Analog Computers

Historical Document

YEW Series 3300 Analog Computer

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Product brochure for the Yokogawa Electric Works (YEW) Series 3300 family of all-solid-state analog computers, covering models 3301 through 3306 with 10 to 72 operational amplifiers in a modular building-block architecture. Describes the 'High Speed Repetitive Computation / Low Speed Conversion' approach unique to YEW, computing-element accuracy of 0.1%, and a full range of linear and non-linear computing elements including multipliers, diode function generators, and comparators. Auxiliary devices such as the waveform translator for X-Y recorder, cathode-ray oscilloscope, digital voltmeter, delay device, and logic assembly units are also described.

Manufacturer
Yokogawa
System
YEW Series 3300
Type
Historical Document
Language
English
Learning track
machine reference
Pages
22
  • YEW Series 3300
  • Yokogawa
  • analog computer
  • operational amplifiers
  • computing elements
  • simulation

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YEW Series 3300 Analog Computer

Series3300 il Z \J \/ o \J -]J C --l Tl-l n Po -]J FN N -]J I r-n From Analog Computation of Summation, Subtraction, Multiplication, Division andSquare Root to Problem Analysis byDifferential Equations andTransfer Functions ! TN YJ C All Solid.State Low-drift and stable operational amplifiers High Speed Computation Low Speed ConversionType While observing wayeforms on a Cathode-ray oscilloscope, you can simultaneously record th€m rvith an X-Y Recorder (in combination with Waveform Translator for Recorder). ComputationImpedanceot O.L% 0.1%computation accuracyis ensu:ed for all linearcomputing elements and such nol-tinear computing elements as multipliers and variable diode function generator. v FEn Y0K0GAWA ELECTRTC W0RKS, LTD. ry -FN Z COIVItrLJTER Srr=,rs3*TDD ' Ihe rnl l og c{ )m!t!1e:" i rI cl ct,i ct tha[ per.fol msconl i nuorLsan<] placlicalli jrslarriltiLcr--us colnpt]laLi!rrtsand:simuta{ions bJ- ,t.leats ()1' e l e c lri cal com pi l nents, n \ i ch, rr herr Jui l abl y.i nte:l onneci ed.behar e i r) ti ..:' rr( .r.. r.r .h..' ti .:1. physi cal pro(c5.c.. \'r : , . . - . c o n rPutef5rra! 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In addi Li ou. ai i rl l og compLl tcrsar.e usu; r lly l e s s c c l npl i cel cri . mol r e:i si l \ pi osl rLr:rnred. l nd nore l eadi i l adip: ed to th e l:l ui cl . comprr.:oi r ol ' l i l l r-ge nLrntbcrof sol ul i ol l s. T h e ri n al og con]D Ll l ef rs erterrsi rej ] used l s a genel al ,pLr:posccl s p e c i fi c -pLr:po-:c coi nptl er or si LD ul i rLoli n r.ari ous sci enti l i ! t qcl i n d u s i | ial i l cl i l :. l he dai l y rcc(i tbr. :r corrpact. h i -eh -ctE ciencl, e c o n o m i caL l l ni tl og cotl tputcr. I.o el :, ri narc et-torsarcl l oss ol ' nr Lr L tt.t-r' .n r' : t' . corrptrtl ti o, r. .e: r' .rpi .,t n(-e.r,:r. O n t n. o l h .r h uni j . rescarchand crter.i ]]rcnt l :rJoratofi esrcqui r.eLargcsclle ' , . r,l i | | Lf\ fo. i 5l ' " " . -,1...l | \' .\ i .] corn-Lt| i l i on. r(l rnal) Si. o c t,n rpl i cl l ed prol rl r' i rr:. i { ccc:Il r i L\ compd!efs becol l tci ti gl - r criLt :tc c u ra cy and l i Lr!at | t ::Lze.i l tet,- i uc,i eel t motc l Lnd morc j Jl slance. , \t l rr-i i l ccni | i tl i ,,c.l .i tntpL!tcf rooi ]l i s cstab]i shedi i )r,comrnolt ( i\ €. 1 ,,fr' r:,L ri | 01| trl ;r' tgs anrl i Lppl i cati onsfor I.hcl nai og col npul ei i e t hLLs 1 1rr:r ied. tl tc tni l l og compal ,er.!\,hi ch has genel al Jr,.been rrL iclir r ' l r, \i h c trri ,n :r J L' i ta, ec np.rter. mu\t h( ..\ -l e. LJo. iu J. r(r rn e cL\i t ed \!:i cLtti l l c;rncl i ndrrstri al requi r.erngnrs.W l ti l i ll of rh f\r e racttng nccds i Lr tl .l d, yE W devel oped Ieri bl e, v€fsat jle . d ' l i .l ( r- .,. 1. nnLr.r' \ F\\ scr.i ejj ' { ,rr r l c \ F\\ Ser ics l -1 0 0 Anal os C ol rpLrLergl oL:p ei rpl oys the,l bui l di ng bi ock" l rct hod . ,ILL,: t,. i i l r, ci fa | ..( r' .I bc e.tcnJ.(t i r. rcqrrr-ed.nn t he b rs i s o f ' ftpe l :l C l ,\nal og C ol r l utcr .rs l l re nri nrnrurr unrt. Six' ' | \u . .trc ;' r111.1J' l:r: rl d . .r.l .,rJ ' i ze.. ,R cl c. to r re l rbl e O f T Y t' I-S ,{ \' .