1. Birla Vishvakarma Mahavidyalaya Gujarat Technological University
Department of Mechanical Engineering
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions
Control Engineering ( )
Group Number: 19
Prepared By: Aashirwad Patel ( )
Darshan Baru ( )
Deep Bhanushali ( )
Sumit Mishra ( )

2. 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

3. 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. t
δ(t) A
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions

4. An example of an Impulse Signal.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions

5. 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 t
u(t) A
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions

6. 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 t
r(t)
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions

7. Parabolic Signal t
p(t)
The parabolic signal imitate the constant acceleration characteristic of actual input signal.
If A=1, the parabolic signal is called unit parabolic signal.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions

8. 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

9. 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

10. Transient Response and Steady-State Response
The time response of a control system consists of two parts namely;
The transient response.
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

11. 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

12. Response for an Elevator
Input : Stimulus
PRESS BUTTON 4
Desired Response
SPEED & FLOOR
LEVELLING ACCURACY
Output : Response
FOURTH FLOOR
Actual response
Performance of
an Elevator:
Desired output-
elevator response is
shown as a
Step Function.
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions

13. 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

14. Thank You! 
Time Response Analysis: Transient and Steady State Response, Standard Test Input Functions