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I I

NAVORD REPORT 2-709

MAGNETIC7AMPLIFIER SERVO COMPENSATION,

19' December 1952

Us, So NAVAL ORDNANCE LABORATORYWHITE' OAK, MARYLAND

i\TV!o'ORD E,, r F o6 :t 2709

Prepared byt:

i-'rbert kil Wocdson

ABDzTIACT: TccluIxt es are reacriberi mhxby a a-wave,. bridge-type magnetic adpli .iei with integral£ee'-cic forni a esatile servo ui.llng block.,Proper adjterant of the polarity anxd amplitude ofthe .,,-a feedbacik wakes thQi cixrcu.it a lead net-worl, ; lag i' twopIk, or' an integrator,. In addition'to thava c;aratercZ..to the oirosuit can be used tomodulate, deou.n.ts, or ampl I.y a-c. or d-c rerelvby e]oWsrng the pioper output oomponent. Thisalr-vit iW usei7 . ,ith vacuum tbibe nipiieo servoco~pt.- ..s , -;- as with magnetlc amplifier6e~rvo cntroex'

'1

A.1, Th."YA O.PJ. ILNCEi Lh 3c aAX ,COb~~t~e ,, " , .O .. ver Spri. ntL 1o, _. Mvr:,:q'! nd /

\J{W LA KS 1 0

_______________

U ""~ < fa£r exceuding those. of ~ ErSIOU$ MuttfPeIRi

Uncec t1± vgno Amlplif"e Sav Lysero Daesopnt pl,:ErYatI,UOLiZla g0-253, atw compensation teohniquae wer& &vqdcpcrc1Trhe 3erti'atlrnni ayl' ko.vtret0 c~ aro -,onr ',,tineo rnth'I's re 1.or i

E.DIgARD L 'G), A

Captas 0311o oMhrft~ndec.

.A~ F .......4.9

GAMNTPS

ILLUSTRAT IONS

F ig~ura I - lagnetio Amp:lifte- witli Integral Feediback -

P I W 32 Feedback Circuititmx MesLed and3 Calculated Freeney-Reponf,.e

Curves for Koead NetworkFigue 4 Magnetic AMiplifier with Attentmated Integral

~a'e5 Ma~x~d ndCalculated Frequermy-Re~pone

Curvs foLagNetwork 0 0 C.0 00 0 'A 110

Figure 6-Block D2Majram og Zero-Velocity-Error Ser~voSy1 /e

NAVORI) Report 0''9

XMA~dkOTIC AMPL~fIYR SERVO C OMPENSATION

MNRODUCT ION

1, Tiz: half -wave, bridge-type magnetic amplifier 1 reap,;coeeryullv well to a-c (modulated carri~er) or d-e (modulation-frcequency) signala and the output is phaze -revere ibe,pulsating d-c. Both the d-c and a,-e components of the outputare linearlty related to control. voltage, The gain of interestin the followin;_ derivations is the d-c gain (d.-c voltz outdivided by d--c '-alts in), This steady state d-c gain will bedesignated KD-

2. This half-wave amplifier has a time delay dependent onlyon the number of stagesl; therefore,, the amplifier transferfLunction~ for voltages of modulation frequency, W,' is:

KA =KDeTA~ (i

where 111 is the time constant de-termined by the number ofstages Tn the amnplifier. This time constant is one cycle ofthe supply frequency, for the first stage and one-half cyclefor eaoh additional stage. For a two-stage,, 4Q-cycle ampli-f ier the time constant is:

T,=3.75 millieecond Eg . (d)

3. In the region of frequencies in which the plhase a4Tle.TAw9 Is evall the assuLmption can be made that

KA F - Eq (3)

In a two-stae, 40OO-cycle arnplifier, the phase shift at asigna I f-equency of. 100 radians per second is approximately20 det ees, For frequencies below 100 radians per secoin.d,the phase shift is assumed to be ero, remember ivr that somesmall error will. be introduced by this assumption.

