Basic of Control System
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P.M.MENGHALFACULTY OF ELECTRONICS
MILTARY COLLEGE OF ELECTRONICS & MECHNICAL ENGINEERING,TRIMULGHERRY,SECUNDERABAD -500 015
ANDRA PRADESH INDIA Mobile: 9440635370
Email:[email protected] [email protected]
BASIC OF CONTROL SYSTEM
Control Engineering Coursework
DE-93 Control System Asst Professor P M Menghal 2
I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation.
For best results, it is always suggested you read the source material
DE-93 Control System Asst Professor P M Menghal 3
INTRODUCTION OF CONTROL SYSTEMS
• Basic Components of a Control SystemObjective of Control SystemControl System ComponentsResult or Output
CONTROL SYSTEM
OBJECTIVES RESULTS /OUTPUTS
DE-93 Control System Asst Professor P M Menghal 4
BASIC TERMINOLOGIES RELATED TO CONTROL SYSTEMS
DE-93 Control System Asst Professor P M Menghal 5
BASIC TERMINOLOGIES RELATED TO CONTROL SYSTEMS
DE-93 Control System Asst Professor P M Menghal 6
Fly ball Governor
DE-93 Control System Asst Professor P M Menghal 7
DE-93 Control System Asst Professor P M Menghal 8
TYPES OF CONTROL SYSTEMS
OPEN LOOP CONTROL SYSTEM
Brown
Heating Time
Light Brown
Black
1.10 Min
2.10 Min
DE-93 Control System Asst Professor P M Menghal 9
A physical system which does not automatically corrects for the variation in output is called as open loop control system.In open loop system the output does not influences the controller.
Advantages 1.Simple in construction 2.Fast response3.Low cost Disadvantages1.Accuracy is less.
OPEN LOOP CONTROL SYSTEM
DE-93 Control System Asst Professor P M Menghal 10
EXAMPLESTraffic Control System Automatic Washing Machine Ceiling fanVacum Cleaner
OPEN LOOP CONTROL SYSTEM
DE-93 Control System Asst Professor P M Menghal 11
Heating Time
Brown
Light Brown
1.10 Min
2.07Min
Brown
Error
CLOSED LOOP CONTROL SYSTEM
DE-93 Control System Asst Professor P M Menghal 12
A physical system which automatically corrects for the variation in its output is called as closed loop control system.
A closed loop control system measures the system output measured by sensor with reference input and according to it produces an error signal.
CLOSED LOOP CONTROL SYSTEM
DE-93 Control System Asst Professor P M Menghal 13
Advantages1.This is less sensitive to disturbance signal.
2.Highly accurate.
EXAMPLES RefrigeratorAir ConditionerHuman Respiration SystemRadar and Missile Railway Reservation System
CLOSED LOOP CONTROL SYSTEM
DE-93 Control System Asst Professor P M Menghal 14
Automobile Steering Control System
DE-93 Control System Asst Professor P M Menghal 15
Human Being
DE-93 Control System Asst Professor P M Menghal 16
Rotating Disk Speed Control
Without Feedback
DE-93 Control System Asst Professor P M Menghal 17
Rotating Disk Speed Control
With Feedback
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Disk Drive Read System
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Disk Drive Read System
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Feedback and Feed Forward System
DE-93 Control System Asst Professor P M Menghal 21
Login T-Expert Learning and Teaching Testing Evaluation Quiz
Measuring of Student Knowledge
Student Knowledge State
Evaluation of student
knowledgeReference Subject Matter and the GoodStudent Model
Leaning & Teaching
Testing
Quiz
Student Knowledge state
DE-93 Control System Asst Professor P M Menghal 22
Positioner
ControllerPosition
Feed back Large Solar collector
SunReference
Control system for a sun seeker solar system
Launch Command
DE-93 Control System Asst Professor P M Menghal 23
Activating signalP K
Feed back signalDrive Marty
Computer (inside)
RADAR antenna
Project position of Air plane when the shell arrives
Anti-air craft RADAR tracking control system
DE-93 Control System Asst Professor P M Menghal 24
Tracking control
Launchcomputer
Amplifier
Launcher
Actual position
Calculated path
Flight path
Control system for a missile launcher
DE-93 Control System Asst Professor P M Menghal 25
Problem
All human have experienced a fever associated with an illness. A fever
is related to the changing of the control input in the body’s thermostat. This thermostat, within the brain, normally regulates temperature near 98oF in spite of external temperature ranging from0o to 100oF or more. For fever the input, or desired, temperature is increased. Even to many scientist, it often comes as surprise to learn that fever doesn’t indicate something wrong with body temperature control but rather well controlled at an elevated level of desired input.Sketch a block diagram of the temperature control system and explain how aspirin will lower fever.
