This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Flight Simulation and Control of an Aircraft Including Turbulent Model ABSTRACT This study deals with the broad area of a control: equation of motions, turbulent models, and simple attitude control and tracking. The each area has a common part, which contains a wind effect. So, the final goal of this study is to control an airplane with the wind effect. I. Introduction There are many sources that make an aircraft unstable. One of them is the atmospheric disturbance. The atmospheric disturbance can make an airplane unstable or stalled suddenly, because the limited angle of attack of an airplane is in the small range generally. To solve this problem, a proper wind turbulent model will be applied to the 6DOF equation of motion. As a turbulent model, the Dryden Power Spectral Density(PSD) function will be applied. Additionally a LQR is adapted for an airplane to be kept stable through the turbulence, and PID control is used to follow the command. II. Modeling A. Translational Dynamics with wind effect. The following equations of motion are derived based on the trim condition. The trim condition has a following assumption : ) , , ( ) , , ( ) , , ( ) , , ( ) , , ( ) , , ( o o r q p u w v u θ θ = Ψ Φ = = Aerodynamics, moments and propulsion are external forces on the aircraft relative to atmosphere, that is, those forces depend on the velocity relative to the atmosphere. So, the external forces on the inertial frame are expressed with the velocity relative to the atmosphere. As the momentums of the translational equations are expressed at the body frame, the external forces are also expressed at the body frame. The only difference between the two frames is the expression. The magnitude of velocity and direction remain same. Inertia Air Air C A Inertia C A V V V + = / / In body frame, --- = - = g g g a a a g a w w v v u u w v u V V V , Translational dynamics, + Φ Φ- + --- = + + = = + = + = = Z Y X mg mg mg pv qu ru pw qw rv m w v u m f f V w mS V m f V V R R m f V R V R m f V R dt d m f mV dt d wt B B B B B B T I B T B T I B T I I θ θ θ cos cos cos sin sin ) ( ) ( ) ( ) ( ) ( With small perturbation theory, w u w u w X u X T X e X g w X u X u e e w w w u u u q w u f X X mg u m o o g w g u T e o w u T T g g a a a a o ∆ ≈ ∆ ≈ ∆ + ∆- ∆ + ∆ + ∆- ∆ + ∆ = ∆ ∆ ∂ ∂ + ∆ ∂ ∂ + ∆- ∆ ∂ ∂ + ∆- ∆ ∂ ∂ = ∆ ∆ ∆ ∆ = ∆ ∆ + ∆- = ∆ α α δ θ θ δ δ δ δ θ θ θ δ δ , ) ( cos X X ) ( X ) ( X ) , , , ( cos v u v u v Y Y Y g r u Y p Y v r u g v Y Y Y r Y p Y v Y v r r r p p v v v a r r p v f Y Y r mu mg v m o o g v a a r r o o r p o o g v a a r r r p v a a r g a a a a a o o ∆ = ∆ = ∆- ∆ + ∆ + ∆Φ + ∆- + ∆ +...
View Full Document
This note was uploaded on 05/05/2008 for the course AE 5001 taught by Professor A during the Spring '08 term at UT Arlington.
- Spring '08