controllers ITS TYPES AND CLASSIFICATION BASED ON APPLICATION

CONTROLLER IN AUTOMATION

1. Design, Implementation, and
Applications of Controllers
Design, Implementation, and
Applications of Controllers
Dr. S. P. Gawande
MIEEE, LMISTE. MIACSIT, MIE(I)
[email protected]

2. Control System Control System
14-Mar-202

3. Design of Controller Design of Controller
•The design of the controller can be carried out either in time
domainorfrequencydomain
•In Time domain the specifications used are Maximum (Peak)
Overshoot,
Rise
Time
and
Settling
time
.
Overshoot,
Rise
Time
and
Settling
time
.
•In frequency domain the specifications used are Gain Margin,
PhaseMargin,Resonant Peak.
•The choice of the controller design depends on the preference
ofthedesignerandthecomplexityofthesystem.

4. Types of Controllers Types of Controllers
Controllers in Time Domain •Proportional Controller
•Proportional Derivative Controller (PD Controller)
•Proportional Integral Controller (PI Controller)
•
Proportional Integral Derivative Controller
(PID Controller)
•
Proportional Integral Derivative Controller
(PID Controller)
Controllers in Frequency Domain •Lead Compensator
•Lag compensator
•Lag-Lead Compensator
•Notch Controller
14-Mar-204

5. Role of Controllers to Improve Transient Response and
Steady state Response
Role of Controllers to Improve Transient Response and
Steady state Response
Transient Response
•Increase in Damping ration ( )
•Reduction in Peak overshoot (MP %)
•Reduction in settling time (Ts)
Steady state Response
ξ
Steady state Response •Reduction in Steady State Error ( E
ss)
•Increase in Gain (k)
•Increase in Type of the System
14-Mar-205

6. Proportional Controller and Addition of Poles and Zeros Proportional Controller and Addition of Poles and Zeros
•The controller has been typically a simple amplifier with a constant gain
Kp. This type of control action is formally known as proportional control,
because the control signal at the output of the controller is simply related to
theinputofthecontrollerbya proportionalconstant(K
p)
•Along with the derivative and integral controller, these co ntrollers add
additional poles and zeros to the open loop or the close loop t ransfer function
oftheoverallsystem.
•Addition or cancellation of undesirable poles and zeros of T F often
necessary in achieving the satisfactory time domain perfor mance of control
system.

7. Uncompensated System (or With Only Proportional
controller)
Uncompensated System (or With Only Proportional
controller)
•Proportional Controller : The controller in which the
controller output is proportional to the error signal
•The uncompensated 2
nd
order system for under damped system
is given by is given by
2
, ( )
( 2 )
n
Where G S
S S n
ω
ξω
=
+
14-Mar-207

8. With Proportional Controller
2
( )
K
p n
G S
ω
=
Effects:
1. Increases the Gain of the System
2. Generate impact similar to the shifting of the p ole away from
the origin
( )
( 2 )
K
p n
G S
S S
n
ω
ξω
=
+
14-Mar-208

9. Derivative Error compensation (Derivative Error Controller)
Error Rate Controller
Derivative Error compensation (Derivative Error Controller)
Error Rate Controller
Objective:
1) To improve Transient Response by improving Damping
( )
3) To reduce the Peak overshoot
(%Mp)
and Settling time
(Ts)
Derivative Controller/PD Controller:The input to the plant is
the
combination/sum
of
two
signals
.
One
is
proportional
to
ξ
the
combination/sum
of
two
signals
.
One
is
proportional
to
the error signal while the other is proportional to the
derivativeoferrorsignal
Where , K
p
= Proportional Gain , K
D
= Derivative Error
Constant / Derivative Gain of the controller
( ( ))
( ) ( )
d e t
Vc t K e t K
p D
dt
= +
( ) ( ) ( )
Vc S K E S K S E S
p D
= +
14-Mar-209

10. 2
(1 ) ( )
2 ( )
( 2 ) (1 )
n SK C SD
R S
S S n n SK
D
ω
ξω ω
+
=
+ + + 1
2
K n
D
ω
ξ ξ
= +
14-Mar-2010

