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Frequency Response Analysis
(Bode & Polar Plot)
Presented by
Mr. C.S.Satheesh, M.E.,
Assistant Professor, Department of EEE,
Muthayammal Engineering College (Autonomous),
Namakkal (Dt), Rasipuram – 637408
MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC, NBA & Affiliated to Anna University),
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu, India.
Introduction - Frequency-Response Analysis
-By the term frequency response, we mean the steady-
state response of a system to a sinusoidal input.
- In frequency-response methods, we vary the frequency
of the input signal over a certain range and study the
resulting response.
Frequency-Response Analysis
4
Frequency-Response Analysis
Advantages of the frequency-response approach
1. We can use the data obtained from measurements on the
physical system without deriving its mathematical model.
2. Frequency-response tests are, in general, simple and can be
made accurately by use of readily available sinusoidal signal
generators and precise measurement equipment.
3. The transfer functions of complicated components can be
determined experimentally by frequency-response tests.
4. A system may be designed so that the effects of undesirable
noise are negligible and that such analysis and design can be
extended to certain nonlinear control systems.
The performance characteristics of a system in frequency domain are
measured in terms frequency domain specifications
Frequency domain specifications are
 Resonant Peak Mr
 Resonant Frequency ωr
 Bandwidth ωh
 Cut – off Rate
 Gain margin Kg
 Phase margin γ
Frequency Domain Specifications
Resonant Peak Mr
The maximum value of magnitude of closed loop transfer
function is called resonant peak.
A large resonant peak corresponds to a large overshoot in
transient response
For second order system
Frequency Domain Specifications
Resonant Frequency ωr
The frequency at which the resonant peak occurs is Resonant
Frequency .
This is related to frequency of oscillation in step response.
Indicative of speed of transient response for second order system
Frequency Domain Specifications
Bandwidth ωh
Range of frequencies for which normalized gain of the system is more
than -3dB
Frequency at which gain is -3dB is called cut-off frequency
Bandwidth is defined for closed loop system and transmit signals
whose frequency are less than cut – off frequency
Measure of ability of feedback system to reproduce i/p signal, noise
rejection characteristics & rise time
Large BW corresponds to small rise time or fast response
Frequency Domain Specifications
Cut – off Rate
•The slope of the log-magnitude curve near the cut off frequency is called
Cut – off Rate
•It Indicates the ability of the system to distinguish the signal from noise
Frequency Domain Specifications
Gain Margin Kg
The value of gain, to be added to system, in order to bring the
system to the verge of instability
•Gain Margin Kg is given by reciprocal of magnitude of open loop
transfer function at phase crossover frequency
•The frequency at which the phase of open loop transfer function is
180° is called the phase crossover frequency ωpc
Frequency Domain Specifications
The gain margin in dB is given by negative of dB magnitude of G(jω) at phase
crossover frequency Indicates the additional gain that can be provided to system
without affecting the stability of the system
EC8391
Frequency Domain Specificatins
Phase Margin γ
The additional phase lag to be added to the gain cross over frequency in
order to bring the system to the verge of instability
The gain cross over frequency ωgc is the frequency at which the magnitude
of open loop transfer function is unity (or is the frequency at which the dB
magnitude is zero)
Phase Margin γ is obtained by adding 180° to the phase angle φ of the
open loop transfer function at the gain crossover frequency
Indicates the additional phase lag that can be provided to system without
affecting the stability of the system
Frequency Domain Specifications
• Indicates the additional phase lag that can be provided to system
without affecting the stability of the system
• Note: The gain margin of second order system is infinite
Frequency Domain Specifications
15
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22
23
24
25
26
27
28
29
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31
32
33
35
36
37
POLAR PLOT
POLAR PLOT
PROBLEM
c1=1/1= 1 rad/sec= c2
c2=1/2= 0.5 rad/sec= c1
Assignment
Problem
References :
 A.Nagoorkani, Control Systems,
RBA Publications.
