balred (Control System Toolbox)

Model order reduction

Syntax

rsys = balred(sys,ORDERS)
rsys = balred(sys,ORDERS,...,'Elimination',METHOD)
rsys = balred(sys,ORDERS,...,'Balancing',BALDATA)

Description

rsys = balred(sys,ORDERS) computes a reduced-order approximation 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. 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

sys = balred(sys,ORDERS,'AbsTol',ATOL,...
             'RelTol',RTOL,'Offset',ALPHA)

to specify additional options for the stable/unstable decomposition. See stabsep for details. The default values are ATOL=0, RTOL=1e-8, and ALPHA=1e-8.

rsys = balred(sys,ORDERS,...,'Elimination',METHOD) specifies the state elimination method. Available choices for METHOD include:

'MatchDC' : Enforce matching DC gains (default)
'Truncate': Simply discard the states associated with small Hankel singular values. The 'Truncate' method tends to produce a better approximation in the frequency domain, but the DC gains are not guaranteed to match.

rsys = balred(sys,ORDERS,...,'Balancing',BALDATA) makes use of the balancing data BALDATA produced by hsvd. Because hsvd does most of the work needed to compute rsys, this syntax is more efficient when using hsvd and balred jointly.

balred uses implicit balancing techniques to compute the reduced- order approximation rsys.

There is more than one balred method available. Type

```
help lti/balred
```

for more information.

References

[1] Varga, A., "Balancing-Free Square-Root Algorithm for Computing Singular Perturbation Approximations," Proc. of 30th IEEE CDC, Brighton, UK (1991), pp. 1062-1065.

See Also
hvsd Computes the Hankel singular values of an LTI model

lti/order LTI model order

minreal Minimal realization and pole-zero cancellation

sminreal Compute a structurally minimal realization

balreal bandwidth