unit-1-introductiontocontrolsystems-170821111427.pdf

Introduction Controller

1. 8/21/2017 1
Hareesha N G, Dept of Aero Engg, DSCE,
Blore

2. •Concept of automatic controls
•Open loop and closed loop systems
•Concepts of feedback systems
•Requirements of an ideal control system
•Types of controllers
–Proportional,
–Integral
–Proportional Integral,
–Proportional Integral Differential controllers
07 Hrs
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 2

3. 8/21/2017
Thecontentsusedinthispresentationaretakenfromthetextbooks
mentionedinthereferences.Idonotholdanycopyrightsforthe
contents.Ithasbeenpreparedtouseintheclasslectures,notfor
commercialpurpose.
HareeshaNG
HareeshaN G, Dept of Aero Engg, DSCE, Blore 3

4. •Automaticcontrolhasplayedavitalroleinthe
advanceofengineeringandscience.
•Itismoreimportantinspace-vehiclesystems,
missile-guidancesystems,roboticsystems,modern
manufacturingandindustrialprocesses.
•Forexample,
–Numericalcontrolofmachinetoolsinthemanufacturing
industries.
–Designofautopilotsystemsintheaerospaceindustries
–Designofcarsandtrucksintheautomobileindustries.
–SpeedGovernors
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 4

5. •Itisalsoessentialinindustrialoperationsas
–controllingpressure,
–temperature,
–humidity,
–viscosity,and
–flowintheprocessindustries.
•Automaticcontrolhelpsinattainingoptimalperformanceofdynamic
systems,improvingproductivity,relievingthedrudgeryofmany
routinerepetitivemanualoperations.
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6. 8/21/2017
Hareesha N G, Dept of Aero Engg, DSCE,
Blore
6
Automatic water lever controller
Automatic Engine speed controller

7. •Anautomaticcontrolsystemisapre-setclosed-loopcontrol
systemthatrequiresnooperator(human)action.
•Automaticcontrolusesapplicationofmechanismstotheoperation
andregulationofprocesseswithoutcontinuousdirecthuman
intervention.
•Thisassumestheprocessremainsinthenormalrangeforthe
controlsystem.
•Anautomaticcontrolsystemhastwoprocessvariablesassociated
withit:
–acontrolledvariable
–amanipulatedvariable.
•Acontrolledvariableistheprocessvariablethatismaintainedata
specifiedvalueorwithinaspecifiedrange.
•Inthepreviousexample,thestoragetanklevelisthecontrolled
variable.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 7

8. •Amanipulatedvariableistheprocessvariablethatisactedonbythe
controlsystemtomaintainthecontrolledvariableatthespecified
valueorwithinthespecifiedrange.
•Theflowrateofthewatersuppliedtothetankisthemanipulated
variable.
FunctionsofAutomaticControl
•Inanyautomaticcontrolsystem,thefourbasicfunctionsthatoccur
are:
–Measurement
–Comparison
–Computation
–Correction
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 8

9. System:
Asystemisacombinationoranarrangementof
differentphysicalcomponentswhichacttogetherasa
entireunittoachievecertainobjective.
•E.g.,
–Aclassroomisaphysicalsystem.Aroomalongwiththe
combinationofbenches,blackboard,fans,lightingarrangement
etc.canbecalledasaclassroomwhichactsaselementarysystem.
–Inaclassroom,professorisdeliveringhislecture,itbecomesa
controlsystemas;hetriestoregulate,directorcommandthe
studentsinordertoachievetheobjectivewhichistoinputgood
knowledgetothestudents.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 9

10. Plant:
–Theportionofasystemwhichistobecontrolledorregulated
iscalledastheplant.
–A plant may be a piece of equipment, perhaps just a set of
machine parts.
–The purpose of plant is to perform a particular operation.
–E.g., mechanical device, a heating furnace, a chemical reactor,
or a spacecraft.
Process:
–Any operation to be controlled is called a process.
–Examples are chemical, economic, and biological processes.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 10

