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HoneywellR - E D 11117

3 January 1961P

SCOUT SYSTEM DESIGN R E P O R T1915 ARMACOST AVENUEWEST 10s ANoELes, CALE

Preparedby: e . ,&&,.Systems Analysis Engineer

Approve d by:Senior Proj tc t Engineer

Approved by: &A&D. C. Gerrieh, Manager


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FOREWORD

This document is submitted to Chance Vought Corporation as a require-me nt of con tract No. CV 300.w i l l be published in the ear ly pa r t of 1961, will complete the abover equi ement.

Two supplements to this document, wbich

The f i rs t supplem ent will be entitled "SCOUT Sy ste m Design Rep ort,Supplement I, Bas ic Sys tem Design Data." This document w i l l containchar t s and g raphs which represen t bas ic char ac te r i s t i c s of the airframeand engines.Design Report , Supplement 11, Design Data Used in Selection of S ys temPara met e rs ." Th is document will contain ch ar t s and graphs whichrep res en t the ' 'large payload" design effect on he system.

The second supplement wil l be entit led "SCOUT Sy ste m

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I

I1

TABLE OF CONTENTS

FOREWORDINTRODUCTIONSUMMARYSCOUT FIRST-STAGE CONTROL SYSTEM

Control Member sStabilization

Page No.i

1 '2 .33

12SCOUT SECOND AN D THIRD-STAGE CONTROL SYSTEMS 63

Reaction -Je t Control Sys tem sSecond-Stage Control Sy st emThird-Stage Control Sy st em

636984

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LIST O F ILLUSTRATIONS

Fig ure No. Pag e No.1234

567

8910

11

121314

1516171819

20

Firs t -Stage Total P i t c h Cont ro l Moment vs T imeFirs t -Stage Total Rol l Control Moment vs Tim eFir st-S tag e Block Diagram of SCOUT Hyd raulic Se rv oEffect of Hinge Moment on First-Sta ge Servo Freq uen cyResponseMa trix of Pi tc h Equations of Motion fo r First StageFirs t -Stage Block Diagram of the Pi tch Control Syste mMa trix of Pitch Ai rfra me and Control Equations fo rFirs t -StageRoot Locus Plot of Uncompensated First-Stage Sys emBode Pl ot of Uncompensated First-S tage Sys temRoot Lsc us P lot of Nominal First-Stage System a t Maximumq ConditionBode Plot of Nominal First-Stage Sys tem at Maximumq ConditionRoot Locus Plot of Nominal F i r s -Stage S ystem at LaunchBode Pl ot of Nominal First-Stage Sys tem at LaunchRoot Locus Plot of Nominal First-Stage System 17 Secondsafter LaunchRoot Locus Plot of Nominal First-Stage System at BurnoutBode Plot of Nominal First-Stage S yst em at BurnoutBode Plot of Nominal First-Stage System after BurnoutFirs t -Stage Hydraul ic Servo Frequ ency Response Toleranc eFirst-Stage Serv o and Network Freq uenc y ResponseToleranceFirs t -Stage Pi tch Tim e Response at Launch

57'911

151820

242528

29313233343538404146

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F i g u r e No.

21

2223

24

25

26

27

23

2930

313233

343536

3'138394041

Fi rs t -S tage P i t ch T ime Responee at Makimum qConditionFi rs t -S tage P i t ch T ime Response at:BurnoutFirst-Stage Tim e Response of Sys tem with ActualHardwareMa trix of Rol l Airf ram e and Control Equat ions fo rFirst -StageRoot Locus Plo t of Nominal Fi rs t -Stage Rol l Sys tem atLaunchRoot Locus Plo t of Nominal Fi rs t -Stage Rol l Sys tem a tMax imum q Condit ion

P a g e No.

474849

52

54

55M at ri x of Coupled Roll-Yaw Ai rf ra m e and C ontrol Equations 59fo r F i r s t -S tageRoot Locus Plo t of the Fir st- Sta ge Coupled Roll-Yaw 60Sys t emFirst-Stage Ti m e Resp onse with Roll-Yaw CouplingBlock Diagram of the Second and Third-Stage Reaction- JetCont rol Sys temSecond and Third-Stage Diagram of Je t A rrangem en t

6164

65Second-StageSecond -StageThr us t LevelSecond-StageSecond-StageSecond-StageT h r u s t Level

Pi t ch Time Response wi th Dual Thr us t Levels 7475i t ch and Yaw F ue l Consumption with Dual

Rol l T im e Respors e 79Pi tc h T ime Response wi th S ing le Thru s t Level 82Pi tc h and Yaw Fu el Consumption with Single 83

Th+*d-Stage Pi tc h T im e ResponseThird-Stage Pi t ch and Yaw Fuel ConsumptionThird-Stage Rol l Tim e ResponseT h i rd-Stage R011 F ie l Colisur1-q ionThi rd-S tage Roll Trans ien t Response to an Extern a lDisturbance

8889929899

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LIST OF TABLESTable No.

