1. The document discusses frequency response analysis techniques, which analyze how a system responds to input signals of varying frequencies. 2. It describes two common frequency response techniques - Bode plots, which show magnitude and phase response as functions of frequency, and Nyquist plots, which plot magnitude against phase on a polar graph. 3. The techniques provide insights into system stability and dynamics and are useful for control system design, but their use requires complex derivations and they do not always directly indicate transient response characteristics.

1. Topic :
SUBMITTED TO : PROFESSOR DR. AZIZA AFTAB
GROUP : MURTAZA SHAH G.L (16CH48)
AWAIS SHAIKH A.G.L (16CH52)
SIKANDAR ALI (16CH45)
IFTIKHAR AHMAD (16CH47)
RAKESH KUMAR (16CH104)
DEPARTMENT OF CHEMICAL ENGINEERING MUET JAMSHORO

2. Contents:
 Introduction to Frequency & its types
 Frequency Response basic concept
 Frequency Response Analysis
 Frequency Response Techniques
Bode Plot
Nyquist Plot
 Bode plot Vs Nyquist plot
 Adv: and dis-adv: of Frequency Response Techniques

3. Introduction to Frequency Response
 What is Frequency?
 The rate at which something occurs over
a particular period of time or in a given
sample.
 For example :
If an object is vibrating 5 times
Per second then its frequency is
Equal to 5 Hertz
 Hertz is the unit of frequency that is equal
to Number of Vibrations per Second

4. Types of Frequency Example
Natural human voice spans a frequency range from
20Hz to 20KHz, however conventional telephone
system passes frequencies from 400Hz to 3.5KHz.
Therefore phone conversation differs from face-to-
face conversation.
Natural Voice Telephone System

5. Concept of Frequency Response
Frequency Response
 it is defined as Analysis of systems through test signal at input and
checking the output.
 It is use to analyze the stability of system. Any deviation taking place in
system can be noted by change in Frequency.
Analysis of System
 System can be analyzed in two ways
1. Analyzing the system with respect to TIME
2. Analyzing the system with respect to Frequency

6. Frequency Response Analysis
 Since analyzing the system w.r.t time is tedious
and difficult process
 We convert time domain signal to frequency
domain signal
 This can be done using LAPLACE
TRANSFORMATION which provides a neat and
better way to analyze system for stability and
other parameters.
the portable device for frequency response
analysis of high voltage equipment insulation
and power transformers windings

7. Explanation of 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
system
SIN ωt
INPUT
ASin (ωt+φ)
Output

8.  Mathematically ;
 Input : SIN ωt
 Output : ASin (ωt+φ)
Where A = Amplitude of System
ω = Angular Frequency of input Signal
φ = Phase of System
 Reference Input r(t)= Sin(wt)
 Since we are giving sin(wt) as input we can substitute s=jω in our Transfer
Function.

9. Continued….
 Transfer Function
G(s) = G( jw ) = |G( jw)| < G(jw)
Where |G( jw)| = Magnitude Spectrum
< G(jw) = Phase Spectrum
 Output Signal we get
c=(t)= A|G(jw)| Sin(wt+<G(jw))
 So this output shows that amplitude vary with transfer function, It can be
obtained by multiplying magnitude with input function
 The Frequency is not going to vary but the phase is going to vary.

10. Frequency Response Techniques
 Frequency Response Techniques refers to the methods
involved in analyzing the frequency output generated by the
system that is being tested for Stability
 There are two techniques of Frequency Response
A. Polar plot or (Nyquist Criterion)
B. Bode Plot

11. Bode Plot:
 The log-magnitude and phase frequency response curves as functions of log(ω) are called Bode
plots or Bode diagrams.
 Sketching Bode plots can be simplified because they can be approximated as a sequence of straight
lines. Straight-line approximations simplify the evaluation of the magnitude and phase frequency
response.
 if we knew the response of each term, the algebraic sum would yield the total response in dB.
Further, if we could make an approximation of each term that would consist only of straight lines,
graphical addition of terms would be greatly simplified.

12. Bode Plots for G(s) = (s + a):
 Consider a function, G(s) = (s + a), for which we want to sketch separate
logarithmic magnitude and phase response plots. Letting s = jω, we have.
 Where a < ω < ∞. Notice from the middle term that the high-frequency
approximation is equal to the low-frequency approximation when ω = a and
increases For ω > a.

13. Magnitude & Phase Plot:

14. Video for plotting BODE plot

15. Polar plot or (Nyquist Criterion):
 The polar plot of any transfer function is a plot of the magnitude Vs phase
angle on a polar coordinates.
 The Nyquist criterion relates the stability of a closed-loop system to the
open-loop frequency response and open-loop pole location.
 This concept is similar to the root locus, where we began with information
about the open-loop system, its poles and zeros, and developed transient
and stability information about the closed-loop system.
 Thus, frequency response techniques are an alternate approach to the root
locus.
 ω varied from 0 to infinity.

16. Derivation of the Nyquist Criterion:
 Consider the system of Figure10.20. The Nyquist criterion can tell us how many closed loop
poles are in the right half-plane.
 Before deriving the criterion, let us establish four important concepts that will be used during
the derivation:(1) the relationship between the zeros of1+G(s)H(s)and the poles of the closed-
loop transfer function, T(s);(2) the concept of Mapping points; and (3) the concept of mapping
contours. Letting
 Next, let us define the term mapping. If we take a complex number on the s-plane and
substitute it into a function F(s), another complex number results. This process is called
mapping

17. Video for Nyquist Plot:

18. Bode Plot Vs Nyquist Plot:

19. Advantages of Frequency Response
Techniques
 Frequency response techniques play an important role in
control system design and analysis.
 It is most reliable and uncomplicated method for the
experimental analysis of a system
 FRT are used to compute the response of the structure
which is actually transient in a static frequency domain.

20. Continued…
 FRT are used to characterize the dynamics of the system and it
is applicable to all orders and types of dynamics model .
 It provides good designs in the face of uncertainty in the plant
model.
 We can determine the stability of non linear systems by using
frequency response techniques.
 it is also a good indicator of transient response.

21. Drawbacks of Frequency Response
Techniques
 Complicated derivations are used.
 Time consuming
 it is not always easy to deduce transient response characteristics from a
knowledge of the frequency response.
 Diagrams represents expected results for a model not necessarily the
real process.
 it can be difficult to generate low-frequency signals and obtain the
necessary measurements.