Chapter 3 Multiplicative Error Reduction
© National Instruments Corporation 3-21 Xmath Model Reduction Module
For mulhank( ), this translates for a scalar system into
and
The bounds are double for bst( ).
The error as a function of frequency is always zero at ω=∞ for bst( )
(orat ω= 0 if a transformation s → s–1 is used), whereas no such particular
property of the error holds for mulhank( ).
Imaginary Axis Zeros (Including Zeros at ∞)
When G(jω) is singular (or zero) on the jω axis or at ∞, reduction can be
handled in the same manner as explained for bst( ).
The key is to use a bilinear transformation [Saf87]. Consider the bilinear
map defined by
where 0 < a < b–1 and mapping G(s) into through
86.9 vidB 20log10
<G
ˆnsr G⁄
insr1+=
ns
∑
–
8.69 vi
insr1+=
ns
∑
<dB
phase error viradians
insr1+=
ns
∑
<
sza–
bz–1+
-------------------=
zsa+
bs 1+
---------------=
G
˜s()
G
˜s() Gsa–
bs–1+
-------------------


=
Gs() G
˜sa+
bs 1+
---------------


=