11. Controller:
–Theelementofthesystemitselforexternaltothesystemwhich
controlstheplantortheprocessiscalledascontroller.
–E.g.,ON/OFFswitchtocontrolbulb.
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12. Input:
–Itisanappliedsignaloranexcitationsignalappliedtocontrol
systemfromanexternalenergysourceinordertoproducea
specifiedoutput.
–Foreachsystem,theremustbeexcitationandsystemacceptsitas
aninput
Output:
–Itistheparticularsignalofinterestortheactualresponse
obtainedfromacontrolsystemwheninputisappliedtoit.
–foranalysingthebehaviourofsystemforsuchinput,itis
necessarytodefinetheoutputofasystem.
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13. Disturbances:
–Disturbanceisasignalwhichtendstoadverselyaffectthevalueoftheoutput
ofasystem.
–Disturbancesareundesirableandunavoidableeffectsbeyondourcontrol,
generatedfromoutsideprocess-environment,andfromwithin.
–Ifsuchadisturbanceisgeneratedwithinthesystemitself,itiscalledasinternal
disturbance.
–Thedisturbancegeneratedoutsidethesystemactingasanextrainputtothe
systeminadditiontoitsnormalinput,affectingtheoutputadverselyiscalled
asanexternaldisturbance.
–Thepresenceofthedisturbanceisoneofthemainreasonsofusingcontrol.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 13

14. 1)NaturalControlSystem
—Universe
—HumanBody
2)ManmadeControlSystem
—Vehicles
—Aeroplanes
3)ManualControlSystems
–RoomTemperatureregulationViaElectricFan
–WaterLevelControl
4)AutomaticControlSystem
–RoomTemperatureregulationViaA.C
–HumanBodyTemperatureControl
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15. 5)Open-LoopControlSystem
–WashingMachine
–Toaster
–ElectricFan
6)Closed-loopControlSystem
–Refrigerator
–Auto-pilotsystem
–Driverlesscars
7)LinearVsNonlinearControlSystem
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 15
A Control System in which output varies linearly with the
input is called a linear control system.

16. 8)TimeinvariantvsTimevariant
–Whenthecharacteristicsofthesystemdonotdependupontimeitselfthenthesystem
issaidtotimeinvariantcontrolsystem.
–Timevaryingcontrolsystemisasysteminwhichoneormoreparametersvarywith
time.
9)ContinuousDataVsDiscreteDataSystem
–Incontinuousdatacontrolsystemallsystemvariablesarefunctionofa
continuoustimet.
–Adiscretetimecontrolsysteminvolvesoneormorevariablesthatareknown
onlyatdiscretetimeintervals.
10)DeterministicvsStochasticControlSystem
–AcontrolSystemisdeterministiciftheresponsetoinputispredictableand
repeatable.
–Ifnot,thecontrolsystemisastochasticcontrolsystem.
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17. 8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 17

18. •Anyphysicalsystemwhichdoesnotautomaticallycorrectfor
variationinitsoutput,iscalledanopen-loopsystem.
•Suchasystemmayberepresentedbytheblockdiagramasshownin
Fig.
•Inthesesystems,outputisdependentoninputbutcontrollingaction
orinputistotallyindependentoftheoutputorchangesinoutputof
thesystem.
•Inthesesystemstheoutputremainsconstantforaconstantinput
signalprovidedtheexternalconditionsremainunaltered.
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19. •Inanyopen-loopcontrolsystemtheoutputisnotcomparedwiththe
referenceinput.Asaresult,theaccuracyofthesystemdependson
calibration.
•Inthepresenceofdisturbances,anopen-loopcontrolsystemwillnot
performthedesiredtask.Open-loopcontrolcanbeused,inpractice,
onlyiftherelationshipbetweentheinputandoutputisknownandif
thereareneitherinternalnorexternaldisturbances.
•Clearly,suchsystemsarenotfeedbackcontrolsystems.Notethatany
controlsystemthatoperatesonatimebasisisopenloop.
•Forinstance,trafficcontrolbymeansofsignalsoperatedonatime
basisisanexampleofopen-loopcontrol.
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20. Advantages: The advantages of open loop control system are,
1) Such systems are simple in construction.
2) Very much convenient when output is difficult to measure.
3) Such systems are easy from maintenance point of view.
4) Generally these are not troubled with the problems of stability.
5) Such systems are simple to design and hence economical.
Disadvantages: The disadvantages of open loop control system are,
1.These systems are inaccurate and unreliable because accuracy of such systems are
totally dependent on the accurate pre-calibration of the controller.
2.These systems give inaccurate results if there are variations in the external
environment.
3.These systems cant sense internal disturbances in the system, after the
controller stage.
4.Recalibration of the controller is necessary, time to time to maintain the quality
and accuracyof the desired output.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 20

