National Instruments Xmath - page 77

Chapter 4 Frequency-Weighted Error Reduction
© National Instruments Corporation 4-7 Xmath Model Reduction Module
Matrix algebra shows that C(s) can be described through a left or right
matrix fraction description
with DL, and related values, all stable transfer function matrices.
In particular:
For matrix C(s), the left and right matrix fraction descriptions are distinct
entities. It is the right MFD which corresponds to Figure 4-1; refer to
Figure 4-2.
Figure 4-2. C(s) Implemented to Display Right MFD Representation
Cs() DL
1–s()NLs() NRs()DR 1–s()==
DLIK
RsI A–KEC+()
1–B+=
NLKRsI A–KEC+()
1–KE
=
NRKRsI A–BKR
+()
1–KE
=
DRICsIA–BKR
+()
1–KE
+=
Cs() Ps()
+
-
K
E
Ps()
+
-1
s
---K
R
++
C
ABK
R
–
+
-