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1. Storey: Electrical & Electronic Systems © Pearson Education Limited 2004 OHT 7.‹#›
CONTROL SYSTEMS
Course Code: 21EC652
•Unit1: Introduction: Types of Control Systems,
Effect of Feedback System s, Differential
equation of Physical Systems –Mechanical
Systems, Electrical Systems, Electromechanical
systems, Analogous Systems.
•Unit2 : Block diagrams: Transfer functions,
Block diagram algebra.

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Unit1:Control and Feedback
•Introduction
•Open-loop and Closed-loop Systems
•Feedback Systems
•Negative Feedback
•The Effects of Negative Feedback
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Introduction
•Earlier we identified controlas one of the
basic functions performed by many systems
–often involves regulationor command
•Invariably, the goal is to determine the value
or state of some physical quantity
–and often to maintain it at that value, despite
variations in the system or the environment
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Basic Components of a Control System
1.Objectives of control (Inputs)
2.Control system components (Controller, plant, actuator, sensor,…)
3.Results (Outputs)
HomeHeatingSystem:Sensors(Temperature,pressure,fluidflow).
Actuators(Motors,pumps,heatsources)
Automobile:Sensors(Displacement,speed,force,pressure,temperature,fluidflow,fluidlevel
voltage,current).Actuators(DCmotors,stepmotors,pumps,heatsources)
Robot:Sensors(Opticalimage,displacement,speed,force,torque,pressurevoltage,current).Actuators
(ACmotors,DCmotors,stepmotors,hydroulicactuators)
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Definition:Acontrolsystemisthatmeansbywhichanyquantity
ofinterestinamachine,mechanism orotherequipmentis
maintainedoralteredinaccordancewithdesiredmanner.
Thefollowingfigureshowsthesimpleblockdiagramofacontrolsystem.

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1.Linear Control Systems
In order to understand the linear control system, we should first understand the principle of
superposition.
The principle of superposition theoremincludes two the important properties :
Homogeneity:A system is said to be homogeneous, if we multiply input with some
constant α then the output will also be multiplied by the same value of constant
i.e. f(αx)=αf(x)
Additivity:Suppose we have a system S and we are giving the input to this system as a
1for
the first time and we are getting the output as b
1corresponding to input a
1. On the second
time we are giving input a
2and correspond to this we are getting the output as b
2.
Now suppose this time we are giving input as a summation of the previous inputs (i.e. a
1+
a
2) and corresponding to this input suppose we are getting the output as (b
1+ b
2) then we
can say that system S is following the property of additivity.
Now we are able to define the linear control systemsas those types of control systems
which follow the principle of homogeneity and additivity i.e .superposition theorem.
In Non linear control systems principle of superposition cannot be applied

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2.Time Varying and Time invariant systems:
i.Time Varying control systems are those in which parameters
of systems varying with time.
Ex: A mass of missile varies as a function of time as fuel is
expended during flight.
ii. Time invariant systems :When parameters of control system are
stationary with respect to time during operation of the system,
the system is called as Time invariant system.
Ex: spectroscopy,seismology,circuits,signal processing,

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3.Continuous data and Discrete data control systems
i. A continuous-data system is one in which the signals at various parts
of the system are all functions of the continuous time variablet. The
signals in continuous-data systems may be further classified as ac or dc.
ii. Discrete-data control systems differ from the continuous-data systems
in that the signals at one or more points of the system are in the form of
either a pulse train or a digital code. Usually, discrete-data control
systems are subdivided into sampled-data and digital control systems.

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Control Systems can be classified as SISO control
systems and MIMO control systems based on the
number of inputs and outputs present.
SISO (Single Input and Single Output) control systems
have one input and one output. Whereas, MIMO
(Multiple Inputs and Multiple Outputs) control systems
have more than one input and more than one output.
4.SISO and MIMO Control Systems

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5.Open Loop and Closed Loop ControlSystems
Control Systems can be classified as open loop control systems and closed loop control
systems based on the feedback path.
1.In open loop control systems(Non feedback), output is not fed-back to the
input. So, the control action is independent of the desired output.
The following figure shows the block diagram of the open loop control system.
Here, an input is applied to a controller and it produces an actuating signal or
controlling signal. This signal is given as an input to a plant or process which is to be
controlled. So, the plant produces an output, which is controlled.

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1.Anelectricclothesdryer:Dependingupontheamountofclothesorhowwet
theyare,auseroroperatorwouldsetatimer(controller)tosay30minutesandat
theendofthe30minutesthedrierwillautomaticallystopandturn-offevenifthe
clotheswherestillwetordamp.
2.Themobilephoneisanexampleofopenloopsystem.Atthetimeof
incomingoroutgoingcallloopbegins.Inthisloopthemobilephoneisconnected
tothesatellitedirectly.Thiscontinuoustilltheuserbreakstheconnectionby
endingthecall.Thusthissystemcanbesaidasopenloopsystemasitcannot
breaktheconnectionbyitselfwithouttheuserinterference.Theactionisnot
doneonanaccountoffeedbackbutmanually.
3.Wecanobserveatrafficlightcontrolleratdifferentroadcrossings.The
signalswhicharegeneratedthroughthecontrolsystemaretime-dependent.At
thedesigningtimeofthecontroller,aninternaltimingcanbegiventothe
controller.Thus,oncethecontrollerofatrafficsignalisfixedatthecrossingafter
thateverysignalcanbedisplayedthroughthecontroller.Herethecontrolsystem
hasnothingtoperformusingtheproducedoutputbecauseitcannotchangeits
inputbasedonthetrafficthereatanyside.Aftersomefixedtimegap,basedon
theprimarilygeneratedinput,thecontrolsystemgeneratestheoutput.
Examples:

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2.Closedloopcontrolsystems
Inclosedloopcontrolsystems,outputisfedbacktotheinput.So,thecontrol
actionisdependentonthedesiredoutput.
Thefollowingfigureshowstheblockdiagramofnegativefeedbackclosedloop
controlsystem.

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Theerrordetectorproducesanerrorsignal,whichisthedifferencebetweentheinputand
thefeedbacksignal.
Thisfeedbacksignalisobtainedfromtheblock(feedbackelements)byconsideringthe
outputoftheoverallsystemasaninputtothisblock.
Insteadofthedirectinput,theerrorsignalisappliedasaninputtoacontroller.So,the
controllerproducesanactuatingsignalwhichcontrolstheplant.Inthiscombination,the
outputofthecontrolsystemisadjustedautomaticallytillwegetthedesiredresponse.
Hence,theclosedloopcontrolsystemsarealsocalledtheautomaticcontrolsystems.
Trafficlightscontrolsystemhavingsensorattheinputisanexampleofaclosedloop
controlsystem.

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Examples:
1.Voltagestabilizer:Thevoltagestabilizerstabilizesthesupplyvoltagein
caseoffluctuations.Modernvoltagestabilizersutilizesolidstateelectronic
componentswhichmeasurethefluctuationinvoltageandreduce/increase
(buck/boost)thevoltagetothedesiredlevel.
2.Temperaturecontrolforahouse:Whenthetemperatureofthehouse
fallstoolow,thethermostatmeasuresitandturnsonaheater.Whenthe
temperatureofthehouseisOK,thethermostatmeasuresitandturnsoffa
heater.Whenthetemperatureistoohigh,itturnsonanAC.
3.Trafficcontrolsystemcanbemadeasaclosedloopsystemifthetime
slotsofthesignalsaredecidedbasedonthedensityoftraffic.Inclosedloop
trafficcontrolsystem,thedensityofthetrafficismeasuredonallthesides
andtheinformationisfedtoacomputer.

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The differences between the open loop and the
closed loop control systems are mentioned in the
following table.

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Ifeithertheoutputorsomepartoftheoutputisreturnedtothe
inputsideandutilizedaspartofthesysteminput,thenitis
knownasfeedback.
Feedbackplaysanimportantroleinordertoimprovethe
performanceofthecontrolsystems.Inthischapter,letusdiscuss
thetypesoffeedback&effectsoffeedback.
There are two types of feedback:
Positive feedback
Negative feedback
Feedback

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PositiveFeedback
The positive feedback adds the reference input, ??????(??????) and
feedback output. The following figure shows the block
diagram of positive feedback control system.

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Consider the transfer function of positive feedback
control system is,
Where,
T is the transfer function or overall gain of positive feedback control
system.
G is the open loop gain, which is function of frequency.
H is the gain of feedback path, which is function of frequency.
??????=
G
1−��
----1

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NegativeFeedback
Negative feedback reduces the error between the reference input, ??????(??????)
and system output. The following figure shows the block diagram of
the negative feedback control system.
Transfer function of negative feedback control system is,
??????=
G
1+��
---2
E(S) G(s)E(s)

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C(S)=E(S)G(S) ----1
E(S) = R(S)-H(S)C(S) ---2
Use value of E(S) into C(S)
Then C(S) =G(S)[R(S)-H(S)C(S)]
C(S) = G(S)R(S)-G(S)H(S)C(S)
C(S)+ G(S)H(S)C(S)=G(S)R(S)
C(S)[1+G(S)H(S)]= G(S)R(S)
T=C(S)/R(S)=G(S)/1+G(S)H(S)
E(S)
G(s)E(s)
C(S)H(S)

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Effect of Feedback on Sensitivity:
Sensitivity of the overall gain of negative feedback closed loop control system (T) to the
variation in open loop gain (G) is defined as

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EffectsofFeedback:
EffectofFeedbackonOverallGain
FromEquation2,wecansaythattheoverallgainofnegativefeedback
closedloopcontrolsystemistheratioof‘G’and(1+GH).So,theoverallgain
mayincreaseordecreasedependingonthevalueof(1+GH).
Ifthevalueof(1+GH)islessthan1,thentheoverallgainincreases.Inthis
case,‘GH’valueisnegativebecausethegainofthefeedbackpathis
negative.
Ifthevalueof(1+GH)isgreaterthan1,thentheoverallgaindecreases.In
thiscase,‘GH’valueispositivebecausethegainofthefeedbackpathis
positive.
Ingeneral,‘G’and‘H’arefunctionsoffrequency.So,thefeedbackwill
increasetheoverallgainofthesysteminonefrequencyrangeanddecrease
intheotherfrequencyrange.