Theory of wing rock

Hsu, C.-H.; Lan, C. E.

doi:10.2514/6.1985-199

Cited by 15 publications

(11 citation statements)

References 3 publications

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“…Typically delta wings with leading‐edge sweeps greater than

76^{\circ}

are known to exhibit wing rock, which is a limit cycling oscillation in roll angle and roll rate or unstable behaviour [30, 31]. For an

80^{\circ}

slender delta, the wing rock motion is described by [30, 32]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \ddot{ϕ} = a_{1} + a_{2} ϕ + a_{3} \dot{ϕ} + a_{4} false| ϕ false| \dot{ϕ} + a_{5} false| \dot{ϕ} false| \dot{ϕ}, \end{matrix}

where

ϕ

is the roll angle,

a_{1}

\dots

a_{5}

are time‐varying coefficients depending on wing characteristics and aerodynamic parameters. Remark 7 The analytical expression of (46) has been derived and experimentally validated in [32].…”

Section: Application To Regulation Of Aircraft Wing Rockmentioning

confidence: 99%

“…For an

80^{\circ}

slender delta, the wing rock motion is described by [30, 32]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \ddot{ϕ} = a_{1} + a_{2} ϕ + a_{3} \dot{ϕ} + a_{4} false| ϕ false| \dot{ϕ} + a_{5} false| \dot{ϕ} false| \dot{ϕ}, \end{matrix}

where

ϕ

is the roll angle,

a_{1}

\dots

a_{5}

are time‐varying coefficients depending on wing characteristics and aerodynamic parameters. Remark 7 The analytical expression of (46) has been derived and experimentally validated in [32]. Concretely, the parameters

a_{i}

i = 1, \dots, 5

are given by

a_{i} = false(P U^{2} S B / 2 I_{x x} false) G_{i}

, where

P

is the density of air,

U

is the freestream velocity,

S

is the wing reference area,

B

is the wing span,

I_{x x}

is the mass moment of inertia, and the parameters

G_{i}

are non‐linear functions of AOA.…”

Section: Application To Regulation Of Aircraft Wing Rockmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive tracking control of uncertain switched non‐linear systems with application to aircraft wing rock

Huang

Zhang

2016

IET Control Theory & Applications

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“…Typically delta wings with leading‐edge sweeps greater than

76^{\circ}

are known to exhibit wing rock, which is a limit cycling oscillation in roll angle and roll rate or unstable behaviour [30, 31]. For an

80^{\circ}

slender delta, the wing rock motion is described by [30, 32]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \ddot{ϕ} = a_{1} + a_{2} ϕ + a_{3} \dot{ϕ} + a_{4} false| ϕ false| \dot{ϕ} + a_{5} false| \dot{ϕ} false| \dot{ϕ}, \end{matrix}

where

ϕ

is the roll angle,

a_{1}

\dots

a_{5}

are time‐varying coefficients depending on wing characteristics and aerodynamic parameters. Remark 7 The analytical expression of (46) has been derived and experimentally validated in [32].…”

Section: Application To Regulation Of Aircraft Wing Rockmentioning

confidence: 99%

“…For an

80^{\circ}

slender delta, the wing rock motion is described by [30, 32]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \ddot{ϕ} = a_{1} + a_{2} ϕ + a_{3} \dot{ϕ} + a_{4} false| ϕ false| \dot{ϕ} + a_{5} false| \dot{ϕ} false| \dot{ϕ}, \end{matrix}

where

ϕ

is the roll angle,

a_{1}

\dots

a_{5}

a_{i}

i = 1, \dots, 5

are given by

a_{i} = false(P U^{2} S B / 2 I_{x x} false) G_{i}

, where

P

is the density of air,

U

is the freestream velocity,

S

is the wing reference area,

B

is the wing span,

I_{x x}

is the mass moment of inertia, and the parameters

G_{i}

are non‐linear functions of AOA.…”

Section: Application To Regulation Of Aircraft Wing Rockmentioning

confidence: 99%

Adaptive tracking control of uncertain switched non‐linear systems with application to aircraft wing rock

Huang

Zhang

2016

IET Control Theory & Applications

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“…납작하고 얇은 날개가 -축에 대해서만 자 유롭게 롤 운동을 하도록 되어 있으며 이 날 개의 Wing Rock 운동은 다음과 같이 미분방 정식으로 모델링할 수 있다 [1,2]. 롤링모멘트 계수는 다음의 형태를 가지고 있다 [1,2].…”

Section: ⅱ Wing Rock Dynamicsunclassified

Adaptive Control System Designs for Aircraft Wing Rock

Shin¹

2011

Journal of the Korean Society for Aeronautical & Space Scie

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At high angles of attack, aircraft dynamics can display an oscillatory lateral behavior that manifests itself as a limit cycle known as wing rock. In this paper, a classical and neural network based adaptive control design methods of adaptively stabilizing the oscillatory motion by adapting uncertainties are described in detail. All methods are simulated and compared using a model for an 80 o swept delta wing.

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“…Therefore, it generates the large-amplitude wing rock, which limits the maneuvering capability of the aircraft. 1 On the other hand, Hsu 2 shows that wing rock is caused by flow asymmetries developed by negative roll damping and sustained by nonlinear aerodynamic roll damping. Wing rock, as one type of lateral-directional instability for modern aircrafts, typically leads to a series of problems of dynamic performances, one of which is the limit cycle in the control field.…”

Section: Introductionmentioning

confidence: 99%

Two novel robust tracking control strategies for eliminating aircraft wing rock

Yin

Zhang

Huang

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part G:

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Nonlinearities are essential features in the model of aircraft wing rock system and limit cycle is a typical phenomenon when flying without any control force. In this work, we concentrate on two robust tracking control schemes for automatic flight control systems by using forwarding technique. Combining forwarding technique with adaptive control and disturbance observer, manifolds are represented as insensitivity to parameter uncertainties and external disturbances. A second-order filter is employed to compute mappings and their analytic derivatives at each step of the design. The global, uniform, and ultimate boundedness of all trajectories are guaranteed by internal stability of filters. Unlike some of the existing control methodologies, modularization and no differential operations together with reduction of computational load are the main advantages for practical applications. Scheme 1 requires no prior knowledge of unknown parameters and scheme 2 analyzes the convergence rate of uncertainty observers. Controller performance and comparison between two approaches are demonstrated via simulations.

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Theory of wing rock

Cited by 15 publications

References 3 publications

Adaptive tracking control of uncertain switched non‐linear systems with application to aircraft wing rock

Adaptive tracking control of uncertain switched non‐linear systems with application to aircraft wing rock

Adaptive Control System Designs for Aircraft Wing Rock

Two novel robust tracking control strategies for eliminating aircraft wing rock

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