Environmental Engineering Reference
In-Depth Information
w
e
u
u
+
−
u
K
(
s
)
G
(
s
)
u
d
−
+
−
y
lin
y
d
u
T
aw
(
s
)
+
+
Fig. 4.12 Anti-windup compensation scheme
K
ð
s
Þ¼
M
ð
s
Þ
K
ð
s
Þ
with K
ð
s
Þ
the controller produced by the optimization algorithm.
The weighting function W
u
(s) is a high pass filter such as
W
u
ð
s
Þ¼
k
u
s
=
0
:
1x
u
þ
1
s
=
x
u
þ
1
with k
u
and x
u
design parameters. This transfer function penalizes the high fre-
quency components of the control signal, thus limiting the pitch activities. High
frequency control action must be also avoided to prevent from rate pitch satura-
tion. Since the modeling errors are covered by additive uncertainty, robust stability
and the limitation of the pitch activity can be expressed as a constraint on the same
closed loop transfer function. Therefore, the weighting function W
u
ð
s
Þ
in Fig.
4.11
is the most restrictive function between W
u
ð
s
Þ
and W
D
ð
s
Þ
.
Notice that if the drive-train damping controller is considered, the plant G
ð
s
Þ
in
Fig.
4.11
must include its dynamics in order to guarantee close loop stability.
Since the pitch controller is only active in region 3, an anti-windup controller is
necessary to ensure good behavior during the transition from region 1 to region 3.
With this purpose an optimal anti-windup controller is added. This controller is not
shown in Fig.
4.6
for a matter of clarity. The anti-windup controller connection is
shown in Fig.
4.12
.
4.5.2 Anti-windup Compensation
In the control scheme of Fig.
4.6
, the pitch controller will be in saturation during
the low wind speed intervals. So, anti-windup compensation is absolutely neces-
sary. To achieve high performance compensation, the anti-windup scheme pro-
posed by [
14
,
15
] is adopted here. It can be seen in Fig.
4.12
. This scheme offers a
good trade-off between stability margin and smooth recovery from saturation.
As can be seen in Fig.
4.12
, the anti-windup compensator produces two terms:
y
d
acting on the controller input and another u
d
acting on the control output. It can