Modern Control Engineering

Example Problems and Solutions 525

Frequency (rad/sec)

Bode Diagrams of G(s) = K/[s(s + 1)(s + 5)], where K = 1, K = 10, and K = 20

− 140

Gain (dB)

− 120

− 100

− 80

− 60

− 40

− 20

20

0

10 −^1100101102

K = 10

K = 1 K = 20

(a)

Frequency (rad/sec)

− 300

− 200

− 150

− 100

− 50

− 250

0

Phase (deg)

10 −^1100101102

K = 10 K = 20

K = 1

(b)

Figure 7–121
Bode diagrams:
(a) Magnitude-
versus-frequency
curves; (b) phase-
angle-versus-
frequency curves.

A–7–5. Prove that the polar plot of the sinusoidal transfer function

is a semicircle. Find the center and radius of the circle.

G(jv)=

jvT

1 +jvT

, for 0 vq