Environmental Engineering Reference
In-Depth Information
Thus, we have
(
e
I
rd
¼
rL
r
V
rd
þ
G
1
e
C
em
¼
p
ð
2
:
14
Þ
V
rq
þ
G
2
M
rL
s
L
r
/
s
To overcome standard sliding mode control chattering, a natural modification is
to replace the discontinuous function in the vicinity of the discontinuity by a
smooth approximation. Nevertheless, such a smooth approximation is not easy to
carry-out. This is why common approaches use current references. Therefore, a
high-order sliding mode seems to be a good alternative.
The main problem with high-order sliding mode algorithm implementations is the
increased required information. Indeed, the implementation of an nth-order con-
troller requires the knowledge of S
;
S
;
S
;
...
;
S
n
ð Þ
. The exception is the super-
twisting algorithm, which only needs information about the sliding surface S [
16
].
Therefore, the proposed control approach has been designed using this algorithm.
Now, lets us consider the following second-order sliding mode controller based
on the supertwisting algorithm [
16
]. In the considered case, the control could be
approached by two independent High-Order Sliding Mode (HOSM) controllers.
Indeed, the control matrix is approximated by a diagonal one. Hence, V
rd
controls
I
rd
(reactive power) and V
rq
controls the torque (MPPT strategy).
(
j
2
sgn e
I
r
ð ;
V
rd
¼
y
1
B
1
e
I
rd
j
y
1
¼
B
2
sgn e
I
r
ðÞ
ð
2
:
15
Þ
j
2
sgn e
T
em
V
rq
¼
y
2
þ
B
3
e
T
em
j
ð
Þ;
y
2
¼þ
B
4
sgn e
T
em
ð
Þ
where the constants B
1
, B
2
, B
3
, and B
4
are defined as
<
:
\U
1
ð
B
2
rLr
þ
U
1
Þ
B
1
[
2r
2
L
r
G
1
;
B
2
[ rL
r
U
1
;
ð
B
2
rL
r
U
1
Þ
2
ð
Þ
p
M
ð
2
:
16
Þ
rL
s
L
r
B
4
þ
U
2
rL
s
L
r
pM
Þ
;
B
4
[
rL
s
L
r
B
3
[ 2
U
2
ð
pM
p
M
rLs Lr
B
4
U
2
\U
2
G
2
In practice the parameters are never assigned according to inequalities. Usually,
the real system is not exactly known, the model itself is not really adequate, and
the parameters estimations are much larger than the actual values. The larger the
controller parameters are the more sensitive will be the controller to any switching
measurement noises. The right way is to adjust the controller parameters during
computer simulations.
The above-described high-order sliding mode control strategy for a DFIG-based
WT is illustrated by the block diagram in Fig.
2.5
[
17
].