\tLA i }LE on page.4. GENEFAL DESCFIPTION One of the most outstanding features of yEW Series3300Analog Computer family is that they have a summing integratorwith a wide range of time constants covering both low speedcomputations and high speedrepetitivecomputations. Due to the employment of this unique integrator,YEW Analog Computerscan provide advantagesof both high spesd and low speed computations. Particularly, the YEW original ,,High SpeedRepetitive Computation Low SpeedConversion,' method makesthe YEW analog computersdistinguished from all other analog computers in the market. The following two types of computing systemsare availablefor any 3300-Series Analos ComDuter: High S peed R e p e ti ti v e C o mp u ta ti o n Low Speed Gonversion Type In this type of computingsysremthe high-speedcomputed solution waveforms are obsetved on a cathode-rayoscilloscope and at the sametime recorded by an X-Y recorder after the solution is low_speedc onr er r ed by th e u n i q u e s a m p l i n g ry p e * uui for. translator. The large waveformson the X_y recorder facilitate highly accurate readout. The adoption of s am pling m et h o d e n a b l e sth e re c o rd e rl o a i curarel v record even such solutionsas conrain high frequency components. This system consistsoi computing ele_ ments accurate to 0.1%. This js recommendedfor high precisionanalysisin generallaboratories. High SpeedT'Low Speed Com put at ions S e l e c ta b l e T y p e This system is provided with a mode selection switch on its hont panel to switch over from the high-speed repetitive computation to the waveform computation so that the solution shown on the cathoderay oscilloscopemay be recorded by an X-y recorder or a pen-writing oscillograph. This system consistsof computing elements with 0.5"1 acatracy This is recommended for simple computation or educational purposes. training To give full play to rhe functions as the analos c om puler .v ar io u sry p e so f l i n e a r a n d n o n -l i n earcoml puting elementsare made compatiblewith the yEW Series3300 Analog Computers. The computing.ele_ ments are all usablecommonly for Types 3301 througb 3306Analog Computers. Therefore,rne same accuracy is guaranreedin borh !mall-sizeand large-sizesystems. and c ons eque n tl yb u i l d i n g u p fro m a s m a l l -si /e uni l . to a large-sizesystem requires no extra device for adjustment. To sum up, the YEW Analog Computers are the products to exactly meet the requirements of today's scientific and industrial activities. They are epochmaking systems designed with an extremely rational mind on the basis of a long time experienceof YEW in analog and pulse techniques. FIELD OF APPLICATION The scope of application of analog computers is limitless. The following ate some examples of phenomena or systemsthat can be simulated by analog compute6 : Fi el d Phenomenaor Systems ElectricPower........-Powersystem, characteristicsof rotors. Electronics ............Linearand non-linearcircuits,distributed constant system. Automatic Control...Processanalysis,designingof control units. Atomic Power.........Dynamicharacteristics of atomic pile, control system. Mechanical Engineering. . . . .. . . .. .Vibrations of beams, vibration s5srem ol spri ngs. P hysi cs....-.............Thermal propagati on,so und system, fluid analysis. Chemistry....... -.......Chemicalreactions,reaction velocity. Automobile ............Ridingcomfort, changegears. A i rcraft................._C omputati of ons vi brations and stability. S hi p .... ... . ...... .... ...y7x1g5 Architecture ..........Eadhquakeresistance of buildings and bridges. Civil Engineering . . .Flood, tidal waves. Mathematics .........Non-linear differential equation, algebraic equation with multiple unknowns. B i ol ogy..................E nvi ronmental ci rcumsta nces and growth of animals and plants. Medicine and Physiology ............Simulationof living bodies. Economics ............Business cycles,economicgrowth. OUTSTANDING FEATURES C ompl etel y S ol i d-S tate with increased All circuitsare silicon-transistorized reliability.and lesspower consumption. Reducedsize provides more conveniencefor operation. H i gh P reci si on Computingelementsare accurateto 0.1%. Highly stable metal film resistorsand polystyrolcondensers are usedas compul i ngi mpedance:. A ccurate R ecordi ng of S ol uti on Accurate recording of any solution waveform is attributed to the sampling type wavelorm translator incorporated. S ummi ng Integrator w i th Tw o S el ectabl e Tim e Constants Time constantfor integratoris changeableto I sec and 1/l0sec fuomthe front panelfor easierobservation and analysisof sohltion variation. E xcel l ent S tabi l i ty FET choppers in operational amplifrers provide very stable operationwith minimum drift. B ui l di ng B l ock S ystem for Increasi ng Fl exi bilit y Series3300Analog Computers employ 'separate power supply system", so that a larger systemcan be made only by building up additional units on the basisof Type 3301,each of which has an rn-asily diviclual power sttpply. Therefore,it is very easy to i ncrea.ethc .omtrul i ngcafabi l i ri e\. Modul ar C onstructi on Computing elementsfully gmploy modular construc(i on to faci l j tal e repl acementor e\pan5j o n as required. TYPES AVAILAFLE Prepatch Board Analog Computer Type 3301 Type 3302 Tvpe 3303 Tvpe 3304 Tvpe 3305 Type 3306 P repatch B oards w i th Graphi c D i spl ay Very convenientfor referenceto block diagrams or drawingsof operatingprinciple Max. 10 Max. 26 Max. 36 Max. 36 Max. 72 Max. 72 Provided Provided A ppl i ca bl e for H ybri d C omputati ons can perform The large-scalesystemof 3100-Series si mpl e hybri d computati onsi f di gi tal l ogi c uni ts ar