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Chapter 2 Additive Error Reduction
© National Instruments Corporation 2-11 Xmath Model Reduction Module
Related Functions
balance(), truncate(), redschur(), mreduce()
truncate( )
SysR = truncate(Sys,nsr,{VD,VA})
The truncate( ) function reduces a system Sys by retaining the first
nsr states and throwing away the rest to form a system SysR.
If for
Sys one has,
the reduced order system (in both continuous-time and discrete-time cases)
is defined by A
11
, B
1
, C
1
, and D. If Sys is balanced, then SysR is an
approximation of
Sys achieving a certain error bound. truncate( ) may
well be used after an initial application of
balmoore( ) to further reduce
a system should a larger approximation error be tolerable. Alternatively, it
may be used after an initial application of
balance( ) or redschur( ).
If
Sys was calculated from redschur( ) and VA,VD were posed as
arguments, then
SysR is calculated as in redschur( ) (refer to the
redschur( ) section).
truncate( ) should be contrasted with mreduce( ), which achieves a
reduction through a singular perturbation calculation. If
Sys is balanced,
the same error bound formulas apply (though not necessarily the same
errors),
truncate( ) always ensures exact matching at s = ∞ (in the
continuous-time case), or exacting matching of the first impulse response
coefficient D (in the discrete-time case), while
mreduce( ) ensures
matching of DC gains for
Sys and SysR in both the continuous-time and
discrete-time case. For a additional information about the
truncate( )
function, refer to the Xmath Help.
Related Functions
balance(), balmoore(), redschur(), mreduce()
A
A
11
A
12
A
21
A
22
= B
B
1
B
2
=
C
C
1
C
2
=