DE-93 Control System Asst Professor P M Menghal 26
With the onset of a fever , the body
thermostat is turned up. The body
adjusts by shivering and less blood flows
to the skin surface. Aspirin acts to lower
the thermal state point in the brain.
ControllerAdjustment with in the body
ProcessBody
MeasurementInternal sensor
XDesigned
Temp orset point from body the most at to the brain.
Measured body
temp
Body
temp-
DE-93 Control System Asst Professor P M Menghal 27
Problem
The role of air traffic control systems is increasing asairplane traffic increases at busy airports. Engineers are developing air traffic control systems and collisionavoidance systems using Global Positioning System (GPS) navigation satellites.GPS allows each aircrafts to know its positions in the airspace landing corridor very preciously. Sketch the block diagram depicting how an air traffic controller might use GPS for aircraft collision avoidance.
DE-93 Control System Asst Professor P M Menghal 28
An aircraft flight path control system
using GPS.
XControllerComputer Auto pilot
Actuators Ailerons, elevators,
Rudder and engine power
ProcessAircraft
MeasurementsMeasured R light
Path
Desired path from
Flight
Path from air traffic
controller
DE-93 Control System Asst Professor P M Menghal 29
The potential of employing two or more helicopters for transporting payloads that are too heavy for a single helicopter is a well addressed issue in the civil and military rotorcraft design arenas. Overall requirements can be satisfied more efficiently with smaller aircraft by using multilift for infrequent peak demands. Hence principle motivation for using multilift can be attributed to the promise of obtaining increased productivity without having to manufacture largerand more expensive helicopter. A specific case of a multilift arrangement where two helicopters jointly transport payloads has been named twin lift Fig shows typical “two point pendant” twin liftconfiguration in the lateral/vertical plane. Develop the block diagramdescribing the pilots action, the position of each helicopter and
position of the load.
Problem
DE-93 Control System Asst Professor P M Menghal 30
DE-93 Control System Asst Professor P M Menghal 31
A control system for a twin lift helicopter
system.
System
X
XController
Process
Helicopter
Measurement
Radar
Measurement
AltimeterMeasurecl Altitude
Separation distance
Altitude
Desired separation distance
Designed altitude
-
DE-93 Control System Asst Professor P M Menghal 32
TYPES OF SYSTEM
Fig : Input –Output Behavior of a System
DE-93 Control System Asst Professor P M Menghal 33
Linear System : Roughly speaking, a linear circuit is one whose parameters do not change with voltage or current. More specifically, a linear system is one that satisfies
(i)Homogeneity property [response of α u(t) equals α times the response of u(t), S(αu(t) = αS(u(t)) for all α; and u(t)].
(ii) Additive property [that is the response of system due to an input {α1u1(t)+α2u2(t)} = α1u1(t) + α2u2(t) .
TYPES OF SYSTEM
DE-93 Control System Asst Professor P M Menghal 34
Non-Linear System : Roughly speaking, a non-linear
system is that whose parameters change with voltage or
current. More specifically, non-linear system does not
obey the homogeneity and additive properties. Volt-
ampere characteristics of linear and non-linear elements
are shown in below .In fact, a circuit is linear if and only
if its input and output can be related by a straight line
passing through the origin as shown in fig Otherwise, it
is a nonlinear system.
TYPES OF SYSTEM
DE-93 Control System Asst Professor P M Menghal 35
Fig. V-I Characteristics of Linear System
Fig. V-I Characteristics of Non Linear System
TYPES OF SYSTEM
DE-93 Control System Asst Professor P M Menghal 36
Electrical Network: A combination of various electric
elements (Resistor, Inductor, Capacitor, Voltage
source, Current source) connected in any manner
what so ever is called an electrical network. We may
classify circuit elements in two categories, passive
and active elements Passive Element: The element which receives energy
(or absorbs energy) and then either converts it into
heat (R) or stored it in an electric (C) or magnetic (L )
field is called passive element.
TYPES OF SYSTEM
DE-93 Control System Asst Professor P M Menghal 37
Active Element: The elements that supply energy to
the circuit is called active element. Examples of active
elements include voltage and current sources,
generators, and electronic devices that require power
supplies. A transistor is an active circuit element,
meaning that it can amplify power of a signal. On the
other hand, transformer is not an active element
because it does not amplify the power level and power
remains same both in primary and secondary sides.
Transformer is an example of passive element.