e incorporated. In addition, complicated large-scale hybri d compul ati ons can al so be made i f a digit al computeri s connectedto the Y E W anal ogcompu t er . ..E}IJILDINGE}LOCK" EXPANSION SYSTEM The YEW Series 3300 Analog Computer family is flexibly built up from the minimum unit of 10 operational amplifien up to the large-scalesystem of 72 opgrational amplifiers, In other words, a system of minimum required size for a particular analysis can easily- be composed by selecting exactly necessary computing elementsonly. The computing elements L ine ar C om put ing Elem ent s t' -Tr g No n - l i n e a r C o m p u t i n g E l e m e n t s I I I I I T ir !r :t *t Type 33Ol Max. l0 Type 3302 M a x.2 6 o p e .a ti o n a l a ftplifier s ope.r r ional am pline.s, $ Auxiliary Devices rrrrtrrrrrr lr r !3Ir I can freely be changed in accordance with the size of the problems. The varietyof computingcapabilitiesof YEW Analog Computgrs satisfiescomputing requirements better than any other analog computer ever produced in the world. The illustration below shows the entire line-up of the YEW Series 3300 Analos C omputersi ncl udi ngrari ous computi ngel ement s. r/- Co m puting Elehenr s ( buitr - in) n u x ir iar r Devic€s ( builr - in) llI A u xiliar y Devices ( exter nally connecr ed) Types 3303 & 3304 ----f lOOitiotat co nputing Type3 3305 & 3306 Max. 36 ope.al i onalampti fi ers Mar(. ?2 ope.ational amplifiers F€arures for incre.siDs eftciency( b!ilFin) FUNCTIONS OF COMPUTING ELEMENTS LINEAF COMPUTING ELEMENTS Coef f ic ient Po te n ti o m e te r Thjs is a 1-turn variable resistorfor setting coefficients and can be set at an accuracy ol 1i1000by making this unit balancewith the referencecoefllcient potentiometer provided in the computation control unit . A lo- tu rn h e l i p o t c a n b e a tta c h e dt o the uni t upon requesl. Dual S um m i n g Amp l i f i e r A pair of summingamplifierelementsare contained in one unit. When a feedbackcircuit is made by shorting its upper right and left holes with a boule plug and multiple inputs are connectedto it, this unit providessumming functions and producesan output of reversedpolarity. " SJ" is a summing junction terminal. In case there is only one input, this unit works just as a polarity reversingunit. If the feedback circuit formed by the bottle plug is removed, this unit becomesa high-gain operationalamplifier, which is used for direct simulation of a control system by connecting arbitrary input impedance and feedback impedancethrough SJ (summing junction) terminals. It can also be used for non-linear coemcieot generation if free diodesare used in combinatioxwith it. Dual Summing Integrator A pair of summing integrators specifically designed for high-speed computation are contained in one unit. When a feedback circuit is made by shorting either of its two upper capacitors with the output side by means of a bottle plug, and then a number of inputs are connected. this unit performs summation and integration and provides an output of reversed polarity. "IC" is a terminal for the initial value of variables at the output side and provides a reversed polarity. (Dual summing integrator specifically designed for low-speed computation to be used for applied measurement is also available upon request.) lntegrator Summer This unit consists of a summingamplifierand a summrng lntegrator for high-speed,llow-speed comp u t a t i o n . T h e s u m m i n g i n t e g r a t o r c o n t a i n s a ca p a ci to r f o r l o w - s p e e d c o m p u t a t i o n w h i c h i s a u t o m a ti cr l l y changed over by the computation mode selecting signal from the computation control unit. The method of patching in this unit is the same as in the unit for high-speed only. Coefficient F€edback Circuit (by 6horting with bottte ptug) D ual S umml ng A mpl i ti er Integrator NON-LINEAF COMPUTING Multiplier {Time DivisionType) This is a high-efficiency multiplierwhichemploys th e t im e div is ion te c l tn i q u e o f mu l ti p l i c a ti o n. B y ch anging t he pos i ti o n o f th e b o ttl e p l u g s , a si ngl e u n i t c an per t br mt h e th re e fu i c ti o n s o f mu l ti p l i cati on, d i vis ionand s quarero o t. Free Diode Resistor This resistorconsistsof a unit which providesreferencevoltagesof +10V and -l0V and two diodes which ar9 incorporatedinto the unit. This resistoris used in combinationwith computing elementsto generate various non-linear elements (saturation, dead band simulation and hysteresis). Va riable Diode Fu n c ti o n Ge n e ra to r This unit approximatesan arbitrary function by meansof l0 broken lines. The position and inclination angle of each broken line can be adjusted from the holes on the surface of the patch board with a screwclrrver. Fi xed Diode F unc ti o n Ge n e ra to r This unit generatesa fixed function which is approximated beforehand by broken lines. Multlpli€r (Time Dlvlsion Typs) Free Diod€ R€slstot Varlbble Diod€ ELEMENTS The following kinds of fixed function generators are avai l abl e: Sine Diode Function Generator Cosine Diode Function Generator X'? Diode Function Generator ?