21. 1)AutomaticToasterSystem
•Inthissystem,thequalityoftoastdependsuponthetimeforwhich
thetoastisheated.
•Dependingonthetimesetting,breadissimplyheatedinthissystem.
•Thetoastqualityistobejudgedbytheuserandhasnoeffectonthe
inputs.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 21

22. 2)TrafficLightController
•Atrafficflowcontrolsystemusedonroadsistimedependent.
•Thetrafficontheroadbecomesmobileorstationarydependingon
thedurationandsequenceoflampglow.
•Thesequenceanddurationarecontrolledbyrelayswhichare
predeterminedandnotdependentontherushontheroad.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 22

23. 3)ResidentialHeatingSystem
•Theindoortemperatureistheresponsevariableofinterest,anditis
affectedbythemaindisturbanceinput—theoutdoortemperature.
•Thedesiredtemperatureissetonacalibrateddial.Thispositionsthe
valvethatadmitsthesteamforcirculationthroughtheradiator.
•Thevalvedialiscalibratedwhentheenvironmenttemperaturehas
certainvalue.
•Whenthisvaluechangessignificantly,thecontrolledtemperaturewill
deviatefromthedesiredvaluebyalargeerrorandhenceprecise
controlwillnotberealized.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 23

24. FeedbackControlSystems.
•Asystemthatmaintainsaprescribedrelationshipbetweenthe
outputandthereferenceinputbycomparingthemandusingthe
differenceasameansofcontroliscalledafeedbackcontrolsystem.
Closed-LoopControlSystems.
•Feedbackcontrolsystemsareoftenreferredtoasclosed-loopcontrol
systems.
•Inpractice,thetermsfeedbackcontrolandclosed-loopcontrolare
usedinterchangeably.
•Inaclosed-loopcontrolsystemtheactuatingerrorsignal(whichis
thedifferencebetweentheinputsignalandthefeedbacksignal)is
fedtothecontrollersoastoreducetheerrorandbringtheoutputof
thesystemtoadesiredvalue.
•Thetermclosed-loopcontrolalwaysimpliestheuseoffeedback
controlactioninordertoreducesystemerror.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 24

25. Thevarioussignalsare,
r(t)=Referenceinput
e(t)=Errorsignal
c(t)=Controlledoutput
m(t)=Manipulatedsignal
b(t)=Feedbacksignal
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 25

26. •Thepartofoutput,whichistobedecidedbyfeedbackelementisfed
backtothereferenceinput.Thesignalwhichisoutputoffeedback
elementiscalledfeedbacksignal,b(t).
•Itisthencomparedwiththereferenceinputgivingerrorsignale(t)=
r(t)±b(t)
•Whenfeedbacksignispositive,systemsarecalledpositivefeedback
systemsandifitisnegativesystemsarecallednegativefeedback
systems.
•Thiserrorsignalisthenmodifiedbycontrolleranddecidesthe
proportionalmanipulatedsignalfortheprocesstobecontrolled.
•Thismanipulationissuchthaterrorwillapproachzero.Thissignal
thenactuatestheactualsystemandproducesanoutput.Asoutputis
controlledone,hencecalledcontrolledoutputc(t).
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27. Advantages
1.Accuracy of these systems is always very high because controller modifies and
manipulates the actuating signal such that error in the system will be zero.
2.closed loop system senses environmental changes, as well as internal disturbances
and accordingly modifies the error.
3.There is reduced effect of nonlinearities and distortions.
4.Bandwidth (operating frequency zone) for such system is veryhigh.
Disadvantages
1.systemsarecomplicatedandtimeconsumingfromdesignpointofviewand
hencecostlier.
2.Duetofeedback,systemtriestocorrecttheerrorfromtimetotime.Tendencyto
overcorrecttheerrormaycauseoscillationswithoutboundinthesystem.
3.Systemhastobedesignedtakingintoconsiderationproblemsofinstabilitydueto
feedback.
4.Thestabilityproblemsaresevereandmustbetakencareofwhiledesigningthe
system.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 27

