Page 164 - Neural Network Modeling and Identification of Dynamical Systems

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

trol system of this class is also visible here, but in the case of a failure situation it performs the
the overall effect of changes in the angle of at- reconfiguration of the motion control algorithm
tack on the longitudinal trajectory motion can and allows us to rapidly cancel the effects of
be considered insignificant. For this reason, it equipment failures and structural damage of the
is perfectly acceptable to use a simpler single- vehicle.
channel model (4.2) instead of the two-channel
model (4.3) for the estimation of the adaptation 4.3.3 Model Predictive Control
algorithms efficiency. Of course, the final evalu- 4.3.3.1 General Scheme of the Model
ation of these algorithms should be performed
Predictive Control
using the complete model of the aircraft motion.
The problem of control with the predictive
Figs. A.36–A.39 show the simulation results
model (MPC) uses the object model, which pre-
for one more class of aircraft, namely, micro- dicts its future behavior, as well as an optimiza-
UAVs and mini-UAVs. Figs. A.36 and A.37
tion algorithm to select the control action that
demonstrate the operation of the adaptive con-
provides the best values of the predicted char-
trol system under normal operation conditions,
acteristics of the system.
and Figs. A.38 and A.39 show how the MRAC Control with the predictive model is based on
system with the compensator copes with the ef- the sliding horizon method, according to which
fect of two successive failures that significantly
the ANN model predicts the output of the con-
affect the dynamics of the object. The first of
trolled object after a predetermined time interval
them leads to a displacement of the centering
(forecast horizon). The obtained forecast results
by 10% back (at 5 sec for micro-UAV “003” and are used by the algorithm of numerical opti-
10 sec for mini-UAV X-04), the second to a de- mization to find the control value u, which min-
crease by 50% of efficiency of the longitudinal imizes the following control quality criterion on
motion control (at 10 sec for micro-UAVs and the given forecast horizon:
20 sec for mini-UAVs). We can see that the adap-
N 2
tation scheme provides operation with a minor 2
◦
error (as a rule, E α ≈±0.05 ) until the first fail- J = (y r (t + j) − y m (t + j))
ure situation occurs. Adaptation to the change j=N 1
N u
in the dynamics of the object caused by this sit- 2
uation occurs quickly enough (approximately + ρ (u (t + j − 1) − u (t + j − 2)) .
1.2–1.5 sec). The error has now become larger j=1
(before the appearance of the second fault sit- Here N 1 , N 2 ,and N u are numerical parame-
uation), but it fits, basically, in the range E α ≈ ters that determine the forecast horizon within
±0.2 ; the stability of the system’s operation is which the values of the tracking error and the
◦
preserved. After the second failure, the stability increments of the control signal are estimated.
is preserved, but the error values become quite The values of y r and y m are the desired output of
significant (mostly, their values lie in the range the controlled object and the output of the ANN
E α ≈±0.5 ). model, respectively, u are trial control actions,
◦

The simulation results presented in this sec- and ρ is the weighting factor, which determines
tion serve as clear evidence that in most cases, the relative share of the contribution of control
the adaptive neural network control system, variations to the overall value of the efficiency
whose structure is represented in Fig. 4.6, suc- criterion J.
cessfully performs its tasks. It allows to take into In addition to the forecast horizon, the second
account the relationship between the angle of at- important parameter in the MPC scheme is the
tack and the thrust of the aircraft engine. Also, value of the control horizon, i.e., the values of