Chapter 4 Frequency-Weighted Error Reduction
Xmath Model Reduction Module 4-16 ni.com
3. Only continuous systems are accepted; for discrete systems use
makecontinuous( ) before calling bst( ), then discretize the
result.
Sys=fracred(makecontinuous(SysD));
SysD=discretize(Sys);
Defining and Reducing a Controller
Suppose P(s) = C(sI–A)–1B and A–BKR and A–KEC are stable (where
KRis a stabilizing state feedback gain and KE a stabilizing observer gain).
A controller for the plant P(s) can be defined by
(with u the plant input and y the plant output). The associated series
compensator under unity negative feedback is
and this may be written as a left or right MFD as follows:
(4-5)
(4-6)
The reduction procedures "right perf" and "left perf" have similar
rationales. We shall describe "right perf", refer to [AnM89] and
[LiA86]. The first rationale involves observing that to reduce C(s), one
might as well reduce its numerator and denominator simultaneously, and
then form a new fraction Cr(s) of lower order than C(s).
This amounts to reducing
(4-7)
x
ˆ
·Ax
ˆBu KECx
ˆy–()–+=
uK
Rx
ˆ
–=
Cs() KRsI A BKRKEC++–()
1–KE
=
Cs() IK
RsI A KEC+–()
1–B+[]
1–KRsI A KEC+–()
1–KE
=
Cs() KRsI A BKR
+–()
1–KEICsIABK
R
+–()
1–KE
+[]
1–
=
Es() KR
C
sI A BKR
+–()
1–KE
=