PPT: Time Response Analysis | Control Systems - Electrical Engineering (EE) PDF Download

 Page 1


Time Domain 
Analysis of First 
Order and 
Second Order 
System
Page 2


Time Domain 
Analysis of First 
Order and 
Second Order 
System
Time Domain Analysis
The Time Domain Analyzes of the system is to be done on basis 
of time. The analysis is only be applied when nature of input 
plus mathematical model of the control system is known. 
Expressing the main input signals is not an easy task and cannot 
be determined by simple equations. There are two components 
of any system's time response, which are: Transient response & 
Steady state response.
Transient Response: This response is dependent upon the 
system poles only and not on the type of input & it is sufficient 
to analyze the transient response using a step input. Steady-
State Response: This response depends on system dynamics 
and the input quantity. It is then examined using different test 
signals by final value theorem.
Page 3


Time Domain 
Analysis of First 
Order and 
Second Order 
System
Time Domain Analysis
The Time Domain Analyzes of the system is to be done on basis 
of time. The analysis is only be applied when nature of input 
plus mathematical model of the control system is known. 
Expressing the main input signals is not an easy task and cannot 
be determined by simple equations. There are two components 
of any system's time response, which are: Transient response & 
Steady state response.
Transient Response: This response is dependent upon the 
system poles only and not on the type of input & it is sufficient 
to analyze the transient response using a step input. Steady-
State Response: This response depends on system dynamics 
and the input quantity. It is then examined using different test 
signals by final value theorem.
Standard Test Input Signals
1
Step Input Signal
A voltage source connected to a voltmeter via a switch. When the switch is open, the voltage is zero. At t = 0, the switch closes, and voltage V 
appears.
2
Mathematical Representation
The unit step function is defined as: Examine the Laplace transform of the unit step function by multiplying by e-st and integrating from 0 to infinity.
Page 4


Time Domain 
Analysis of First 
Order and 
Second Order 
System
Time Domain Analysis
The Time Domain Analyzes of the system is to be done on basis 
of time. The analysis is only be applied when nature of input 
plus mathematical model of the control system is known. 
Expressing the main input signals is not an easy task and cannot 
be determined by simple equations. There are two components 
of any system's time response, which are: Transient response & 
Steady state response.
Transient Response: This response is dependent upon the 
system poles only and not on the type of input & it is sufficient 
to analyze the transient response using a step input. Steady-
State Response: This response depends on system dynamics 
and the input quantity. It is then examined using different test 
signals by final value theorem.
Standard Test Input Signals
1
Step Input Signal
A voltage source connected to a voltmeter via a switch. When the switch is open, the voltage is zero. At t = 0, the switch closes, and voltage V 
appears.
2
Mathematical Representation
The unit step function is defined as: Examine the Laplace transform of the unit step function by multiplying by e-st and integrating from 0 to infinity.
Ramp Function
A ramp function is represented by a straight line starting from 
the origin and inclining upwards. It begins at zero and increases 
or decreases linearly over time.
Here in this above equation, k is the slope of the line.
Now let us examine the Laplace transform of ramp function. As 
we told earlier Laplace transform of any function can be 
obtained by multiplying this function by e-st and integrating 
multiplied from 0 to infinity.
Page 5


Time Domain 
Analysis of First 
Order and 
Second Order 
System
Time Domain Analysis
The Time Domain Analyzes of the system is to be done on basis 
of time. The analysis is only be applied when nature of input 
plus mathematical model of the control system is known. 
Expressing the main input signals is not an easy task and cannot 
be determined by simple equations. There are two components 
of any system's time response, which are: Transient response & 
Steady state response.
Transient Response: This response is dependent upon the 
system poles only and not on the type of input & it is sufficient 
to analyze the transient response using a step input. Steady-
State Response: This response depends on system dynamics 
and the input quantity. It is then examined using different test 
signals by final value theorem.
Standard Test Input Signals
1
Step Input Signal
A voltage source connected to a voltmeter via a switch. When the switch is open, the voltage is zero. At t = 0, the switch closes, and voltage V 
appears.
2
Mathematical Representation
The unit step function is defined as: Examine the Laplace transform of the unit step function by multiplying by e-st and integrating from 0 to infinity.
Ramp Function
A ramp function is represented by a straight line starting from 
the origin and inclining upwards. It begins at zero and increases 
or decreases linearly over time.
Here in this above equation, k is the slope of the line.
Now let us examine the Laplace transform of ramp function. As 
we told earlier Laplace transform of any function can be 
obtained by multiplying this function by e-st and integrating 
multiplied from 0 to infinity.
Parabolic Function
Definition
Here, the value of function is zero when time t<0 and is quadratic 
when time t > 0. A parabolic function can be defined as,
Laplace Transform
Now let us examine the Laplace transform of parabolic function. As we 
told earlier Laplace transform of any function can be obtained by 
multiplying this function by e-st and integrating multiplied from 0 to 
infinity.