Dynamic Response of Second Order Systems Notes

: Dynamic Response of Second Order Systems Notes

 Page 1


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Dynamic Response of Second Order Systems
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
Page 2


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Dynamic Response of Second Order Systems
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
This Lecture Contains
?Standard Forms of a 2nd order system
?Transient response of a second order system
?A 3-D representation of unit step response
?Unit Impulse Response
? ?Unit step response
?NormalisedRise-time
?System with Additional Pole and Zero
Joint Initiative of IITs and IISc - Funded by MHRD
Page 3


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Dynamic Response of Second Order Systems
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
This Lecture Contains
?Standard Forms of a 2nd order system
?Transient response of a second order system
?A 3-D representation of unit step response
?Unit Impulse Response
? ?Unit step response
?NormalisedRise-time
?System with Additional Pole and Zero
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Standard Forms of a 2
nd
order system y
?i th tt) ?in other texts)
Joint Initiative of IITs and IISc -Funded by MHRD
Page 4


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Dynamic Response of Second Order Systems
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
This Lecture Contains
?Standard Forms of a 2nd order system
?Transient response of a second order system
?A 3-D representation of unit step response
?Unit Impulse Response
? ?Unit step response
?NormalisedRise-time
?System with Additional Pole and Zero
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Standard Forms of a 2
nd
order system y
?i th tt) ?in other texts)
Joint Initiative of IITs and IISc -Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Transient response of a second order system
) s ( R ) s ( Y
n
2
?
?
A Second order system may be represented as follows:
) s ( R
s s
) s ( Y
n n
2 2
2 ? ?? ? ?
?
Where, R(s) is the excitation signal and the second order plant is 
1
1 ) t i( ) t (
t ?
? ß
??
defined by it’s natural frequency ?
n  
and damping ratio ?. The 
response of the system in time domain may be written as:
1
1
2
) (
) t sin( e ) t ( y
n
t
n
?
? ? ?
? ß
? ß ?
ß
??
1
1
cos
) (
?
? ?
?
?
? ?
? ß
1 0to ? ?
Joint Initiative of IITs and IISc -Funded by MHRD
Page 5


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Dynamic Response of Second Order Systems
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
This Lecture Contains
?Standard Forms of a 2nd order system
?Transient response of a second order system
?A 3-D representation of unit step response
?Unit Impulse Response
? ?Unit step response
?NormalisedRise-time
?System with Additional Pole and Zero
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Standard Forms of a 2
nd
order system y
?i th tt) ?in other texts)
Joint Initiative of IITs and IISc -Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
Transient response of a second order system
) s ( R ) s ( Y
n
2
?
?
A Second order system may be represented as follows:
) s ( R
s s
) s ( Y
n n
2 2
2 ? ?? ? ?
?
Where, R(s) is the excitation signal and the second order plant is 
1
1 ) t i( ) t (
t ?
? ß
??
defined by it’s natural frequency ?
n  
and damping ratio ?. The 
response of the system in time domain may be written as:
1
1
2
) (
) t sin( e ) t ( y
n
t
n
?
? ? ?
? ß
? ß ?
ß
??
1
1
cos
) (
?
? ?
?
?
? ?
? ß
1 0to ? ?
Joint Initiative of IITs and IISc -Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 2- Lecture 10
A 3-D representation of unit step response
Joint Initiative of IITs and IISc -Funded by MHRD
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