UMM-25 REV. B IMPROVEMENTS IN THE CHARACTERISTICS OF AC LEAD NTETWORKS FOR SERVOMICHANI SMS By Donald McDonald July 26, 1949

FNG1IEERING LIBRARY.-/o-s50 IMItoJh IN THE OHABACTTRISTICS OF A-C L3AD ETWORK7S FOR SRVOtMECHANISMS Eleetric lead networke are used quite extensively to impro've the response of servomechanisms. Such lead networks may be required to operate on the servo error voltage, on the input or output signal voltages separately, on the feedback voltage from an output tachoometer, on various, internal loop voltages, and on other signals. In many cases the input voltage to the lJad network is a modulated, suppressed-carrier voltage, and it is necessary that the output voltage of the lead T network also be a modulated, suppressed-carrier voltage of the.same carrier frequency. Consequently, the basic d-c lead network of Figure 1A, which is noramtally used where the output signal may be d-c, is not applicable by itself to these problems, and an a-c lead network must be used. Tae conventional a-c lead networks do not operate on their input signals so effectively as does th1e network of Figure lA in a d-ec servolaecilanisrm. it is the purpose of this article to suggest modifications in design and in the components used which will improve the characteristics of a-c lead networks. Before considering improvements in thfe characteristics of 4ac lead networks, it is desirable to summarize the general characteristics of these conventional a-c lead networks. Conventional A-O Lead Networks When the input and output voltages of a lead network must be modurlated, suppressed-carrier voltages, two general classes of a-c lead networks are normally used. In the first class, illustrated by Figure 1, the a-c signal is demodulated, then the demaodulated signal is passed through a d-c lead network, like the one of Figure 1A, and lastly, the carrier is modulated with the output voltage of the d-e lead network, Tiis

class of a-c 1eld networiswill be called E Class I network. Regardless of the type of lead network, it may be stated that the essential characteristic of an a-c lend network is tnhat it produce a pronounced, positive phase shift of tne modulating envelope over specific portions of the modulating frequency bend. The analytical expressions (1A-2), (1A-3), and (lA-4) gnow tsat thie Class I lead network of Figure 1 and Figure 1A does have a pronounced positive phase shift 0 which reaches a maximum value of 0sm at a signal frequency of w. Graph 1 is a plot of the phase shift and magnitude charncteristics of this lead network. In general, for all lend networks, either a-c or d-c, the ratio of the lead-network transfer-function at infinite signal frequency to the lead-network transfer-function at zero signal frequency (for example Equation (IA-o) ) will be aef ned as t:ne lead network attenuation,. The aemodulaetor and modulator circu its of tne first class of a-c lead networks produce noise. Filter circuits added to t.iie demodulsptor and iaodulator tend to reduce the imagnitude of this noise. Unfortunately tLie reduction in noise by this:netrnoo is accompanied by a time del.y or an effective negative phase shift of tne;uodult-inge envelope. Such m negative phase shift may be partially compensated for by an increase in the attenustion of tne d-c lead network. This increase in the attenuation will result in an increase of toiLie overall noise-to-signal ratio. Hence, in t'he Class I a-c lead network', an engineering compromise must be reached between (1) ttie amount of noise suppressed by filters in the demodulator and modnulator snd (2) the increase in noise-tosinmal ratio resulting from the increase in attenuation required to offset the effect of the filters. These several factors cause this Class I network to produce a smaller maxiumr positive phase shift than the d-c lead network can produce by itself

An example of the second class88 of a-c lead networks is shown in Figure 2, and this class will be referred to as Class II networks, The parallel T network of Figure 3 is snother simple a-c lead network of Class II. Equations (2-2) through (2-5) and Equations (3-3) tnrogl-..h (3-7) of Figures 2 and 3, respectively, demonstrate that tnese networks aiondify the envelope of the inodulated signal in a.pproximately the same fashion as does th5e circ;-it of Figure 1. The application of these Cl0ss II networks is restricted by the following two factorsi 1. A-C lead networks of t.e seconr class are e qute eitive t o cu11e iaf thnw 8arrier f requency becaui-se a cAange in carrier frequea;cy can reduce tahe effective lead developed by tiaese networks and cen, in some cases, produce lag inateaid of lead. This effect is more noticeable at 400 cps. than at 60 cps., because it is tfhe absolPute change in carrier frequency which affects tlie -networkc, an{a, in general, 60 cps. sources are better frequency-regulnated on an absolute basis then 400 ops. sources. 2. The maximum value of the lead time constant T of the second cless of a-c lead networAkis limited and this limits ththe minimum value of Was, the frequency at which the maximnum oositive phase shift of the modulating envelope occurs. (For the network of' L Figure 2, tne maximum value of T 2 - and for the network 1 of Figure 3, tne maximum value of T' ) In some csSes when the minizmu, val-ue of w is too large, it is possible to increase tie phase shift at lower fretq.enicies by increasing the atteaulation. Unfortunatel.y tnlls cn.er'as-e in attenuation may increase the noi-e-to-signal r:-tio of the lead network sufficiently to offset any improvemeent derived from an increase in positive phase shift at lower frequenci-es.