L Coefficients of Pitch Equations of Motion forFirs -Stage

2 Second-Stage Control Parameters for Vehicles Oneand Two

3 Second-Stage Control Parameters for Veh icles Threeand Four

4 Third-Stage Control Parametezs for Veh icle One5 Third-Stage Control Param eters for Vehicles T hreeand Four

Page No.16

80

85

95101.

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INTRODUCTION

The SCOUT is a four-stage, sol id fuel , rocket re se ar ch vehiclecapable of carr ying mode rate s iz e payloads to high al t i tudes o r ofplacing them in orbi ts .l i f t t ra jec tory by a stor ed pr og ram of atti tude commands, and itder ives its attitude fr o m three body-mounted gyros.for each s tage except the f i r s t a r e provided by a t im er in the guidanceunit.by movable jetwaneq and aerod yna mic surfac es.th i rd s tages a r e controlle d by hydrogen peroxid e rea ctio n jets, whilethe fourth stage at t i tude is maintained by spin stabiliza tion only.

The SCOUT vehic le i s guided along a zero-

Ignition sig nals

The vehicle is control led f ro m launch to second -stage ignit ionThe second and

This re por t pres ents the methods and resul t s of the sys te m des ignof the SCOUT controls fo r the f i r s t three vehicles . These ear lySCOUTS were characte rized by a 20-inch diamete r fourth-stageand by a payload weight of 150 lbs.vehicle, which has a different fourth& tage s tru ctu re, will followth i s r epor t as a n addendum.

The an aly sis of the fou rth

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SUMMARY

This rep ort documents the con sideratio ns involved in the design of theSCOUT first , second, and third-stage control system s. The consider-ations of the control members of each stage a s determ ined by disturbancemoments, je t vanes, aerod ynam ic surface s, and control-surfaceac tua tion a r e d i scusse&

Stabilization of the thre e axes of the first -st ag e is reviewed withrespec t to a description of the ai r f r am e, cont rol sys tem des ign, andthe nominal control system .

The second and th i rd-s tage cont ro l sys tems a r e d iscussed with reg ardto the selection of con trol pa ra me ter s for the f i r s t four vehicles.A descript ion of the air fra me is al so included.

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SECTION ISCOUT FIRST-STAGE CONTROL SYSTEM

CONTROL MEMBERS

During fir st- sta ge operatio n the SCOUT is control led by m ean s ofmovable, aerodynamic su rfaces and by je t vanes located in the engineexhaust. The aerody namic surfaces, which are actually the tip s of e achof the four f ins, a r e connected to the sam e shaft that dr ives the je t vanes.During the few s econd s imme diately following launch, the je t vanesprovide most of the contro l; then as the dynamic pre ssu re incr eas es ,the t ip sur faces become more ef fec tive.

Gsturbance Moments

The s iz es of both the vanes and the tips we re chose n to provide controll-ing forc es adequate to overcom e disturbance mo ments due to thru stmisal ignment, f in misal ignment, and winds. Thrust misal ign mentmoments , at the max imum specified angle of 0.25 degree , va ry f rom11,100 to 20,400 ft-lbs during flight.mis alig ned the sp ecified maximum of 0.15 degree , the resulting m omen twould reach a peak of about 16,600 f t - lbs. The disturbance momen t dueto wind is about 55,000 ft-lbs within the wind and attitude specificatio:isf o r SCOUT.

If both fins in one plane w e r e

In the body roll axis, dis turbance mom ents a re produced mainly bydifferential misalignm ent of the four fins.the maxi mu m allowable amount of 0.15 deg ree , the peak rollin g mo men t

If eac h fin we re m isaligned

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would be 1120 ft-lb s under conditions of an 80-deg ree vehic le launchangle.

Je t Vanes

The je t vane used on SCOUT produces a n average l i f t of 48 lb s/ d egdeflection; the act ua l value depends upon the Algol engine thru st andthe state of ero si on of the vane surfa ce. Sta tic firin g tests of the v a n eshow norm al ero s ion of about eight pe rce nt of the effective area duringengine burning.amount.l in ea r with deflect ion over t h e range of deflections used.

