Environmental Engineering Reference
In-Depth Information
The effect of disturbance on the linear model is assumed to affect the platform
pitch angle and the rotor- and generator speed. In this analysis, the disturbance
vector is chosen to be:
T
:
B
1
¼
0
1
9
½
ð
6
:
16
Þ
0
:
111
This means that the platform pitch speed will not be as influenced by the
disturbance as the rotor- and generator speed. The performance measure matrices
are considered as
2
3
97C
t1
C
t2
C
t3
ð
:
Þ
4
5
;
C
z
¼
ð
6
:
17
Þ
D
z
¼
diag
f
100
;
80
;
10
g
;
ð
6
:
18
Þ
where
ð
:
Þ¼
10 0 10 0 10 0 0
1
½
and C
ti
represent the i-th row of C
t
.
The first row of C
z
handles drive train oscillations. Rotor speed times the gearing
ratio minus the generator speed should be kept zero, i.e., minimizing oscillations.
In row 2, the platform pitch movement is penalized and row 3 handles the blade
pitch motion. Suitable results were found with a diagonal structure on the matrix
D
z
.
Figures
6.5
and
6.6
show the outputs (first column) and the blade pitch angles
(second column) for the closed-loop linear system. Simulation is carried out with
initial values for platform pitch angle, generator speed and rotor speed. In Fig.
6.5
,
no faults occur in the system and both controllers achieve an acceptable perfor-
mance. In Fig.
6.6
, a sensor failure is imposed on the system. For the full structure
of the control gain K, values for all three blades are calculated and the output
values are not too different from the results in Fig.
6.5
. For the diagonal structure
of the control gain K, only values for blades 1 and 2 are calculated, the value for
blade 3 is depending on a working sensor nr. 3. In the case of a failure in sensor nr.
3, the two systems do not behave too different. It is worth mentioning that sce-
narios where sensor nr. 1 and nr. 2 fails have also been investigated. Only one
sensor fails at the time. Now, the behavior of the two systems become very
different. Results from these scenarios show that the system with the diagonal gain
is stable regardless of which of the sensors that fails. In contrast to tests done with
the full gain, where the system becomes unstable if sensor nr. 1 or nr. 2 fails, but as
the figure shows, stays stable when sensor nr. 3 fails.
The full and the diagonal controllers are given in (
19
) and (
20
), respectively,
and the c-values for the two cases are compared in Table
6.2
.
2
3
0
:
9676
0
:
01
0
4
5
;
K
full
¼
0
:
0037
0
0
:
0125
ð
6
:
19
Þ
0
:
1988
0
:
0021
0
:
0043
