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RADIAL BASIS FUNCTION NEURAL
NETWORK DESIGN
 (k )
r
enn
h1
w1
iq* (k )
h2
r (k 1)
w2
wq
r (k  2)
Input layer
+
-

rbf
hq
Hidden layer
Output layer
The multivariate Gaussian function was used
as the activated function for2 hidden layer:
hr  exp( 
X  cr
2
2
r
), r  1,2,3,4,....q
RADIAL BASIS FUNCTION NEURAL
NETWORK DESIGN
 (k )
r
enn
h1
w1
iq* (k )
r (k 1)
r (k  2)
Input layer
+
-
h2

w2
wq
hq
Hidden layer
Output layer
Output layer:
q
rbf   wr hr
r 1
rbf
RADIAL BASIS FUNCTION
NEURAL NETWORK DESIGN
Based on the gradient descent method, the
learning algorithm of weights, node center and
variance were designed as follows:
wr (k  1)  wr (k )  enn (k )hr (k )
X s (k )  crs (k )
crs (k  1)  crs (k )  enn (k ) wr (k )hr (k )
2
 r (k )
 r (k  1)   r (k )  enn (k ) wr (k )hr (k )
X ( k )  cr ( k )
 (k )
3
r
2
RADIAL BASIS FUNCTION NEURAL
NETWORK DESIGN
Adjusting mechanism of fuzzy controller
q
cr1  iq* (k )
r 1
 r2
cm,n (k )  e(k )( K p  K i )d n,m  wr hr
SIMULATION MODEL
VHDL codes of all system were embedded to
Modelsim block:
1: Neural Fuzzy controller
2: Current control and coordinately transforms
3: SVPWM
NEURAL FUZZY CONTROLLER
r* (k )
a0
+
x
a1
m (k  1)
m (k  2)
b1
b2
x
e( k  1)
-
x
m (k )
+
+
e(k )
-
x
r* (k  1)
r* (k  2)
a2
+
r (k )
+
s1
-
s3
s4
s6
s5
c j ,i
x
Ki
+
c j 1 ,i
d i , j 1
+
+
uf
x
+
x
x
dek
s9
s8
-
+
Fuzzification
iq* ( k )
ui
r (k )
+
r (k 1)
Neuro-1
computation
Defuzzification
s20
Neuro-3
computation
out2
rbf
di, j
x
+
+
s22
s23
s15
s24
s25
Computation of current
command
s26~s87
s16
r
c j ,i 1
x
+
Computation of RBF NN
s89
r
c j ,i
+
c j ,i 1
c j 1 ,i 1
d i 1 , j 1
c j 1 ,i 1
x
Kp
s88
c j ,i
Jaco
J3
d i 1 , j 1
Defuzzification
r
+
J2
d i , j 1
x
d i 1 , j
Ki
s21
d i 1 , j
s14
+
Neuro-2
computation
x
x
J1
out3
c j 1 ,i 1
s19
 Ai 1 ( e )
Look-up fuzzy table
x
s18
 B j 1 ( de )
+
 B j (de )
+
s13
s12
d i  1, j  1
s17
1
s11
s10
di, j
x
-
RS,1
 B j (de ) -
out1
ui
iq* ( k )
c j ,i 1
d i  1, j
 B j (de )
 B j (de )
de j 1
 Ai (e )
1
 Ai (e )
SD
s7
Kp
x
j
 Ai (e )
RS,1
de(k )
+
Computation of speed error
and error change
Computation of reference model output
di, j
-
+
&
c j ,i
c j ,i 1
c j 1 ,i
c j 1 ,i 1
Look-up
Fuzzy rule
table
j&i
e( k  1)
x
s2
e i 1
ek
e(k )
s0
SD
-
i
α
e(k )
r
+
x
x
x
s90
s91
s92
s93
s94
r
c j 1 ,i
x
+
d i , j 1
s95
+
c j 1 ,i
s96
s97
s98
Tuning of fuzzy rule parameters
Implement by FSM (Finite state machine)
6
s99
Speed Control IC
NEURAL
ModelSim FUZZY CONTROLLER

*
r
Reference
Model
(RM)
Speed loop
m
+
uf
e
+
KI
1  Z 1
i
Fuzzy Controller
_
KP
r
de
Adjusting Mechanism
Jacobian
iq*
Z
1
Z 2
RBF
Neural Network
iq**
+q
Current
controlle
+
enn
PI
—
id*  0
v
PI
+
—
i
rbf
i
_
+
r
7
NEURAL FUZZY CONTROLLER
8