Controller reduction, Figure 6-3. open-loop gain using redschur, Controller reduction -5 – National Instruments NI MATRIXx Xmath User Manual
Page 100
Chapter 6
Tutorial
© National Instruments Corporation
6-5
Controller Reduction
This section contrasts the effect of unweighted and weighted controller
reduction. Unweighted reduction is at first examined, through
redschur( )
(using
balance( )
or
balmoore( )
will give similar
results). The Hankel singular values of the controller transfer function are
6.264
Ч10
–2
4.901
Ч10
–2
2.581
Ч10
–2
2.474
Ч10
–2
1.545
Ч10
–2
1.335
Ч10
–2
9.467
Ч10
–3
9.466
Ч10
–3
A reduction to order 2 is attempted. The ending Hankel singular values, that
is,
σ
3
,
σ
4
, ...,
σ
8
, have a sum that is not particularly small with respect to
σ
1
and
σ
2
; this is an indication that problems may arise in the reduction.
[syscr,hsv] = redschur(sysc,2);
svalsRol = svplot(sys*syscr,w,{radians});
plot(svalsol, {keep})
f3=plot(wc, constr,{keep,!grid,
legend=["reduced","original","constrained"],
title="Open-Loop Gain Using redschur()"})
Figure 6-3. Open-Loop Gain Using redschur