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

+

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

+

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

+

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.

+

r(t) u(t)G(s)

H(s)

c(t)e(t)

-+

+

+

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

rfafa iLE

+

-

er T,LT

+

-

ar

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!!!