iigure 2A2 shows a modified foria of' thie basic Class II a-c lead network. As will be noted fromn EquEations (ZA- ), (2A-6), and (2A-7), wnen tne maximuIm puhas-e shnit ni is t1e same for both the circuits of Figures;~ and 2A, thle minimum vlue oz w is gm smaller for Figure 2A tran for Figure 2 by a factor of c. Inasmuch as the minimuma valuae of r" is 1, tiae maximum value of c under the condition off Equaioi (2A-5) is r3 Modifications of the Cla.ss I A-V Lead Network As was mentioned before, the demodulal.tor and.odulator filters of Figure 1 produce time delays or effective negative phase shifts of the modulatinug envelope. Figure 4 snows a circuit where the demod-ulator.and mouDtlator filt.ers a-re used to an adveantage. TAhe arreniement of the componentsi of Figure 4 snell be relferred tos s a feedback type mooifiL cation of Clas.s - To imrr ify t"he consic!ertiofn of this circuits the time delays or pnase shift5 created by tne filters of the demodlIetor and moculatIor have been lumped in the single RC time lag network of Figure 4. Taus tne minixmvu value of tne time cncnstant of tne TR ne twork of Figre 4 wll b e 1ieter.mln in by tihe fiIters in te deneoduilator and modulator, but 1i required, ad ditlonal filtering or delays may be added to increase this equivalent time constant, The analytical expressions (4t-0), (4-11), and (4-12) of Figure 4 show that the cnaracteristics of this system are the same as for the basic Class I network. The attenuation r may be adjusted by adjusting the gains of the amplifier, demodulator or modulator. The lead time coanmta.nt T mit be wde pa large a depired hut dos have lea mlnimm value determined by the equivalent time constant of the demodulator and modulator filters which- pr od ul>ce en a.cceptable noise level.

Figure 4A shows another arrangement of the components of the basic Class I a-c lead network ant will be referred to as a parallel type modification of Class I a-c lead network. The assumptions made in representing the circuit of Figure 4 are carried over into the circuit of Figure 4A. The analytical expressions (4A-9), (4A-10), and (4A-11) show that the response of this network is similar to that of Figure 4. The parallel type has the limitation that, as noted from Equation (4A-8), tne minimum value of the le;ad time constant is esa]el to r times the minimu=m value of tne equivalent time constant of the demodulator and modulator filters. Inasmuch as this value may t-be too large for some servomecthanism application-s, tle parallel type may not always be as useful as the feedback type. The effectiveness of the aemodulator and modulator filters or ti:e comnplexities of the demodulpator and modulator plus filters may be suCh as to limit the degree of suppression of noise generated. Such a. limitation will establish tue noise-to-signal ratio and determine the applicability of these circuits. By a cnange in the type of components as well as tne arrangement used in the basic Class I network a system can be evolved having demodulators and modulators with excellent noise-to-signal ratios. Such a system will be referred to as an Elentromechanical A-C Lead NetworK Class I. El ectromechanical A-C Lead Networks - Class I Figure 5 is an example of such a modified Class I network. In its most general form, this network is equally applicable for d-c and a-c operation, but in this article, only its a-c form is discussed. In this system the motor functions as a demodulator and the generator as a modu