28. 1.HumanBeing
•Thebestexampleishumanbeing.Ifapersonwantstoreachfora
bookonthetable,Positionofthebookisgivenasthereference.
•Feedbacksignalfromeyes,comparestheactualpositionofhands
withreferenceposition.Errorsignalisgiventobrain.
•Brainmanipulatesthiserrorandgivessignaltothehands.This
processcontinuestillthepositionofthehandsgetachieved
appropriately.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 28

29. 2.HomeHeatingSystem
•Inthissystem,theheatingsystemisoperatedbyavalve.
•Theactualtemperatureissensedbyathermalsensorandcompared
withthedesiredtemperature.
•Thedifferencebetweenthetwo,actuatesthevalvemechanismto
changethetemperatureaspertherequirement.
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30. 3. Manual Speed Control System
•A locomotive operator driving a train is a good example of a manual
speed control system.
•The objective is to maintain the speed equal to the speed limits set.
•The entire system is shown in the block diagram in the Fig.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 30

31. 8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 31
Open Loop Closed Loop
Any change in output has no effect
on the input i.e. feedback does not
exists.
Changes in output, affects the input
which is possible by use of feedback.
Output measurement is not
required for operation of system.
Output measurement is necessary.
Feedback element is absent.Feedback element is present.
Error detector is absent. Error detector is necessary.
It is inaccurate and unreliable.Highly accurate and reliable.
Highly sensitive to the disturbances.Less sensitive to the disturbances.
Highly sensitive to the environmental
changes.
Less sensitive to the environmental
changes.
Bandwidth is small. Bandwidth is large.
Simple to construct and cheap.Complicated to design and hence costly.
Generally are stable in nature.Stability is the major
consideration while designing
Highly affected by nonlinearities.Reduced effect of nonlinearities.

32. Toachievetherequiredobjective,agoodcontrolsystemmustsatisfy
thefollowingrequirements.
1.Accuracy:
–Agoodcontrolsystemmustbehighlyaccurate.
–Theopenloopsystemsaregenerallylessaccurateandhence
feedbackisintroducedtoreducetheerrorinthesystem.
2.Sensitivity:
–Agoodcontrolsystemshouldbeveryinsensitivetoenvironmental
changes,ageetc.But,mustbesensitivetotheinputcommands.
–Theperformanceshouldnotbeaffectedbysmallchangesinthe
certainparametersofthesystem.
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33. 3)Externaldisturbanceornoise:
–Allthephysicalsystemsaresubjectedtoexternaldisturbances
andnoisesignalsduringoperation.
–Arequirementofagoodcontrolsystemisthatsystemis
insensitivetonoiseandexternaldisturbancesbutsensitivetothe
inputcommands.
–Itshouldbeabletoreducetheeffectsofundesirable
disturbances.
4)Stability:
–Aconceptofstabilitymeansoutputofsystemmustfollow
referenceinputandmustproducedboundedoutputforbounded
input.
–Agoodcontrolsystemisonewhichisstableinnature.
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34. 5)Bandwidth:
–Thisrequirementisrelatedtothefrequencyresponseofthe
system.
–Fortheinputfrequencyrange,itshouldgivesatisfactoryoutput.
6)Speed:
–Asystemshouldhavegoodspeed.Thismeansoutputofthe
systemshouldapproachtoitsdesiredvalueasquicklyaspossible.
–Systemshouldsettleddowntoitsfinal,valueasquicklyas
possible.
7)Oscillations:
–Thesystemshouldexhibitssuitabledampingi.e.thecontrolled
outputshouldfollowthechangesinthereferenceinputwithout
undulylargeoscillationsorovershoots.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 34