4, The Z~ii of a. half-wave, bridge type ampiier Is greatest* when the control sjouyrce iuipedartze is the smallest poss ible.,

For inany servo applicati~ons, the amplifier muot be operatedfrom a control transfoxnaer, The load impedance on the outputof the control transformer is frequently required to be atleast 10,;000 ohms.~ Amplifiers of the above type are asuallydezigned, therefore, with a, 109000 ohm resistov in aeries1wIth the input winding* In which case the d.-o input resistancela very nearly 10,000 ohmo ainoe the d--c reail'.tance of the'control wian3 ings Ix s~i iWic ,-:tmller than this va~lue,

INVORD RC!ort 210~9

5 hen 'the output of the amp li~iee toi fed 1. ao1,. tb cuoi ares tanae eapac itance networas 5J, hown in figure 1, only theC-c component of the amplifir output will appear across hecaeetor if the RC tMe constant to lon compaved to thep .. cd of the sapply voltage and the anipJJfter Input Pe'ltana'doea not load the RO neptwork too severe ly. When ther n 'zome

Sof the network by the ampi~fier input rezistai7jv.-; thefce.ieitaclc function will. be changed fromi that of a inXi-lnetrw4 Wether or riot ther.e to loading of thc! l25twor,,/ thc,.capacltor voltage Is the input voltage to the armplific.'! 'omthe feedback~ networ~k; theretore, from flgre 2 AI is zwen thatthe feedbaok function of figure 1 is:

where I, -c(+c R~T C and RO is the amplifier i Ppi0;resietance. Using the above value off feedback functiort., Mheclosed loop transfer functilon of figure 1 izs:

Ej o I ( Tji-l 1dKr

Lead Nyetwork

6 I When the'feedback of ftgure I is negative, equation()reduces to:

This in a lead circult 2 with lower break frequency 1/op, Txbreak-frequency spread (i~~~,and zero frequency lainKr)/(l+,-,K) This va.Lu~e of 2ero-trequency gain is based onthe assumption that the only unable portion of the output Wsthe d-c component. The output of this network is actunAlypulsating d-c;, consequently, when the output of this networkIs fed directly into the Input of a half-wave amplifier,which responds to both d-e and Zundamental a--c components,the zero frequeney gain will be somewhat greater than thatindicated by equation (6)~.

7t Since this netwovk will rson equally w-elX to a--c oid-a inputs, and since the output contains both gt-o and No-components, it is a uaeful and ver'satile oservo building bloeKBy using the appropriate component of the output for a giveninput, a--c or d--c It Is oeen that this network can be usedas a modulator, demodvlatov, a-c ampl ifier, or cl-e amplifiereach with the same lcia6 chraterAKYi given by the frequency-variant portion off equat~ion ()

"'Luo %. igure 3 ar CSICU:1at,.d and Aieaaredi ofthe~ t;aqatnay variant portion of~ equation (6), The are rBM1'clo cz ex:~r~ 7cept ~at high rrequenote:C Were~ the phas s'hiptDii tIbe ari ,IiJ.eo eS ted in the aaalyf;0.8 Int. c e V,c'roniuab:le err~or, Fr~ont the resul.ts of7 fig11, _-s It. -T e

~j'~ eh ctei~~ie~of' each a net-vor~q can be pe.&dis simnple servo' theory with sufXiciant aci~raey fco'.r:

mt e-0 (I) orflpi nsaie a practie al servo kstenI134

9.-i ci. ;,*Ltion muot be obsev~ved wihen asing thia lead~ zk t'ork,When th~e x'hate tahiit around the loop to 180 degrees,~ the loop

i '.a tixs c be les than. one to Insmyre stabillity'L The Gborqplaj:l.oop~ gin is-.

--TA

For o&iccuit, 18T0 degrea p~hase sihift will 000aX

in whieh eage the phase ,ghif~t of the devominator of equa.tior.(i) kiear.lyy 7r,/20W radians, la view ofI thisk the qhas e

shift of 180O degrees KJ11J ocatur when.

