lecture time domain analysis of 2nd order systems
DESCRIPTION
Lecture Time Domain Analysis of 2nd Order SystemsTRANSCRIPT
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Control Systems (CS)
Engr. Mehr Gul
Lecturer Electrical Engineering Deptt.
LectureTime Domain Analysis of 2nd Order Systems
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Introduction
We have already discussed the affect of location of poles and zeroson the transient response of 1st order systems.
Compared to the simplicity of a first-order system, a second-ordersystem exhibits a wide range of responses that must be analyzedand described.
Varying a first-order system's parameter (T, K) simply changes thespeed and offset of the response
Whereas, changes in the parameters of a second-order system canchange the form of the response.
A second-order system can display characteristics much like a first-order system or, depending on component values, display dampedor pure oscillations for its transient response.
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Introduction A general second-order system is characterized by
the following transfer function.
22
2
2 nn
n
sssR
sC
)(
)(
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Introduction
un-damped natural frequency of the second order system,which is the frequency of oscillation of the system withoutdamping.
22
2
2 nn
n
sssR
sC
)(
)(
n
damping ratio of the second order system, which is a measureof the degree of resistance to change in the system output.
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Example#1
42
42
sssR
sC
)(
)(
Determine the un-damped natural frequency and damping ratioof the following second order system.
42 n
22
2
2 nn
n
sssR
sC
)(
)(
Compare the numerator and denominator of the given transferfunction with the general 2nd order transfer function.
sec/radn 2 ssn 22
422 222 ssss nn 50.
1 n
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Introduction
22
2
2 nn
n
sssR
sC
)(
)(
Two poles of the system are
1
1
2
2
nn
nn
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Introduction
According the value of , a second-order system can be set intoone of the four categories:
1
1
2
2
nn
nn
1. Overdamped - when the system has two real distinct poles ( >1).
-a-b-c
j
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Introduction
According the value of , a second-order system can be set intoone of the four categories:
1
1
2
2
nn
nn
2. Underdamped - when the system has two complex conjugate poles (0 <
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Introduction
According the value of , a second-order system can be set intoone of the four categories:
1
1
2
2
nn
nn
3. Undamped - when the system has two imaginary poles ( = 0).
-a-b-c
j
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Introduction
According the value of , a second-order system can be set intoone of the four categories:
1
1
2
2
nn
nn
4. Critically damped - when the system has two real but equal poles ( = 1).
-a-b-c
j
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Example : Determine the un-damped natural frequency and dampingratio of the following second-order system.
Second Order System
93
9)(.1
2
sssG
168
16)(.2
2
sssG Solve them as your own
revision
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