Modern Control Engineering

Example Problems and Solutions 373

(z=0.7 corresponds to a line having an angle of 45.573° with the negative real axis.) Hence, the

desired closed-loop poles are at

The open-loop poles and the desired closed-loop pole in the upper half-plane are located in the

diagram shown in Figure 6–83(b). The angle deficiency at point s=–0.35+j0.357is

This means that the zero at must contribute 11.939°, which, in turn, determines the

location of the zero as follows:

s=-

1

Td

=-2.039

s=- 1 Td

- 166.026°-25.913°+ 180 °=-11.939°

s=-0.35;j0.357

+

(a)

(b)

Kp(1+Tds)^1

10000 (s^2 – 1.1772)

0

jv

s

45.573°

j 3

j 2

j 1

• j 1


• j 3


• j 2

25.913°

166.026°

Closed-loop pole

• 4 – 3 – 2.039 –1.085 1.085 2

Figure 6–83
(a) PD control of an
unstable plant;
(b) root-locus
diagram for the
system.