11. Derivative Output compensation (Derivative Output
Controller) Output Rate Controller
Derivative Output compensation (Derivative Output
Controller) Output Rate Controller
Objective:
1) To improve the Transient Response by improving ( )
3) To reduce the Peak overshoot (%Mp) and Settling time (Ts)
Derivative Controller/PD Controller:The derivative of the
output
signal
is
compared
with
the
error
signal
and
the
ξ
output
signal
is
compared
with
the
error
signal
and
the
resultantisgivenasinputtotheplant.
[ ( )]
( ) ( ) ( ) ( ) ( )
d C t
V t e t K
c o
dt
V S E S K S C S
c o
= −
= −
Where , K
o
= Derivative output Constant / Tachometer
feedback constant
14-Mar-2011

12. 2
( )
2 2 2
( )
(2 )
C S n
R S
S K S n
n o n
ω
ξω ω ω
=
+ + +
1
2
K
o n
ω
ξ ξ
= +
14-Mar-2012

13. Effect of Addition of Zero to the Close loop Transfer Function
(Unity Feedback System)
Effect of Addition of Zero to the Close loop Transfer Function
(Unity Feedback System)
Consider a closed loop T.F. of second order uncompensated system
Consider a zero S= -1/K
D
to be added to the prototype of second
order T.F.
2
2
( )
2 2
( )
2
Y S n
R S
S nS n
ω
ξω ω
=
+ +
2
(1 ) ( )
2 2 ( )
2
2 2
( )
2 2 2 2
( )
2 2
[ ( )] ( )
1
( )
1
( )
n K S Y S
D
R S
S nS n
K S n Y S n
D
R S
S nS n S nS n
d Y t Y S
Y t KD
R S dt
ω
ξω ω
ω ω
ξω ω ξω ω
+
=
+ +
= +
+ + + +
= +
Forω
n= 1, ξ= 0.5 and K
D= 0, 1, 3, 6, 10
14-Mar-2013

14. •AsK
D
increases, zero will move closer to the origin, thus decreas ing the
risetime andincreasingthepeakovershoot(Mp)
•ThusY1(t)increases by after adding a zero to the close loop T.F..
ThusitincreasestheMpanddecreasestherisetime.
•AsK
D
approaches to infinity, Mp also approaches to infinity and y et the
system is stable as long as peak overshoot (Mp) is finite and d amping is
positive.
[ 1( )]
d Y t
K
D
dt
14-Mar-2014

15. Effects of PD Controller Effects of PD Controller
•TheDampingratio/Factorisincreasedfrom byfactor
as compared with damping factor of uncompensated system. (The
damping ratio can be increased to any desired value with suit able choice of
K
o
orK
D
)
•The increase in damping reduces the Peak overshoot as
2 2
k K
D n o n
ω ω
=
πξ
−
1
ξ ξ
−
•The Increase in damping reduces the Settling Time a s
•At optimal value of K
pand K
d, controller reduces the settling time
and also rise time.
•Improves Bandwidth and improves GM, PM and Mr. (In frequency
Domain)
2
1
%Mp e
πξ
ξ
−
−
=
4 3
T
s
n n
ξω ξω
= =
14-Mar-2015

16. Integral Controller/Compensation/Integral Error
Compensation (PI Controller)
Integral Controller/Compensation/Integral Error
Compensation (PI Controller)
Objective:
1) To improve the Steady State Response of the system
2) To increase the Type of the system
Integral or PI Controller:The input to the Plant is the
combination
of
sum
of
two
signals
.
One
is
proportional
to
the
combination
of
sum
of
two
signals
.
One
is
proportional
to
the
error signal and other is proportional to integral of error
signal.
( ) ( ) ( ).
0
( ) ( ) ( )
V t e t K e t dt
c i
Ki
V S E S E S
c
S∞
= +∫
= +
Where , K
i
= Integral Error Constant/ Gain of the Integral
controller
14-Mar-2016

17. Thus the Loop Transfer function of the compensated system
with integral controller is
2
( )
( ) ( )
2
( 2 )
n S K
i
G S H S
S S
n
ω
ξω
+
=
+
Thus with integral controller, the Type of the system increases
to 2 from 1.
14-Mar-2017

