National Instruments NI MATRIXx Xmath - Manual (Page 85)

Chapter 4 Frequency-Weighted Error Reduction
© National Instruments Corporation 4-15 Xmath Model Reduction Module
From these quantities the transformation matrices used for calculating
C
sr
(s), the stable part of C
r
(s), are defined
and then
Just as in unweighted balanced truncation, the reduced order transfer
function matrix is guaranteed stable, the same is guaranteed to be true in
weighted balanced truncation when either a left (output) weight or a right
(input) weight is used. It is suspected to be true when both input and output
weights are present. The overall algorithm is not, however, at risk in this
case, since it is stability of the closed-loop system which is the key issue of
concern, (except for
type="input spec" , but here there is only a single
weight, and so the theory guarantees preservation of stability).
Related Functions
balance() , redschur() , stable() , fracred()
fracred( )
[SysCR,HSV] = fracred(Sys,Kr,Ke,type,{nscr,Qyy})
The fracred( ) function uses fractional representations to calculate a
reduction of a continuous-time compensator comprising a state estimator
with state feedback law.
Restrictions
1. The closed-loop system ( SCLR,NSCLR ) is calculated from
sysol=scr*sys # open loop system
syscl=feedback(sysol) # closed loop system
2. Initial state values, state names, and input and output names are not
considered by
fracred( ) .
S
lbig
V
lbig
V
ebig
S
ebig
1 2 ⁄ –
=
S
rbig
V
rbig
V
ebig
S
ebig
1 2 ⁄ –
=
AC
R
S
lbig
′
A
C
S
rbig
= B
CR
S
lbig
′
B
C
=
AC
R
C
C
S
rbig
= B
CR
D
C
=