Gure 4-4, with – National Instruments NI MATRIXx Xmath User Manual
Page 79
Chapter 4
Frequency-Weighted Error Reduction
© National Instruments Corporation
4-9
Figure 4-4. Redrawn; Individual Signal Paths as Vector Paths
It is possible to verify that
and accordingly the output weight
can be used in an
error measure
. It turns out that the calculations for frequency
weighted balanced truncation of G and subsequent construction of C
r
(s) are
exceptionally easy using this weight.
The second
fracred( )
option is the dual of this. The error measure is
where:
It is possible to argue heuristically the relevance of these error measures
from a second point of view. It turns out that:
K
R
C
sI
A
BK
R
+
–
(
)
1
–
K
E
C s
( )
P
ˆ s
( )
+
-
-
+
P s
( ) I
+
-
I PˆG
+
(
)
1
–
Pˆ
CsI A K
E
C
+
–
1
–
B
[
=
I C sI
A K
E
C
+
(
)
1
–
K
E
–
(
)
–
]
I PˆG
+
(
)
1
–
Pˆ
W
=
W G G
r
–
(
)
H H
r
–
(
)V
V
I K
R
sI A BK
R
+
–
(
)
1
–
B
–
C sI A BK
R
+
–
(
)
1
–
B
=
D
L
N
L
W
1
–
W
2
V
1
N
R
–
V
2
D
r
I 0
0 I
=