balredOptions
Create option set for model order reduction
Syntax
opts
= balredOptions
opts
= balredOptions('OptionName
', OptionValue
)
Description
returns
the default option set for the opts
= balredOptionsbalred
command.
accepts
one or more commaseparated name/value pairs. Specify opts
= balredOptions('OptionName
', OptionValue
)OptionName
inside
single quotes.
Input Arguments
NameValue Arguments

State elimination method. Specifies how to eliminate the weakly coupled states (states with smallest Hankel singular values). Specified as one of the following values:
Default:  

Error bound type, specified as either '
Relative error gives a better match across frequency
while absolute error emphasizes areas with most gain. For more
information, see Default: '  

Regularization level value that ensures a welldefined relative error
at all frequencies. When you set Default: '  

Frequency intervals for computing frequencylimited Hankel singular
values, specified as a matrix with two columns. Each row specifies
a frequency interval
The default value, If If both the frequency and time intervals do include DC, you
can still set Default:  

Time intervals for computing timelimited Hankel singular values,
specified as a matrix with two columns. Each row specifies a time
interval
The default value, If If both the frequency and time intervals do include DC, you can still set
Default:  

Maximum loss of accuracy value in stable and unstable decomposition.
For models with unstable poles, Default:  
 Offset for the stable/unstable boundary. Positive scalar value. In the stable/unstable decomposition, the stable term includes only poles satisfying
Increase the value of Default: 
For additional information on the options and how to use them,
see the balred
reference page.
Examples
Algorithms
The SepTol
and Offset
options are only used for
models with unstable or marginally stable dynamics. Because Hankel singular values (HSV)
are only meaningful for stable dynamics, balred
must first split such models into the sum of their stable and
unstable parts:
$$G={G}_{s}+{G}_{u}$$
This decomposition can be tricky when the model has modes close to the stability
boundary (e.g., a pole at s=1e10
), or clusters of modes on the
stability boundary (e.g., double or triple integrators). While balred
is able to overcome these difficulties in most cases, it
sometimes produces unexpected results such as
Large HSV for the stable part. This happens when the stable part G_{s} contains some poles very close to the stability boundary. To force such modes into the unstable group, increase the
'Offset'
option to slightly grow the unstable region.Too many modes are labeled "unstable." For example, you see 5 red bars in the HSV plot when your model had only 2 unstable poles. The stable/unstable decomposition algorithm has builtin accuracy checks that reject decompositions causing a significant loss of accuracy in the frequency response. For instance, such loss of accuracy arises when trying to split a cluster of stable and unstable modes near
s = 0
. Because such clusters are numerically equivalent to multiple poles ats = 0
, it is actually desirable to treat the whole cluster as unstable. In some cases, however, large relative errors in lowgain frequency bands can trip the accuracy checks and lead to a rejection of valid decompositions. Additional modes are then absorbed into the unstable part G_{u}, unduly increasing its order. Such issues can be easily corrected by adjusting theSepTol
tolerance.
If you use the TimeIntervals
or FreqIntervals
options, then balred
bases the computation of state
energy contributions on timelimited or frequencylimited controllability and
observability Gramians. For information about calculating timelimited and
frequencylimited Gramians, see gram
and [1].
References
[1] Gawronski, W. and J.N. Juang. "Model Reduction in Limited Time and Frequency Intervals." International Journal of Systems Science. Vol. 21, Number 2, 1990, pp. 349–376.