This eros ion causes the l i f t to decre ase by the sam eThe l i f t (and hence the c on trol mom ent) of the vane is quite

Lift natura l ly dec re as es during the engine th rus t decay after burning.Seve ra l je t vane des igns were cons idered with a view to m inimizing t h ehinge moment, reducing variat ion s due to erosio n, and preventing f la .meleakage into the drive-shaft area.low hinge moments which vary fr om ini t ial ly unstable to s ta ble mom entsin about 19 seconds.diverging mo ment of 570 in- lbs, while jus t p r i or t o engine tai loff, a20-degree def lec t ion resu l t s in a restoring moment of 476 in-lbs.Hinge moments a re not predictable within a small range due to e r o s i o nof the vane and flame shield, and it is expected tha t b ias and asy mm et r ic amoments exist in opera tion .

The design chosen produces relat ively

At engine ignition full deflection pro duc es a

The aerodynamic t ip cont ro l sur face s produce l i f t dependent upon dynam icpre ssu re and M ach num ber .total pitch o r yaw contro l moment (which is a function of the vehicle ce nt eof mass) is plot ted again st t ime in f igure 1.

Assuming an 80-degree launch angle, t h e

Note that the total con trolR-ED 11117

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0 0 0 0 00 0 0 0 0

0 0 0 09 In -? m N0

3m3za/saNnod m 0 . z

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momen t pe r degre e deflect ion va rie s fro m 2660 to 5600 f t- lbs / deg(a fa ct or of 2.1) dur ing powered flight.momen t due to differen tial deflection of two s ur fac es and vane s var ie sfr om 1280 to 4460 ft-lbs during fir st- sta ge burning, as m ay be seenfr o m the plot of figu re 2.

In rol l the total control

A e ro dynamic Surfac e s

The aerodynamic t ip cont ro ls a re s ta tica l ly uns table a t all Mach numhe rs ,but above Mach 2 their hinge moment coefficient is very low.mom ents due to the t ips a re nonlinear with deflect ion, and a re depend-ent upon the dynamic pr es su re , Mach nu mb er, and angle of attack . Inthe SCOUT design, to ta l momen ts w e r e calculated with a four-degreeangle of at tack of the m ost conservat ive sign.al l hinge moment, occu rring about 11 seconds af ter launch, is 600 in-lb s at 20 de gre es of deflection and four deg re es angle of attack . Th isi s t rue for an 80-degree launch angle.between hinge moment and deflection causes the equivalent "springrate" of the control surfac es to be so m w ha t higher than indicated bythe moment a t 20 degrees of deflection.i t em s such as l i f t and moment coefficients will be given in SCOUTSyste m Design Report , Supplement I.

Hinge

The m os t s eve re ove r -

The nonlinear relat ionship

More comp lete data on bas ic

Control Surfa ce Actuation

Movement of the control surfaces on SCOUT s accomplished by meartsof a hydraulic piston actuator opera ted by an electro-hydraulic valve.Thes e components , together with a power amplifier and a feedback

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t ran sdu cer , fo rm a servo unit , one of which is used for each cont ro lsur face .The actuator , valve combination mu st be chosen to be capable ofovercoming the maximum expected hinge moment and providing as lewing ra te adequate f o r contro l.and slewing rat e requir eme nts we re not known at the t im e of componentselection, rath er conservat ive values we re chosen. Accordingly theSCOUT actu ator and valve can produce a stall hinge mom ent of 1700in-lbs and a no-load slewing rate of 250 deg/sec.m uch g rea te r t ha n r equ i red , but a r e incorpora ted because of the eas eof attaining th em with a hydraulic servo . The rea son , ho wev er, fo rleaving a sizable hinge moment margin is due par t ly to t h e uncer ta intyin requi rement r esu l t in g f rom eros ion, and par t ly due to the m e r e f a c tthat the moment i s som etim es unstable. The serv o valve cons ists ofa solenoid-driven f lapper valve which dir ec ts hyd raulic oi l to posi tiona four-way spool . The spool in tur n controls the f low to the actuator .Sys tem operat ing pre ssu re i s obtained by mea ns of a b a t t e r y - d r i v e nelec t r ic pump, a hydraulic accumulator , and a regulator s et at 3000psi .ar e a of 0.419 squ are inches and a total s t roke of 0 . 8 6 inches. It ac t sa t a m o m en t a r m ( at ze ro deflection) of 1.375 inche s and can prod ucea total angular con trol surf ace deflect ion of 37 deg ree s. The closedloop dynamic response of the se rvo depends upon amplif ier and valvelags, the ine rt ia of the load (v an es and t i p s) , and the open-loopgain. With the SCOUT compon ents, the l a g s a r e v e r y s m a l l ( l e s sthan one ms ) , so that at low gains, the gain alone det erm ine s thedynamic respo nse .exhibi ts primari ly a f i r s t -o rd e r r e sponse up to f r equenc ies of 50o r 60 r a d / s e c .

