Page 152 - Neural Network Modeling and Identification of Dynamical Systems

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

FIGURE 4.7 Structural diagram of the neural network implementation of model reference adaptive control (MRAC). TDL
(c)
is time delay line; W is the matrix of the synaptic weights of the connections between the input and the first processing
1
(c) (p)
layer of the ANN; W , W ,i = 2,3,4,j = 1,2,3 are the matrices of the synaptic weights of the connections between
i j
(c) (c) (p) (p)
1
4
the ANN processing layers; b , b , b , b are the sets of biases of the ANN layers; f ,...,f are the sets of activation
1 2 1 2
functions of the ANN layers; are sets of summation units of the ANN layers; v (i) (t), i = 1,...4 are sets of scalar outputs
of summation units; y (j) (t), j = 1,2,3 are sets of scalar outputs of activation functions; r(t) is the reference signal; y p (t) is
the output of the plant; y(t) is the output of the ANN model; y rm (t) is the output of the reference model; u ∗ (t) is the control
produced by the neurocontroller; u add (t) is an additional control from the compensator; u(t) is the control used as the input
of the plant; ε(t) = y p (t) − y rm (t) is the difference between the outputs of the plant and the reference model.
lowing form: periment, closely resembles the behavior of the
model (4.7).
ω 2 rm If the motion of the aircraft is described by
W α = . (4.3), then in addition to the system (4.6), rep-
2
2
((1/ω act )p + 1)(p + 2ω rm ζ rm p + ω )
rm
resenting the angle of attack channel, we have
(4.7) to add the reference model for the tangential g-
load channel, i.e.,
Fig. 4.8 demonstrates the desired behavior
˙ x 1 = x 2 ,
of the controlled object given by the reference (4.8)
2
model (4.7). 2 The behavior of the reference ˙ x 2 =−2ω rm ζ rm x 2 + ω rm (r − x 1 ),
model (4.6), as shown by the computational ex-
or, in the transfer function form,
2 We can see characteristics of this model in the time and fre- ω 2 rm
2
quency domain in Fig. 4.8. W n x = (p + 2ω rm ζ rm p + ω ) . (4.9)
2
rm