Design of Robust Controllers for Load Reduction in Wind Turbines - Wind Turbine Control and Monitoring - page 104

d(s)

Augmented Plant

D

y ( s)

u(s)

+ +

G(s)

1/D

D

Zp 1 (s)

W 1 (s)

Z p 2 (s)

W 2 (s)

Zp 3 (s)

W 3 (s)

r(s)

e(s) - +

K(s)

Fig. 5.6 Mixed control sensitivity problem

controller. The other plants of the family are considered as additive uncertainties in
the pitch control design because these plants present differences. The inputs of the
augmented plant are the output disturbances d 1 (s), d 2 (s) and the control signal u(s).
The outputs are the y 1 (s) and y 2 (s) from the scaled plant and the performance
output channels Z p11 (s), Z p12 (s), Z p2 (s), Z p31 (s) and Z p32 (s).

0
@

1
A

0
@

1
A

Z p11 ð s Þ
Z p12 ð s Þ
Z p2 ð s Þ
Z p31 ð s Þ
Z p32 ð s Þ
y 1 ð s Þ
y 2 ð s Þ

ð D u = D e1 Þ G 11 ð s Þ W 11 ð s Þ
ð D u = D e2 Þ G 12 ð s Þ W 12 ð s Þ
W 2 ð s Þ
ð D u = D e1 Þ G 11 ð s Þ W 31 ð s Þ
ð D u = D e2 Þ G 12 ð s Þ W 32 ð s Þ
ð D u = D e1 Þ G 11 ð s Þ
ð D u = D e2 Þ G 12 ð s Þ

ð D d1 = D e1 Þ W 11 ð s Þ
0
0
0
0
ð D d1 = D e1 Þ
0

0
ð D d2 = D e2 Þ W 12 ð s Þ
0
0
0
0
ð D d2 = D e2 Þ

0
@

1
A

d 1 ð s Þ
d 2 ð s Þ
u ð s Þ

¼

ð 5 : 7 Þ

5.3.1.1 Multivariable Generator Torque H ? Control

The H ? Torque Controller solves two of the control objectives: to reduce the wind
effect in the drive train mode and to reduce the wind effect in the first tower side-
to-side mode. The H ? Torque Controller has two inputs (generator speed w g and
tower top side-to-side acceleration a Tss ) and one output (generator torque T H? ).
The selected nominal plant to design the controller is the linearized plant at the
19 m/s wind speed operational point because it is a representative plant in the
above rated zone. The nominal plant has the input of generator torque and two
outputs: generator speed and tower top side-to-side acceleration. This nominal
plant G(s) (Eq. 5.8 ) is represented by the state space matrices A PT, B PT, C PT and
D PT and it has 55 states. Uncertainties are not considered because the nominal
plant is valid for all operating points in the above rated zone.