A block d iagram of a SCOUT servo is given in f igure 3.

Since the maximum hinge momen t

T h e se n u m b e r s a r e

The hydraulic a ctuator is a cylinder and piston having an effecti-ie

Without introducing extrane ous lags, the ser vo

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If the loop gain is rais ed even more,the effect of the s yst em lags beginsto become ev ident, and the s erv o eventually beco mes underdamped inthe region of 100 to 150 rad / sec .desig ner to know the response of each component in his s ys te m a sclosely a s possi ble, the s erv o loop gain on SCOUT was m ade variable.During the sy st em desig n of the f i r s t stage, a se r vo response wasdetermined which gave the best overall operation, and th is wasapproximated in the actual equipment by adjusting the loop gain.resul tant behavior is near ly a s imple , f i r s t -o r der response with abre ak f requency of 31 rad /sec .s imp le brea k f requency var ies d i rect l y with loop gain ,and in fact , isnumerical ly equal to it .

Since it is neces sa ry fo r the con t ro l

The

Within the region of operation, the

The response of the SCOUT servo depends upon extern al par am et erssuch a s hydraul ic pressure and spr ing rate of the load a s well a supon loop gain.which should allow a variati on of f 3 percen t in the s e rv o b reakfrequency.effective s pr in g ra te due to hinge mom ent ra i ses or lowers thefrequency a s l ight amount merely by adding a pos it ion te rm to thecha rac ter i s t ic equat ion. Also, the pre sen ce of a static load requ i restha t the ac tua to r assum e a cer ta in pr es su re level , which reduces thep r e s s u r e d r o p a c r o s s t h e va lv e an d d e c r e a s e s its gain.of se rv o f requency response were m ade with lar ge hinge mom ents and

The to lerance on supply pr es su re is f 10 percent ,

The load affects the se r vo respo nse in two ways. Thena tura l

M e a s u r e m e n t s

the resu l t s a r e shown in figure 4. Investigation of the effect of lowhydrau l ic p r es su re ind ica ted t ha t deviat ions i n respo nse w er e withinth e m e a s u r e m e n t e r r o r . -._. .

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0

L.--- 1

--.D

-.--.*-.--

-------.-.-,

--

-.N

0 09 m

00,"mc-

m

rr)

N

0HOImI-\o

m*m

d

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The choice of hydrau lic rath er than ele ct ric s erv o actuation was madea t a t im e when the hinge moment, slewing rat e, and frequency resp ons erequ irem ents could only be estim ated .the advantage of being m ore than adeq uate in hinge m oment whilegiving a n adjustable response . The hydraul ic ser vo is capable offir st -o rd er behavior up to relatively high frequenc ies, and due to itsl a r g e m a r g in of effectiveness, it i s af fected ve ry l i t t le by loadvar ia t ions .

The hydraulic ser vo has

STABILIZATION

P it c h And Yaw Axes

Air f rame Descr ip t ion :by the control sys t em is a long, sle nd er body and is aerodynamical l j -stable. The l i f t due to angle of attack is dis t r ibuted over the body ina ma nne r dependent on Mach num ber.distr ibution was lumped a t four body stations, this being practicalsince the loads tend to concentrate a t the nose, the D-section flare,the B-sect ion f lare, and a t the fins. The lumped distr ibutions willbe given in SCOUT Sys tem Design Report , Supplement l , f o rth ree Mach numbers .

The SCOUT i r f r am e, which must be s tabi liaed

F o r purpose s of analysis the

To proper ly s tabi l ize the SCOUT vehicle, the effects of body flexibil!.tyhad to be c onsidered .to des crib e the deflections and angles a t each body station.

The fir st thre e body-bending modes w ere usedBending

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mode shapes, s lopes , and f requencies wil l be given for sev era l f lightconditions in "SCOUT System Design Rep ort, Supplement I. In flightthe actual l i f t distribution is determined by the loca l angles of attackalong the body, and the se ar e affected by bending. Hence, the totaldescr ipt ion of the a i r f r am e is accomplished by wri ting the ordin aryrig id equ atio ns of motion in conjunction with a s e t of wave equationsfor the body flexibility.