-Log Z Dtode Function Generator 6'Comparator This unit containssix voltagecomparatols.In combi nati on w i th an 8-A nal og or an 8-E l ect r onic or used Switch, this unit is usedfor signalchangeover as a non-linear element such as saturation, absolute value,etc. This unit is also used in combinationwith x Logi c A ..embl ) l or l ogi c computrti on.. S .A nal og S w i tch 8-E l ectroni c S w i tch The 8-Analog and 8-ElectronicSwitchesare electronic switches,the former using mechanicalrelays and the l atterusi ngFE T' S . E l ch oftheseuni ts i s composed of four pairs each of make-contactsand break-contacts, which are used being connected to the SJ terminals of Summer or Integrator. S i ne D i od€ Xt Oiode Gon€rator Gsnerator 6-comParator 8'Electronlc \NAVEFOFM TtrANSLATOF] solutionwaveFor analysisof low-speed-computed forms, a pen-writing oscillographhaving a liequency responseof about l00Hz is generallyused. Hotyever, the recording width of a pen-writing oscillograph is 40mm or so, and it is difficult to expect a better accuracy than 2-3% from it, This means that the record analysisby low-speed conversionplaces a limit on the final recording accuracy even if the accuracy of the computing element is increased. In high-speed computation, each single computation is performed within a very short time and this computation is repeated. Once the coemcient is fixed, the same solution waveforms are repetitively obtained. Using pulse tgchniqugs, this Waveform Translator samples these continuously repetitive waveforms point by polnt and strings up these points, thereby converting them into waveforms which are completely analogous to thg original waveforms,changing so slowly that the X-Y recorder can follow. Since the amplitude and timg saaleon the recording paper accurately correspond to those of the solution waveform and only the recording speed is converted to a lower speed,the waveform is reproducedon the recording paper with an accuracy of +0.5%, however complicatedit may be. Since high-speed computation is continued even when recording is being carried out, there is no need of changing over the integrating time constant (capacitor of integrator) from a high speed to a low speed by means of a relay or the like. FOF trECORDEF Consequently,the translator reliability increases and it provides a solution waveform which is very stable and has excellent reproducibility. A solution waveform at a different parameter can also be recorded being superposed on the same recording paper, and this feature provides convenient comparative observation. Waveform Tran.lator for Recorder - (S horti nc rvi th bottl e P l uc ) Setti ne of ti m e bas e + (shorti nc w i th bottl e pl uc ) Setti ne of r ec or c l i ng sPeed S tart and reset contro l + Output Y .-- Output X (T) Function Generation with Free Diodes o Absolute Value Dsad Band Simulation Hysteregig 9 COMPUTATION CONTFIOL UNITS AND AUXIUAFIY DEVICES TYPE A CONTtrOL UNIT This is a control unit to be used for Types 3301 and 3302 Analog Computers. It consists of a computation controller for sta , rest and stop, a voltmeter to measurecomputation output voltages or set the coefficient potentiometer accumtely, and a refgrence coefficient potentiometer. The high-speed computation time is a constant 55 ms. TYPE A CONTFIOL PANEL This is a console-typecontrol panel for Types 3303 (3304)and 3305 (3306)and consists of the following componenls: a Power source for refergnce voltage (provided with a referencecoemcientpotentiometer and a voltmeter) a Control signal generator (high-speed)(Computation time can be switched in four stagesof lOl2DlsOllOO ms.) a Control signal generator (low-speed)(This unit performs low-speedcomputation control and switching of high-speedcomputations.) a Signal distribution (This unit distributes control signals and computation signals to their respective panels,) a Waveform Translator (A two-channel wavgform translator is built in.) CATHODE-FAY OSCILLOSCOPE FOFI MONITOFIING This oscilloscope is used lor monitoring the solution waveformson a high-speed computer. Withthisoscilloscopeemploying the brightness modulation system, it is possiblg to observg the waveforms and phasesof four channels (maximum six channels) simultaneously. The cathode-ray oscilloscopeis a 9 inch square type ano very easy Io se9. Sys t em : Brightness modulation system 9-inch electromagnetic deflecCathode-ray : tion type Oscilloscope Number of Channels: 4 ll2l5 Y ; accuracy *51 Vertical Amplifier : Time Base: Synchronizedwith control signal generator 10 a,,h /r-"1 ty 2r z DIGITAL VOLTMETEFI <TYPE 2BO5> fl t t' This is an extremely stable, noise-rejectedintegrating type digital voltmetercapableof lopv resolution. It is used for calibration of computing voltages,measurement of output voltagesof computing elementsand setting of the