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
 
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