Environmental Engineering Reference
In-Depth Information
controller design. For example, the quadratic parameterisation dynamic output
feedback controller can correspondingly be reduced to a linear parameterisa-
tion dynamic output feedback controller to control the wind turbine.
The aim is to develop a controller whose gain varies with wind speed. For
example, in the low wind speed range of operation the control aim is to maximise
the amount of power extracted from the available wind power through tracking
the optimal rotor rotational speed reference signal. Hence, to derive the T-S model
with minimum uncertainty, the wind speed (v) and the rotor speed (x
r
) are con-
sidered as fuzzy premise variables.
During the low wind speed of operation (Region 2) v varies within the operating
range:
ms
1
v
2
v
min
;
v
max
½
where in the benchmark wind turbine considered in this thesis v
min
¼
4m s
1
and
v
max
¼
12
:
5m s
1
. According to these limits the other premise variable (x
r
)is
bounded by:
rad s
1
x
r
2
x
min
;
x
max
½
where x
min
¼
0
:
56 rad s
1
and x
max
¼
1
:
74 rad s
1
. The bounds of x
r
are deter-
mined using Eq. (
7.2
) using k
opt
¼
8.
The membership function is selected as follows:
9
=
;
M
1
¼
x
r
x
min
x
max
x
min
M
2
¼
1
M
1
N
1
¼
v
v
min
v
max
v
min
N
2
¼
1
N
1
ð
7
:
8
Þ
Based on the two premise variables four local linear models of the wind turbine
can be determined to approximate the non-linear system at different operating
points in the low range of wind speed. Hence, Eq. (
7.9
) gives the four rule T-S
fuzzy model of the non-linear wind turbine in Eq. (
7.7
):
9
=
x
¼
P
r
h
i
ð
v
;
x
r
Þ½
A
i
x
þ
Bu
þ
E
i
v
ð
7
:
9
Þ
i
¼
1
;
y
¼
Cx
where h
1
¼
M
1
N
1
;
h
2
¼
M
1
N
2
;
h
3
¼
M
2
N
1
, and h
4
¼
M
2
N
2
.
