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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