18. Effect of Addition of zero to the Forward Path Transfer
Function
Effect of Addition of zero to the Forward Path Transfer
Function
Consider a second order unity feedback system with forward path
T.F.
Consider a zero
S
=
-
1
/
K
i
to be added to the prototype of second
2
( )
( 2 )
n
G S
S S n
ω
ξω
=
+
Consider a zero
S
=
-
1
/
K
i
to be added to the prototype of second
order T.F.
Therefore,
2
(1 )
( )
( 2 )n K S
i
G S
S S nω
ξω
+
=
+
2
(1 ) ( )
2 2 2 ( )
2
2
(1 ) ( )
2 2 2
( )
(2 )
n K S Y Si
R S
S nS n n K S
i
n K S Y Si
R S
S n n K S n
i
ω
ξω ω ω
ω
ξω ω ω
+
=
+ + +
+
=
+ + +
14-Mar-2018

19. •Thus, in this case , the effect of adding zero is not only the
term (1 +K
iS) appears in the numerator but the denominator
alsocontainsK
i.
•The term (1+K
iS) in the numerator increases the Peak
overshoot(Mp)butK
iappearinginthecoefficientof‘S’term
in denominator has effect of improving the damping or
reducing
Mp
.
reducing
Mp
.
14-Mar-2019

20. Effects of PI Controller Effects of PI Controller
•Thus, the Integral controller improves the steady state
performanceofthesystembyincreasingthetypeofthesystem
andreducingthesteadystateerror.
•IncreasesRiseTime(T
s)
•DecreasesBandwidth(BW)
•
Improves
GM,
PM
and
M
r
•
Improves
GM,
PM
and
M
r
•ImprovesDampingandreducesMaximumOvershoot
14-Mar-2020

21. Proportional Integral Derivative Controller
(PID Controller)
Proportional Integral Derivative Controller
(PID Controller)
Objective:
1) To improve the Transient and Steady State Response of the
system
PID Controller:In PID Controller, input to the plant is a
combination /sum of three signals. First is the proportional to
the
error
signal,
second
is
proportional
to
derivative
of
error
the
error
signal,
second
is
proportional
to
derivative
of
error
signal and the third is proportional to the integral of error
signal.
[ ( )]
( ) ( ) ( ).
0
( ) ( ) ( ) ( )
d e t
V t e t K K e t dt
c D i
dt
K
i
Vc S E S K S E S E S
D
S
∞
= + +∫
= + +
Where , K
D
and K
i
= Gains of Derivative and Integral
Controllers, respectively.
14-Mar-2021

22. 14-Mar-2022

23. Effects of PID Controller Effects of PID Controller
•In PID controller, Derivative controller part increases the
damping ratio. This reduces the peak overshoot (% Mp) and
Settling time (Ts) of the system. This reduces the response
timeofthesystem.
•
The
Integral
controller
part
improves
steady
state
response
by
•
The
Integral
controller
part
improves
steady
state
response
by
increasingthetypeofthesystemandreducingthesteadystate
error.
•Hence,PIDcontrollerimprovesthetransientaswellassteady
stateperformanceofthesystem.
14-Mar-2023

24. Design with PD Controller Design with PD Controller
( )
G S K K S
c p D
= +
Transfer function of the
controller
2
( )
2 1
R
G S R C S
c
R
= +
( )
2 1
1
G S R C S
c
R
= +
On Comparison
2
2 1
1
R
Kp KD R C
R
= =
Thus, for Large value of K
D
, the
capacitor value will be larger
14-Mar-2024

25. Design with PI Controller Design with PI Controller
( )
K
i
G S K
c p
S
= +
Transfer function of the
controller
2 2
( )
R R
G S
c
R R C S
= +
( )
1 1 2
G S
c
R R C S
= +
On Comparison
2 2
2
1 1
R R
K K
p i
R R C
= =
Thus, for Small value of K
i
, the
capacitor value will be larger
14-Mar-2025

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14-Mar-2026
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27. Thank You ? Thank You ?
14-Mar-2027