National Instruments Xmath K, +(), +Ps()I, s(), Cs() P, C, sI A BK, K, +

Chapter 4 Frequency-Weighted Error Reduction
© National Instruments Corporation 4-9 Xmath Model Reduction Module
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 Cr(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
Cs() P
ˆs()
+
-
-
+Ps()I
+
-
IP
ˆG+()
1–P
ˆCsI A KEC+– 1–B[=
ICsI AK
EC+()
1–KE
–()–]
IP
ˆG+()
1–P
ˆW=
WG G
r
–()
HH
r
–()V
VIK
RsI A BKR
+–()
1–B–
CsI A BK
R
+–()
1–B
=
DLNL
W1 –W2
V1NR –
V2Dr
I0
0I
=