coefficient potentiometer. MeasurementMethod: Feedback pulse width modulatio[ counting method Max. Indication: 59900 Accuracy : IO.0l% of reading +l digit u DELAY o ll tf DEVICE As a dead time element, this device is used for a procasssimulator and for forecasting business cycles. It maintains the amplitudes of input signals as they are and delays time only. Delay time can be changed with the dial. Since this device adopts the delay circuit of a newly developed / t modulation system, there is no disturbance in waveforms at rise time as is gxperienced with the Pad6 system. LOGIC ASSEMBLY <TYPES 3351 S.3352> This assembly widens the scope of application of analog computers. lt is capable of such functions as logic judgement, counting and storage, and makes possible such automatic computations as A-D/D-A conversion and sequencecontrol. Type 3351Logic Assembly consistsof the followina C.P. Res is t or Count er .. .......................1 G . P . I nd i c a to r .....................1 Cloc k a n d C .P . In d i c a ro rT e rm i n a l................1 F lip- f lo p In d i c a to r ...............1 Cloc k G e n e ra to r ..................1 T ie P oi n ts ...........................1 For details,a separatecatalog is available. X-Y FIECOFDEFI <TYPE 3077> This is a single-penX-Y recorderto be usedin combination with the Waveform Translator for Recorder. It has a recordingarea of 250X250mm and records the solution waveform of an analog computer accurately and in a large form. Voltage Divider: 0.1mV/cm- l0 V/cm (changedover in l6-steps) +0.3% of full scalespan HO\N TO SELECT COMPUTING ELEMENTS 1. F ir s t det er m in e th e a p p ro x i ma te n u mb er of unit s of ope ra ti o n a l a m p l i fi e rs a c c o rd i ng t o t he s c ale o f y o u r c o mp u ta ti o n a n d the pr obable f ut u re e x p a n s i o n o f y o u r a n al og c om put er . Select the most suitablg analog computer from the following according to the number of units (operational amplifiers) required (see page 5). If you require lessthan 10 units: Type 3301 Analog Computer 'fype 3302 If you require 1l to 26 units: Analog Computer If you require 25 to 36 units: Type 3303 or Type 3304 (Prepatch system) Analog Computer If you require 37 to 72 units: Type 3305 or Type 3306 (Prepatch system) Analog Computgr Then select the ones you require out of a variety of computing elements,while making sure that the number of computing elements,you have selectedis within the number of units shown in the following table (Do not include the Coefficient Potentiometer nor Dual Free Diode Resistorin the number): Type Number of Units 3301 3302 13 3303 . 3304 3305 . 3306 18 How to Select Coefficient Potentiometer The one-turn Coeffcient Potgntiometeris suffcient for all purposes. The ten-turn Coefficientpotentiometer has the advantage of making the setting of coemcients slightly smoother. The number of Coefficiehtpotentiometers that can be equipped to various analog computers is shown in the following table: Type 3301 3302 Number of Units 8 16 3303 . 3304 3305 . 3306 36 72 4. How to Select Type A Gontrol Panel (For Types 3303-3306 A nal og C omputersl The component units of the panel vary according to computing systems. High-speed computation: Control Signal Generator (low-speed) is not required. High-speed/low-speedcomputation selectabletype : Waveform Translator is not required. Low-speed computation : Neither Control Signal Genehator (high-speed)nor Waveform Translator is required. Three units of Signal Distributors arg required in any case. 36 Count the Waveform Translator for Recorder as one of the above-mentioned computingelements. 2. How t o S elect S u m m i n g In te g ra to r For high-speed computation and high-accuracy analysis,use: Dual Summing Integrator (Code 33l7ll) Note: When Type 3301or 3302AnalogComputeris employed for high-speedcomputationand highaccuracyanalysis, addoneWaveformTranslator for Recorder, For high-speedcomputation plus low-speed-computed solulion waveform recording,use: Integrator Summer (Code 331811) For low-speedcomputation such as in applied measurement! use: Dual Summing Integrator (Code 331751) L2 3, 5. Other Devices The 36-unit Analog Computer can be provided with the following devices: One Monitoring Oscilloscop9, or any two units out of the Digital Voltmeter, Delay Device and Logic Assembly. The 72-unit Analog Computpr can be equipped with one each of all the above-mentioneddevices. > For EducationalTraining Use { The fol l ow i ng compuri ng el emenrshavi ng 0. 5oo computation impedance accuracy are also available for training students on analog computers: Dual Summing Integrator Code 331721 (for high-speed) Dual Summing Integrator C ode 331761 (for low-speed) Integrator Summer Code 331821 Dual Summing Amplifier Code 331621 Coefficient Potentiometer C ode 331531 o tta i r .r r i* ! a.Ar .t I I I t I t t l. r illr ; 1-i;.i-f f -' , " -: I l ;n,l a t a.-t I tl_:N I -,:.,^ | t:l1i r !-r. '-. 