Environmental Engineering Reference
In-Depth Information
where
2
4
3
5
s
g
0
0
0
0
0
0
0
I
0
0
0
x
n
I
2fx
n
I
0
0
0
0
1
J
r
o
T
a
ob
B
dt
þ
B
r
ð
Þ
þ
1
J
r
oT
a
ox
r
B
dt
n
g
J
r
K
dt
J
r
0
0
J
r
A
¼
1
J
g
B
dt
þ
n
g
B
g
K
dt
n
g
J
g
B
dt
n
g
J
g
0
0
n
g
J
g
1
n
g
0
0
0
1
0
2
4
3
5
2
4
3
5
2
4
3
5
1
s
g
0
0
0
0
T
g
b
b
x
r
x
g
h
D
2
3
100000
010000
000100
000010
00
0 x
n
I
00
00
00
4
5
1
J
r
oT
a
ov
0
0
B
¼
;
E
¼
;
C
¼
;
x
¼
;
T
gr
b
r
u
¼
o
T
a
ob
¼
2x
r
qAv
3
oC
p
1
ob
oT
a
ox
r
1
2x
r
qAv
3
o
C
p
ox
r
1
2x
r
qAv
3
C
p
¼
o
T
a
ov
¼
1
2x
r
qAv
3
o
C
p
3
2x
r
qAv
2
C
p
ov
þ
where T
g
is the generator torque, b is the pitch angle, x
r
and x
g
are the rotor and
generator speed respectively, and h
D
is the torsional angle. It is clear from the state
space model given in Eq. (
7.7
) that the system matrix A and the disturbance matrix
E are not fixed matrices and depend on state variables, the uncontrollable input v,
and the partial derivatives of the usually non-analytical function of k and b, C
p
.
Hence, to cope with system non-linearity, a non-linear control strategy is required
to achieve the aim and objectives of wind turbine operation.
Multiple-model based non-linear control is one of the approaches to verify non-
linear controllers. The basic concept is to design local controller responsible for
controlling the local behaviour of the non-linear system. In the literature, the
Takagi-Sugeno (T-S) fuzzy inference modelling approach for dynamical systems
[
43
] is an important and systematic tool for multiple model control. The T-S fuzzy
model consists of a set of IF-THEN rules which represent local linear model of the
non-linear system. The main feature of this approach is that it can express the local
dynamics of each fuzzy rule by a linear system model. The overall fuzzy model is
achieved by connecting the local linear model of each rule by membership
