Module 12
Frequency Response and
Nyquist Diagram
(2 hours)
12.1 Introduction of the Frequency Response
12.1.1 Why do we should study the Frequency Response
(P223,Paragraph 2)
12.1.2 What is the Frequency Response?
—The frequency response of a system is defined as the
steady-state response of the system to a sinusoidal input
signal,The sinusoid is a unique input signal,and the
resulting output signal for a linear system,as well as
signals throughout the system,is sinusoidal in the steady-
state; it differs from the input waveform only in amplitude
and phase angle.
–– The frequency response is a kind of model of
system,
jssGjG )()(
Differential Equation
Transfer
Function
Frequency Response
System
dt
ds?
js?
dt
dj
Nyquist Diagram
12.2 Different forms of the Frequency Response
Bode Diagram
Nichols Diagram
12.3 Nyquist Diagram
Im
Re
0
K
90?
Im
Re
0
1?n
2?n
3?n
Im
Re
0 )1(rM
)1(
Im
Re
0
490 1 tg
490 1 tg
Other Example (P232-P237)
SP,12.1 (P232)
)13)(12(
1.0)(

sss
sGH
Determine the frequency ωg at which the phase angle is –
180°,
Ex,1 The unstable open-loop system
1
1)(
Ts
sGH
Ex,2
)1)(1)(1(
)(
321
sTsTsT
KsGH
Ex,3
)1)(1(
)(
21
sTsTs
KsGH
Ex,4
)1(
)( 2
Tss
KsGH
Ex,5
)1(
)1()(
2
2
1

sTs
sTKsGH
Ex,6
3)( s
KsGH?
Ex,7
3
21 )1)(1()(
s
sTsTKsGH
Ex,8
)1(
)(
Tss
KsGH
Instructional objectives:
At the end of this lecture students
should be able to
Plot the Nyquist diagram of the basic
system
Plot the Nyquist diagram of the open-loop
system