Control System Toolbox™

balred - 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.

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 NNZ of nonzero Hankel singular values using an eps-level relative threshold)

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

hsvd, lti/order, minreal, sminreal

balreal

bandwidth