'i}r .ti I I , ,I I I I , ,. I I I a I . tl, I .l /*l l {L'r r *t r' ftl ? ? I l, tI f, f. I I t a, j {tr flit ili.r {-:-r ? ? I the a a a , .i ,-.1 r;i , I .ga In a series resonancecircuit, the switch K is placed to E side to charge the capacitor C, and next, the switch is placed to L-R side, Then, let us observe the state of this discharging current, E:6.94 V, C:1,2 pF, L:5.1 mH, R:201) (I) FROMFORMATION TO PREPARATION OF EQUATION OF BLOCKDIAGRAM (Ti me S cal i ng) Although the equation (7) has given the yoltage which is within the range of +10V, the solution contains (r: /i^5-taaq a frequency component of L or + r R i- i(l.i, a t- o ....................................(r) about 2 kHz. Becauseof the frequency response of the computing SinceI idt:q. we obtain J element and the necessity of recordi.og the solution, A2^ A^ L:- ; - R * +1 .:o; ir r:0. q .cE ......... . . . . . . \ 2 )it is necessaryto do time scaling to reach near @:1. dr. dt L T:Ft ................ ........... . . . ( 8) 1f we divide the equation (2) by L and substitutenumeriwhere T is the computer time after the time scaling cal values, we obtain and p is the so-called "time scale factor." A2a d^ To make <o:1 in this problem, it is necessaryto make 1. 92 103 = + 1 .6 3Y l 0 3 q :0 ; (lt' ot x loa, but we adopt i3:10a for the F: lt'lxrc":t.Z8 -+ convgnienceof later conversion. Now, since T:10!t, we. obtain dQ _ ,n,,dQ drQ _ ,.,, dQ -' " -' " dt dr' dt, dr If we substitute the above into the equation (7) and learrange it, we obtain (Formation of Equation) If the circuit current at the time switch K is placed to L-R side is denoted by i, we obtain dza'\ :--:1! (Scaling) In computation with an analog computer, the indspendent and dependent variables are replaced by time and a voltage respectively. Since the range of computation voltages of the YEW Series 3300 Analog Computersis -10V through +10V, it is necessary that variations in th9 voltage of dependent variables be within this range. If we assumethat the variable in the computer, which correspondsto the actual variable q, is Q volts, we obtain the following conv9tslon I . . ... . ..... . ..(4) Q : aq . . . . . . . . .. . .. d is called the " scale factor " and can generally be obtained from the following equatlon: Max. computation voltage d< Max. value of dependent variable In the presentproblem, we obtain from the equation (3) 10 t.2 z 1 0 c ..................... . . ...(6) " . T J - l0" In consideration of convenience in later conversion, we selecta:106. The equation after the scaling will be .lat n tot-:- a I <1a\-n. " --- dr i f t:0, Q:8.33 Here, the differential term of the highest degreein the above equation is kept at the left side, while the rest of the terms are transposedto the right side for preparation of the next step. dT, d2a't *: qr. .ln -0.392#ol 1.630: (P reparati on of B l ock D i agram) Now we will illustlate by block diagrams(Figs. 13) how to solve the equation (9) by the combination of computing elements. Set up a seriesconnection of two Summi:rg Integrators and assumethat the input terminal a is drQ/dTr. Eyely time the input signal passesthrough one com.12rl drl puting clement, the sigq is invelted, and the yoltages F1.92. r03F+ 1,63/l03Q 0r ii at points b and c bring about the relation illustrated if t-0, Q-8.33................... ...................(7) in Fig. 1. 74 a - (rrlPATGHING Patch cords are used in connecting computing elements according to the Block Diagram. The time constant of the Summing Integrator is ordinarily set at 15. A bottle plug can be conveniently used for connecting two adjoining units, Take out these signals of -dQ/dT and Q and form the terms on the right side of the equation (9). Now, a value above I aannot be set.by the Coefficient Potentio- d! meter. Therefore, in order to set the value of 1,63,set or 0.163 on the Coemcient Potentiometer and multiDly the gain of the computing elementten times. ff F "o.o. ",.," (III)SETTINGOF COEFFICIENT POTENTIOMETER ( 0 .3 e 2 :;+r .n a ) (".*,j$_r.o:o) The equation (9) means that the voltages at points a and d in the diagram (Fig. 2), which was formed in the way explained aboye, are equal. Therefore, the Block Diagram can be completed for the time being by connectingthese two points by a dotted line. The initial yalue of Q is given to the IC terminal of INT, by inverting its sign at the output side. On looking gloser at the dia$am in Fig. 2, it is found that INTI, a Summing Integrator, can add aqd integrate a multiple number of inputs. Thus SM2 and SMg become unn€cessary;an{ finally, the Block Diagram shown in Fig.3 is completed. INT ' - Set the computationmode swilch to RS and rhe voltmeter function switch to PS, For setting the value of, say, 0.29, first set the REF POT of the Computation Control Unit to 0,29, Then while depressingthe setting push-button of the Coemcient potentiometer to be set, using the index finger of the right hand, turn the kDob with the thumb and middle finger, so that the pointer deflection of the voltmeter comes to zero (center). 