The SCOUT fir st -s ta ge control sy ste m was designed by investigatingthe a i r f r am e behav ior a t severa l d i sc re te cond it ions . These werelaunch, the t ransonic region, maximum dynamic pr es su re , and burn-out.points on the trajec tor y. The launch case w as of in te re st because thebending f requen cies wer e lowest the re and becau se the effect ive cant:-olgain was low (due to both the abs enc e of ae rody nam ic co ntrol and to theiner t ia cen ter-o f-m ass s ituat ion).considered because the s ta t ic s tabil i ty ma rgin is very la rg e near Machone, and the t ip controls a r e espe cially effective. Maximum dynamicpre ssu re i s of p r im ary impor tance s ince the t ip con t ro ls a r e ve ryeffective, the aero dy nam ic coupling of bending mo des is large , and themom ent due to angle of attack i s near maximum.was used p r ima r i ly to check the pe r fo rmance jus t p r io r to the f i r s t - s tag ecoas t ; a t that t ime the l i f t forc es ar e sm al l and the control effect ivenesshas been g rea tly reduced due to the los s of je t vane control .

These conditions w er e felt to be rep rese ntati ve of the mo st se ve re

The tran so nic condition was

The burnout condition

The equations of motion of the veh icle a r e composed of aerodynam ic andstr uc tur a l ter m s; the fo rc e on the body i s the summation of l i f ts at thefour aerodyn amic load s ta t ions and these , in tu rn , a r e functions

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of the loc al ang les of at tac k.i s that of the r ig id a i r f ra me plus that due to bending.two angle-of-attack te rm s at each station; one i s the actu al bendingslope (the sum of the sl opes due to each of the thr ee mo des), and theo ther is that caused by the bending deflection rate.

The angle of a tta ck at eac h body sta tionBending produc-ss

In wri t ing the a i r f ra m e equations in the pi tch plane, s tandard termin-ology has been used w herever possible.and Z ' s to displacement.is w(x, t ) E Cp (x) z( t ) where w is the generalized deflection at t im e,t , and body station, x.z i s the normalized t ime response.the mode and to the number of the body station, in that or de r.p i j is the n orm aliz ed deflection of the i th bending mode at the j thbody station.flight condition is given in figure 5 fo r fo rc e applied by a control su rfa cedeflection, 6.

Capital M ' s re f e r to momentsThe wave desc ription of str uc tu ra l deflecticn

c) is the normalized bending mode shape andSubscr ipts ref er to the number of

Thus

The matrix of pitch equations of motion at a par t icu la r

eH e r e a i s the rigid-body angle of attack, 0 the rigid pitch rate, V isthe vehicle velocity, and S s the Laplace (complex f requency)opera to r .f i r s t mode due to rate of deflection of the second, while the coefficientZ1z1, f o r ex am ple , i s the s quare of the nat ur al frequ ency of the f i rs tmode including aerod ynam ic influence. The coefficients ar e definedin table 1.

Coefficients such a s Z1z2 r ef er to fo rc es excit ing the

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-0N"

L oNNI

a imNII 1

iuI II 1d *a "N NN mN

mEN

SN+v) m

NE N

iN+m

N

4

E N

iN+cn "

+cnI

E d

mN"N+m mN"* N

NNN"+O N

N"4

NN"

m 4+N+cnN I

*2N

cr)NNN+v1a K lN

mN

cuNNN+cn- NN

N

N+rnI

4N6 1N+- 8 9NN

*aNN

dNN

mNmN+ m.NmN+cnI

NNmN+cn N.N

cr)N

*amN

dmN

W0

Q-l0x.r(k

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La. ij f o r i = 1, 2, and 3V j J

-x. +..M ii = J 111

- -M b = x b + K b x b

1

Z ia = cLa, Qijm.1 j J -

2.;. = - 2 S i wi 51 1m .1

j

m.V

m.j

where:

q = dynamic pressu reS = reference are a for the l if t coefficientV = vehicle velocityI vehicle in ert iam 5 vehicle mas s

CLa. = lift coefficient at the jth body station due to angle of attackz. = dis tance f rom the th ody station to the cen ter of mass,1 posit ive if j is forward of the center of m a s s+ = mode slopem . = generalized ma ss of the i* mode

i. k = mode numberssubscr ipt b = the control surface stat ionsubscr ipt T = the engine thrust stat ion (the nozzle throat)

CL . = lift coefficient of the aerod ynam ic contro l sup e r unit deflection

Kb = lift of the jet v anes p er unit deflectionT = engine th Ns t

miSi

= natu ral bending frequen cy of the ith mode= stru ctur al damping ratio of he ith mode

Table 1 Coefficients of Pitch Equations of Motion for Firs t Stage

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Note that the engine thru st level ap pe ars in the mom ent coefficients.This i s ne ce ss ar y to account for the effect of ta i l deflections due tobending which tilt the thru st vector away fr om the center of m as s .Many of the coefficients a r e negligibly sm all when prac tic al da ta isused.design sinc e they do not add significantly to the work and they ca nbecome important under cer ta in c i rcumstances .

