Page 161 - Neural Network Modeling and Identification of Dynamical Systems

4.3 APPLICATION OF ANN MODELS TO ADAPTIVE CONTROL PROBLEMS UNDER UNCERTAINTY CONDITIONS 151
system with the compensator under the influ- The angle of attack reference signal, sup-
ence of the traditionally used stepwise reference posed to be tracked by the control system, was
signals. Fig. A.12 shows the operation of such a constructed by the same rules as the actuator
system for a sequence of stepwise reference sig- command signal during the training set gener-
nals, following the intervals during which the ation for the ANN model. Namely, a random
previous disturbance has already been canceled, sequence of stepwise values of the reference an-
i.e., these stepwise effects can be considered iso- gle of attack was generated, with frequent and
lated. This kind of verification of the dynamic significant differences between adjacent values
properties of a controlled system remains essen- of the elements of the sequence. This approach is
tial for the systems of the class considered in this applied in order to provide the broadest possible
chapter since it makes it possible to observe vi- variety of states of the simulated system (in or-
sually and evaluate the nature of the response der to cover the entire state space of the system
of the controlled system when some disturbance as uniformly and densely as possible), as well as
effect occurs. the highest possible variety of changes in the ad-
However, in the modern practice of the non- jacent states (in order to reflect the dynamics of
linear system testing, instead of isolated step- the object as accurately as possible in the control
wise disturbances, which we use traditionally algorithm implemented by the neurocontroller).
for linear systems, we have to use more complex See Fig. 4.13.
input (reference) signals that allow testing in a Figs. A.13–A.16 show the operation of a con-
much more strict mode. Namely, the input sig- trol system with a reference model and a com-
nal is generated, which often and significantly pensator for the case when the F-16 aircraft was
changes in magnitude, so the control system has considered as a controlled object and two emer-
to start reacting to some ith disturbance even gency situations happened that led to a shift of
before the transient process associated with the the center of mass of the aircraft, as well as to a
reaction to the (i − 1)th (and possibly also to decrease of the effectiveness of its longitudinal
the (i − 2)th, (i − 3)th, ...) disturbance has com- control.
pleted. In other words, with this approach to Fig. A.17 shows how an adaptive control
testing, the system is required to react regularly system with reference model and compensator
not to any single disturbance, but to their combi- deals with the influence of two consecutive fail-
nation (“mixture”), the components of which are ures, which significantly affect the dynamics of
at different stages of the completion of the tran- the hypersonic research vehicle X-43. The first
sient processes generated by them, and this com- of them leads to a displacement of the center
bination is changing randomly. Here, the control of gravity by 10% (at t = 20 sec), the second to
system has to work in much more difficult con- a 50% decrease in the effectiveness of the lon-
ditions than with the traditional stepwise effect, gitudinal motion control (for t = 50 sec). We
but this approach is better suited to the nature can see that the adaptation scheme provides
of the problems arising in the control of non- operation with a small error (E α ≈±0.05 deg)
linear systems operating under uncertainty. For until the first failure situation occurs. Adapta-
example, atmospheric turbulence, affecting the tion to the change in the dynamics of the object
aircraft, will not wait until the control system caused by this situation occurs quickly enough
has fulfilled its previous impact. (approximately 1.2–1.5 sec). The error has now
For this reason, in the examples of testing become larger (up to the moment of occurrence
adaptive control algorithms considered below, a of the second emergency situation), but it fits,
difficult reference signal is used. This input sig- basically, in the range E α ≈±0.2 deg; the sta-
nal usually changes frequently and significantly. bility of the system operation is preserved. Af-