5' LNT. F la . 3 15 coiii'!' "r' 1T:'1i' {lv) }'llc$l"SPEED rjil ,i{, .F,1,,.. .i,: -i tria..lill..r,_,i.,,i iltii Airer ' r he s et t ing of t he pot ent iom c t c i i s c o m p l c t e d , turn thc c om put lt ion m ode s \ r it c h i o R O , a n d t h c l n t r o d u c c t h e s o l u {i o n \ o l t a g e i n t o th e j n p u t tcr hjg h-spe ed c onr p! r t at ion s t at e is as s u m e d . l n t r o d u c e n t i n r l o i t h e Wa \ c l o r n l T r a n s l a t o r a n d co n n e ct i ts thc soL ut ion \ olt ages int o t he os r llln s t o p e . a n d t h e o r . r r n u r t e r m i n a l w i t h t h e X - y R e c o rd e r . Se t TIM E so lutio n wav ef or n' r sc an be obs c r v c d. If l h e o u t p u t o f B A S E o r d i n a r i i y t o 5 0 m s , a n d s e t pEN Sp EED to the TRIG terminal of the Computation Control Urlit FAST il the wavcforms are simple ones, to SLOW if is used as thc horizont:rl synchronizing signal of the lhe waveforms are complicated oncs, and to MEDIUM -;." Oscilloscopc, stationary waveforms ccn bc obtnin,;d., cases. Short the holes of SHORT RESET . in ordi1,]nr,v Tf the ti nr e c ons t ant of t he Sum m ing I n t e g r o t o r i s s e t b e l o r e h a n d w i t h a b o t t l e p 1 u g . Wh i l e m a j n ta i n i n g ' the state of high,speed computation, lower the pen of at 0.1S, *aveforms, u,hich are made slower, as if the computation tinc {ere elongated ten times, can be ihe X-y Recorcler, remove the bottle plug, and the obtaioed, Therefore, you can analyze the initial statc wavelorm will be recorded from left to rjsht. Lift in detail at the setting of 1S and find the general trend the pen and jnsert the bottle p1ug, and the pen will at the setting of 0.1S. return to its original position. Futing I llme il t 's e t rd for S OLU TION WA V E FOR M ar o.ls nd the ! \'aluo mputarng the ometer hand, ger, so mes to RECORDING N) SOLUT]ON BY LOW-SPEED COMPUTATION lntroduce the solution voltage into the input terminal of the pen recorder. Set the computation mode switch first to RS. Select the proper sensitivity of the pen-recorder and start feeding the recording paper. Then cha.ge over the computation mode switch to OP, and the low-speed computation will start and the solution waveform will be obtained on the recording paper. The waveforms on the cathode-ray oscilloscope n atu rall y dis appear dur ing low- s peed c o m p u t a t i o n . 15 L€t us analyzethe followingMathieu's equationx: i*+ ot" 12(1+ €coszt)v:0 ; if t:0, y:2 *Mathieu's equation is used when Laplace'$ equation i$ analyzed by m€ans of cylindrical coordinates and when vortex movement in an elliptical cylinder or attenuation of magnetic force in a metallic cyli[der is analyzed. It is orle of the most important equations in eleatrical and mechanical engineering. If we assume that coemcients I and 6 haye th€ following values, we can procefd \trith programming immediately without scaling : 10Z t ) 0, 12e) 0 (Programming) I-et us proc€cd with programming by modifying the given equation, :-L: - )z {y +€ cos2t.y}; if t=O, y:2 dt. (Generatlon of cos 2t) The generalized cos (1rt can be obtained as the solution of the following €4uation : A2! E + ar 2x = 0: dtz if t= 0 - x = 1 The above equation can b€ made into the following Block Diagram : Olle Coefficient Potentiometer could set the value of d but the method shown in the above Diagram has been adopted, because a, can be directly read out and the unbalance among the computation voltageo of the respectivecomputing elements can be diminishe.d. (Ghcle T€rt) A tri&snometrical function is generated by setting th€ above-mentioned 4, to 1, and ths quantity of attenuation of its amplitude is us€d as a guide in judgement of the characteristics of the analo! computing clement (sce the specifications on p. 20). Clrclo To3t I 4 9 - xtn % I L7 EXAMPLE OF SOLUTION WAVEFORIiI U=rO, t=1.O1 F I 2 L€t us analyze the following simultaneous difrerential equations with two unknowns : 2i+ l+ 3Y+ 66x 8y : 0 4y + i+ 8i+ 16y - 1' 15x : 0 I f t : 0, x : 3, y : 5, i: i: 0 First we divide the above equationsrespectively with the coemcientsof i and y,and obtain i + 0. 5i + l. 5i + 3 3 x 4 y :0 y + 0.25Y+ 2i + 4y + 3.75x:0 Then we assumethat T:2t and perform the time scaling of the above equationsto obtain X - - 0. 25X - 0. 7 5 Y - 8 .2 5 X+ Y Y: 0. 125Y x Y 0 .9 3 7 5 x I f T : 0, X : 3 , Y: 5 , * :V:0 n. ti I or5 Let us solve the following equation : xri 2x- 5x + 6:0 algebraic The analysisof differentialequationsis the specialty of an analog computer,but variousstudieshave been carried on to solve algebraicequationsalso with an analog computer. The following is one of the examplesof this type application: We divide the above-mentionedequation by 5 to facilitate setting th9 coemcient.and obtain 0.2x3 0.4x'?-x + 1.2:0 W e usex= t and consi der(t):0.2tr 0.4t' : t+ 1. 