TYPES OF SYSTEM
DE-93 Control System Asst Professor P M Menghal 38
Bilateral Element: Conduction of current in both
directions in an element (example: Resistance;
Inductance; Capacitance) with same magnitude is
termed as bilateral element.
TYPES OF SYSTEM
DE-93 Control System Asst Professor P M Menghal 39
Unilateral Element: Conduction of current in one
direction is termed as unilateral (example: Diode,
Transistor) element.
Meaning of Response: An application of input signal to the system will produce an output signal, the behavior of output signal with time is known as the response of the system.
TYPES OF SYSTEM
DE-93 Control System Asst Professor P M Menghal 40
TYPES OF SYSTEM• TIME VARIANT SYSTEM
Parameters of system are
functions of time
Input
r(t)
Output
c(t)
Examples:1.Space vehicle whose mass (weight ) decreases with time, as it leaves earth.
2.Rocket ,aerodynamic damping can change with time as the air density change with altitude.
DE-93 Control System Asst Professor P M Menghal 41
Parameters of system are
constant and not functions of time
Input
r(t)
Output
c(t)
Examples: Different electrical networks consisting of the elements as resistances,inductances and capacitances are time invariant systems as the values of the elements of such system are constant and not the functions of time.
TIME INVARIANT SYSTEM
DE-93 Control System Asst Professor P M Menghal 42
TRANSFER FUNCTION
System Parameters
Selected
Input
Output
Performance of system can expressed in terms of its outputOutput = Effect of system parameters on the selected inputOutput = Input X Effect of system parametersEffect of system parameters = Output / Input
DE-93 Control System Asst Professor P M Menghal 43
T(s)= C(s)/R(s)
Definition:
It is defind as the ratio of Laplace transform of Output (response) of the system to the Laplace transform of Input (Excitation or driving function) under the assumption that all initial conditions are zero.
System r(t) c(t)
T(s)R(s) C(s)
Laplace Transform of OutputTransfer Function =
Laplace Transform of Input
DE-93 Control System Asst Professor P M Menghal 44
ADVANTAGES & FEATURES OF
TRANSFER FUNCTION It gives mathematical models of all system
components and hence of the overall system. Individual analysis of various components is also
possible by the transfer function approach. As it uses a Laplace approach, it converts time
domain equations to simple algebraic equations. The transfer function is expressed only as a function
of the complex variable 's‘.lt is not a function of the real variable, time or any other variable that is used as the independent variable.
DE-93 Control System Asst Professor P M Menghal 45
It is the property and characteristics of the system itself. Its value is dependent on the parameters of the system and independent of the values of inputs.
Once transfer function is known, output response for any type of reference input can be calculated.
It helps in determining the important information about the system i.e. poles', zeros, characteristic equation etc.
It helps in the stability analysis of the system.
ADVANTAGES & FEATURES OF
TRANSFER FUNCTION
DE-93 Control System Asst Professor P M Menghal 46
DISADVANTAGES
Only applicable to linear time invariant systems.
It does not provide any information concerning the physical structure of the system. From transfer function, physical nature of the system whether it is electrical, mechanical, thermal or hydraulic, cannot be judged.
Effects arising due to initial conditions are totally neglected. Hence initial conditions loose their importance.
DE-93 Control System Asst Professor P M Menghal 47
TERMINOLOGIES RELATED TO TRANSFER FUNCTION
A Transfer function is a ratio of L.T. of output to input which can be expressed as a ratio of polynomials in ‘S’.
Transfer Function = P(s)/Q(s) = a0Sm + a1Sm-1 + a2Sm-2 + -- + am
b0Sn + b1 Sn-1 + b2 Sn-2 + -- + bn
= K (S-Sa) (S-Sb)- - - - -(S-Sm)
(S-S1) (S-S2)- - - - -(S-Sn)
DE-93 Control System Asst Professor P M Menghal 48
Poles: The value of ‘S’ which makes the T.F.infinite after substitution in the denominator of a T.F.are called as Poles of T.F. So values S1,S2,S3 - - - -Sn are called as poles of the T.F.
Zeros: The value of ‘S’ which makes the T.F. zero after substitution in the numerator of a T.F.are called as Zeros of that T.F. So values Sa,Sb,Sc - - - -Sm are called as zeros of the T.F.
Characteristics Equation The equation obtained by equating denominator of atransfer function to zero whose roots are the poles of the transfer function is called as characteristics equation
TERMINOLOGIES RELATED TO TRANSFER FUNCTION
DE-93 Control System Asst Professor P M Menghal 49
Pole-Zero Plot: Plot obtained by locating all poles and zeros of aT.F.in S plane is called pole-zero plot.