lator. Both of these functions are approximate with the limitations that w5 and the motor-generstor speed be small compared to the carrier frequency and synchronous speeds, respectively. The analytical expressions of (5-11), (5-12), and (5-13) of Figure 5 snow that the characteristics of t:iis system arse tre same as for the basic Class I a-c lead network. By proper adjustment of K1, K2, and K3, it is possible to establish any value of attenuation r. The lead time constalnt T can be made as large as desired by the addition of inertia to thle commorn motor-gexlerastor shaft. Unfortunately the minimum value J2 J of T is a3 nd this value may be too high for some servo applications. f The arrengement of the components of the circuit of' Figure 5 is such that this type of electromechanical network will be referred to as a feedback type. Another arrangement of the components of Figure 5 is shtown in Figure 6 arid will be referred to as an electromechsanical a —c lead network of tie parallel tyj:e. This parallel type of electromechanical network has characteristics similar to thiose of tie, feedback type except that its lead time constant T is greater byr a f&actor equal t'o the atte-onuation r. Uonsequently in many cases, tue prallei typie is not so useftul as the feedb Kcc t-ea t f- e ctr ecacl f a-e lead netvworiC.< It i~s If fnteree4 tt to note tlhat the aruplifier K can be omitted in the parallel type. Figure 7 is a scnematic of Enother electromechanicel a-c lead network - Class I It is of the feedbsck type but, as indicated by Equation (7-12), does not have tue phase and amlitude chara.cteristics of tle bapsic Class I a-c network. Tnis network i e. resonant lead controller of Class I. Graprhs 2, 3, 4, 5, and 6 show t:,e phane aidu amplitude chlaracteris.tics of this electromechlanic4l svste..

Figure 8 srows tne parallel type counterpaT't of tie electromchanicl a-c lead network of Figure 7. Its characteristics are similar to those of the feedback type. Of the several. types of electromechanical a-c lead networks di.cussed, that of Figure 7 appears to have the most desirable cihiaracteristics arnd also to be tne simplest to manufstctu.re, FigJre 9 is a cu.t-awa.y view of a pilot design of this electromechanical system. The main corpTonents of the system are (1) an induction torque motor, (2) a combination induction pickoff and electric spring, (3) an edd. y-current damper, and (4) inertia weights. The induction torque motor and tie coombination induction pickoff and electric spring are made of simple, pulched laminations and bobbinwound coils and are called Microsyn elemeanti. The induction torque:,otor is excited by a fii ed a-c reference volteage and by tihe signal voltage, It develops a torque pro.portionea. tao the signJ-l v'ol.tage which Ji virtua..elly indeperl.Ient of the anguilar disila@e~ ment of its rotor. The coi] ot t:ie co;b oif ati cn inidution p iccoff i an electric p, ring arre so arr8i ng. d thltt tt!.ere i 8a s eprate cifrc'uit f1cr boita the pickoff and electric spring, The pici<off circuit is excitce. wti th a-c voltage and the circuit rf tfle electr-ic 4 [ring is xcited with d-c voltage. This comin:i.ntion then1;roduces a si.gna. voltaE e and a tc'Vc~e, both of which are proportional to thne anoflar dtsplacement of the rotor from neutral. By ch-ng:ii t-.e d-c excitatior of the electric sp ring circuit, the torque gradient of tLe electrt-ic r ring m-ay be adiutE. The eddy-current da.mper is uce. lnp of an aluminum, dampirng disc and a multi-pole, Alnico permarent a.;rnvet wit[i its!:oles parallel to thie axis of rotation. Thist magg:.t i.s t*'ea aal,.ly into the ousi no g; and

-8therefore it is possible to adjust the spacing between the magnet and damping disc, thus changing the damping coefficient f, The total moment of inertia of the system may be changed by adjutting the position of trle inert ia weights. Thus as t-iere are three continuously adjustable p-ranmeters —the spring constent, tuie dCmsping, and tne moment of' inerti. —it is possible to adjust txe two variables wn and c independently. The attenuation factor h can also be adjusted independently by chanrginlg the pickoff sensitivity or the s.a:pIifier gain. As planned, w and c are to be cont inuously adjust-hble from 1 cps. to 6 cps. and 5 tto 1, respectively. Over tihese ranges of network parameters, the maximai pfower con;sumption of the torque motor should not exceed one.third of a WEtt. (K..en.' A) Cnranes in carrier frecue,;cy whicnr will not prevent proper operation of any electromecnani c. l components in the complete servo loop (such as mortors annr indicatori,) will not affect tue operation of the electroteecharEicel a —c lted networke described. Graphs 2, 3, 4, 5, and 6 show th-t w1 occ-: is nea r w, enc, s s noted above, w and hence Wm ma.y be.adJsuted to cover tne region of frecuencies 1 to 6 cps. Also the maximum value of phasesnift 5sm may be made larger for the network of Fig' re 4 tain for a simple lead network having tie same attenuation or noise-tosignal ratio. An example of tilo application of tihe electromech-nical lead network of Figu.re 7 is shown in Figuxre 1C0 Here a twro-plase induction servo is beinr stabilized by the use of this electromechanical a-c lead network. As will be noted, tnhe azlifier driving the servo motor is a.lso ussed to

