Dynamic Stability Analysis of Aircraft Flight in Deep Stall

Cunis, Torbjørn; Condomines, Jean-Philippe; Burlion, Laurent; Cour-Harbo, Anders la

doi:10.2514/1.c035455

Cited by 11 publications

(14 citation statements)

References 25 publications

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“…The elevator deflection η is, by convention, negative when causing a positive pitching moment. The linear damping coefficient kq q accounts for non-static aerodynamics (see [21]).…”

Section: A Equations Of Motionmentioning

confidence: 99%

“…In [21], we applied bifurcation theory as well as optimization techniques to derive the linear pitch-damping model in Eq. (3).…”

Section: Preliminary Stability Analysismentioning

confidence: 99%

“…Remark In [18], analysis of a six-state polynomial aircraft model has been considered, omitting inter alia the aircraft's speed from the state vector. Since deep-stall transition maneuvers span a large range of airspeeds [21], this approach would not be applicable here. Instead, we restrict this study to the four-state longitudinal motion (later, we will include the elevator deflection as a fifth state); however, as we consider piecewise-defined polynomial equations of motion of higher order, this model is in fact more complex than [18].…”

Section: Region Of Attraction At Trim Pointmentioning

confidence: 99%

“…for all 1 ≤ i ≤ k. As the degree of P is predefined, the equality constraints in (21) are linear in the decision variables (the coefficients of P).…”

Section: Computing Quasi-ellipsoids With Sosmentioning

confidence: 99%

“…In this article, we synthesize controllers for and verify deep-stall recovery of a small unmanned aircraft using SOS programming and a piecewise, 5th-order polynomial model. The choice of aircraft, a fixed-wing capable of stable deep-stall transition, descent, and recovery [21], allows us to isolate longitudinal dynamics.…”

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confidence: 99%

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Sum-of-Squares Flight Control Synthesis for Deep-Stall Recovery

Cunis

Condomines

Burlion

2020

Journal of Guidance, Control, and Dynamics

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Certification of inflight loss-of-control recovery is complicated by the highly nonlinear flight dynamics beyond stall. In lieu of extensive Monte-Carlo simulations for flight control certification, sum-of-squares programming techniques provide an algebraic approach to the problem of nonlinear control synthesis and analysis. However, reliance on polynomial models has hitherto limited applicability to aeronautical control problems. Taking advantage of recently proposed piecewise polynomial models, this paper revisits sum-of-squares techniques for recovery of an aircraft from deep-stall conditions using a realistic yet tractable aerodynamic model. Local stability analysis of classical controllers is presented as well as synthesis of polynomial feedback laws with the objective of enlarging their nonlinear region of attraction. A newly developed synthesis algorithm for infinite-horizon backwards-reachability facilitates the design of recovery control laws, ensuring stable recovery by design. The paper's results motivate future research in aeronautical sum-of-squares applications. Nomenclature α Angle of attack (rad); α 0 Low-angle of attack boundary (α 0 = 16.2949°); γ A Flight-path angle relative to air (rad); η Elevator deflection (rad), negative if leading to positive pitch moment;

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“…The elevator deflection η is, by convention, negative when causing a positive pitching moment. The linear damping coefficient kq q accounts for non-static aerodynamics (see [21]).…”

Section: A Equations Of Motionmentioning

confidence: 99%

“…In [21], we applied bifurcation theory as well as optimization techniques to derive the linear pitch-damping model in Eq. (3).…”

Section: Preliminary Stability Analysismentioning

confidence: 99%

Section: Region Of Attraction At Trim Pointmentioning

confidence: 99%

“…for all 1 ≤ i ≤ k. As the degree of P is predefined, the equality constraints in (21) are linear in the decision variables (the coefficients of P).…”

Section: Computing Quasi-ellipsoids With Sosmentioning

confidence: 99%

mentioning

confidence: 99%

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Sum-of-Squares Flight Control Synthesis for Deep-Stall Recovery

Cunis

Condomines

Burlion

2020

Journal of Guidance, Control, and Dynamics

Self Cite

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Analysing dynamic deep stall recovery using a nonlinear frequency approach

2022

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Based on bifurcation theory, nonlinear frequency response analysis is a recent development in the field of flight dynamics studies. Here, we consider how this method can be used to inform us on how to devise the control input such that the system transitions from an undesirable equilibrium solution—an aircraft deep stall solution in our case—to a desirable solution. We show that it is still possible to induce a large-amplitude oscillation via harmonic forcing of the pitch control device and escape the otherwise unrecoverable deep stall, despite very little control power available in such a high angle-of-attack flight condition. The forcing frequencies that excite these resonances are reflected as asymptotically unstable solutions using bifurcation analysis and Floquet theory. Due to the softening behaviour observed in the frequency response, these unstable (divergent) solutions have slightly lower frequencies than the value predicted using linear analysis. Subharmonic resonances are also detected, which are reflected in the time-domain unforced responses. These nonlinear phenomena show strong dependency on the forcing/perturbation amplitude and result in complex dynamics that can impede recovery if the existing procedures are followed. The proposed method is shown to be a useful tool for nonlinear flight dynamics analysis as well as to complement the rather thin literature on deep stall analysis—a topic of relevance for recent research on unconventional landing techniques in unmanned aerial vehicles. A full description of the aircraft model used, the unstable F-16 fighter jet, is provided in the appendix.

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Investigation of longitudinal stability analysis of general aviation aircraft by phase plane method

Yan,

Tu,

et al. 2024

Nonlinear Dyn

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Dynamic Stability Analysis of Aircraft Flight in Deep Stall

Cited by 11 publications

References 25 publications

Sum-of-Squares Flight Control Synthesis for Deep-Stall Recovery

Sum-of-Squares Flight Control Synthesis for Deep-Stall Recovery

Analysing dynamic deep stall recovery using a nonlinear frequency approach

Investigation of longitudinal stability analysis of general aviation aircraft by phase plane method

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