Modern Control Engineering

482 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

peak value Mrand the resonant frequency vrcan be found from the M-circle tangency

to the G(jv)locus. (In the present example,Mr=2andvr=v 4 .)

Nichols Chart. In dealing with design problems, we find it convenient to construct

theMandNloci in the log-magnitude-versus-phase plane. The chart consisting of the

MandNloci in the log-magnitude-versus-phase diagram is called the Nichols chart.

The G(jv)locus drawn on the Nichols chart gives both the gain characteristics and

a

=

G

1

+

G

M

=

G

1

+

G

Im

Re

Im

Re

2

0 0

• 2


• 2


• 4


• 4 – 4 – 2

2

• 2


• 4

M= 1.2

M= 1.4

M= 1.1

M= 1.1

M= 2

M= 0.6

M= 1.2

G(jv)

v 1 G(jv)

(a) (b)

(c)

20 °

60 °

• 20 °
  
  
  • 40 °
  
  
  
  


• 10 °

v 1

v 2

v 2

v (^3) v 3
v 4
v 4
v 5 v 5
2
1.5
1
0.5
0
0 °

• 90 °


• 180 °


• 270 °
  v 1 v 2 v 3 v 4 v 5 v

v

Figure 7–83

(a)G(jv)locus

superimposed on a

family of Mcircles;

(b)G(jv)locus

superimposed on a

family of Ncircles;

(c) closed-loop

frequency-response

curves.

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