Environmental Engineering Reference
In-Depth Information
T
2R
n
x
a
¼
x
T
u
1
u
2
u
3
... u
q
2
4
3
5
A
ð
p
Þ
0 ... 00
00... 00
0
I
... 00
2R
n
n
A
a
ð
p
Þ¼
.
.
.
.
.
.
.
00...
I
0
B
a
¼½
B
T
00... 0
T
2R
n
m
E
a
ð
p
Þ¼½
E
T
00... 0
T
2R
n
m
v
G
¼½
0 I
k
0 ... 0
T
2R
n
g
C
a
¼½
C 00... D
f
2R
l
n
n
¼ð
n
þ
w
Þþ
gq
The following T-S fuzzy PMIO is proposed to simultaneously estimate the
system states and sensor faults:
x
a
¼
A
a
ðÞ
x
a
þ
B
a
u
þ
E
a
ðÞ
v
þ
R
a
y
r
þ
L
a
ðÞ
y
a
y
a
ð
Þ
ð
7
:
26
Þ
y
a
¼
C
a
x
a
The state estimation error dynamics are obtained by subtracting Eq. (
7.26
) from
Eq. (
7.25
) to yield:
Þ
e
x
þ
Gf
s
þ
E
a
ðÞ
e
v
e
x
¼
A
a
ðÞ
L
a
ð
p
Þ
C
a
ð
ð
7
:
27
Þ
where e
v
is the difference between the effective wind speed and the measured wind
speed (v). The augmented system combining the augmented state space system
[
25
], the controller [
24
], and the state estimation error [
27
] is given by:
x
a
ð
t
Þ¼
X
r
h
i
ðÞ
A
i
x
a
þ
N
i
d
ð
7
:
28
Þ
i
¼
1
where:
A
ð
p
Þþ
BK
ð
p
Þ
B
½
K
ð
p
Þ
0
m
q
0
A
i
¼
A
a
ðÞ
L
a
ð
p
Þ
C
a
2
4
3
5
v
e
v
y
r
f
s
;
N
i
¼
;
d
¼
E
ð
p
Þ
x
e
x
0
R
0
x
a
¼
0
E
a
ðÞ
0
G
