Page 163 - Neural Network Modeling and Identification of Dynamical Systems

4.3 APPLICATION OF ANN MODELS TO ADAPTIVE CONTROL PROBLEMS UNDER UNCERTAINTY CONDITIONS 153
well as the different versions of control schemes and the largest ones, when the reference signals
(with or without compensator in one or both on both channels are random, with a sharply,
channels). All experiments were performed for often and significantly varying amplitude. Such
the MRAC scheme. These experiments include behavior is not usual for an aircraft of the class
the following: under consideration in its normal flight regimes.
It will rather be adequate to some abnormal sit-
1. Constant reference g-load n x = 0,random uation, in which the parameters of the flight of
reference angle of attack. Compensators in-
the aircraft are changed abruptly and often. But
cluded for both channels.
even in this rather complicated situation, the
2. Constant reference g-load n x = 0,randomref-
control system has performed quite successfully.
erence angle of attack, there is no compen-
In the case when the compensator was used
sator in the g-load channel.
only for the angle of attack channel, and not
3. Constant reference angle of attack (2 degrees),
for the g-load channel, the quality of control
random reference g-load, compensators in-
deteriorated somewhat. Namely, the magnitude
cluded for both channels.
of the error in this case lies in the range from
4. Constant reference angle of attack (2 degrees),
and from
random reference g-load, no compensator in
−(0.06 ÷ 0.10) to +(0.05 ÷ 0.08) in n x a
−(0.12÷0.60) to +(0.4÷1.2) with respect to α.It
the g-load channel.
can be seen that the relative error has increased.
5. Both reference signals are random stepwise.
In particular, the error has increased to a greater
Compensators included for both channels.
extent for g-loading rather than for the angle of
6. Both reference signals are random stepwise.
attack. However, the absolute errors remain per-
There is no compensator in the g-load chan-
nel. fectly acceptable, i.e., the adaptation algorithm
7. Both reference signals are random stepwise. works quite efficiently, despite the complicated
conditions.
There are no compensators in all channels.
The absence of compensators in both chan-
The results of the computational experiments nels is more significant. The error value in this
for the abovementioned conditions are shown in case lies in the range from −0.10 to +0.08 in n x a
Figs. A.22–A.35. Since for each of the variants, and from −1.2 to +2.1 in α.Thus,theroleofthe
there are eight graphs, they are divided into two compensator in the considered adaptive control
parts in four graphs for each of the variants. The scheme is quite significant, but it is not critical.
first graph in each pair shows the behavior of the We can estimate the effect of the change of
object, the reference model, and control signals, the angle of attack on the longitudinal trajectory
while the second graph shows tracking errors motion due to the relation between the angle of
and the reference signals. attack and the engine thrust from the dynamics
The results obtained in this series of exper- and boundaries of the change in the g-load val-
iments allow us to draw the following conclu- ues n x a .
sions. The accuracy of the angle of attack track- From the results presented in Figs. A.22–A.35,
ing when using the extended motion model (4.3) we can see that the g-load in the case of using
is somewhat reduced. compensators in both channels lies in the range
In the case when the compensator is used from −(0.03 ÷ 0.15) up to +(0.01 ÷ 0.15),inthe
for both channels, the error value ranges from absence of a compensator in the g-load chan-
and from nel in the range from −(0.10 ÷ 0.18) to +(0.10 ÷
−(0.02 ÷ 0.04) to +(0.01 ÷ 0.02) by n x a
−(0.05÷0.20) to +(0.7÷1.1) with respect to α.In 0.17), and in the absence of compensators in
this case, the lowest error values are obtained by both channels from −0.18 to +0.19.Thus, the
maintaining the regime with α = const = 2 deg, positive effect of the compensators in the con-