Never th eless a l l of the t e rms wer e retained during the SCOUT

Control S ystem Design:co nsi sts of ra te and position gyros, a ser vo , a compensation network,and of course , the a i r f ra m e.resp ons e which contributes to the complexity of the a naly sis.of the body flex ibilit y, comb inations of s om e of the component dynam icsa r e not s imple .at different body station s, so that the angles and r a t es they detecta r e diffe rent mi xt ur es of bending slope and rigid-body motion.actu al inputs se en by each gyro a re:

The control sy s tem fo r the SCOUT f i rs t -s tag e

Ea ch of thes e i tems h as its own dynamicBecause

F o r ins tance the r a te and posi t ion gyros a re located

The

rat e input

A block dia gra m of the pitch sy st em is shown in figu re 6.dynamic re spon se of the posit ion gyro i s that of a sim ple t im e constantof 0 . 4 m s, while the rate gyro responds as a second-order devicewith a natu ral f requency of 2 2 cps and a damping ra tio of 0.5.

The

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Ea,m*ro0kI:0u

c,

.-(

c,

5ii9E

E

c,

a,w0rakMra

xV04a,boldIc,k

smtzZI9a,k.r(cr

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The dynam ic behav ior of the ser vo sy ste m and the com pensation devicea r e , wi th in ce r ta in l imi t s , unde r the contro l of the designer.each can be re pres ente d by equat ions of second ord er o r less , a lthoughhighe r o rde r compensat ion te rm s have been cons ide red .

In general

The SCOUT control problem was a t tacked by consider ing the ent i reset of a i r f ra m e and control equat ions together .t h i s r e s u l t s i n a twelf th-order square matr ix, the e igenvalues ofwhich a r e the roo ts of the closed loop sy ste m equation.m a t r i x is shown in f igure 7.

In the pitch plane

The zero

In represent ing equat ions this way sev era l assump tions a r e made.First, the ae rodyn amic and s t ruc tura l coef f ic ien t s a r e cons ide redto be constant a t the t im e the equations we re writ ten, i .e . , theya r e inva rian t wi th t ime . Second, the coef ficient s a r e a s su med t o beinvariant with the dependent vari able , making the equations l ine ar.Str ic t ly speaking, both assumptions a r e false but their effect canbe es t imated.s ignif icant problem, but nonl inear i ties a r e important in some cases .Changes with t ime a r e always

too s m a l l t o be a

The va lues of C and CL 6 a r e both dependent upon the i r va r ia b le s ,L aand for s tab i l ity ana lys i s , the i r g r ea te s t va lues were used (cor re spokdingto ze ro angle of attack o r control deflection).

I *

The desig n lati tude included selection of rate and posit ion gains, ofcourse , and as much va r ia t ion i n se rv o re sponse a s could be reasonzblyjus ti f ied with e le c tr ic o r hydraul ic ac tua tors .sys tem was accomp lished by de termin ing the most advantageous serv obehavior , ga ins , compensat ion, and a s i t developed la ter , loca t ion of

Synthes is of the control

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0

0

0-0

0

-0

0

-0

-9-N

0

s

--N29c

2 29 0

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the gyros in the a i r f ram e .the fl ight were left as a possibility.chosen so hat predetermined design cr i ter ia could be met in spite ofvar ia t ions and to ler ance s .

