An Adaptive Nonlinear Aircraft Maneuvering Envelope Estimation Approach for Online Applications

Abstract

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.

Flight Safety Assessment and Management for Takeoff Using Deterministic Moore Machines

“…McDonough et al [10], McDonough and Kolmanovsky [23], and Lombaerts et al [24,25] proposed methods to estimate degrading envelope constraints under conditions such as icing. Yu et al [11] and Schuet et al [26] developed system identification techniques to estimate the dynamics of an aircraft following adverse onboard conditions. Information from these systems can be used by FSAM to make efficient decisions to prevent catastrophes.…”

Effects of Structural Failure on the Safe Flight Envelope of Aircraft

“…The estimation of safe flight envelope as a reachability set problem has been researched in the recent past [12,14,20,21,25]. This approach with uncertainty quantification and robustness in the estimated values of aerodynamic derivatives is also discussed in detail [26,27]. The idea is to observe the dynamic behavior of the trim states as they evolve over a certain time horizon T i.e., reachability from the trim envelope.…”

Envelope-Aware Flight Management for Loss of Control Prevention Given Rudder Jam

“…A safe set O ∞ is the set of aircraft initial states for which the nominal closedloop response does not violate the imposed constraints. The literature on computing safe sets and closely related forward and backward reachable sets for constrained aircraft dynamics is extensive; for example, see [22][23][24][25][26][27][28][29] and references therein. Many of the existing approaches exploit nonlinear models and require extensive computations to solve partial differential equations.…”

“…Many of the existing approaches exploit nonlinear models and require extensive computations to solve partial differential equations. Consequently, their onboard use for scenarios in which aircraft models must be identified online may be infeasible unless significant simplifications are made and short horizons are assumed [25]. Because the EA-FMS relies on identified linearized models, information about changes in parameters, such as C D0 and C L0 , that impact the global flight envelope can be inferred from identified models [11].…”