35. •Theconceptofacontrolsystemistosensedeviationoftheoutput
fromthedesiredvalueandcorrectit,tillthedesiredoutputis
achieved.
•Thedeviationoftheactualoutputfromitsdesiredvalueiscalledan
error.Themeasurementoferrorispossiblebecauseoffeedback.
•Thefeedbackallowsustocomparetheactualoutputwithitsdesired
valuetogeneratetheerror.
•Thecontrollerisanelementwhichacceptstheerrorinsomeform
anddecidesthepropercorrectiveaction.
•Theoutputofthecontrolleristhenappliedtotheprocessorfinal
controlelement.Thisbringstheoutputbacktoitsdesiredsetpoint
value.
•Thecontrolleristheheartofacontrolsystem.Theaccuracyofthe
entiresystemdependsonhowsensitiveisthecontrollertotheerror
detectedandhowitismanipulatingsuchanerror.
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 35

36. Mostindustrialcontrollersmaybeclassifiedaccordingtotheircontrol
actionsas:
1.Two-positionoron-offcontrollers
2.Proportionalcontrollers
3.Integralcontrollers
4.Proportional-plus-integralcontrollers
5.Proportional-plus-derivativecontrollers
6.Proportional-plus-integral-plus-derivativecontrollers
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 36

37. •Themostelementarycontrollermodeisthetwo-positionorON/OFF
controllermode.
•Itisthesimplest,cheapest.
•Themostgeneralformcanbegivenby:
P=0% ep<0
P=100% ep>0
•Therelationshowsthatwhenthemeasuredvalueislessthanthe
set-point(i.e.ep>0),thecontrolleroutputwillbefull(i.e.100%),
•whenthemeasuredvalueismorethanthesetpoint(i.e.ep<0),the
controlleroutputwillbezero(i.e.0%).
8/21/2017 HareeshaN G, Dept of Aero Engg, DSCE, Blore 37
Ex. ON/OFF switch

38. 8/21/2017
•Inthiscontrolmode,theoutputofthecontrollerissimpleproportional
totheerrore(t).
•Therelationbetweentheerrore(t)andthecontrolleroutputpis
determinedbyconstantcalledproportionalgainconstantdenotedasK
p.
•Theoutputofthecontrollerisalinearfunctionoftheerrore(t).
•Thuseachvalueoftheerrorhasauniquevalueofthecontrolleroutput.
•Therangeoftheerrorwhichcovers0%to100%controlleroutputis
calledproportionalband.
•Thebasicrelationshipbetweenoutputofthecontrolleranderrorsignal
isgivenby,
p(t)=K
pe(t)
TakingLaplacetransform,
P(s)=K
pE(s)
HareeshaN G, Dept of Aero Engg, DSCE, Blore 38
K
p= Proportional gain constant

39. 8/21/2017
•Thoughthereexistslinearrelationbetweencontrolleroutputandthe
error,forazeroerrorthecontrolleroutputshouldnotbezero,
otherwisetheprocesswillcometohalt.
•HencethereexistssomecontrolleroutputP
oforthezeroerror.Hence
mathematicallytheproportionalcontrolmodeisexpressedas,
p(t)=K
pe(t)+P
o
HareeshaN G, Dept of Aero Engg, DSCE, Blore 39
K
p= Proportional gain constant
P
o= Controller output with zero error

40. 8/21/2017
•Intheproportionalcontrolmode,errorreducesbutcannotgoto
zero.
•Itfinallyproducesanoffseterror.Itcannotadaptwiththechanging
loadconditions.Toavoidthis,anothercontrolmodeisoftenusedin
thecontrolsystemswhichisbasedonthehistoryoftheerrors.This
modeiscalledintegralmodeorresetactioncontroller.
•Insuchacontroller,thevalueofthecontrolleroutputp(t)ischanged
ataratewhichisproportionedtotheactuatingerrorsignale(t).
Mathematicallyitisexpressedas,
TakingLaplacetransform,
sP(s)=KiE(s) or P(s)=(Ki/s)E(s)
HareeshaN G, Dept of Aero Engg, DSCE, Blore 40
teK
dt
tdp
i

K
i = Constant relating error and rate

41. 8/21/2017
•TheconstantK
iisalsocalledintegralconstant.
•Integratingtheaboveequation,actualcontrolleroutputatanytimet
canbeobtainedas,
Where
p(0)=Controlleroutputwhenintegralactionstartsi.e.att=0.
HareeshaN G, Dept of Aero Engg, DSCE, Blore 41  0
0
pdtteKtp
t
i