Discrete changes in control gains duringT h e s e p a r a m e te r s w e r e t o b e

During the design it was intended that the "nominal sy stem " (thatsy ste m fo r which no allowance was made f or component variation,para met er to le rances , o r accuracy of basic data) should mainta ingain and ph ase m ar gi ns of stab ility of 12 db and 30 degrees , respect ively .The cr i t er ia wa s l at er , changed to 10 db and 20 degrees in the presenceof the wor s t para me ter var ia t ion. Other facto rs of importance we rehigh loop gain and good damping. In or de r to cope with steady o rs lowly varying dis turbances such a s thrust misal ignment , winds , andf in misal ign ment , the control gain should be larg e . Sudden mom entsf r om gus t s o r shar p changes in th rus t misa l ignment a re con t ro l ledbe t te r if the effective overall damping rati o i s high enough to p reve ntm or e than one overshoot . I t w a s decided that the control gain should bekept above five if possible and that the damping ratio of the "rigid-body"response ( the response i n the region of 0 . 5 cps) should exceed 0 .2 .Actually the t ransi ent response is so complex (s ince it includes allthe bending frequenc ies and seve ral control frequenc ies and t im econstants ) that damping ratio has l i t t le meaning.than 0.3 o r 0 .4 was deemed unnecessary since the wavelength of theoscil lat ions is ve ry long and s ince the pi tch-over maneu ver is m o r eaccura te at low damping.as possible, however, at frequencies of three cps and lower.

Higher damping

The sett l ing t ime wa s maintained as low


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Originally th er e we re two outstanding diffic ulties connected withstabil ization of the f i r s t stage: the unfavorable phase shift introducedto the gyro s by the second body-bending mode, and the pro xim ity infreq uen cy of the f i r s t bending mode and the rigid-body res po nse a tconditions of high q (dynamic pre ssu re) .upon the g yros when mounted in T rans it ion Section D (a t body station120 ) was qui te seve re . At tempts to filter the forward control loopby low-pass networks w er e handicapped by the adve rse effect of thef i l t er on the f i r s t mode behavior.and lag compensation dynamics is chosen for the rigid and f i r s t bend-ing frequ enci es, the second bending frequency is sti l l not sufficientlyattenuated . A combination low freq uen cy lag and second-mo de notchf i l ter was considered which produced sa t is factory response to acer tai n extent, but which allowed too much trans mi ssi on a t highfrequency, thus making the system m ore suscept ib le to noise andto third-mo de instabil ity.to the prob lem would be to reduce the second -mod e coupling L t itssou rce by moving the ra t e gyros to a more favorable location.The location of the rate gyros i s mo re cri t ic al than that of thedisplacement gyros , s ince a ra te gyro output is higher a t body-bendi.ig

The second mode effeck

If the pr op er com bination of se rv o

It wa s decided that th e be st ov era ll soluticm

frequencies .body sta tion 214 in Transit ion S ection C because the second-modenormal ized s lope is v e r y s m a l l at this location.Bkeferred over locations of low slope in other sections because ofthe advantage of retaining the ra te gy ros through third - stag e operation.Although the roll ra te g yro location is not pa r t i cu la r ly c r i t i ca l , th i sgyro was aI'so re located s ince i t is a n integr al pa rt of the Gnat Packa.ge

The ra te-g yro Gnat Packag e Assembly was located at

Section C w as

,AAsscr;lZ?.- . P.,y --A # L ~ b A A A ~- -4: - - t h c g y r o p e k z g c , t k z s e C G d - k c d i c g =odeeffect was reduced by a lmos t 16 db.

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A s the concu rrent se lect ion of compensation and servo dynamicsproceeded, * itbecame clear that the addit ional response required wasof low -pas s na ture . The root locu s plot of figu re 8 and the Bode plotof figure 9 show the situation at maxim um q with no co mpen sation anda perf ect ( ins tantaneous response) servo.ra t io , which produce s a low-frequency rea l z er o in the open-loop W ansferfunction, has been a rb i t ra r i ly se t at 0.33.syst em roo ts a s the loop gain is increased, i t can be seen that considerablephase shift is needed at the f ir st bending mode frequency. If one ormo re lag te rm s (poles) wer e added a t low frequency, the f i rs t modelocu s would s ta r t into the left half plan e and the rigid-body locu s wouldnot bend so far to the left .in the behavior of the rigid body and the fi r s t bending mode, and thesep aratio n of the ir frequencies dete rmi nes i ts feasibil i ty.the locus is a ls o affected by the locat ion of the rate gain z er o which i :3alm os t equal to the posit ion-to-rate gain ratio. As th i s ze ro is movedclos er to the origin the rigid-body locus is bent mor e to the left , improv ingthe syst em damping. Unfortunately, such movement of the zer o isaccom plished by raisi ng the rate gain, which inc rea ses the sensit ivityto bending modes.quency of the zero.

