This document contains slides about time domain analysis prepared by Syed Hasan Saeed. It defines concepts like transient response, steady state response, and steady state error. It also discusses commonly used test signals for time response analysis, including step functions, ramp functions, parabolic functions, and impulse functions. The Laplace transforms of these signals are provided.
This presentation gives complete idea about time domain analysis of first and second order system, type number, time domain specifications, steady state error and error constants and numerical examples.
this is presentation about time response analysis in control engineering. this is presentation on its types and many more like time responses with best example
Time Response Analysis of system
Standard Test Signals
What is time response ?
Types of Responses
Analysis of First order system
Analysis of Second order system
ppt on Time Domain and Frequency Domain Analysissagar_kamble
in this presentation, you will be able to know what is this freq. and time domain analysis.
At last one example is illustreted with video, which distinguishes these two analysis
Giving description about time response, what are the inputs supplied to system, steady state response, effect of input on steady state error, Effect of Open Loop Transfer Function on Steady State Error, type 0,1 & 2 system subjected to step, ramp & parabolic input, transient response, analysis of first and second order system and transient response specifications
This presentation gives complete idea about time domain analysis of first and second order system, type number, time domain specifications, steady state error and error constants and numerical examples.
this is presentation about time response analysis in control engineering. this is presentation on its types and many more like time responses with best example
Time Response Analysis of system
Standard Test Signals
What is time response ?
Types of Responses
Analysis of First order system
Analysis of Second order system
ppt on Time Domain and Frequency Domain Analysissagar_kamble
in this presentation, you will be able to know what is this freq. and time domain analysis.
At last one example is illustreted with video, which distinguishes these two analysis
Giving description about time response, what are the inputs supplied to system, steady state response, effect of input on steady state error, Effect of Open Loop Transfer Function on Steady State Error, type 0,1 & 2 system subjected to step, ramp & parabolic input, transient response, analysis of first and second order system and transient response specifications
Time response of continuous data systems, Different test Signals for the time response, Unit step response and Time-Domain Specifications, Time response of a first-order and second order systems for different test signals, Steady State Error and Error constants, Sensitivity, Control Actions: Proportional, Derivative, Integral and PID control. Introduction to Process Control Systems, Pneumatic hydraulics, Actuators.
time domain analysis, Rise Time, Delay time, Damping Ratio, Overshoot, Settli...Waqas Afzal
Time Response- Transient, Steady State
Standard Test Signals- U(t), S(t), R(t)
Analysis of First order system - for Step input
Analysis of second order system -for Step input
Time Response Specifications- Rise Time, Delay time, Damping Ratio, Overshoot, Settling Time
Calculations
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Time domain definition 6
1. NOTE: This ppts are prepared by Syed Hasan
Saeed and was uploaded in slideshare.com
These ppts are reused here by same owner Syed
Hasan Saeed
SYED HASAN SAEED 1
2. TIME DOMAIN ANALYSIS
Email: hasansaeedcontrol@gmail.com
URL: http://shasansaeed.yolasite.com/
2SYED HASAN SAEED
3. BOOKS
1. AUTOMATIC CONTROL SYSTEM KUO & GOLNARAGHI
2. CONTROL SYSTEM ANAND KUMAR
3. AUTOMATIC CONTROL SYSTEM S.HASAN SAEED
SYED HASAN SAEED 3
4. DEFINITIONS
TIME RESPONSE: The time response of a system is the
output (response) which is function of the time, when
input (excitation) is applied.
Time response of a control system consists of two parts
1. Transient Response 2. Steady State Response
Mathematically,
Where, = transient response
= steady state response
SYED HASAN SAEED 4
)()()( tctctc sst
)(tct
)(tcss
5. TRANSIENT RESPONSE: The transient response is the
part of response which goes to zero as time
increases. Mathematically
The transient response may be exponential or
oscillatory in nature.
STEADY STATE: The steady state response is the part of
the total response after transient has died.
STEADY STATE ERROR: If the steady state response of
the output does not match with the input then the
system has steady state error, denoted by .
SYED HASAN SAEED 5
0)(
tcLimit t
t
sse
6. TEST SIGNALS FOR TIME RESPONSE:
For analysis of time response of a control system,
following input signals are used
1. STEP FUNCTION:
Consider an independent voltage source in series with
a switch ‘s’. When switch open the voltage at
terminal 1-2 is zero.
SYED HASAN SAEED 6
7. Mathematically,
;
When the switch is closed at t=0
;
Combining above two equations
;
;
A unit step function is denoted by u(t) and defined as
;
;
SYED HASAN SAEED 7
0)( tv 0 t
Ktv )( t0
Ktv
tv
)(
0)( 0 t
t0
1)(
0)(
tu
tu 0t
t0
8. Laplace transform:
£f(t)=
2. RAMP FUNCTION:
Ramp function starts from origin and increases or
decreases linearly with time. Let r(t) be the ramp
function then,
r(t)=0 ; t<0
=Kt ; t>0
SYED HASAN SAEED 8
ss
e
dtedtetu
st
stst 1
.1)(
000
K>0
t
r(t)
10. 3. PARABOLIC FUNCTION:
The value of r(t) is zero for t<0 and is quadratic function
of time for t>0. The parabolic function represents a
signal that is one order faster than the ramp function.
The parabolic function is defined as
For unit parabolic function K=1
SYED HASAN SAEED 10
2
)(
0)(
2
Kt
tr
tr
0
0
t
t
2
)(
0)(
2
t
tr
tr
0
0
t
t
12. IMPULSE RESPONSE: Consider the following fig.
The first pulse has a width T and height 1/T, area of the
pulse will be 1. If we halve the duration and double
the amplitude we get second pulse. The area under
the second pulse is also unity.
SYED HASAN SAEED 12
13. We can say that as the duration of the pulse
approaches zero, the amplitude approaches infinity
but area of the pulse is unity.
The pulse for which the duration tends to zero and
amplitude tends to infinity is called impulse. Impulse
function also known as delta function.
Mathematically
δ(t)= 0 ; t ≠ 0
=∞ ; t = 0
Thus the impulse function has zero value
everywhere except at t=0, where the amplitude
is infinite.
SYED HASAN SAEED 13
14. An impulse function is the derivative of a step function
δ(t) = u(t)
£δ(t) = £
SYED HASAN SAEED 14
1
1
.)(
s
stu
dt
d
INPUT r(t) SYMBOL R(S)
UNIT STEP U(t) 1/s
UNIT RAMP r(t) 1/s2
UNIT PARABOLIC - 1/s3
UNIT IMPULSE δ(t) 1