Use of Bifurcation and Continuation Methods for Aircraft Trim and Stability Analysis - A State-of-the-Art

Abstract

The bifurcation and continuation methodology has evolved over the last two decades into a powerful tool for the analysis of trim and stability problems in aircraft flight dynamics. Over the years, bifurcation methods have been employed to deal with a variety of problems in aircraft dynamics, such as predicting high angle of attack behavior, especially spin, and studying instabilities in rolling maneuvers. The bifurcation methodology has served as a tool for the design of flight control systems, and is promising to be a useful tool in the aircraft design, simulation, testing, and evaluation process. In the present paper, we describe the state-of-the-art in the use of bifurcation and continuation methods for the analysis of aircraft trim and stability with a few illustrative examples. Both the standard and extended bifurcation analysis procedures are discussed and typical results for instabilities in high-α flight and in inertia-coupled roll maneuvers are shown. This is followed by several problems in nonlinear flight dynamics where bifurcation and continuation methods have been fruitfully applied to yield effective solutions. Finally, the use of bifurcation theory to arrive at analytical instability criteria is demonstrated for the aircraft roll coupling and wing rock problems. 76 references have been cited in the text.

Flight mechanics of a tailless articulated wing aircraft

“…The aerodynamic forces on the aircraft wings and the horizontal tail are modelled using strip theory with aerodynamic data from Dickinson, Lehmann and Sane [13]. Bifurcation analysis [14] is used to study the performance and stability of a six degree-of-freedom aircraft model which incorporates the effect of dynamic CG location as a function of the aircraft geometry. Performance metrics of interest are (a) trim angle of attack, velocity, and flight path angle for longitudinal flight assessment, and (b) sideslip angle and turn rate for the lateral motion.…”

“…Performance metrics of interest are (a) trim angle of attack, velocity, and flight path angle for longitudinal flight assessment, and (b) sideslip angle and turn rate for the lateral motion. Co-ordinated turns are analysed using a modified version of the constrained bifurcation analysis [14].…”

“…In this case, the aircraft performs a steady coordinated turn. to analyse a turning maneuver, a simplified version of constrained bifurcation analysis (CBA) [14] is employed. In CBA, constraint equations are added to the ordinary differential equations and the corresponding control parameters are "freed," i.e., treated as state variables.…”

Dynamics and Performance of Tailless Micro Aerial Vehicle with Flexible Articulated Wings

“…A bifurcation analysis [26] of turning flight is performed assuming quasi-statically deformed wings to identify the nature of the instabilities, and the performance and control deflections are compared with those of a rigid winged aircraft. Bifurcation analysis of turning flight demonstrates two salient features of a flexible winged aircraft.…”

Upset Dynamics of an Airliner Model: A Nonlinear Bifurcation Analysis

“…Full bifurcation analysis of civil airliner flight dynamics models is not common practice, although the same approach has been successfully applied to open loop military aircraft models [16][17][18][19][20] and to augmented aircraft dynamics [21][22][23][24]. An overview of flight dynamics applications can be found in [25][26][27]. Bifurcation analysis has already been applied to the GTM in [28,29]; where a rigorous assessment of the ability to control and regulate an aircraft around bifurcations is provided, with a focus on loss-of-control; the controllability and observability of a closed-loop GTM model is studied, leading to the definition of safe sets in which the aircraft can be positively controlled.…”