Page 363 - Modern Control Systems

Section 5.7 Performance Indices 337
1.2

& 0.8

Normalized time
FIGURE 5.30 (c)
[Continued)
The standard form for a third-order system given in Table 5.6 requires that
_
,.3
.2
2£&>o = 1.75w„, 0)1 = 2.15(0% , and K aK„,o)Q 0)„
Examining Figure 5.30(c) for n = 3, we estimate that the settling time is approxi-
mately 8 seconds (normalized time). Therefore, we estimate that
a) nT s = 8.
Because a rapid response is required, a large o)„ will be selected so that the settling
time will be less than 1 second. Thus, o)„ will be set equal to 10 rad/s. Then, for an
ITAE system, it is necessary that the parameters of the camera dynamics be
(o 0 = 14.67 rad/s
and
C = 0.597.
The amplifier and motor gain are required to be

(t>, t
K K = - 3 = = 4.65.
0)1 2X50)1 2.15
Then the closed-loop transfer function is
1000
T(s) = 3
s + 17.5 J + 2155 + 1000
2
1000
(5.49)
(s + 7.08)(5 + 5.21 + /10.68)(5 + 5.21 - /10.68)