Environmental Engineering Reference
In-Depth Information
a fixed reference frame, so M
tilt
and M
yaw
are proportional to the Coleman
transformation outputs and the controller can be easily scaled. The inverse of the
Coleman transformation C
-1
is used to transform the fixed frame to the frame in
blades.
0
1
M
flap1
M
edge1
M
flap2
M
edge2
M
flap3
M
edge3
0
1
0
1
@
A
cos h
T
þ
b
ð
Þ
sin h
T
þ
b
ð
Þ
00 00
M
oop1
M
oop2
M
oop3
@
A
¼
@
A
00 cos h
T
þ
b
ð
Þ
sin h
T
þ
b
ð
Þ
00
00 00 cos h
T
þ
b
ð
Þ
sin h
T
þ
b
ð
Þ
0
1
M
flap1
M
edge1
M
flap2
M
edge2
M
flap3
M
edge3
@
A
¼
T
ð
5
:
14
Þ
For the 'Upwind' model cos h
T
þ
b
ð
Þ
0
:
8716 and sin h
T
þ
b
ð
Þ
0
:
4903
0
@
1
A
M
oop1
M
oop2
M
oop3
M
tilt
M
yaw
cos w
1
cos w
2
cos w
3
¼
ð
5
:
15
Þ
sin w
1
sin w
2
sin w
3
P
ipc
¼
C
1
PTC
¼
PT
ð
5
:
16
Þ
The new plant P
ipc
(Eq.
5.16
) uses the mathematical properties of the Coleman
transformation to simplify the construction of the plant. P
ipc
has three outputs (a
Tss,
M
tilt
and M
yaw
) and two inputs (b
tilt
and b
yaw
). The plant P
ipc
linearized at the
operating point of 19 m/s is used in the H
?
IPC control design.
In this case, one MIMO (3 9 2) mixed sensitivity problem is necessary to
design a MIMO controller based on the H
?
norm reduction. The scale constants
are shown in (Eq.
5.17
). The weight functions used in this mixed sensitivity
problem are W
11
(s)
,
W
12
(s)
,
W
13
(s)
,
W
21
(s) and W
22
(s)
.
The weight functions
W
31
(s)
,
W
32
(s)
,
W
33
(s) are not used, so their value is the unit when using the
MATLAB Robust Toolbox. Regarding to the weigh functions, W
11
(s)isan
inverted notch filter centered at the tower first side-to-side mode frequency to
reduce the wind effect in this mode, W
12
(s) and W
13
(s) are inverted high pass filters
to guarantee the integral control activity to regulate the tilt and yaw moments.
W
21
(s) and W
22
(s) are inverted low pass filters to reduce the controller activity in
high frequencies with an inverted notch filter at the first blade in-plane mode
frequency to include a notch filter at this frequency in the controller dynamics.
Figure
5.12
shows the Bode diagrams of these weight functions.