A2

At he frequeney4 dete rm~ied by eqmmton ()the magrtue Q~Bff/;, ru;t be leas than one., hence:

LT10. When the feedback in figure 2 is wade positive and W~ezerox-freque~ncy 1ooP NaInM KVj I i ess than Ones ecquat iOn(5beomres;

Thia; io seen to be a~ lag net o: wit~h apec break~ freuency

ga in KD/(l P,")r cequno ,

4., -,XhAI 1,ag netwol*k., like the levtI netwo)rk. .ceev iously.. 18 a vereatile vevo building block. For the rtainu-.ivein Pre 1.u'sly. this 1aS network can be ased fo~r wodtsla.:to n

demodlibotio,ig a-rc amplif icat Ion,, or d-.c amplif ication.

. is bef'ore~ the zero-frequenoy gain gtven by equ~t:;.?-, (13,itbe basis of' the d-c component of the output,, D'0t

ci o t nd a -c components of the output are used,, as In 61& Jgaro~cma rnuntic ampliffier, the zero-frequency gain wl. o

sove-iihal .ie than that indicated by equation (11).

I If' a -Lven- amplifiter has isufficient gain that 0SK agreater thau one,~, the circuit conf iguration of f iguwe cnbe used to obtain the proper lag charateristic while ke~epingthe maximum possible zero-frequeney gain. In this caso,ref'erring to figure 4., the feedback function is now:

*where a R2 /(R3,+R-)Y. Of course, the total. resistance (RI+R2)must be much less than R for the above expresoion to hold.The output impedance of the magnetie amplifier ls su~ffficlentlirlow that this condition is easily met in any practical case.Using the circuit of figure 4, we see that the transfer functionIs now:

Eo L~~~~3Ei j

The detatllo of this lag funetion are very similar to thoaeof' equation (ll).

14. Shown In f igure 5 are measured and calculated ouv S of*a typical lag function as given by equation (111 or (13),,Once again the agreement between curvez io good except that

*f or higher frequencies the error between calculated and* measured phase angles becomes appreciable Que to the assumption

of negligible amplifier phase shift in the calculations. Thigscircuit has been used succebsfully to raiLse the velocity

p'. constant of a servo without appreciably affecting the servobandwidth.

V: Integrator

15. When the feedback of figure 4 is positive and the factor"KD is equal to one,, the over-all traaafer function from

equation (5) 'is:

E 0 KD' Tjw)1

Ta *

.h4-- , -

. .~o t: £ t, e q o c , c- je s , CA.3 h t b.O l I,,. ;:

', :-e 2>, < K U: E:q t (1 )

the wirouit described by aqcvtion to a4 L n integrator withth,. a:sfc funcJtion"

to K. D E t G \

When gs ,.teady signtal tom put Into this circuti-, the otxthu:..

beinS proportlonal to the inteSral of the input signal,, Iill

buIld up until the amplifler saturateo iences, a constanti outpat voltage is obtained from this circuit only when the

1input voltaZe is zero, This type o.C transfer fLunotion whenplaced in a servo loop with the proper tvpes of stabil;ationwil.l yield a zero-velocity-error system. Suc.,h a systevi.bvxing the block diagram rhcwr in figure 6, hae been e;coeusfull,synthesize4d

V Ono.~E !1 .ion,

1.6, The techniques described above are ueful In vacuum tabeservo ytems az well as in ivanetie, rpiifer servo sys~temls,The usefulness is enhanced by the ease with whioh circuitcharacteristics can be computed wth suffliet aao teay fordescn purposes,e

7 hen these desiga methods are used with half-wave bridge-type magnetic amplif iers the resulting coiiipensat ion netiwyorkscan be used with any combination of a-c and/or d-c input,and a-c and/or d-c output. The,

to line Thse netw;ox is are only as sews it:'.veto line voltaege and frequency varlations as the amplifier usetin the network. ien the amplifier components are properlymatched, the amplifier is extremely insenafltive to these

variations,.

1 ,

IZI

I jl"t

MWVOhD Riepor't 27(09

LC. W. -ACYb, ik. j3- Schnid~ . W,, Barnart,, "An YiproyedMnett S3ervc AnpifiexQ' AK IE Technical PaPer 5:-235,

S1952.

