Control Engineering (2151908)
Time Response Analysis: Transient and Steady
State Response, Standard Test Input Functions
Group Number: 19
Prepared By:
Aashirwad Patel (130080119001)
Darshan Baru (130080119002)
Deep Bhanushali (130080119003)
Sumit Mishra (130070119101)
Standard Test Signals
• The characteristics of actual input signals are a sudden shock, a
sudden change, a constant velocity, and constant acceleration.
• The dynamic behavior of a system is therefore judged and
compared under application of standard test signals – an
impulse, a step, a constant velocity, and constant acceleration.
• Another standard signal of great importance is a sinusoidal
signal.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Impulse Signal
• The impulse signal imitate the
sudden shock characteristic of
actual input signal.
A
 (t )  
0
δ(t)
A
t0
t0
• If A=1, the impulse signal is called
t
0
unit impulse signal.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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• An example of an Impulse Signal.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Step Signal
• The step signal imitate the sudden
change characteristic of actual input
signal.
A
u( t )  
0
u(t)
A
t0
t0
• If A=1, the step signal is called unit
t
0
step signal
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Ramp Signal
• The ramp signal imitate the constant
velocity characteristic of actual input
signal.
t0
 At
r(t )  
t0
0
• If A=1, the ramp signal is called unit
ramp signal
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
r(t)
t
0
6
Parabolic Signal
• The parabolic signal imitate the
constant acceleration characteristic
of actual input signal.
 At 2

p(t )   2
0

p(t)
t0
t0
• If A=1, the parabolic signal is called
t
0
unit parabolic signal.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Which Test Signal to Choose and When?
• Which of these typical input signals to use for analyzing
system characteristics may be determined by the form of
the input that the system will be subjected to most
frequently under normal operation.
• If the inputs to a control system are gradually changing
functions of time, then a ramp function of time may be a
good test signal.
• Similarly, if a system is subjected to sudden disturbances, a
step function of time may be a good test signal.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Typical Test Signals
• For a system subjected to shock inputs, an impulse
function may be best.
• Once a control system is designed on the basis of
test signals, the performance of the system in
response to actual inputs is generally satisfactory.
• The use of such test signals enables one to compare
the performance of all systems on the same basis.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Transient Response and Steady-State Response
• The time response of a control system consists of
two parts namely;
1. The transient response.
2. The steady-state response.
• By transient response, we mean that which goes from
the initial state to the final state.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Transient Response and Steady-State Response
• The transient is the way in which the system
responds during the time it takes to reach its steady
state.
• Transient means “short lived”. This depends on
system characteristics.
• By steady-state response, we mean the manner in
which the system output behaves as ‘t’ approaches
infinity.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Response for an Elevator
Input : Stimulus
PRESS BUTTON 4
Desired Response
SPEED & FLOOR
LEVELLING ACCURACY
ELEVATOR
Output : Response
FOURTH FLOOR
Actual response
Performance of
an Elevator:
Desired outputelevator
response is
shown as a
Step Function.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Transient Response and Steady-State Response
• The system response c(t) may be written as:
c(t) = ctr(t) + css(t)
• Where ctr(t) is the transient response and css(t) is the
steady state response.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
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