by linearizing with respect to a nominal reference trajectory. Disturbances due to random parametric uncertainty, atmospheric turbulence, and static wind shear are considered. Probabilistic uncertainty in the aerodynamic coefficients and mass parameters is quantified efficiently by applying a polynomial chaos series expansion. This generalized Fourier series is applied after employing a linear fractional transformation. The computational benefits of expanding uncertain interconnections in linear fractional representation build an appealing advantage of the applied analysis methods. Probabilistic and worst-case perturbations around the reference trajectory are quantified. The analysis results are compared with nonlinear Monte Carlo simulations of the complete closed-loop system.