National Instruments Xmath KrsI A KEC+(), Ps(), B, K, + -

Chapter 4 Frequency-Weighted Error Reduction

Xmath Model Reduction Module 4-8 ni.com

The left MFD corresponds to the setup of Figure4-3.

Figure 4-3. C(s) Implemented to Display Left MFD Representation

The setup of Figure 4-2 suggests approximation of:

whereas that of Figure 4-3 suggests approximation of:

In the LQG optimal case, the signal driving KE in Figure 4-2 is white noise

(the innovations process); this motivates the possibility of using no

frequency dependent weighting in approximating G(s) [but observe that

after approximating, the signal will no longer be white noise, so that

argument is questionable]. Simple appeal to duality motivates using no

frequency dependent weighting for H(s). These are two of the options

offered by fracred( ).

Two more fracred( ) options depend on examining stability robustness

(the options are duals of one another). From the stability point of view, the

set-up of Figure 4-3 is identical to that of Figure 4-4, with .

KrsI A KEC+–()

1–

BPs()+-

Gs() Kr

=sI A–BKr

+()

1–KE

Hs() KRsI A–KEC+()

1–BK

ˆPI