7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 1/13

Analogue computers

Introduction:

Defnitions o the Analogue Computers

An analogue computer is a form of computer that uses electrical,

mechanical  or hydraulic phenomena to model the problem being

solved. More generally an analog computer uses one kind of 

physical quantity to represent the behaviour of another physical

system, or mathematical function. Modeling a real physical system

in a computer is called simulation.

Characteristic unction o an analogue computer:

An analogue computer is a computing device that has two

distinguishing characteristics:

1. It can perform operations in a truly parallel manner which

means that it is capable of handling and performing so many

calculations simultaneously or at the same time.

. It also operates using continuous variables i.e. it uses

numbers that that change not in steps, but change in a

smooth continuous manner.

A brie history o analogue computers:

 !he simulation of control systems has been done using analogue

computers for decades. !he analogue computer played an

important role in the advent of system simulations as mentioned

above" some of the control system in use today could not have been

done without the developments of analogue computer owing to the

fact that the analogue computers provided a platform for new

development and advancements of such development

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 2/13

Analogue computer has been very useful in the engineering industry

as well fro military uses.

#uring the $rst and the %econd &orld &ar" the analogue computer

proved such an important item in war $ghting and commands andcontrol for the military.

'elow is a brief timeline of developments and of analogue

computers.

Early Analogue Computers

 !he Antikythera mechanism is the earliest known mechanical analog

computer. It was designed to calculate astronomical positions. It was

discovered in 1()1 in the Antikythera wreck o* the +reek island of 

Antikythera, between ythera and -rete, and has been dated to

circa  1)) '-. In 1) A#, the Iraqi  inventor Al/0aari created the

earliest programmable computer in the form of a humanoid robot.

 !he evolution of the analogue computer resulted directly from the

&&II and the post era the accelerated race to develop newer and

better weapons. A good e2ample of the analogue computers is the

type employed in aircrafts"

Timeline o Analogue Computers

 !he slide rule is a hand/operated analogue computer for

solving multiplication and division problems was invented

around 1)314), shortly after the publication of the concept

of the logarithm.

In 156 a mechanical analogue computer was invented as a

di*erential analyser. It was designed to solve di*erential

equations by integration, using wheel/and/disc mechanisms to

perform the integration. Although it was invented year earlier,

they were $rst built in the 1()s and 1(4)s.

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 3/13

&orld &ar II era gun directors and bomb sights used

mechanical analogue computers.

The fgure below shows part o an analogue computer:

+eneral 7recision %ystem8s electronic analogue computer c.

1(9) was a very adaptable machine that could be con$gured

to solve a range of problems.

 !he M;IA- -omputer was a hydraulic model of a national

economy built in the early 1(9)s

<eathkit =-/1. An educational analogue computer made by

the <eath -ompany, >%A c. 1().

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 4/13

#/&ave %ystems? @rion quantum computing system@, the

world8s $rst working quantum computer operates as an

analogue computer.

In the today8s control and simulation" the rich history of analogue

computers is only remembered when it is randomly mentioned" it is

almost forgotten even though it dates back to prehistory. !he

advent of microprocessor has been largely responsible for demise of 

analogue computers. !he microprocessor" been able to function in

several devices and applications has proved huge and popular in the

control and simulation applications therefore leading to the

analogue computers been discarded and forgotten to history.

ne of the earliest computing machines in industries was analogue,

before the digital age, the analogue computers were very popular

with industries and most importantly with engineering and control

systems industries.

Functions:

In analogue computers, a physical system can be used to represent

a set of di*erential equations, especially useful when the system is

rather complicated and hard to set up. or e2ample, in setting up a

model of a large vibrating system could be demanding, however the

equations for this system could be modelled on an analogue

computer.

Also numerical quantities can be represented by, for e2ample, the

angle of rotation of a shaft or a di*erence in electrical potential

hence the output voltage of the machine at a time might represent

the momentary speed of the obBect being modelled.

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 5/13

Parts o the Analogue Computer:

1. The Operational Amplifer Op Amp!.

 !he operational ampli$er is a high gain ampli$er with a wide variety

of applications. !he ampli$er is usually described in terms of its

gain, input impedance, output impedance, bandwidth, and o*set

characteristics. An operational ampli$er usually has two input

terminals. !he two input terminals are marked with a CDE to indicate

the no inverting input and a C3E to indicate the inverting input. An

equivalent circuit for an op amp and a standard symbol are shown in

igure 1.1.

"igures1.1: a! The Circuit #ymbol or an Op Amp$ b! AnE%ui&alent Op Amp Circuit.

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 6/13

'. #ummers an( )n&erters.

 !he electrical circuit whose transfer characteristics are analogous to

the mathematical operation of summation is shown in igure 1.9 Cfor

ann3input summerE. Applying ircho*8s current law at the summing

 Bunction gives

Or$

In terms of voltagesF

;ote that since V A V o v x G / , then equation C1.6E can be rewritten

&here,

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 7/13

"igure 1.': #umming Amplifer

'y isolating Vo $ we obtain,

%ince the op amp has a very high voltage gain Cusually H E, we

assume that Av  . !hus, equation reduces to

>sually, analogue diagrams are given in terms of symbols which

represent the electrical circuit. or this weighted summation, the

analogue symbol is shown in igure 1.4, and we have the output

equation

And

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 8/13

"igure 1.*: +eighte( #umming Amplifer

*. )ntegrators.

