National Instruments Xmath

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:

–()G1–

∞G1–GG

–()

∞

–()

*GG*

()

1–GG

–()

∞

X*s() X′s–()=sj

X*jω() X*jω()=

–()G*G()

1–GG

–()

*∞