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Wk 12 fr bode plot nyquist may 9 2016
1. Chapter 5
Week 12 -Frequency Response Analysis
Topics:
Control System Engineering
PE-3032
Prof. CHARLTON S. INAO
Defence Engineering College,
Debre Zeit , Ethiopia
3. Terminologies- Frequency , Amplitude ,
Phase
• Frequency, or its inverse, the period- is the
number of occurrences of a repeating event
per unit time. The number of cycles per unit
of time is called the frequency.
The hertz (symbol Hz) is the SI unit of frequency defined as the
number of cycles per second of a periodic phenomenon. One
of its most common uses is the description of the sine wave,
particularly those used in radio and audio applications, such
as the frequency of musical tones. The word "hertz" is named
for Heinrich Rudolf Hertz, who was the first to conclusively
prove the existence of electromagnetic wave.
• Period is the inverse of frequency
4.
5. Bode Plot :Introduction
• The plot of magnitude as well as phase angle
versus frequency may represent a sinusoidal
transfer function.
• Hendrik Wade Bode used the logarithmic
scale extensively for the study of the
magnitude of the transfer function and the
frequency variable. The logarithmic plot is
called Bode Plot.
6. • A Bode plot, named after Hendrik Wade Bode,
is usually a combination of a Bode magnitude
plot and Bode phase plot:
• A Bode magnitude plot is a graph of log
magnitude against log frequency often used in
signal processing to show the transfer
function or frequency response of a linear,
time-invariant system.
7. Phase and Gain Cross Over
Frequency
The gain cross over frequency is the frequency
at which the magnitude of the open loop
transfer function is UNITY.
The phase cross over frequency is the
frequency at which the phase of the open loop
transfer function is 180o.
34. Frequency VS Magnitude
ω (rad/sec)
A(magnitud
e)
0.5 -12 dB
5 28 dB
50 48 dB
100 48 dB
First corner
frequency, ωc1
second corner
frequency, ωc2
Chosen Lower limit
frequency, ωL
Chosen pper limit
limit frequency, ωh
55. Example: Bode diagram of the open loop systems
G(s)H(s) could be regarded as:
Then we have:
101.0
1
s
1
1)(s10
)101.0(
)1(10
)()(
22
sss
s
sHsG
① ② ③ ④
0dB, 0o
1001010.1
)(log
)(),( L
③
④
②
①
20dB, 45o
-20dB, -45o
-40dB, -90o
40dB, 90o
-80dB,-180o
-60dB.-135o
-40dB/dec
-20dB/dec
20dB/dec
-40dB/dec
-20dB/dec
-40dB/dec
5/30/2016 55
82. (rad/sec)
dB Mag
Phase
(deg)
1 1 1 1 1 1
wlg
This is a sheet of 5 cycle, semi-log paper.
This is the type of paper usually used for
preparing Bode plots.
Semi log paper used in Bode Plots
84. Week 12 Frequency Response Analysis
Topics:
Control System Engineering
PE-3032
Prof. CHARLTON S. INAO
Defence Engineering College,
Debre Zeit , Ethiopia
85. Instructional Objectives
At the end of this lecture, the students shall be able to:
1. Conduct review of Frequency Response
fundamentals
2. Discuss the parameters in Nyquist Plot construction
3. Understand Nyquist Stability Criterion
116. Summary
Gain Margin= reciprocal of the magnitude of
the locus of frequency response as it first
touch the real axis, i. e.,at the phase cross
over frequency. Kg=1/G(jw)pc
Phase Margin= the angle through which the gain
cross over line must be rotated to reach the real axis
and pass through the unit circle(gain cross over
frequency)
(-1, j0). γ= 180 +φgc