National Instruments Xmath Additive Error Reduction

Additive Error Reduction

This chapter describes additive error reduction including discussions of

truncation of, reduction by, and perturbation of balanced realizations.

Additive error reduction focuses on errors of the form,

where G is the originally given transfer function, or model, and Gr is the

reduced one. Of course, in discrete-time, one works instead with:

As is argued in later chapters, if one is reducing a plant that will sit inside

a closed loop, or if one is reducing a controller, that again is sitting in a

closed loop, focus on additive error model reduction may not be

appropriate. It is, however, extremely appropriate in considering reducing

the transfer function of a filter. One pertinent application comes specifically

from digital filtering: a great many design algorithms lead to a finite

impulse response (FIR) filter which can have a very large number of

coefficients when poles are close to the unit circle. Model reduction

provides a means to replace an FIR design by a much lower order infinite

impulse response (IIR) design, with close matching of the transfer function

at all frequencies.

Gjω()Grjω()–∞

jω

()Grejω

()–∞