42. 8/21/2017
•Thecontrollerproducesacontrolactionthatisproportionaltothe
rateatwhichtheerrorischangingde(t)/dt.
•Themathematicalequationforthemodeis,
where K
d= Derivative gain constant.
Taking Laplace transform
P(s) = K
ds E(s)
HareeshaN G, Dept of Aero Engg, DSCE, Blore 42

dt
tde
Ktp
d


43. 8/21/2017
•This is a composite control mode obtained by combining the
proportional mode and the integral mode.
•The mathematical expression for such a composite control is,
Taking Laplace transform,
HareeshaN G, Dept of Aero Engg, DSCE, Blore 43   0
0
pdtteKKteKtp
t
ipp    sE
s
KK
KsP
ip
p 





  sE
s
K
KsP
i
p 





1

44. 8/21/2017
•The series combination of proportional and derivative control modes
gives proportional plus derivative control mode.
•The mathematical expression for the PD composite control is,
•Taking Laplace transform,
•The addition of a derivative mode to a proportional controller
modifies its response to inputs.
•A PD controller provides an element to the response which is largest
when the rate of change of the error is greatest and diminishes as it
becomes smaller.
•The derivative mode is never used alone because it is not capable of
maintaining a control signal under steady error conditions.
•It is always used with the proportional mode and often additionally
with the integral mode.HareeshaN G, Dept of Aero Engg, DSCE, Blore 44 

0p
dt
tde
KKteKtp
dpp
  sEsKKKsP
dpp


45. 8/21/2017
•Thecompositecontrollerincludingthecombinationofthe
proportional,integralandderivativecontrolmodeiscalledPID
controlmodeandthecontrolleriscalledthreemodecontroller.
•Itisverymuchcomplextodesignbutverypowerfulinaction.
•Mathematicallysuchacontrolmodecanbeexpressedas,
HareeshaN G, Dept of Aero Engg, DSCE, Blore 45  

0
0
p
dt
tde
KKdtteKKteKtp
dp
t
ipp    sEsKK
s
KK
KsP
dp
ip
p 





   sEKsKs
s
K
sP
id
p

2

46. 8/21/2017
•Thismodehasadvantagesofallthemodes.
•Theintegralmodeeliminatestheoffseterroroftheproportional
modeandtheresponseisalsoveryfastduetoderivativemode.
•Thesuddenresponseisproducedduetoderivativemode.
•Thusitcanbeusedforanyprocesscondition.
•WiththePIDcontrolaction,thereisnooffset,nooscillationswith
leastsettlingtime.
•Sothereisimprovementinbothtransientaswellassteady
stateresponse.
HareeshaN G, Dept of Aero Engg, DSCE, Blore 46

47. 8/21/2017
A
The Fulcrum can be adjusted horizontally by turning
knob A
BThe Float can be adjusted vertically by turning knob B
HareeshaN G, Dept of Aero Engg, DSCE, Blore 47
DesiredValue(DV) = Therequiredlevelofwaterinthetank
MeasuredValue(MV) = Theactuallevelofwaterinthetank.
OffsetorError(E) = Thedifferencebetweentherequiredandactual
level(DV-MV)
Gain(K) = Theratiooffloatmovementtovalvemovement
•The water level and the Float continue to drop and the Supply Valve
continues to open until the water flow into the tank equals the flow out of
the tank at which point the water level stops falling.
•Thesystemhas now reached steady state but the tank level is now lower
than the required level (DV>MV) and there is an Offset.
•In a Proportional onlysystemunder load there will always be an Offset
and that offset will vary dependant on the size of the load.
Courtesy: http://aeroquad.com

48. 8/21/2017
•Proportional control will always result in an Offset between
Measured Value and Desired Value and for every load there will be a
different steady state water level.
•As the Gain increases the Offset decreases.
•As the Gain increases the stability decreases until the system
becomes unstable.
•With Proportional only control a compromise must be reached
between size of Offset and stability by adjusting the Gain.
•In some systems an Offset is acceptable, as in the water tank
described above, and Proportional only control is acceptable.
•However in other systems an offset of any size is unacceptable and
some other form of control is required.
HareeshaN G, Dept of Aero Engg, DSCE, Blore 48