Integration is the most important operation available on the

analogue computer. In fact, analogue computers owe their e2istence

to their ability to integrate rapidly. Integration is di*erent from

inversion and summation because it is time dependent. Integration

can be accomplished by replacing the feedback resistor of the

summer with a capacitor. !he resulting electrical circuit for an

integrator is shown in igure1..

"igure 1.,: Electrical Circuit or an n- )nput )ntegrator.

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 9/13

=2periment

Aims an( ob-ecti&es:

1. amiliarisation with the

operation and -omputing elements of an Analogue -omputer.

. >se of a summer and summer / integrator.

4. %imulation of a $rst order system

. %imulation of a second order system

9. btaining graphs of $rst J %econd order responses and

commenting on the results.

Apparatus:

1. !he 'I--/Kero Analogue -omputer.

. 7-, #ata Acquisition %oftware for plotting the response of

simulated systems and =+ALA%= %creen #ump program.

4. 7rinter.

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 10/13

Eperimental Proce(ure:

#umming amplifer e%uation or  /#ummers0

( )   [ ])(10)(10)()()( 59321  t  E t  E t  E t  E t  E t V 

o

  ++++−=

ote E*$ E, 2 E3 are set at 4ero. #o the system e%uation

re(uces to

[ ])()()( 21   t  E t  E t V o

  +−=

1.1 #imulation o the "irst Or(er #ystem:

 !he analogue computer is now used to solve a $rst order

di*erential equation as follows:

02

1

2

3=+=

 x

dt 

dx  i.e. 05.05.1

.

=++   x x  &ith 2 C)E G ( )3

10   = x  or initial

condition

irst the formula is arranged to isolate the highest derivative term:

[ ]5.05.1

.

+−=   x x

;ow start by assuming the solution 2 is available at the output of an

pAmp. 'ecause there is an.

 xterm in the equation, it is reasonable

to e2pect this solution to be at an output of an integrators as shown

below.

Eperimental 5esults an( Discussions:

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 11/13

 !he simulation of 1st and nd order systems using the 'I-- 3Keroanalogue computer:

Eperiment 1:

#tep 1:

-hoosing value for =1 and setting the value of = at ero.

7ot 4 7ot 9 >!7>! N O/).9)M> ) ).91/).)1M> ) ).9/).6)M> ) ).64)/).5))M> ) ).5)

/).()M> ) ).(1

#tep ':

Karying 7! 9 and repeating the procedure for a set of di*erentvalues for 7! 9 and 7! 4.

7ot 4 7ot 9 %>MM= >!7>! NO =

/).9)1 /).)) ).6)/).)) /).) 1.11/).6)) /).)9 1.4/).5)) /).6) 1.91/).(1 /).5)4 1.91

Obser&ation:1. 7! 9 values are not stable CluctuatingE" it might be due to

error in the system.. It was also ob served that the values of the output cannot

e2ceed 1.91 even after trying several values above /).6)for 7! 9

#tep *:

Karying the values with reversed polarity in 7! 9

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 12/13

7ot 4 7ot 9 >!7>! N O/).9)) D ).1 ).)1/).) D ).5 ).114/).6)) D ).999 ).)4)

/).5)) D ).641 ).)6/).()) D ).5 ).)(1

bservation J -onclusion for %ummer Ampli$er:

1. nce 7! 9 reaches /).6) and above, the value of the outputremains the same regardless.

. !he output value of the summer ampli$er gives readings inabsolute vaules that corresponds to the addition of the two7!s using =quation .

4. !here were little Puctuations in output values, these valuesare negligible as it is due error which has been accounted forby introducing the N O =rror.

Eperiment ':

%ummer Integrator

7! (: /).1 M> I - 7! G )

&hen the above values were set and the output was switched on

the digital voltmeter to 7 mode" it was observed that the output

value ramped up to

D1 M> and over in less than 1)seconds

 !his step was repeated by switching polarity and tried with several

di*erent values.

 !he following values were noted and recorded.

7! ( I - 7! >!7>! !IM= CsecED).)1 ) 1.41 9D).41 ) 4.9D).)1 ) D).9)4 ) /).1)) ) 6.5/).)1 ) .1

/).4)1 ) 4.5/).)) ) 4.)1

7/21/2019 Control Report 2

http://slidepdf.com/reader/full/control-report-2 13/13

'. AdBusting 7! 11 to /).1M> initial condition and repeating the

above test.

7! ( 7! 11 >!7>! !IM= CsecED).1) /).1 1.5) 11/).) /).1 4D).) /).1 1.)5 D).4)) /).1 1.) /).4)) /).1 4/).)) /).1 4D).)) /).1 4/).1) /).1 .(

bservation:

1. It was observed that a negative 7! ( value ramped up to

D1M> and over in about 4 seconds.

. !he reading showed that the positive input in 7! ( takes a

longer time to reach D1.)M>

4. !he negative value generally reaches the targeted D).1M>

in a short time.. A value was tried to con$rm the e*ect of a negative which

was /).)) on 7! (, the output and time were the same

with the earlier inputs.

9. !he output time was 4 seconds when the polarity of 7! (

was switched at input value of D).))M>

. It was observed that the output time remains the same

regardless of the input if it is a negative value, but forpositive input, the output time is getting shorter as the

input value rises.