Page 145 - Neural Network Modeling and Identification of Dynamical Systems

4.2 PERFORMANCE EVALUATION FOR MULTILAYER NEURAL NETWORK MODELS OF AIRCRAFT MOTION 135
mand signal δ e, act . This model has the form ing parameters and characteristics for these air-
craft, required for modeling as source data, were
¯ qS T cr sinα g taken from the papers [14,15]for theF-16air-
˙ α = q − C L (α,δ e ) + + cosθ,
mV mV V craft, [21–25] for the hypersonic research vehicle
c
¯ qS ¯ T cr h T X-43, [16–18] for the NASP research vehicle, and
˙ q = C m (α,q,δ e ) + ,
I z I z [26]for theUAVs.
2
T ¨ =−2Tζδ e − δ e + δ e, act , For each of the abovementioned aircraft, a
˙
δ e
computational experiment was performed in or-
T cr = ω eng (T ref (δ th ) − T cr ),
˙
der to evaluate the performance of the corre-
¯ qS T cr cosα sponding ANN models. Some of the results of
n x =− C D (α,δ e ) + .
mg mg these experiments are shown in Fig. 4.3 for F-16
(4.3) and Figs. 4.4 and 4.5 for the UAVs.
In Figs. 4.3A, 4.4A, and 4.5A, examples of
Here T ref = T ref (δ th ) is the specified thrust training samples used for learning of the ANN
level (linear function), T cr is the current thrust models are shown. We can see that for the for-
level, ω eng is the frequency of the aperiodic link, mation of each of the samples very active work
which describes the dynamics of the engine is carried out by the longitudinal motion control
(here ω eng = 1 was assumed). The thrust mo- element (elevons for UAV, the controlled stabi-
ment arm is assumed to be equal to h T = 0.5 m; lizer for F-16), expressed in the frequent change
it is calculated relative to the center of mass of in the value of command signal δ e, act of the com-
the aircraft in the vertical plane, so the change mand control signal at significant differences be-
δ th causes a change in the angle of attack. In the tween its neighboring values (this command sig-
model (4.3), the variables α, q, δ e , δ e ,and T cr are nal was formed at random). The purpose of us-
˙
and δ th are ing this method for synthesis of a training set is
the states of the controlled object, δ e act
its controls, and n x is the tangential load factor, to provide the broadest possible variety of states
i.e., load factor along the velocity vector of the of the modeled system (to cover, as much as pos-
aircraft. sible, evenly and densely the entire state space
A series of computational experiments has of the system), as well as the highest possible
been performed to evaluate the properties of variety of time derivative values that reflect the
the ANN model under consideration and its dynamics of the simulated system.
suitability for modeling of the aircraft motion. Since we consider the optimal tracking con-
To demonstrate the efficiency of adaptive con- trol problem for the angle of attack, we evaluate
trol under various conditions, aircraft of essen- the accuracy of the designed model by compar-
tially different classes were chosen as examples: ing the actual trajectory of this variable for the
a maneuverable aircraft F-16 [14,15], a heavy controlled object described by the system of dif-
hypersonic aircraft (one of the options [16–18], ferential equations (4.2)or(4.3) with the trajec-
which were considered by NASA within the tory predicted by the ANN model. We estimate
framework of the National AeroSpace Plane the accuracy of the model by the error e α ,com-
[NASP] program, aimed at creating a single- puted as the difference between the angles of
stage aerospace plane with a horizontal launch, attack for the controlled object and the ANN
putting a payload on the orbit of the artificial model at the same time instant.
Earth satellite, and horizontal landing), the hy- We can see from these examples that the pro-
personic research vehicle X-43 [19–25], and UAV posed approach makes it possible to build rea-
“003” and X-04 micro and minidimensions, re- sonably accurate ANN models (e α values lie
spectively [26]. The values of the correspond- within the range ±(0.5 ÷ 0.7) deg). However, in