National Instruments Xmath ophank( )

Chapter 2 Additive Error Reduction

Xmath Model Reduction Module 2-14 ni.com

For the discrete-time case:

When {bound} is specified, the error bound just enunciated is used to

choose the number of states in SysR so that the bound is satisfied and nsr

is as small as possible. If the desired error bound is smaller than 2σns,

no reducti on is mad e.

In the continuous-time case, the error depends on frequency, but is always

zero at ω=∞. If the reduction in dimension is 1, or the system Sys is

single-input, single-output, with alternating poles and zeros on the real

axis, the bound is tight. It is far from tight when the poles and zeros

approximately alternate along the jω-axis. It is not normally tight in the

discrete-time case, and for both continuous-time and discrete-time cases,

it is not tight if there are repeated singular values.

The presentation of the Hankel singular values may suggest a logical

dimension for the reduced order system; thus if , it may be

sensible to choose nsr = k.

Related Functions

ophank(), balmoore()

ophank( )

[SysR,SysU,HSV] = ophank(Sys,{nsr,onepass})

The ophank( ) function calculates an optimal Hankel norm reduction

of Sys.

This function has the following restriction:

• Only continuous systems are accepted; for discrete systems use

makecontinuous( ) before calling bst( ), then discretize the

result.

Sys=ophank(makecontinuous(SysD));

SysD=discretize(Sys);

jω

()GRejω

()–∞2σnsr 1+σnsr 2+... σns

+++()≤

σkσk1+