National Instruments NI MATRIXx Xmath - Manual (Page 60)

Chapter 3 Multiplicative Error Reduction
Xmath Model Reduction Module 3-14 ni.com
There is one potential source of failure of the algorithm. Because G(s) is
stable,
certainly will be, as its poles will be in the left half plane circle
on diameter . If acquires a pole outside this circle
(but still in the left half plane of course)—and this appears possible in
principle—G
r
(s) will then acquire a pole in Re [s] > 0. Should this difficulty
be encountered, a smaller value of
ε should be used.
Related Functions
redschur() , mulhank()
mulhank( )
[SysR,HSV] = mulhank(Sys,{nsr,left,right,bound,method})
The mulhank( ) function calculates an optimal Hankel norm reduction of
Sys for the multiplicative case.
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
j
ω-axis.
• Only continuous systems are accepted; for discrete systems use
makecontinuous( ) before calling mulhank( ) , then discretize
the result.
Sys=mulhank(makecontinuous(SysD));
SysD=discretize(Sys);
Algorithm
The objective of the algorithm, like bst( ) , is to approximate a high order
square stable transfer function matrix G(s) by a lower order G
r
(s) with
either or (approximately) minimized,
under the constraint that G
r
is stable and of prescribed order.
The algorithm has the property that right half plane zeros of G(s) are
retained as zeros of G
r
(s). This means that if G(s) has order NS with N
+
zeros in Re[s] > 0, G
r
(s) must have degree at least N
+
—else, given that it
has N
+
zeros in Re[s] > 0 it would not be proper, [GrA89].
G˜ s ( )
ε
– j0 0 ,
=
( ) G˜
r
s ( )
G G
r
–
( )G 1 –
∞
G
1 – G G
r
–
( )
∞