National Instruments NI MATRIXx Xmath User Manual
Page 101
Chapter 6
Tutorial
6-6
ni.com
Figures 6-3, 6-4, and 6-5 display the outcome of the reduction. The loop
gain is shown in Figure 6-3. The error near the unity gain crossover
frequency may not look large, but it is considerably larger than that
obtained through frequency weighted reduction methods, as described
later.
Figure 6-3 also shows the inability to suppress all three plant resonances,
in contrast to the full-order controller. Two are such as to cause violation
of the specifications. The closed-loop gains differ by some 4 to 5 dB
between the full-order and reduced-order controller, in the vicinity of
0.1 radians per second. The step response has overshoot of 50% as opposed
to 40% and the ripple persists for longer.
We use the
compare( )
function (refer to the
section of
) to reproduce Figures 6-4 and 6-5. Calculate the
full-order closed-loop system, then the closed-loop system with the
reduced-order compensator:
syscl = feedback(sysol);
sysolr=sys*syscr;
sysclr=feedback(sysolr);