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 :TWOBODE 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

Section of TF can be represented as straight lines =asymptotic

approximation

Example:


Constructing bode diagram

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:


Bode diagram

Engineering

Transcript of Bode diagram