-\rR, APdwencd an'd J. F. Tapli., "Automtic Feedack. to)~Wo~raw-HiJJ. Book Comnpany, Inc,,~, New York,~ N. Y.9 19§

74; 1-1, 11. Uoodson, A,, E, Saebmid, C. V. Thrower, "Compesationof a Vagnetle Aplifier Servo Sysitem," paper presen~ted atthe VAtiona]. Electronics Conferene,~ Chicago, lllinoio,

K 6

NAVORD Report 2709

MAGNETIC -Ei ~ Ee AMPLIFIER E

Ef K+FEEDBACK

R

T= RO

FIGURE I

R

E 1 R ~ Ef0 1FIGURE 2

NAVORD Report 2709'

S331403a NI 31ONVIa 00 0

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NAVORD Report 2709

Rc

MAGNETIG

RR

Ei+0

R

T:RG CRKR 0( -R+

FIGURE 4

9

NAVOlID Report 2709

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NAVORI) Report 2709

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RN AI. Ac. Foel BLud, Reb

DrIRoype I We 3.er e Na~val Air Miusile Test Center, Point

Drw - kibrt ( Ball. Asoistaznt Director~ of Rezearch, Bood~iRareare~h Laboratory. )4855 Foaoth Streett Detroito

Mr.~ S. Edlwardt Dawson, Code 216, David Taylor~ Model Basi,.Wshington 25, DC 0 0,003 3~ 03~'

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C. Krill~, c/o Libraiscopa, Ine., 1607 Flower Stret, Glanda.e,Cal~ifornxia .

ik. 0, Hiartley, Raytheon Nhnu~aetvriA% Compary, .t48 Callornlf;Street1 , 1Ne~-ton 58~, Mssaahasetts 0 .I

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Kearfott Company, Inc. 1150 MBride Avenue, Litt~le Falls,K N~~~ew Jersey, Attn: J, A. JBronnon . .3

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Mr. E. V. Weir, Magnetics, Inc., E. Butler, Pennsylvania. I

Senior Naval Liaison Offlcer~. tY3 S. Navy Electronics LiaisonOfficep Ft.. ?4orouth, New Jersey . . . . 0

H. MA. Roseman, RCA Victor Division, Camden, New Jersey 3I

F. S. Maliek, Air Arm Divisioni, Westinghouse Electric Corp.,Friendship Airport, Baltimoref, Maryland . .1

Dr. Williamson, Reseach Division, Bu rouali Adding rrahineCompany, 511 N. Broad Street, Philadelphia 25k.

:4 ~~Penneylvanja ( 3 . .C S

,hAVORiD ieort 2409

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S. M. Hidebrand~ Conrol Enineering Campany, 560O PL-.)4dfa-ce~tght y.NXorwood, Masachuseetts '.. .3

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'A owE~ Gabert Rm 20.-D-216, DAGfA., Tisschtu3etta InstitoiPe,ct1 ~chcoy, Camnbridge Wss ~achuoettz

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Mr,. U J. ft~acbmnan, Norcien laboratoriesIn 121. Wes,'u;~3.kcAvenie,. White Plains, New York . 3 3C~3:

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Hi. F. McKinrieyq Ford Instrunient Company,, 31 10.IC ThomsonAVenue, L~ong Island City 1v New York 1

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13,

"17-'

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V. , L Conair G, M D.C auput~ r oupq Pom~onaq

SDieo,,o CaliforniaI

.X~o'V-,e ofi Teen~~ ':5300 S.' Fedex al Street,, Chleao,

L, C. 14. N4rr t0 C he~ Elo E~ Resarch,~ Armour RsacSof> -l"liwisi In 0 titute of Technology rPech-ologyK A ~~~Cener; Chi l.,11lot 0 0e AA

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F -V f e a ip r G0 C Newt o2An, 0jr, S rvic ha L m La bo r at or y

0~ a0

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Dul ,c~~ a~ o a' c. mo

Cre NaG113m, Haa Diiin a.lOdae

tampls Inia

Voamo D.0 ItEetia n~ern eat~bon 018 ascaet Isiueo ehooy

Coidbidge assacusett