Environmental Engineering Reference
In-Depth Information
Since
D
2
=
0,
⎡
⎤
A
2
C
d
B
2
D
d
C
c
0
0
⎣
⎦
0
A
d
B
d
C
c
0
0
T
ba
=
B
c
C
1
0
A
c
B
c
C
w
0
.
0
0
0
A
w
B
w
C
1
0
0
C
w
0
Once the controller
C
is designed, the stability of the system can be verified by checking
T
ba
∞
. Moreover, according to (Weiss and Hafele 1999; Weiss
et al.
2004), a small value
γ
0
1
−
γ
for
, where
γ
0
=
T
e
w
∞
and
γ
=
T
ba
∞
, results in a small steady-state error. Hence,
γ
0
the weighting parameters
ξ
and
μ
can be chosen to minimise
while keeping
γ<
1. The
1
−
γ
realisation of the transfer function from
w
to
e
=
e
u
, assuming that
v
=
0, can be found as:
1
A B
2
C
1
A
d
B
d
C
d
D
d
A
c
B
c
C
c
−
1
A B
1
C
1
D
1
T
e
w
=
−
0
0
⎡
⎤
A
2
C
d
B
2
D
d
C
c
0
A B
1
C
1
D
1
⎣
⎦
0
A
d
B
d
C
c
0
=
B
c
C
1
0
A
c
B
c
C
1
0
0
1
⎡
⎣
⎤
⎦
A
2
C
d
B
2
D
d
C
c
0
0
0
A
d
B
d
C
c
0
0
=
B
c
C
1
0
A
c
B
c
C
1
B
c
D
1
0
0
0
A
B
1
C
1
0
0
C
1
D
1
⎡
⎣
⎤
⎦
A
2
C
d
B
2
D
d
C
c
0
B
1
0
A
d
B
d
C
c
0
0
=
B
c
C
1
0
A
c
0
B
c
D
1
0
0
0
A
B
1
C
1
0
0
0
D
1
⎡
⎤
A
2
C
d
B
2
D
d
C
c
B
1
⎣
⎦
.
0
A
d
B
d
C
c
0
=
B
c
C
1
0
A
c
B
c
D
1
C
1
0
0
D
1
5.3 Design Example
The parameters of the inverter are given in Table 3.1. The nominal low-pass filter
W
is chosen
according to (5.5) as
−
2550
2550
W
=
1
0
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