control report 2
TRANSCRIPT
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.