First & second order of the control systems

Mr. C.S.Satheesh, M.E.,
First order of the control systems
second order of the control systems

1. First & Second Order of the Control Systems
Presented by
Mr.C.S.Satheesh, M.E.,
Assistant Professor, Department of EEE,
MuthayammalEngineering College (Autonomous),
Namakkal(Dt), Rasipuram–637408
MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC, NBA & Affiliated to Anna University),
Rasipuram -637 408, NamakkalDist., Tamil Nadu, India.

2. Order system

3. Introduction -First order system
Thefirstordersystemhasonlyonepole.
Where
KistheD.Cgainand
Tisthetimeconstantofthesystem.
Timeconstantisameasureofhowquicklya1
st
order
systemrespondstoaunitstepinput.
D.CGainofthesystemisratiobetweentheinputsignal
andthesteadystatevalueofoutput.1

Ts
K
sR
sC
)(
)(

4. First order system
Examples:
Thefirstordersystemgivenbelow.13
10


s
sG)( 5
3


s
sG)( 151
53


s/
/
•D.Cgainis10andtimeconstantis3seconds.
•Forthefollowingsystem
•D.CGainofthesystemis3/5andtimeconstantis1/5seconds.

10. Second Order System
Wehavealreadydiscussedthetransientresponseof1
st
order
systems.
Comparedtothesimplicityofafirst-ordersystem,asecond-order
systemexhibitsawiderangeofresponsesthatmustbeanalyzed
anddescribed.
Whereas,changesintheparametersofasecond-ordersystemcan
changetheformoftheresponse.
Asecond-ordersystemcandisplaycharacteristicsmuchlikea
first-ordersystemor,dependingoncomponentvalues,display
dampedorpureoscillationsforitstransientresponse.
10

15. ttc
ncos1)(

17. Problem 142
4
)(
)(
2


sssR
sC
Determinetheun-dampednaturalfrequency
anddampingratioofthefollowingsecond
ordersystem.4
2

n 22
2
2
nn
n
sssR
sC




)(
)(
•Comparethenumeratoranddenominatorofthegiventransfer
functionwiththegeneral2
nd
ordertransferfunction.2
n ss
n22  422
222
 ssss
nn 50. 1
n
17

18. Problem 2

20. Problem 3

28. Static error constant for various type number
of system

29. Steady state error for various types of input

36. Problem 4

37. Problem 5

53. References :
A.Nagoorkani, Control Systems,
RBA Publications.
4/5/2021 53

54. Thank You
54