Modern Control Engineering

Section 7–5 / Nyquist Stability Criterion 445

|G

| in dB

20

10

0

–10

–20

–180° 0 ° 180 °

G

|G

| in dB

20

10

0

–10

–20

–180° 0 ° 180 °

G

|G

| in dB

20

10

0

–10

–20

–180° 0 ° 180 °

G

|G

| in dB

20

10

0

–10

–20

–180° 0 ° 180 °

G

|G

| in dB

20

10

0

–10

–20

–180° 0 ° 180 °

G

|G

| in dB

20

10

0

–10

–20

–180° 0 ° 180 °

G

v

v

0

v = 1





G =j^1 v G^ =

1

1 + jvT

v v = 0

G =(jv)

(^2) + 2zvn(jv) + vn 2
vn^2
G = 1 + jvT
G =e–jvL
G =^1
jv(1 + jvT)
 v
v = 0

v = 0 v

v
v = 0

v
v
0

Table 7–2 Log-Magnitude-versus-Phase Plots of Simple Transfer Functions

7–5 Nyquist Stability Criterion

The Nyquist stability criterion determines the stability of a closed-loop system from its

open-loop frequency response and open-loop poles.

This section presents mathematical background for understanding the Nyquist sta-

bility criterion. Consider the closed-loop system shown in Figure 7–44. The closed-loop

transfer function is

C(s)

R(s)

=

G(s)

1 +G(s)H(s)