Basic of Control System

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.

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INTRODUCTION OF CONTROL SYSTEMS

• Basic Components of a Control SystemObjective of Control SystemControl System ComponentsResult or Output

CONTROL SYSTEM

OBJECTIVES RESULTS /OUTPUTS


BASIC TERMINOLOGIES RELATED TO CONTROL SYSTEMS


BASIC TERMINOLOGIES RELATED TO CONTROL SYSTEMS


Fly ball Governor



TYPES OF CONTROL SYSTEMS

OPEN LOOP CONTROL SYSTEM

Brown

Heating Time

Light Brown

Black

1.10 Min

2.10 Min


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.



EXAMPLESTraffic Control System Automatic Washing Machine Ceiling fanVacum Cleaner



Heating Time

Brown

Light Brown

1.10 Min

2.07Min

Brown

Error

CLOSED LOOP CONTROL SYSTEM


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.



Advantages1.This is less sensitive to disturbance signal.

2.Highly accurate.

EXAMPLES RefrigeratorAir ConditionerHuman Respiration SystemRadar and Missile Railway Reservation System



Automobile Steering Control System


Human Being


Rotating Disk Speed Control

Without Feedback


Rotating Disk Speed Control

With Feedback


Disk Drive Read System


Disk Drive Read System


Feedback and Feed Forward System


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


Positioner

ControllerPosition

Feed back Large Solar collector

SunReference

Control system for a sun seeker solar system

Launch Command


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


Tracking control

Launchcomputer

Amplifier

Launcher

Actual position

Calculated path

Flight path

Control system for a missile launcher


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.


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-


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.


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


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



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

-


TYPES OF SYSTEM

Fig : Input –Output Behavior of a System


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


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


Fig. V-I Characteristics of Linear System

Fig. V-I Characteristics of Non Linear System

TYPES OF SYSTEM


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


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


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


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


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.


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


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


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


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.


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


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.


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)


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



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



PB: Derive the Transfer Function of the circuits I(s)/Vi(s)

Vi(t)i(t)


Step:1 Convert the given network in to laplace

Vi(s)I(s)


Apply KVL to circuit Vi(s) = (R +1/Cs)I(s)

I(s)/Vi(s) = Cs / (1 + sCR)


Vi(t) Vo(t)

Determine the transfer function Vo(s) / Vi(s)

Step1: Convert the given network in to Laplace network


Vi(s)Vo(s)

I(s)


Apply KVL to given Network.

Vi(s) = (R +1/Cs)I(s)

Vo(s) = R I(s)

Vo(s) sCR

=

Vi(s) (1+sCR)


Vi(t) Vo(t)

Determine the transfer function Vo(s) / Vi(s)

i(t)

Step1: Convert the given network in to Laplace network


1/Cs

R2

R1

Vo(t)Vi(t)

I(s)


R1(1/Cs)(R1+ 1/Cs)

R2

Vi(s) Vo(s)I(s)


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)


Vo(s) K(1+s 1ז )

Vi(s) (1+s 2ז )

Where 1ז =CR1 2ז = CR1R2 / (R1 +R2) and

K= R2/(R1+R2)


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



Negative Feedback

G(s)

H(s)

R(s) +

-

C(s)

V(s)

E(s)

All practical systems are negative feedback system

TYPES OF FEEDBACK


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


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)


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)


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Basic of Control System