The document discusses the time response of control systems, focusing on both transient and steady-state responses. It outlines important time domain specifications including delay time, rise time, peak time, maximum overshoot, and settling time, as well as standard test signals like impulse, step, ramp, and parabolic signals. Lastly, it highlights the relevance of Laplace transforms in analyzing these test signals.

1. Time Response in systems
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. Time Response
System
• The time response of any system has two components
• Transient response
• Steady-state response.
• Time response of the system is the output of closed loop system
expressed as a function of time.

3. Time Response
• When the response of the system is changed from equilibrium it
takes some time to settle down.
• This is called transient response.
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
6
x 10
-3
Step Response
Time (sec)
Amplitude
Response
Step Input
Transient Response
Steady
State
Response
• The response of the
system after the transient
response is called steady
state response.

4. Time Response
• The response c(t) can be obtained from the transfer function of the
system and the input to the system

5. Time domain specifications
• The desired performance characteristics of control systems are
specified in terms of time domain specifications.
• The time domain specifications are
1. Delay Time (td)
2. Rise Time (tr)
3. Peak Time (tp)
4. Maximum Overshoot (Mp)
5. Settling Time (tS)

6. Time domain specifications

7. Time domain specifications
1. Delay Time (td)
• The delay (td) time is the time required for the response to
reach half the final value the very first time.

8. Time domain specifications
2. Rise Time (tr)
• It is the time required for the response to rise from 0% to
100% of its final value.
• For under damped second order systems, the 0% to 100%
rise time is normally used.
• For over damped systems, the 10% to 90% rise time is
commonly used.

9. Time domain specifications
3. Peak Time (tp)
• It is the time required for the response to reach the peak
value for the first time.
• The peak time is the time required for the response to reach
the first peak of the overshoot.

10. 4. Maximum Overshoot
10
Peak overshoot Mp is defined as the deviation of the response
at peak time from the final value of response. It is also called
the maximum overshoot.
Mathematically, we can write it as
Where,
c(tp) is the peak value of the response.
c(∞) is the final (steady state) value of the response.
Time domain specifications

11. Time domain specifications
5. Settling time
It is the time required for the response to reach the steady
state and stay within the specified tolerance bands around the
final value.
In general, the tolerance bands are 2% and 5%.

12. Time domain specifications

13. Standard Test Signals
 The knowledge of input signal is required to
predict the response of a system.
 In most of the system the input signals are not
known ahead of time and also it is difficult to
express the input signal mathematically by simple
equations
 The characteristics of actual input signals are
Sudden shock,
Sudden change,
Constant velocity, and
Constant acceleration.

14. Standard Test Signals are
1. Impulse signal
2. Step signal
3. Ramp signal
4. Parabolic signal

15. Standard Test Signals
1. Impulse signal
- The impulse signal imitate the
sudden shock characteristic of
actual input signal.
- If A=1, the impulse signal is called
unit impulse signal.
0 t
δ(t)
A






0
0
0
t
t
A
t)
(


16. Standard Test Signals
2. Step signal
- The step signal imitate the
sudden change
characteristic of actual
input signal.
- If A=1, the step signal is
called unit step signal






0
0
0
t
t
A
t
u )
( 0 t
u(t)
A

17. Standard Test Signals
3. Ramp signal
- The ramp signal imitate the
constant velocity
characteristic of actual
input signal.
- If A=1, the ramp signal is
called unit ramp signal






0
0
0
t
t
At
t
r )
(
0 t
r(t)
r(t)
unit ramp signal

18. Standard Test Signals
4. Parabolic signal
- The parabolic signal
imitate the constant
acceleration characteristic
of actual input signal.
- If A=1, the parabolic signal
is called unit parabolic
signal.








0
0
0
2
2
t
t
At
t
p )
(
0 t
p(t)
Unit parabolic signal
p(t)

19. Laplace Transform of Test Signals
 Impulse
 Step






0
0
0
t
t
A
t)
(

A
s
t
L 
 )
(
)}
(
{ 







0
0
0
t
t
A
t
u )
(
S
A
s
U
t
u
L 
 )
(
)}
(
{

20. Laplace Transform of Test Signals
 Ramp
 Parabolic
2
s
A
s
R
t
r
L 
 )
(
)}
(
{
3
)
(
)}
(
{
S
A
s
P
t
p
L 







0
0
0
t
t
At
t
r )
(








0
0
0
2
2
t
t
At
t
p )
(

21. References :
 A.Nagoorkani, Control Systems,
RBA Publications.
4/5/2021 21

22. Thank You
22