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# hossain - AAE 666 Final Presentation Final Backstepping...

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February 24, 2005 1 AAE 666 - Final Presentation Final Presentation Backstepping Based Flight Control Backstepping Based Flight Control Asif Hossain

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February 24, 2005 2 Overview Modern Aircraft Configuration Aircraft Dynamics Force, Moment and Attitude Equations Current Approaches to Flight Control Design Backstepping Approaches to Flight Control Design Backstepping Backstepping Design for Flight Control Flight Control Laws Simulation
February 24, 2005 3 Modern Aircraft Configuration

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February 24, 2005 4 Aircraft Dynamics , Aircraft position expressed in an Earth-fixed coordinate system; , The velocity vector expressed in the body-axis coordinate system; , The Euler angles describing the orientation of the aircraft relative to the Earth-fixed coordinate system; , The angular velocity of the aircraft expressed in the body axes coordinate system; T E N h p p ) ( = P T w v u ) ( = V T ) ( ψ θ φ = Φ T r q p ) ( = ω
February 24, 2005 5 Aerodynamics Forces and Moments Body axis coordinate system

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February 24, 2005 6 Force Equations (Body-axes) Z m g pv qu w Y m g ru pw v F X m g qw rv u T 1 cos cos 1 cos sin ) ( 1 sin + + - = + + - = + + - - = θ φ θ φ θ Rewrite the force equations in terms of T V and , β α β α β β α cos sin sin cos cos T T T V w V v V u = = = 2 2 2 arcsin arctan w v u V V v u w T T + + = = = β α
February 24, 2005 7 Force Equations (wind-axes) ( 29 1 cos cos 1 mg F D m V T T + + - = β α ) sin ( cos 1 tan ) sin cos ( 2 mg F L mV r p q T T + - - + + - = α β β α α α ) sin cos ( 1 cos sin 3 mg F Y mV r p T T + - + - = β α α α β ) cos cos sin sin sin cos sin sin cos (cos ) sin sin cos cos (cos ) cos cos cos sin sin cos sin sin cos cos ( 3 2 1 φ θ β α θ α β φ θ β θ α φ θ α φ θ β α φ θ β θ β α - + = + = + + - = g g g g g g Where the contributions due to gravity are given by,

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February 24, 2005 8 Moment and Attitude Equations Moment Equations: Attitude Equations: N c L c q r c p c r Z F M c r p c pr c q N c L c q p c r c p TP T 9 4 2 8 7 2 2 6 5 4 3 2 1 ) ( ) ( ) ( ) ( + + - = + + - - = + + + = θ φ φ ψ φ φ θ θ φ θ φ cos cos sin sin
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