Design of Robust Controllers for Load Reduction in Wind Turbines - Wind Turbine Control and Monitoring - page 105

_ X ðÞ¼ A PT X ðÞþ B PT T ðÞ
w g ð t Þ
a Tss ð t Þ

¼ C PT X ðÞþ D PT T ðÞ

ð 5 : 8 Þ

The nominal plant is generalized including the performance output channels
and the scale constants (Eq. 5.9 ) D u , D d1 , D d2 , D e1 , D e2 to scale the different
channels of the mixed sensitivity scenario.

D u ¼ 90
D e1 ¼ 0 : 1; D e2 ¼ 1
D d1 ¼ 0 : 1; D d2 ¼ 1

ð 5 : 9 Þ

Finally, five weight functions are included in the generalized plant. In this
mixed sensitivity problem, W 11 (s) , W 12 (s) , W 2 (s) are used. The weight functions
W 31 (s) and W 32 (s) are not used, so their value is the unit when using the MATLAB
Robust Toolbox. Like Fig. 5.7 shows, W 11 (s) is an inverted notch filter centered at
the drive train frequency to mitigate the wind effect in this mode, W 12 (s)isan
inverted notch filter centered at the tower side-to-side first mode to also mitigate
the wind effect in this mode and W 2 (s) is an inverted low pass filter to reduce the
controller activity in high frequencies.
After developing the controller synthesis, the obtained controller has to be
re-scaled to adapt the input and the output to the real non-scaled plant. A high pass
filter is included in the DTD channel if the input of the controller is changed to be
the generator speed value instead of the generator speed error. The gain of this
controller channel is reduced at low frequencies with this high pass filter. As it is
defined in the augmented plant, the designed H ? Torque Controller has two inputs
(generator speed in rad/s and tower top side-to-side acceleration in m/s 2 ) and one
output (generator torque contribution T H? in Nm). This designed controller is state
space represented and its order is 39. Finally, the controller is reduced to order 25
without losing important information in its dynamics. After reducing, the last step
is the controller discretization using a sample time of 0.01 s. The Bode diagram of
the discretized state space represented controller (Eq. 5.10 ) is shown in Fig. 5.8 .

w g ðÞ
a Tss ðÞ

Xk þ 1 ð Þ¼ A TD X ðÞþ B TD

ð 5 : 10 Þ

w g ðÞ
a Tss ðÞ

T H 1 ðÞ¼ C TD X ðÞþ D TD

5.3.1.2 Multivariable Collective Pitch H ? Control

The H ? Pitch Controller solves two control objectives: the generator speed reg-
ulation increasing the output sensitivity bandwidth and reducing the output sen-
sitivity peak compared to the classical control design, and to reduce the wind effect