Chapter 3 Multiplicative Error Reduction
Xmath Model Reduction Module 3-4 ni.com
The objective of the algorithm is to approximate a high-order stable transfer
function matrix G(s) by a lower-order Gr(s) with either inv(g)(g-gr) or
(g-gr)inv(g) minimized, under the condition that Gr is stable and of the
prescribed order.
Restrictions
This function has the following restrictions:
• The user must ensure that the input system is stable and nonsingular at
s = infinity.
• The algorithm may be problematic if the input system has a zero on the
jω-axis.
• Only continuous systems are accepted; for discrete systems use
makecontinuous( ) before calling bst( ), then discretize the
result.
Sys=bst(makecontinuous(SysD));
SysD=discretize(Sys);
Algorithm
The modifications described in this section allow you to circumvent the
previous restrictions.
The objective of the algorithm is to approximate a high order stable transfer
function matrix G(s) by a lower order Gr(s) with, in the square G(s) case,
either or (approximately) minimized,
under the constraint that Gr is stable and of prescribed order nsr. In case
Gis not square but has full row rank, the algorithm seeks to minimize:
Recall that so that when ,
When G is not square but has full column rank, the algorithm seeks to
minimize:
GG
r
–()G1–
∞G1–GG
r
–()
∞
GG
r
–()
*GG*
()
1–GG
r
–()
∞
X*s() X′s–()=sj
ω
=
X*jω() X*jω()=
GG
r
–()G*G()
1–GG
r
–()
*∞