Page 227 - Neural Network Modeling and Identification of Dynamical Systems

218 6. NEURAL NETWORK SEMIEMPIRICAL MODELING OF AIRCRAFT MOTION

⎧
form 1 ⎨ 1.0, if (P c − P a )≤ 25,
= 0.1, if (P c − P a )≥ 25,
⎧
⎪ R x = F T (h,M,P c )cosα −¯qSC x (V,α,φ,q) ˜ τ eng ⎩ 1.9 − 0.036(P c − P a ), otherwise,
⎪
⎪
⎪
⎪ − mg sinγ, (6.18)
⎪
⎨
R z = F T (h,M,P c )sinα +¯qSC z (V,α,φ,q)
1 5, if P a ≥ 50,
⎪
⎪
⎪ − mg cosγ, = 1 (6.19)
⎪ , otherwise.
⎪
⎪ τ eng
⎩ ˜ τ eng
¯
M = q p S ¯cC m (V,α,φ,q),
(6.15)
The function F T (h,M,P a ) from (6.15)isgiven
in [20] as follows:
where α is the angle of attack, deg; V is the air-
2
speed, m/sec; S is the aircraft wing area, m ; ¯c is ⎧
2
the mean aerodynamic chord, m; q p = (ρV )/2 is ⎪ T idle + (T mil − T idle )(P a /50),
⎪
⎪
2
dynamic pressure, N/m ; M is the Mach num- ⎨ if P a ≤ 50,
F T =
ber. Here C x , C z are the dimensionless coeffi- ⎪ T mil + (T max − T mil )((P a − 50)/50),
⎪
⎪
cients of the axial and normal forces and C m ⎩ if P a ≥ 50,
is the pitching moment coefficient, which are
(6.20)
nonlinear functions of their arguments listed in
(6.15). In addition, F T is a nonlinear function de- where T idle , T mil ,and T max are the thrust of
scribing the dependence of the engine thrust on
the engine in the idle, military, and maximum
the altitude H, the Mach number M, and the cur-
modes, respectively. These quantities are the
rent value of the relative thrust P a . functions of flight altitude and Mach number,
The function F T (H,M,P a ), which determines
interpolated using the experimental data given
the altitude-velocity and throttle characteristics
by [20] (page 93, Table VI). As an example, these
of the engine, was obtained using data from [20,
21]. The mathematical model (6.14) also includes values are T idle = 111.2 N, T mil = 41421.9 N,
the equation that describes the engine dynamics. and T max = 74997.0 Nfor H = 3000 mand M =
0.4.
It is represented by a differential equation for the
actual relative thrust value P a and depends on The values of the atmosphere parameters (air
the corresponding command value P c as well as density ρ and local speed of sound a) at a given
the relative position of the engine throttle δ th .We altitude H required by the model (6.14)–(6.20)
have are estimated using the International Standard
Atmosphere (ISA) model. The gravitational ac-
⎧
⎨ 64.94δ th , if 0 ≤ δ th ≤ 0.77, celeration g is assumed to be constant and equal
∗
P = 217.38δ th − 117.38, if 0.77 ≤ δ th ≤ 1.0,
c to its value at sea level.
⎩ ∗
P .
c We consider the maneuverable F-16 aircraft as
(6.16)
an example of a specific simulated object. The
experimental data for this specific aircraft given
The dependence of the time constant τ eng of
the engine on the actual P a value and the com- by wind tunnel tests are presented in [20]. Some
additional data are contained in [21].
mand P c value of the relative thrust is deter-
The following particular values of the cor-
mined by the following equations:
responding variables in (6.14)–(6.20)wereused
⎧
⎨ 60, if P ≥ 50 and P a < 50, for the simulation: the mass of the aircraft m =
∗
c
2
∗
P c = 40, if P < 50 and P a ≥ 50, (6.17) 9295.44 kg; the wing area S = 27.87 m ; the mean
c
⎩ ∗ aerodynamic chord of the wing ¯ = 3.45 m; mo-
P , otherwise, c
c