790 Chapter 10 / Control Systems Design in State SpaceOutputyt (sec)Unit-Step Response of
(302s^2 + 303s + 256)/(s^5 +18s^4 + 114s^3 + 320s^2 + 416s + 256)0.60.811.21.40.40.20
012345678910Figure 10–30
Unit-step response of
the control system
shown in Figure
10–29.Configuration 2: A different configuration of the control system is shown in Figure
10–31. The observer controller is placed in the feedback path. The input ris introduced
into the closed-loop system through the box with gain N. From this block diagram, the
closed-loop transfer function is obtained as
We determine the value of constant Nsuch that for a unit-step input r, the output yis
unity as tapproaches infinity. Thus we choose
The unit-step response of the system is shown in Figure 10–32. Notice that the maxi-
mum overshoot is very small, approximately 4%. The settling time is about 5 sec.
N=
256
113
=2.2655
Y(s)
R(s)
=
NAs^2 +18s+ 113 B
sAs^2 + 1 BAs^2 +18s+ 113 B+302s^2 +303s+ 256
Nr+u y- u
r
+–302 s^2 + 303 s+ 256
s^2 + 18 s+ 1131
s(s^2 + 1)NFigure 10–31
Control system with
observer controller
in the feedback path.Openmirrors.com