49. 8/21/2017
•With thesystemwe described above, under load, assuming the Gain
of system has been adjusted to its optimum value, the water level will
settle with an Offset from the Desired Value.
•By adjusting knob B so that the float moves upwards, relative to the
water level, the Supply Valve will open more, the flow in will increase
and the Offset will reduce.
•Eventually a new height of the Float will be found where the flow into
the tank equals the flow out , the Measured value equals the Desired
Value and Offset will be zero.
HareeshaN G, Dept of Aero Engg, DSCE, Blore 49Courtesy: http://aeroquad.com

50. 8/21/2017
•The speed at which the Float height is adjusted can be fast or slow.
•If it is too fast thesystemcan become unstable (hunting) and if it is
too slow time will be wasted.
•With Integral control the speed at which Offset is removed is made
directly proportional to the size of the Offset.
•In the water tanksystem,we could achieve this by operating knob B
with a variable speed servo motor.
•The amount of integral action applied would be controlled by
adjusting the ratio between Motor speed and size of Offset.
HareeshaN G, Dept of Aero Engg, DSCE, Blore 50Courtesy: http://aeroquad.com

51. 8/21/2017
•NotallsystemscanbecontrolledbyProportionalandIntegralcontrol
only.
•Inthewatertanksystem,anincreaseinloadresultsinanimmediate
dropinwaterlevelandtheFloat.
•TheSupplyValveisimmediatelyopenedallowingwaterintothetank.
•Insomesystemsthereisadelayorlaginresponsetoachangein
load.
•Forexample,awindtunnelhasalargeheavyfan.Ifmorepoweris
appliedtoincreasethefan'sspeedtherewillbeasignificantdelay
beforethenewspeedisachievedduetothetimeneededto
overcometheinertiaofthefan.
•Toovercometheinertiamorepower(thanactuallyrequired)is
requiredtomaintainthedesiredspeed(DV),toacceleratethefans
speedchange.
HareeshaN G, Dept of Aero Engg, DSCE, Blore 51

52. 8/21/2017
•Theadditionalpoweristhenreducedtothelevelrequiredto
maintaintherequiredspeed.
•Inthewatertanksystem,underProportionalandIntegralcontrol,
knobBisoperatedbyavariablespeedservomotor.
•Iftherewasinertiainthesystem,duetofrictioninthelinkage
betweentheFloatandtheSupplyValve,Derivativeactionwould
temporarilyapplyahigherspeedtotheservomotorthanwas
necessarytoremovetheOffset.
HareeshaN G, Dept of Aero Engg, DSCE, Blore 52
Summary:
1.Derivative action speeds up the removal of the Offset.
2.It is required in systems which have large time delays due to
Inertia or large capacities.
3.It tends to make asystemmore stable as it is increased it can
cause hunting and instability

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Proportional
action (P)
Arrests
It arrest the change of the Measured Value
but always with an Offset from the
Measured Value
Integral action
(I)
RestoresIt removes the Offset ​
Derivative
action (D)
AcceleratesIt speeds up the removal of the Offset
HareeshaN G, Dept of Aero Engg, DSCE, Blore 53

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1.ModernControlEngineering,KatsuhikoOgatta,Pearson
Education,2004.
2.ControlSystemEngineering,U.A.Bakshi
3.ControlSystems,W.Bolton,ElsevierLtd.
4.http://aeroquad.com/showwiki.php?title=A-Guide-To-Proportional-
Integral-and-Derivative-PID-Control
HareeshaN G, Dept of Aero Engg, DSCE, Blore 54

55. 8/21/2017
Thecontentsusedinthispresentationaretakenfromthetextbooks
mentionedinthereferences.Idonotholdanycopyrightsforthe
contents.Ithasbeenpreparedtouseintheclasslectures,notfor
commercialpurpose.
HareeshaNG
HareeshaN G, Dept of Aero Engg, DSCE, Blore 55

56. Please to me if you have any
suggestions/criticisms.
[email protected]
8/21/2017
Hareesha N G, Dept of Aero Engg, DSCE,
Blore
56