Page 219 - Neural Network Modeling and Identification of Dynamical Systems

210 6. NEURAL NETWORK SEMIEMPIRICAL MODELING OF AIRCRAFT MOTION

2
2
2
the axes of the wind frame, m/sec , i.e., 85552.1 kg·m , I xz = 1331.4 kg·m , I xy = I yz =
2
⎧ 0 kg·m ; center of gravity place is 5% of the mean
⎪ g 1 = g(−sinθ cosα cosβ + cosφ cosθ sinα cosβ
⎪ aerodynamic chord; time constants of actuators
⎪
⎪
⎪ + sinφ cosθ sinβ), T e = T r = T a = 0.025 sec; relative damping coef-
⎪
⎨
g 2 = g(sinθ cosα sinβ − cosφ cosθ sinα sinβ ficients for actuators are ζ e = ζ r = ζ a = 0.707.
⎪ During the transient processes of the angu-
⎪
⎪ + sinφ cosθ cosβ),
⎪
⎪ lar motion for the aircraft, the airspeed V and
⎪
⎩
g 3 = g(sinθ sinα + cosφ cosθ cosα).
the flight altitude H do not change significantly.
(6.13) Thus, we assume them to be constant and do
not include the corresponding equations that de-
In addition, in Eqs. (6.11), (6.12)weusethe
scribe the translational motion in the model. In
¯ ¯ ¯
following notation: X, Y, Z are the aerodynamic
the experiments carried out, we used the follow-
axial, lateral, and normal forces; S is the area
2
of the aircraft wing, m ; b, ¯c are the wingspan ing constant values: altitude above sea level H =
3000 m; airspeed V = 147.86 m/sec. Accord-
and mean aerodynamic chord of the wing, m; q p
is the dynamic air pressure, kg·m −1 sec −2 .Also, ingly, the other variables, which depend only on
constants V and H, have the following values:
C x , C y , C z denote the dimensionless coefficients 2
gravitational acceleration g = 9.8066 m/sec ;
of axial, lateral, and normal forces, and C l , C m , 3
air density ρ = 0.8365 kg/m ; local speed of
C n denote the dimensionless coefficients of roll,
pitch, and yaw moments. All these aerodynamic sound a = 328.5763 m/sec; the free stream Mach
coefficients are nonlinear functions of their argu- number M 0 = 0.45; dynamic air pressure q p =
−2
−1
ments, as listed in (6.11)and (6.12). 9143.6389 kg·m sec .
It should be noted that the dependencies of In the model (6.6)–(6.9), the 14 variables p, q,
˙
˙
˙
the coefficients of aerodynamic forces and, espe- r, φ, θ, ψ, α, β, δ e , δ r , δ a , δ e , δ r , δ a represent the
cially, of the aerodynamic moments on their re- state of the controlled object, and the other three
act
act
act
spective arguments are highly nonlinear within variables δ e , δ r , δ a represent the controls.
the domain of interest, which significantly com- The values of the control variables are restricted
act
plicates the process of the aerodynamic charac- to the following ranges: δ e ∈[−25,25] deg,
act
act
teristics identification for a maneuverable air- δ r ∈[−30,30] deg, δ a ∈[−21.5,21.5] deg for
craft. As an example, in Fig. 6.8 we show the the command signals to the actuators of the con-
cross-section of the hypersurface given by the trolled stabilizer, rudder, and ailerons, respec-
tively.
function C m = C m (α,β,δ e ,q) at δ e ∈{−25,0,25}
During the process of the training set gen-
deg, q = 0 deg/sec within the domain α ∈
[−10,45] deg, β ∈[−30,30] deg. eration, as well as during the testing of the
We consider the maneuverable aircraft F-16 final semiempirical ANN model, the control
as an example of a simulated object. The source actions were applied to the aircraft simultane-
data for it were taken from the report [20], which ously along all three channels (elevator, rudder,
presents experimental results obtained by wind ailerons). We utilized the polyharmonic excita-
tunnels tests. tion signals δ act , δ r act , δ a act for the training set
e
The following particular values of the corre- generation and random excitation signals for the
sponding variables in (6.6)–(6.13) were adopted test set generation.
for the simulation: the mass of the aircraft m = The computational experiments for the model
9295.44 kg; wing span b = 9.144 m; the wing (6.6)–(6.9) were performed on the time interval
2
area S = 27.87 m ; the mean aerodynamic chord t ∈[0,20] sec in the ANN model training phase
c
of the wing is ¯ = 3.45 m; moments of iner- and on the interval t ∈[0,40] sec in the test-
2 2
tia I x = 12874.8 kg·m , I y = 75673.6 kg·m , I z = ing phase. In both cases we used the sampling