Examples: C(s)/R(s) = (S+2) / S[S2+2S+2] [S2+7S+12]
Poles: S = 0,-1± j, -3, -4
Zeros: S = -2
Imj (Jω)
Real (σ)
X
X
j
-j-1-2
XX -3-4
S Plane
Imj (-Jω)
Real (-σ)X s= 0
TERMINOLOGIES RELATED TO TRANSFER FUNCTION
DE-93 Control System Asst Professor P M Menghal 50
PB: Derive the Transfer Function of the circuits I(s)/Vi(s)
Vi(t)i(t)
DE-93 Control System Asst Professor P M Menghal 51
Step:1 Convert the given network in to laplace
Vi(s)I(s)
DE-93 Control System Asst Professor P M Menghal 52
Apply KVL to circuit Vi(s) = (R +1/Cs)I(s)
I(s)/Vi(s) = Cs / (1 + sCR)
DE-93 Control System Asst Professor P M Menghal 53
Vi(t) Vo(t)
Determine the transfer function Vo(s) / Vi(s)
Step1: Convert the given network in to Laplace network
DE-93 Control System Asst Professor P M Menghal 54
Vi(s)Vo(s)
I(s)
DE-93 Control System Asst Professor P M Menghal 55
Apply KVL to given Network.
Vi(s) = (R +1/Cs)I(s)
Vo(s) = R I(s)
Vo(s) sCR
=
Vi(s) (1+sCR)
DE-93 Control System Asst Professor P M Menghal 56
Vi(t) Vo(t)
Determine the transfer function Vo(s) / Vi(s)
i(t)
Step1: Convert the given network in to Laplace network
DE-93 Control System Asst Professor P M Menghal 57
1/Cs
R2
R1
Vo(t)Vi(t)
I(s)
DE-93 Control System Asst Professor P M Menghal 58
R1(1/Cs)(R1+ 1/Cs)
R2
Vi(s) Vo(s)I(s)
DE-93 Control System Asst Professor P M Menghal 59
R1(1/Cs) Vi(s) = I(s) + R2I(s)
(R1+1/Cs)
Vo(s) =R2I(s)
Vo(s) R2 (1+sCR1) = Vi(s) (R1+R2) 1 + sCR1R2
(R1+R2)
DE-93 Control System Asst Professor P M Menghal 60
Vo(s) K(1+s 1ז )
Vi(s) (1+s 2ז )
Where 1ז =CR1 2ז = CR1R2 / (R1 +R2) and
K= R2/(R1+R2)
DE-93 Control System Asst Professor P M Menghal 61
G(s)R(s) C(s)
r(t) c(t)
Output signal of any block = Input signal to that block X gain of that block
C(s)= R(s) X G(s)
T.F. = C(s) / R(s) = G(s)
G(s) = Forward path transfer function
TRANSFER FUNCTION OF
OPEN LOOP CONTROL SYSTEM
DE-93 Control System Asst Professor P M Menghal 62
Negative Feedback
G(s)
H(s)
R(s) +
-
C(s)
V(s)
E(s)
All practical systems are negative feedback system
TYPES OF FEEDBACK
DE-93 Control System Asst Professor P M Menghal 63
Positive Feedback
G(s)
H(s)
R(s) +
+
C(s)
V(s)
E(s)
Ex: Oscillator
Unity Feedback
G(s)
H(s) =1
R(s) +
-
C(s)
V(s)
E(s)
Ex: Voltage Regulator
DE-93 Control System Asst Professor P M Menghal 64
TRANSFER FUNCTION OF CLOSED LOOP CONTROL SYSTEM
Consider negative feedback system
H(s) = Feedback Path Transfer Function
E(s) = R(s)-V(s)
Output of the system = C(s) = G(s) E(s)
= G(s)[ R(s)- V(s)]
V(s) = C(s)H(s)
G(s)
H(s)
R(s) +
-
C(s)
V(s)
E(s)
DE-93 Control System Asst Professor P M Menghal 65
C(s) = G(s)[ R(s) – C(s)H(s)]
[1+G(s)H(s)] C(s) = R(s)G(s)
T.F. = C(s)/R(s) = G(s)/{1+G(s)H(s)}
Open Loop Equivalent Of Closed Loop System
G(s)/{1± G(s)H(s)}
+ = Negative Feedback - = Positive Feed Back
R(s) C(s)
DE-93 Control System Asst Professor P M Menghal 66
"A person who learns but does not think is lost"
"A person who thinks but does not learn is in great danger."