Page 144 - Neural Network Modeling and Identification of Dynamical Systems

134 4. NEURAL NETWORK BLACK BOX MODELING OF AIRCRAFT CONTROLLED MOTION

dow, thrust control is also not introduced, and con-
T
k =[ y i−l , y i−l+1 ,..., y i ] , trol is used on a single channel. This channel
y
provides changing the value δ e, act ,whichis the
where l is the length of the sliding window, the command signal for the elevator actuator. This
index i refers to the time instant (sampling step), model has the following form [8–13]:
and the index k indicates the estimate number.
To save time, we do not perform the parame-
ter estimation at each sampling step, but at each ¯ qS g
˙ α = q − C L (α,δ e ) + cosθ,
tenth step (the sampling step is 0.01 sec, and mV V
c
the network parameters are updated in 0.1 sec). ¯ qS ¯ (4.2)
˙ q = C m (α,q,δ e ),
The computational experiment shows that such I z
a coarsening is quite acceptable since it does not T ¨ =−2Tζδ e − δ e + δ e, act ,
2
˙
δ e
significantly affect the accuracy of the model.
where α is the angle of attack, deg; θ is angle
4.2 PERFORMANCE EVALUATION of pitch, deg; q is the angular velocity of the
FOR ANN MODELS OF pitch, deg/sec; δ e is the deflection angle of the
elevator (controlled stabilizer), deg; C L is the
AIRCRAFT MOTION BASED ON
lift coefficient; C m is pitch moment coefficient;
MULTILAYER NEURAL
NETWORKS m is mass of the aircraft, kg; V is the airspeed,
2
m/sec; ¯q = ρV /2 is the dynamic air pressure,
3
kg·m −1 sec −2 ; ρ is air density, kg/m ; g is the ac-
The performance evaluation of the ANN 2
celeration of gravity, m/sec ; S is the wing area,
model under consideration we carry out con- 2
cerning, as an example, the angular longitudinal m ; ¯c is mean aerodynamic chord of wing, m; I z
is the moment of inertia of the aircraft relative to
motion of the aircraft, which was described us- 2
ing traditional mathematical models for flight the lateral axis, kg·m ; the dimensionless coeffi-
dynamics [8–13]. cients C L and C m are nonlinear functions of their
Since the problems of synthesis and analysis arguments; T , ζ are the time constant and the
of adaptive control algorithms have to be solved relative damping coefficient of the actuator; δ e act
for aircraft of various types, we considered two is the command signal to the actuator of the all-
versions of this model. In one version, the rela- turn controllable stabilizer (limited to ±25 deg).
tionship between the angle of attack α and the In the model (4.2), the variables α, q, δ e ,and δ e
˙
thrust of the engine T cr , which is typical for hy- are the states of the controlled object, the vari-
personic vehicles, was taken into consideration. able δ e, act is the control.
In another case, as applied to the F-16 maneu-
The second motion model (“two-channel”),
verable aircraft, this relationship was not taken
which was used only for hypersonic research ve-
into account as it is not characteristic. hicles X-43 and NASP, is a version of the model
The first of the considered models (“single-
channel”) uses an implicit relationship between (4.2), expanded by including the thrust control
channel and the explicit relationship between
the values of the variables α and T cr .Itisgiven
through the value of the coefficient m z (α,T cr ); angle of attack and engine thrust, in addition to
additional changes in the effect of thrust on the the implicit one, mentioned above. Thus, the en-
angle of attack and of the angle of attack on the gine thrust control via the command signal δ th is
thrust are not taken into account in this model, introduced in this model in addition to the com-