Environmental Engineering Reference
In-Depth Information
with
⎡
⎣
⎤
⎦
,
R
f
+
R
d
1
L
f
−
−
L
f
A
u
=
1
C
f
0
⎡
⎤
R
d
L
f
⎡
⎤
1
L
f
0
0
⎣
⎦
,
⎣
⎦
,
B
u
1
=
B
u
2
=
1
C
f
−
0
C
u
1
=
−
1
,
R
d
−
D
u
1
=
R
d
1
,
D
u
2
=
0
.
The corresponding plant transfer function is then
A
u
B
u
1
B
u
2
C
u
1
D
u
1
D
u
2
P
u
=
.
(6.3)
6.3.2 Formulation of the Standard H
∞
Problem
In order to guarantee the stability of the inner voltage loop, an
H
∞
control problem as shown in
Figure 6.6 is formulated to minimise the
H
∞
norm of the transfer function
T
z
u
w
u
=
F
l
(
P
u
,
C
u
)
[
z
u
1
z
u
2
]
T
, after opening the local positive feedback loop of
the internal model and introducing weighting parameters
w
u
]
T
to
z
u
=
from ˜
w
u
=
[
v
u
ξ
u
and
μ
u
. The closed-loop system
can be represented as
z
u
y
u
˜
w
u
u
u
P
u
=
,
(6.4)
u
u
=
C
˜
u
y
u
,
~
a
u
ξ
u
v
u
~
w
u
e
u
+
b
u
P
u
W
u
~
u
μ
u
C
u
~
u
u
Formulation of the
H
∞
control problem for the voltage controller
Figure 6.6
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