Page 12 - Neural Network Modeling and Identification of Dynamical Systems

List of Notations

∗ ∗
U = S ∪ E universe of reasoning C n yawing moment coefficient
S ∗ dynamical system ∂C L ∂C y ∂C m
C L α = ; C y β = ; C m α = ;
∗
E environment ∂α ∂β ∂α
K = S,E system-complex ∂C m
C m q =
S system-object, S ⊂ S ∗ ∂q
∗ T thrust of the engine
E system-environment, E ⊂ E
x = (x 1 ,...,x n ) ∈ X, T ref specified thrust level
x 1 ∈ X 1 ⊆ R,...,x n ∈ X n ⊆ R, T cr current thrust level
n T idle thrust of the engine in the idle mode
X = X 1 × ... × X n ⊆ R
state (phase) vector of system S T mil thrust of the engine in the military mode
R real number line T max thrust of the engine in the maximum mode
y = (y 1 ,...,y p ) ∈ Y P c command relative thrust value
observation vector of system S P a actual relative thrust value
u = (u 1 ,...,u m ) ∈ U δ th relative position of the engine throttle
control vector of system S α angle of attack
w = (w 1 ,...,w s ) ∈ W β angle of sideslip
φ roll angle
vector of parameters for system S
ψ yaw angle
ξ = (ξ 1 ,...,ξ q ) ∈
θ pitch angle
vector of perturbations for system S
p angular velocity about x-axis
ζ = (ζ 1 ,...,ζ q ) ∈ Z
r angular velocity about y-axis
vector of measurement noises for system S q angular velocity about z-axis
t ∈ T ⊆ R time

q turb increment in angular velocity q due to
λ(t i ) situation for time instant t i atmospheric turbulence
λ ext (t i ) external components of situation for time in-
γ flight path angle
stant t i
δ a angle of aileron deflection
λ int (t i ) internal components of situation for time in-
δ e angle of elevator deflection
stant t i
δ r angle of rudder deflection
γ(t i ) goal of the system for time instant t i V airspeed
D aerodynamic drag
M 0 free stream Mach number
L lift force
H altitude of flight
Y side force dynamic air pressure
q p
C D drag coefficient (wind axes) ρ air density
C L lift coefficient (wind axes) p atmospheric pressure
C y side force coefficient (wind axes) g acceleration due to gravity
D axial force (body axes) W wind speed
Z normal force (body axes) S wing area
Y lateral force (body axes) b wing span
C x axial force coefficient (body axes) ¯ c mean aerodynamic chord (MAC)
C y lateral force coefficient (body axes) m aircraft mass
C z normal force coefficient (body axes) W aircraft weight
L rolling moment I x moment of inertia in roll
M pitching moment I y moment of inertia in pitch
N yawing moment I z moment of inertia in yaw
C l rolling moment coefficient I xz product of inertia about ox and oz axes
C m pitching moment coefficient ω rm natural frequency of the reference model
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