A nonlinear aircraft model is presented and used to develop an overall unified approach to online trim and maneuverability envelope estimation with uncertainty quantification without any requirement for active input excitation. The concept of time scale separation makes this method suitable for the adaptive characterization of altered safe maneuvering limitations based on aircraft performance after impairment. The results can be used to provide pilot feedback and/or be combined with flight planning, trajectory generation, and guidance algorithms to help maintain safe aircraft operations in both nominal and off-nominal scenarios.
Nomenclature
R nSet of real n-vectors S n , S n ++ Set of n × n symmetric matrices, Set of n × n positive definite symmetric matrices tr Trace operator, i.e., tr A is the sum of the diagonal elements ofEuclidean norm for vector inputs V, γ, χ True airspeed, flight path angle, course angle F T Magnitude of net thrust force produced by engines F L , F D , F Y Magnitude of lift, drag, and side forces f Continuous dynamics model x, x State vector, Collection of state observations u, u Virtual input vector, Collection of virtual input observations B Set of allowable or achievable states and input vectors x Average current and next state, i.e.,x(Angle of attack, Side-slip angle, Roll angle g, m, S Acceleration due to gravity, Mass of the aircraft, Surface area of the aircraft wings ρ,qAir density, Dynamic pressure (q = ρV 2 /2) N (μ, Σ)Multivariate normal distribution with mean μ and covariance matrix Σ.
p(x|y)Probability density function for the variable x given y L i , D j , Y k Expansion coefficients for the non-dimensional coefficient of lift, drag, and side force c Aerodynamic coefficient parameter vector, e.