User's Manual

Chapter 6 Tutorial
© National Instruments Corporation 6-5 Xmath Model Reduction Module
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
6.264×10
–2
4.901×10
–2
2.581×10
–2
2.474×10
–2
1.545×10
–2
1.335×10
–2
9.467×10
–3
9.466×10
–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