2. By programming this equation,we obtain lhe Block Diagram as shown below. We are going to obtain the value of t just when the output (t) has passed through 0 in its downward curve. In caseof x<0, (becauset cannot bg a negative value) we use -x-t and repeat th9 same procedure after re-writing the equation accordingly. o 0 .6 f +0 . 8 r + I rrl \r rl \r +l 0 V ( - lOV) 18 10V 1 0 V X >0 ( +1 0 V )- 1 X <0 ) ! controller Suppose there is an automatic control system that maintains a constant level of water in a tank. Let us analyze the level variations that may occur when the piping undergoes pressure changes (external disturbances). The transfer function of the water level svstem can be exDressedby the following equation: -nR: Tl S +r m w her e i- T S +r P b: Lev el c hans e c odponent of l be r ank R : Pi pi ns .es i s l anc e /.: C hange c om ponent of pr es s ur e head of pi pi ng m : C hans € c om ponent of fl ow r ar e T : T i m € c ons tant of the tank Ifwe assumgthat the controller performs Pl (proportional+integral)control,this systemcan be expressed by the following Block Diagram: SOLUTION WAVEFORM Desired value Kcn+;t ) Now we will find the variation of h when we assume T:12 sec R:6.8 m3/sec p- l m ( : + l 0 V) and causg the constants Kc and Ti to change. Since we are dealing with analysis of the changecompodent, the desired value *ill be 0. SPECIFICATIONS 1. GENERALSPECIFICATIONS R efe ren ceVo ltag e: +10V, l0v wit h ac c ur ac y+ 0. 1 % circle Test : High PrecisionHigh Speedtype ; +0.05%lcycle (r-1 0 J, coe lllcre nt= l) . High- SpeedLow- Speed( om p u ' c y c lel- - l. c oem c r enl - 1 , ratio ns Se leclab lellpe; ' ip% Normal Operating Condition: Temperature;5-35"C (41' 95'F) Hu midity; 80% M ax . Power Supply: AC 220V +10%,50-60 Hz. OtherVoltages are also availableupon tequest. Dimensions: 166x 497x 400m m ( 6% x l9% x 15 %" ) T yp e 3 30 1........-... . . . . 316x 497x 400m m ( 12% x r g% x 15 %" ) T yp e 33 02 ........... . . . . Types 3303& 3304......992x570x550mm(39x22)ix20%") 1100x 550mm (39x 43% x 20%'/) Types 3305& 3306......992x 2. COMPUTATION CONTROLUNITS T Y P E A CONTROL UNI T for Types 3301 & 3302 Analog Computers ReferenceVoltage : + 10V, - 10V with accuracy*0.1 %. O utp ut Cu rren t: 5 0m A M ax . Mode Control: OFF; power olT. RS; reset, OP; o pe rate . HD; hold. RO; repetitiveoperation.ComputationTime; 55ms+3ms. Re stTime ;5ms + 3 m s at 50H2, 12m s * 3 m s at 6 0 H z EXT; Computation control from external signal CoefficientSetting Potentiometer: 5 k!). Linearity , +0.1% DC Voltmeter; Measuringrange; 0.1/0.3/l/3/10/10 V (center-zeroscale) TYPE A CONTROL PANEL for Types 33O3-3306 Analog Computers ReferenceVoltage: +10V, 10V with accuracy+0.05% Output Current: 200mA Max. Mode Co ntro l: RS; r es et . CO M ; oper at e. HLD; h o t d . REP COM ; repelitive operation. Computation Time ; 10/20/50rrl00 nsec CoefrcientSetting Potentiometer: 5k O. Li neariry; + 0.05% DC Yoltmeter : Measuringrange; 0.1/0.3ril V //3/l0,/30 Mode Control Signal Distribution: Cr : COMPUTE/RESET signal Cr; ./100 sisnal C a; HOLD sign al Sampling Type Waveform Translator : Number of Channels; 2 Input; + l/2,/5/10 v Time Base; 5/10,120i 50/100 m sec Outp ut Yolta ge ; + lV Recording Speed; 30-120sec/trace Accl.Iracy| +0.5% 3. LINEARCOMPUTINGELEMENTS D UAL SUMMING AM PLI FI ER C o d e3 3 1 6 1 1 Input and FeedbackResistors: 100kO X5, 10k0 X 2, accuracy+ 0 .1 % Inpu t Termin al: 1, 1 , 1, 1, 1, 10, 10,SJ C oeficie nt: 0.1 ,I,1 0 DUAL SUMMING INTEGRATOR Code 331711 (Repetitive Mode only) Integrating Capacitors: 0.| 7rF. 0.01,,rF.accuracy+0.1% Input Resistors: 100k O X 3, l0 k O X 2, accuracy+0.1% Dielectric : Pol)styrene I n p u t T e r m i n a l : I , l . l . I 0 . 1 0 ,S J , l C DUAL SUMM ING INTEGRATOR Code 331751 (Operate Mode only) I n t e s r a t o r C a p a c i t o r s : I / ! F ( +0 . 1 %) , 0 . 1t F ( +0 . 1 %) Input Resistors: I MO Xl, 100kO X2, acc\r^cy +0.\% Dielectric: Polystyrene l n p u t T e r m i n a l : l , I , l , 1 0 .1 0 ,S J ,I C INTEGRATOR SUMMER Code 331811 (Operate and Repetitive Mode) INTEGRATOR Integrating Capacitors: 0.1tF, 0.01/rF, accl]ja.y +0.1% ; l 0 r F , l , , r F ,a c c u r a c y+0 . 5 % Input Resistors: 100kO x I, l0 kO x 2, accuracy+0.1% Dielectric: Polystyrene (0.1,/r F,0.01fF) polycarbonare( 10,,/F, I /,F) l n p u t T e r m i n a l : l , l , l , 1 0 ,1 0 ,S J ,I C SUMMING AMPLIFIER Iftput and FeedbackResistors: 1 0 0k O x 5 , l 0 k O x 2 , a c c u r a c y +0 . 1 % Input Terminal: l. l. l. t. t, t0, t0,S. COEFFICIENTPOTENTIOMETER Code 331511 Type : Wire-wound resistor R o t a t i o n : 1 0t u r n s Resistance: 50000,acclrracy+5% Linearity | *0.25% COEFFICIENTPOTENTIOMETER Cod€ 331521 Type: Metal film resistor Rotation: I turn Resistance: 50000,accuncy + l0% 4. NON-LINEAR COMPUTINGELEMENTS MULTIPLIER (Time division type) Code 331911 O p e r a t i o n s: M u l t i p l i c a t i o n ,d i v i s i o n ,s q u a r er o o t Multiplication Functi on: F!,F. E at t: D C A ccuracy: Frequency # IU + 0.1%( * l 0mV ) at 20"C -10'C (68-86'F) C haracteri sti c