User`s guide

modred
11-142
11modred
Purpose Model order reduction
Syntax rsys = modred(sys,elim)
rsys = modred(sys,elim,'mdc')
rsys = modred(sys,elim,'del')
Description modred reduces the order of a continuous or discrete state-space model sys.
Thisfuncti on is usually used in conjunctionwith
balreal. Two order reduction
techniques are available:
•
rsys = modred(sys,elim) or rsys = modred(sys,elim,'mdc') produces a
reduced-orde rmodel
rsys with matching DCgain(orequivalently, matching
steady state in the step response). The index vector
elim specifies the states
to be eliminated. The resulting model
rsys has length(elim) fewer states.
This technique consists of setting the derivative of the eliminated states to
zero and solving for the remaining states.
•
rsys = modred(sys,elim,'del')simply deletes the statesspecified by elim.
While this method does not guarantee matching DC gains, it tends to
produce better approximations in the frequency domain (see example below).
If the state-space model sys has been balanced with
balreal and the gramians
have small diagonal entries, you can reduce the model order by eliminating
the last states with
modred.
Example Consider the continuous fourth-order model
To reduce its order, first compute a balanced state-space realization with
balreal by typing
h = tf([1 11 36 26],[1 14.6 74.96 153.7 99.65])
[hb,g] = balreal(h)
g'
MATLAB returns
ans =
1.3938e–01 9.5482e–03 6.2712e–04 7.3245e–06
m
m
hs()
s
3
11s
2
36s 26+++
s
4
14.6+ s
3
74.96s
2
153.7s 99.65+++
------------------------------------------------------------------------------------------------------=