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,
Muthayammal Engineering 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, Namakkal Dist., Tamil Nadu, India.

2. Order system

3. Introduction - First order system
 The first order system has only one pole.
 Where
K is the D.C gain and
T is the time constant of the system.
 Time constant is a measure of how quickly a 1st order
system responds to a unit step input.
 D.C Gain of the system is ratio between the input signal
and the steady state value of output.
1


Ts
K
s
R
s
C
)
(
)
(

4. First order system
 Examples:
 The first order system given below.
1
3
10


s
s
G )
(
5
3


s
s
G )
(
1
5
1
5
3


s
/
/
• D.C gain is 10 and time constant is 3 seconds.
• For the following system
• D.C Gain of the system is 3/5 and time constant is 1/5 seconds.

10. Second Order System
 We have already discussed the transient response of 1st order
systems.
 Compared to the simplicity of a first-order system, a second-order
system exhibits a wide range of responses that must be analyzed
and described.
 Whereas, changes in the parameters of a second-order system can
change the form of the response.
 A second-order system can display characteristics much like a
first-order system or, depending on component values, display
damped or pure oscillations for its transient response.
10

15. t
t
c n

cos
1
)
( 


17. Problem 1
4
2
4
)
(
)
(
2



s
s
s
R
s
C
 Determine the un-damped natural frequency
and damping ratio of the following second
order system.
4
2

n

2
2
2
2 n
n
n
s
s
s
R
s
C






)
(
)
(
• Compare the numerator and denominator of the given transfer
function with the general 2nd order transfer function.
2

 n
 s
s
n 2
2 
 
4
2
2 2
2
2




 s
s
s
s n
n 

5
0.

 
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