Bode diagram

Control system
Bode diagram
Copyright © 2014 Addaani

Group names:
1. A/rizak mohamed ahmed……31
2. A/kadir A/llahi adan…………34
3. Abukar Hassan Takow………38
4. Ahmed A/aziiz yasiin…………64
Lecturer:
ENG-mahamuud A/qadir

Outline
part: one
Introduction to frequency response
Amplitude ratio and phase
part: two
Introduction to bode diagram
System analysis using bode diagram

Frequency response
• System response to sinusoidal input is known us
frequency response
• Range of frequency used
• Used for system identification
• Used for stability analysis

Frequency response
System behavior determined from the steady state
response to sinusoidal input in the form
R =Asineᾢt
Sine wave used :
 Easy to analyse
 Easy to generate
 Easy to measure experimentally

Cont……
Sinusoidal applied to linear system:
 Output will be sinusoidal
 Output amplitude is proportional to input
 Harmonic input produces harmonic output at same
frequency
 Variation amplitude and phase
 Function of frequency

CONT……
If output flows input is known lag system

BODE DIAGRAM
PART :TWO
BODE DIAGRAM

INTRODUCTION
Hendrik Wade Bode (1905–1982), while working at Bell
Labs in the United States in the 1930s, devised a simple
but accurate method for graphing gain and phase-shift
plots.
These bear his name, Bode gain plot and Bode phase plot.
Copyright © 2014

What is Bode plot?
The Bode plot is the frequency response plot of the
transfer function of a system.
Bode plot consists of two graphs:
 One is the plot of magnitude of sinusoidal transfer
function versus log .
 The other is a plot of the phase angle of a sinusoidal
function versus log .

BODE DIAGRAM

BODE PLOTS
A Bode plot is a standard format for plotting frequency
response of LTI systems.
Becoming familiar with this format is useful because:
 It is a standard format, so using that format facilitates
communication between engineers.
 Many common system behaviors produce simple shapes
(e.g. straight lines) on a Bode plot, so it is easy to either
look at a plot and recognize the system behavior, or to
sketch a plot from what you know about the system
behavior.

cont
• That format is a log frequency scale on the horizontal axis and, on the
vertical axis, phase in degrees and magnitude in decibels. Thus, we begin
with a review of decibels:
 Decibels
Definition: for voltages or other physical variables (current, velocity, pressure,
etc.)
(Since power is proportional to voltage squared (or current, velocity,
pressure, etc.,
squared)

Constructing bode diagram
Constructing bode diagram
 Section of TF can be represented as straight lines =asymptotic
approximation
Example:

Phase

Cont…..
Phase plot :this has three asymptotes
 A LF horizontal asymptote at 0
 A HF horizontal asymptote at -45
 A mid –frequency asymptote that intersects between
HF and LF asymptote -90

Cont…..
Each of TF has certain type of frequency response:
Building blocks:
 Gain
 Differentiator
 Integrator
 First order/second order

Gain………K
• Constant terms such as K contribute a straight
horizontal line of magnitude 20 log10(K)
• A positive constant, K has no effect on phase

Differentiator…….. | j |
• A zero at the origin occurs when there is an s or j?
multiplying the numerator. Each occurrence of this
• causes a positively sloped line passing through ? = 1
with a rise of 20 db over a decade.

Cont…….
• Effect of Zeros at the origin on Phase Angle:
• Zeros at the origin, s, cause a constant +90 degree
shift for each zero.

Integrator………1/s or 1/jw
• A pole at the origin occurs when there are s or j?
multiplying the denominator. Each occurrence of this
• causes a negatively sloped line passing through ? = 1
with a drop of 20 db over a decade.

Cont……
• Effect of Poles at the origin on Phase Angle:
• Poles at the origin, s -1, cause a constant -90 degree
shift for each pole.

first order lead

1’s order lag

Rules for Making Bode Plots

Bode plots
Where do the Bode diagram lines comes from?
1) Determine the Transfer Function of the system:
2) Rewrite it by factoring both the numerator and denominator into
the standard form
where the z s are called zeros and the p s are called poles.

Con…….
3) Replace s with j? . Then find the Magnitude of the Transfer
Function.
If we take the log10 of this magnitude and multiply it by 20 it takes
on the form of

Example 1:
For the transfer function given, sketch the Bode log magnitude
diagram which shows how the log magnitude of the system is
affected by changing input frequency. (TF=transfer function)
Step 1: Repose the equation in Bode plot form:

Con……..

Example 2:
Your turn. Find the Bode log magnitude plot for the transfer
function,
Start by simplifying the transfer function form:

Technique to get started:

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FOR YOUR
LISTENING

Bode diagram

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