63
Thank You
64

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Frequency response analysis

  • 1. Frequency Response Analysis (Bode & Polar Plot) Presented by Mr. C.S.Satheesh, M.E., Assistant Professor, Department of EEE, Muthayammal Engineering College (Autonomous), Namakkal (Dt), Rasipuram – 637408 MUTHAYAMMAL ENGINEERING COLLEGE (An Autonomous Institution) (Approved by AICTE, New Delhi, Accredited by NAAC, NBA & Affiliated to Anna University), Rasipuram - 637 408, Namakkal Dist., Tamil Nadu, India.
  • 2. Introduction - Frequency-Response Analysis -By the term frequency response, we mean the steady- state response of a system to a sinusoidal input. - In frequency-response methods, we vary the frequency of the input signal over a certain range and study the resulting response.
  • 5. Advantages of the frequency-response approach 1. We can use the data obtained from measurements on the physical system without deriving its mathematical model. 2. Frequency-response tests are, in general, simple and can be made accurately by use of readily available sinusoidal signal generators and precise measurement equipment. 3. The transfer functions of complicated components can be determined experimentally by frequency-response tests. 4. A system may be designed so that the effects of undesirable noise are negligible and that such analysis and design can be extended to certain nonlinear control systems.
  • 6. The performance characteristics of a system in frequency domain are measured in terms frequency domain specifications Frequency domain specifications are  Resonant Peak Mr  Resonant Frequency ωr  Bandwidth ωh  Cut – off Rate  Gain margin Kg  Phase margin γ Frequency Domain Specifications
  • 7. Resonant Peak Mr The maximum value of magnitude of closed loop transfer function is called resonant peak. A large resonant peak corresponds to a large overshoot in transient response For second order system Frequency Domain Specifications
  • 8. Resonant Frequency ωr The frequency at which the resonant peak occurs is Resonant Frequency . This is related to frequency of oscillation in step response. Indicative of speed of transient response for second order system Frequency Domain Specifications
  • 9. Bandwidth ωh Range of frequencies for which normalized gain of the system is more than -3dB Frequency at which gain is -3dB is called cut-off frequency Bandwidth is defined for closed loop system and transmit signals whose frequency are less than cut – off frequency Measure of ability of feedback system to reproduce i/p signal, noise rejection characteristics & rise time Large BW corresponds to small rise time or fast response Frequency Domain Specifications
  • 10. Cut – off Rate •The slope of the log-magnitude curve near the cut off frequency is called Cut – off Rate •It Indicates the ability of the system to distinguish the signal from noise Frequency Domain Specifications
  • 11. Gain Margin Kg The value of gain, to be added to system, in order to bring the system to the verge of instability •Gain Margin Kg is given by reciprocal of magnitude of open loop transfer function at phase crossover frequency •The frequency at which the phase of open loop transfer function is 180° is called the phase crossover frequency ωpc Frequency Domain Specifications
  • 12. The gain margin in dB is given by negative of dB magnitude of G(jω) at phase crossover frequency Indicates the additional gain that can be provided to system without affecting the stability of the system EC8391 Frequency Domain Specificatins
  • 13. Phase Margin γ The additional phase lag to be added to the gain cross over frequency in order to bring the system to the verge of instability The gain cross over frequency ωgc is the frequency at which the magnitude of open loop transfer function is unity (or is the frequency at which the dB magnitude is zero) Phase Margin γ is obtained by adding 180° to the phase angle φ of the open loop transfer function at the gain crossover frequency Indicates the additional phase lag that can be provided to system without affecting the stability of the system Frequency Domain Specifications
  • 14. • Indicates the additional phase lag that can be provided to system without affecting the stability of the system • Note: The gain margin of second order system is infinite Frequency Domain Specifications
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  • 43. PROBLEM c1=1/1= 1 rad/sec= c2 c2=1/2= 0.5 rad/sec= c1
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  • 63. References :  A.Nagoorkani, Control Systems, RBA Publications. 63