Modeling and Bifurcation Analysis of Longitudinal Dynamics of an Air-Breathing Hypersonic Vehicle

TL;DR

The paper addresses the nonlinear longitudinal dynamics of an Air-Breathing Hypersonic Vehicle (ABHV) with coupling between propulsion and aerodynamics. It employs a four-state model with continuation-based bifurcation analysis using AUTO-07p to map steady-states as control parameters ($\delta_e$ and $\phi$) vary, identifying stability boundaries and bifurcations such as LP, BP, and Hopf, including transitions to limit cycles. Four case studies illustrate pervasive open-loop instability, with fold and Hopf bifurcations and level-flight Pareto-fronts revealed through Extended Bifurcation Analysis (EBA). Time-domain simulations corroborate the bifurcation results, underscoring the need for stability augmentation and guiding future closed-loop ABHV dynamics research.

Abstract

A nonlinear model of an Air-Breathing Hypersonic Vehicle (ABHV) longitudinal dynamics characterized by coupling of aerodynamic and propulsive terms is presented in this paper. The model is verified using modal analysis carried out around a design operating condition with results available in the literature. Further, parametric dynamic behavior is computed for the model as steady states with local stability with respect to its control inputs, elevator and fuel-equivalence ratio in four different cases using a numerical continuation algorithm. Detailed analysis of the qualitative longitudinal dynamics of the model is carried out based on bifurcation theory methodology. Numerical simulation results are presented to verify bifurcation analysis results.

Figures (14)

• Figure 1: Hypersonic Air-Breathing Vehicle Geometry2007bolender_nonlinear.
• Figure 2: Scramjet Cross-section2007bolender_nonlinear.
• Figure 3: Aerodynamic coefficients at three elevator settings and thrust variation for different values of angle of attack ($-5,0,5~\mathrm{deg}$).
• Figure 4: Total pitching moment coefficient consisting both aerodynamic and thrust components.
• Figure 5: (a) Pole/transmission zero maps of the Jacobian linearization of ABHV, (b) Open-loop time simulation around the nominal condition.