Page 566 - Linear Control System D'Azzo (5th Edition)

548 Chapter 14

FIGURE 14.5 Control: (a) unity feedback; (b) state feedback; (c) state feedback,
H-equivalent. The nominal values are p1 ¼ À1, p2 ¼ À5 and A ¼ 10.

Note that M is the control ratio. The passband frequency is ob ¼ 0.642 for the
system of Fig. 14.5a with nominal values, and ob ¼1.0 for the state-feedback
system of Figs. 14.5b and 14.5c with nominal values.

The control ratios for each of the three cases to be analyzed are

Figure 14.5a:

M ðsÞ ¼ s3 À ðp1 þ 10A p1p2s þ 10A ð14:24Þ
p2Þs2 þ

Figure 14.5b:

10A
M ðsÞ ¼ s3 þ ð2Ak3 À p1 À p2Þs2 þ ½p1p2 þ 2Að5k2 À k3p2ފs þ 10Ak1

ð14:25Þ

Figure 14.5c:

M ðsÞ ¼ s3 þ ð2Ak3 À p1 À p2Þs2 þ 10A þ 10Aðk3 þ k2ފs þ 10Ak1
½p1p2

ð14:26Þ

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