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The stator is directly connected to the grid, then, the stator electrical angle
h
s
is
calculated only with the grid voltage.
h
s
¼
h
1
2
ð
9
Þ
arctan u
s
b
u
s
a
is the stator voltage vector angle in the stationary
reference frame abc as shown in Fig.
1
.
Our control objective is the design of a controller for the DFI-Motor which
ensures reactive power regulation at stator side and speed tracking reference with
unknown load torque. It will be demonstrated that the stator-side reactive power
regulation problem can be formalized as the requirement to guarantee that the line
voltage vector and the stator
where
h
1
¼
flux vector are orthogonal.
Considering the stator equations expressed in terms of stator
fl
fl
uxes and currents
in the line voltage reference frame
u
sd
¼
R
s
i
sd
þ x
s
u
sq
u
sq
¼
ð
Þ
10
R
s
i
sq
x
s
u
sd
þ
u
s
From the second equation of (
5
), the unity power factor objective is equivalent to
i
sd
¼
0. In steady-state condition, all the derivatives are zero. According to the
rst
equation of (
10
),
u
sq
¼
0 is necessary to ensure i
sd
¼
0. Then, the stator-side unity
power factor control is reformulated as a stator
fl
flux orientation control objective
(the stator
flux vector is required to be orthogonal to line voltage vector).
In the following section, the fuzzy logic system used to approximate the
uncertain functions will be described in detail.
fl
4 Description of the Fuzzy Logic System
The basic con
guration of a fuzzy logic system consists of a fuzzi
er, some fuzzy
IF-THEN rules, a fuzzy inference engine and a defuzzi
er, as shown in Fig.
2
. The
fuzzy inference engine uses the fuzzy IF-THEN rules to perform a mapping from an
input vector x
T
to an output f
¼½
x
1
;
x
2
; ...;
x
n
2
R
n
2
R. The ith fuzzy rule is
written as
and x
n
is A
i
n
then f is f
i
R
ð
i
Þ
if x
1
is A
i
1
and
:
...
ð
11
Þ
where A
i
1
;
A
i
2
; ...;
and A
i
n
are fuzzy sets and f
i
is the fuzzy singleton for the
output in the ith rule. By using the singleton fuzzi
er, product inference, and center-
average defuzzi
er, the output of the fuzzy system can be expressed as follows:
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