Any Practical system is a control system
+
+
+
RVr(t)
MVu(t)
CONTROLLERD(s)
PLANTG(s)
SENSORH(s)
Error Detector
ActuatingErrore(t)
CVc(t)
Feedback signalb(t)
DisturbanceN(s)
+-
^
Disturbance signalw(t)
Typical Block Diagram model for a Feedback Control System
Proportional control
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r(t) u(t) G(s)K
H(s)
c(t)e(t)
-
Control action:- u(t)=Ke(t)Effect on Steady State Response:- Reduces the steady state error
Effect on Transient Response:- Increases the speed of response.
Limitations and shortcomings:- Saturation, noise and instability.
Hence new control schemes (PI, PD) are conceived.
Proportional and Integral (PI) control
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r(t) u(t)K G(s)
H(s)
KI/s
c(t)e(t)
- +
+
Control action:- u(t)=Ke(t)+KI∫e(t)dt
U(s)=(K+ KI/s)E(s) where KI=1/TI , TI=Integral or reset time
Effect on Steady State Response:- steady state error can be reduced to zero exactly.Effect on Transient Response:-Increases peak overshoot & reduces the speed of response.Limitations and shortcomings:- Reduces the stability margin of the system.
Proportional and Derivative (PD) control
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r(t) u(t)K G(s)
H(s)
sKD
c(t)e(t)
- +
+
Control action:- u(t)=Ke(t)+KD(de/dt)
U(s)=(K+ sKD)E(s) where KD=KcTD , TD=Derivative or rate time.
Effect on Steady State Response:-Almost no effect.Effect on Transient Response:-Decreases the peak overshoot by improving the effective damping of the system.Limitations and shortcomings:-Amplifies the high frequency noise signals.
Proportional ,Integral & Derivative (PID) control
Control action:-By proper adjustment of K, KD,KI the transient and dynamic responses are properly shaped.Problems:-Tuning of PID controller is a difficult job.
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r(t) u(t)G(s)
H(s)
c(t)e(t)
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+
+
Let
M = Mass=1kg
b =co-efficient of damping= 10 N.s/m
k = spring constant=20 N/m
MASS,SPRING,DAMPER system-A simple 2nd order system
System without any controller
Response of the system without any controller
System with P controller
Response of the system with P controller
System with PD controller
Response of the system with PD controller
System with PI controller
Response of the system with PI controller
System with PID controller
Response of the system with PID controller
VOLTAGE
SUPPLY
LOAD
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-
er T,LT
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ai
arr
aL
frr
fi
fr
fu
fL
auaxisquadrature
axisdirect
armature
field
Speed Control system of Separately excited DC motor
BLOCK DIAGRAM MODEL
w+Tm
+wr er
KP D(S) KT/Ra 1/(Js+B)
Kb
Kt
TW
eb
ea
-+ -+
et
Kp=Potentiometer constant
Kt= Tacho-generator constant
Kb=Back emf constant
KT=Torque constant
Tw=Disturbance torque/ load torque.
Tm=Electromagnetic Torque developed by motor.
D(s)=Controller Transfer Function.
PROS & CONS
Very popular industrial controller due to its simplicity.Almost 75-85% industrial process controllers are still of this kind.3 way independent control action.
The Tuning of PID controller is a cumbersome.‘Online’, ‘Ziegles Nichols’ , ‘Software Based’, ‘Cohen Coon’ all these tuning methods possess problems.
Futuristic Controller:- Fuzzy logic /Neuro fuzzy logic controller
ACKNOWLEDGEMENT
•en.wikipedia.org
•www.youtube.com
•‘Modern Control Engineering ‘ by k.Ogata.
•‘Control Systems: Principles and Design’ by Madan Gopal.
•‘PID -controllers, Theory Design and Tuning’ by K Astrom andT Hagglund
•‘Automatic Control Systems’ by B.C Kuo
!!!!THANK YOU!!!