-9drive the torque motor of the lead network. This is possible because of the very low power consumption of the torque motor. In closing, if the feedback paths of Figures 4, 5, and 7 are connected regeneratively, instead of degeneratively, and the parallel paths of Figures 4A, 6, and 8 are connected so as to add, instesd of subtract, these systems will become lag or integral networks instead of l ead networks. In general, it may be stated that the modifications in the circuit arrangements and tie change in the type of components of tihe basic Class I lead network produces an s-c lead network which rias all of the a.dvantsrgec of the Class I lead network with its disadvantages kept to a minlimm. The general approach used in modifying tne bEsic Clas I a. lead rletwr:< has been to place all of the elements with negp.tive pnase snifts in a parallel; or feedbacc branch where they will eff+ect.ietly pro.~uc, a lead instead of a lag. Thus by this procedure, trne inherent and unaeoidable delays that occur in many networks, such as in denodulators fr:d modulators, can be put to an advantage instead of being a handicap. The characteristics of the Class II a-c lead networks have been described iA this article in order to contrast more effectively the two classes, but no attempt will be made in tnis article to describe metnos.of improving trie cnaracteristics of the Class II a-c lead networks. Acknowled ements I should like to thank Messrs. K. C. Mathews and F. E. Theobeld of the Tniversity of Michigan Aeronauttical iResearch Center for te r assi+t ance in the mechanical design of tne system of Figure 9 and Mr. Ezrnest B. Therkelsen of tne Unlversity of Michigan Aeronautical Resesacr Cernter for his assistanre in prepsring some of the data and graphs for this article and for his haelpful criticism.

-10References 1. Parellel "T" Stabilizing e tworks for A-C Servos Report 811, Radiation Laboratory, Massachisetts Institute of Technology 2. Differetiati Networks and Lead Networks by G. T. Coate, Department of Electrical Engineering, Massachusetts Institute of Technology 3. A New Servomechanisms Technia. by D. McDonald Report UMM-24 Aeronautical Research Center, University of Mic.higan "Stabilizinge Servomecaenisms" Electronics November 1948 4. The Microsyn elements were developed by the Massacnusetts Institute of Technology Instrumertetion Laboratory arnd are wore fully described in Electronic Instrinents, McGraw-~11ill Book Company,y Inc., 1948, pp. 36f-366. TLhe comlinatticn of the induction pickoff and electric spring into one Microsyn element was developed by Mr. K. C. Mathews of tiie University of Michigan Aeronauticel ReneTrch Center while he was a,member of the Doeleam Coruoration, Newton, Messachu)setts. Addendum A If th'e electromechanical sys te m of Figure 9 i. used in the circuit of Fia.rre 11, it, nptu.ral fre1quency wn cen be increased and its design can be simplified. In Figure 11 the spring Ks of Fi..lre 7 has been replaced by tre amplifier K4. As may be noted from EqusFtions (11 —2) and (11-3), when KG Kz K-4 is s',b tituted for (s the rs,tio ~, Equation (11~),'becomries the slame s PEtru)tio (?6)o Hence the respoose of tne ci.orcuit of Figure r 1 ie the same as the response of tie circ-uit of Figare 7 and Equat ion (I7-1?) a;n.i Graphs 2, 3, 4, 5, and 6 apply for both circuit:s..

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(3-2) then if e esinwt -- sin t ) i l tjwrTi (3-1) For balance: RlCl = w_ (3-2) then if ei = e sin wit sin wct (_ _ 1 1 t j wsr W r + 1 variable denotes the envelope of the (3-6) w 1 variable Sm - TV e 5, I (8-6) (3-7) 2.j = / FIG. 3

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