Bifurcation Analysis of the Generic Transport Model with a view to Upset Recovery

Abstract

There is a trend developing in research focusing on commercial aircraft safety, especially with respect to upset recovery and loss-of-control. In seeking to address the upset recovery problem from a control perspective and owing to the fact that upsets involve flight outside the regular flight envelope, the requirement for a wide-envelope non-linear model arises, along with the requirement for non-linear analysis techniques. These needs are addressed by NASA's Generic Transport Model (GTM) and bifurcation theory respectively, with the latter having been used extensively in the analysis of non-linear flight dynamics of military aircraft operating in broad flight envelopes. This paper focuses on the application of bifurcation theory to the GTM and includes an analysis of the initial results thereof. It covers the difficulties involved in combining the two tools, especially the changes that need to be made to the GTM simulation in order to make it compatible with the mathematics performed in bifurcation analysis. Bifurcation theory is applied primarily to the longitudinal dynamics of the aircraft to investigate the effects of the aircraft elevator and throttle on the aircraft behaviour. The results agree with other research that suggests the classical role these controls play in established upset recovery doctrine is effective, but often not correctly executed. The paper also investigates the coupling between the longitudinal and lateral dynamics of the aircraft, highlighting how aerodynamic stall negatively affects the lateral dynamics. NomenclatureGTM Generic Transport Model LOC Loss-of-Control UAV Unmanned Aerial Vehicle FTC Fault Tolerant Control V velocity magnitude α angle of attack β sideslip angle P x body-axis relative angular rate Q y body-axis relative angular rate R z body-axis relative angular rate Φ Euler 321 roll attitude angle Θ Euler 321 pitch attitude angle Ψ Euler 321 yaw attitude angle δ e absolute elevator deflection angle δ a absolute aileron deflection angle δ r absolute rudder deflection angle δ t absolute throttle percentage * PhD Student, Department of Electrical and Electronic Engineering, sjpauck@sun.ac.za. † Senior Lecturer, Department of Electrical and Electronic Engineering, jengelbr@sun.ac.za, AIAA Senior Member.

Bifurcation Flight Dynamic Analysis of a Strake-Wing Micro Aerial Vehicle

“…Given the experience from numerous research (based on the bifurcation analysis and continuation technique), the following, three-stage test diagram for a non-linear aircraft motion was formulated [8][9][10][11][12][13][14]18,[21][22][23][24][25][26][27][28]34,48,49,[51][52][53][54][55][56] 1.…”

Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective

“…This simulation tool of the sub-scale aircraft is known the Generic Transport Model (GTM), and it has been used extensively in upset/LOC studies. The recent application of bifurcation analysis to the open-loop GTM [30,31] has provided an enhanced understanding of its upset/LOC behaviour: the resulting bifurcation diagrams are essentially a 'map' of the vehicle's various nonlinear responses. Figure 4 shows an example of a one-parameter bifurcation diagram of the GTM, where the continuation parameter is elevator angle δ e , with all other parameters fixed, and the solution is represented by the bank angle state φ.…”

Upset Dynamics of an Airliner Model: A Nonlinear Bifurcation Analysis

“…In this paper, as part of recent initiatives to apply this technique to the open-loop GTM behaviour [30,31,36], we present the application of bifurcation analysis to an eighth-order version of the NASA GTM to build an understanding of the underlying flight mechanics. The work identifies possible upset scenarios and, moreover, provides a deeper insight into the complex interactions that govern upset.…”

“…In Ref. [30], bifurcation analysis was used to classify the different types of behaviour of the open-loop GTM; both elevator and throttle variations were considered, however no specific upset scenarios were discussed. Using these bifurcation diagrams a sequential upset recovery strategy was developed in [31].…”