Environmental Engineering Reference
In-Depth Information
found as follows:
P
2
C
)
−
1
P
1
T
e
w
=
(1
−
1
A
A
c
B
c
C
c
D
c
−
1
A B
1
C
1
D
1
B
2
=
−
C
1
0
⎡
⎤
A
+
B
2
D
c
C
1
B
2
C
c
B
1
+
B
2
D
c
D
1
⎣
⎦
.
=
B
c
C
1
A
c
B
c
D
1
C
1
0
D
1
3.3 Design Example
The parameters of an inverter are given in Table 3.1. The low-pass filter
W
is chosen as
−
for
f
2550
2550
W
=
=
50 Hz. The weighting parameters are chosen to be
ξ
=
44
1
0
hinf syn
algorithm, the
H
∞
and
μ
=
0
.
26. Using the MATLAB
R
controller
C
which nearly
minimises the
H
∞
norm of the transfer matrix from ˜
w
to
z
is obtained as
300)(
s
2
10
8
)
604785473
.
5899(
s
+
+
9189
s
+
4
.
04
×
C
(
s
)
=
10
8
)
.
(3.13)
(
s
+
3
.
41
×
10
8
)(
s
+
2550)(
s
2
+
1
.
236
×
10
4
s
+
3
.
998
×
The factor
s
+
3
.
41
×
10
8
in the denominator can be approximated by the constant
10
8
without causing any noticeable performance change (Weiss and Hafele 1999).
The poles and zeros that are close to each other can be cancelled as well. The resulting reduced
controller is
3
.
41
×
1
.
7736(
s
+
300)
C
(
s
)
=
.
(3.14)
s
+
2550
The Bode plots of the original and reduced controllers in the continuous time domain are
shown in Figure 3.5, which shows little difference at low frequencies. The Bode plots in the
discrete time domain are almost identical at the sampling frequency of 5 kHz that was used
for implementation.
Table 3.1
Parameters of an inverter
Parameter
Value
Parameter
Value
L
f
150
μ
H
L
g
450
μ
H
R
f
0
.
045
R
g
0
.
135
C
f
22
μ
F
R
d
1
f
s
5 kHz
f
s
w
12 kHz
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