Page 170 - Neural Network Modeling and Identification of Dynamical Systems

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

in two time intervals with a duration of 20 sec number and up to 4 km in flight altitude. Never-
each: in the first one the adaptation of the con- theless, the adaptation mechanisms (both in the
trol law is carried out by feeding a disturbing MPC scheme and in the MRAC scheme) in prac-
influence to the input of the control system (a tically all cases successfully coped with the task
highly changing signal for the angle of attack); of adjusting the control law to the changed flight
in the second interval with the same duration, conditions, restoring the accuracy of tracking the
the system is tested using a sequence of stepwise prescribed angle of attack.
input signals that are separate in time so that the
disturbed motion caused by the applied signal MODEL PREDICTIVE CONTROL
can be decayed until the next signal is applied. The results of computational experiments on
If this condition is met, then we can assume that the estimation of the influence for inaccuracy in
the system in one session is tested by a set of the initial model concerning the adaptive MPC
independent stepwise input signals, differing in schemeareshowninFigs. A.70–A.78.
magnitude.
The value of the natural frequency of the ref- 4.3.4.3 Estimation of the Importance of the
erence model in these experiments was chosen, Adaptation Mechanisms in the
for the reasons stated in Section 4.3.2.4, equal to Problem of Controlling the Angular
2/sec. Motion of an Aircraft
The analysis of the data shown in Figs. A.61– The neural network control system in the
A.69 allows us to draw the following conclu-
variants studied in this chapter consists of two
sions. The quality of the control, estimated by
parts: the proper neural network and an ad-
the error of tracking the given angle of attack, ditional compensating loop. These two parts
reaches in most cases acceptable values within are independent; each of them performs their
3–5 sec from the process of adjusting the control
law to the changed flight conditions. Thus, the specific functions. The neural network part is
time interval of adaptation of the control system adaptive, and its task is to provide the desired
with a length of 20 sec is clearly redundant; it dynamics of the system. The compensating el-
can be substantially reduced, as a rule, to several ement reduces errors arising from inaccuracy
seconds. of the ANN model and provides a robustness
The considered mechanisms of adaptation property for the system.
provide sufficiently high accuracy of the con- As showninSection 4.3.2.3, the presence of
trol: the tracking error of the prescribed angle the compensating element is fundamentally es-
of attack does not exceed, as a rule, values in the sential for the MRAC and MPC adaptive con-
range from ±0.25 deg up to ±0.45 deg, and this trol schemes. In these schemes, the basic idea
is true for both the MRAC and the MPC scheme. is that we use an ANN model as the source
In steady-state regimes during testing (when the of information about the behavior of the con-
disturbance from the stepwise disturbance was trolled object when forming the values of the
attenuated), the error in tracking the angle of at- regulator parameters. Due to the approximate
tack became practically zero. At the same time, nature of the ANN model, the results obtained
the initial error (at that moment in time when with its help inevitably differ from the real val-
the adaptation mechanism was activated) in ues of the variables describing the motion of the
some cases reached ±1 deg. As we can see from object. The approach to compensating such an
Table 4.1, the gap between the flight regimes error was proposed in Section 4.3.2.3. Accord-
at which the control law was synthesized and ing to this approach, we interpret an inaccuracy
tested was large enough: up to 2 units in Mach of the ANN model as some disturbance acting