Model order reduction
rsys
= balred(sys
,ORDERS
)rsys
= balred(sys
,ORDERS
,BALDATA
)rsys
= balred(___,opts
)
computes
a reduced-order approximation rsys
= balred(sys
,ORDERS
)rsys
of the LTI model sys
.
The desired order (number of states) for rsys
is
specified by ORDERS
. You can try multiple orders
at once by setting ORDERS
to a vector of integers,
in which case rsys
is a vector of reduced-order
models. balred
uses implicit balancing techniques
to compute the reduced- order approximation rsys
.
Use hsvd
to plot the Hankel
singular values and pick an adequate approximation order. States with
relatively small Hankel singular values can be safely discarded.
When sys
has unstable poles, it is first
decomposed into its stable and unstable parts using stabsep
, and only the stable part is
approximated. Use balredOptions
to
specify additional options for the stable/unstable decomposition.
When you have System Identification Toolbox™ software
installed, sys
can only be an identified state-space
model (idss
). The reduced-order model is also an idss
model.
uses
balancing data returned by rsys
= balred(sys
,ORDERS
,BALDATA
)hsvd
.
Because hsvd
does most of the work needed to compute rsys
,
this syntax is more efficient when using hsvd
and balred
jointly.
computes
the model reduction using options that you specify using rsys
= balred(___,opts
)balredOptions
. Options include offset
and tolerance options for computing the stable-unstable decompositions.
The options also allow you to limit the identification of low-energy
states to eliminate to particular time and frequency intervals. See balredOptions
for details.
Note:
The order of the approximate model is always at least the number
of unstable poles and at most the minimal order of the original model
(number |
[1] Varga, A., "Balancing-Free Square-Root Algorithm for Computing Singular Perturbation Approximations," Proc. of 30th IEEE CDC, Brighton, UK (1991), pp. 1062-1065.