National Instruments NI MATRIXx Xmath User Manual
Page 22
Chapter 1
Introduction
© National Instruments Corporation
1-15
Low Order Controller Design Through Order Reduction
The Model Reduction Module is particularly suitable for achieving low
order controller design for a high order plant. This section explains some of
the broad issues involved.
Most modern controller design methods, for example, LQG and H
∞
, yield
controllers of order roughly comparable with that of the plant. It follows
that, to obtain a low order controller using such methods, one must either
follow a high order controller design by a controller reduction step,
or reduce an initially given high order plant model, and then design a
controller using the resulting low order plant, with the understanding that
the controller will actually be used on the high order plant. Refer to
Figure 1-2.
Figure 1-2. Low Order Controller Design for a High Order Plant
Generally speaking, in any design procedure, it is better to postpone
approximation to a late step of the procedure: if approximation is done
early, the subsequent steps of the design procedure may have unpredictable
effects on the approximation errors. Hence, the scheme based on high order
controller design followed by reduction is generally to be preferred.
Controller reduction should aim to preserve closed-loop properties as far
as possible. Hence the controller reduction procedures advocated in this
module reflect the plant in some way. This leads to the frequency weighted
reduction schemes of
wtbalance( )
and
fracred( )
, as described in
Frequency-Weighted Error Reduction
. Plant reduction logically
should also seek to preserve closed-loop properties, and thus should involve
the controller. With the controller unknown however, this is impossible.
Nevertheless, it can be argued, on the basis of the high loop gain property
within the closed-loop bandwidth that is typical of many systems, that
High Order Plant
Plant
Low Order Plant
High Order Controller
Controller
Low Order Controller
Reduction
Reduction