The rate-to-posit ion gain

F r o m the movement of the

Lag compensation thus involves a compromise

The shape of

Thus there is a p rac t ica l lower l imi t to the f r e -

Be ca use of the small f requency separat ion between the r ig id and f i r s tmodes the re i s l i t t le chance of com pensating the first-mo de locus byattenuation of the high er frequency. Accordingly, it was recognizedthat the se rvo and compensation dynamics together m ust producesuffic ient phase shif t a t the f i rs t -mod e f requency to s tabi l ize the f i rp tmode without adverse ly affecting the rigid-body locus. The phase

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NO NETWORK, IDEAL SERVOPOSITION TO RATE GAIN RATI O = 3

MAX. q CONDITIONSECONDBENDINGMODE

Figure 8 Root Locus Plot of Uncompensated First -Stage System

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Figure 9 Bode Plot of Uncompensated First-Stage System

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synthesized with the existing hydraulic s er vo and a s imple , second-orderla g network.a frequency of -31 n e p e r s p e r sec .by the network and one pole by the servo.have roughly verifi ed predictions of the resp on se obtainable. Atfrequencies of in teres t (40 r a d / s e c a n d l o w er ) t h e s e r v o t r a n s f e rfunction was n ear ly ch aract erized by a single pole which vari ed infrequency dir ect ly with loop gain. Actually the ear ly ser vo s exhibitedh igher -o rder po les a t approximately -300 and -500 nepers per second.The locat ions of these poles w ere ra th er unpredic table s ince they var iedfr om unit to uni t a s well a s with loop gain.consider ing these pole chara cter is t ics became unnecessa ry because i.:was found that the poles moved t o higher frequ enci es on la ter se rvos .Because of the s l ight var ia t ion in ser vo high-frequency behavior , se ve ra lpoles w ere included in the s tabi l i ty analysis to dete rmin e their effect.By using a two-pole t ran sfe r function, the actual ser vo could be s imu -la ted a s closely a s was neces sa ry in a l inea r ana lys i s.

T h r e e real poles we re placed very c lose together ne arTwo poles w ere to be generated

Te s t s of the se rv o ac tua to r

However, the pro ble m of

The double-lag network could not be syn thesiz ed with its poles tooclose together and still be pa ssi ve and non-inductive.two break f requencies we re s l ight ly separa ted; the nominal se t t ingsbeing -29 and -33 nepe rs p e r second.

Accordingly the

Nominal Control System: Fig ure s 10 and 1 1 give the root-locus plotand Bode plot of the nominal system a t the maximum q condition.The posit ion-to-rate gain ratio which gives the best ove ral l operat ionis 3.0; it was considered bet ter to use th is mor e sa t is fac tory ra t i oand switch gains a t second-s tage ig ini tion than to com promise it with

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MAXIMUM DYNAMIC PRESSURE CONDITIONNOMINAL SERVO AND NETWORK

-35 / - 3 0 - 2 -25 -20 -1 5 -10 -5(NET WORK)

POLES Q (SEC'l)

Figure 10 Root Locus Plot of Nominal First-Stage System at Maximum q Condi

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-100

- 2 0 0

-300

. 1

-0

.-50

' -100

1-150

I

1 10 100 1000FREQUENCY% RADISEC

Figure 11 Bode Plot of Nominal First-Stage System at Maximum q Condition

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a ra tio which could include the upper sta ges. The nominal pa ram ete rvalues w er e cho sen only af te r reviewing the effects of changes in e a c hof them, a s well a s reviewing var ia t ions in bas ic data and in f l ightcondition.the nominal sys tem at launch, 17 seconds af ter launch, and at burnout(with je t vanes stil l fully effective).deg rees of con trol surf ace def lection pe r degre e a t t i tude er ro r .that a t launch the r igid-body locus becomes ve ry damped at high gain,but a t a ga in of 5.0 , the damping is poor.is g r e a t at launch (due to the absence of aerodyn amic t ip control andthe separa t ion between r ig id and f i rs t - mo de f requencies) , the gainmight have been increase d to 10.0 fo r the f i rs t few seconds of flight,thus improving the damping. I t was felt , however, that al though thedamping was low, it was adequate and that the improv emen t couldnot justify the us e of gain switching.

F i g u r e 12 through 16 show root-locus and Bode plots fo r

The nominal posit ion gain is 5.0Note

Becau se the gain margin

The stab il i ty of the SCOUT firs t-s tag e control system was checked ata va rie ty of conditions. Variations of the following pa ra m et er s w er einvestigated:

0 Bending frequency0 M a x im u m d y n am ic p r e s s u r e0 Rate-gy ro locat ion0 Rate and posit ion-gyro natural frequency0 Rate-gy ro damping0 Serv o dynamic response

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NOMINAL SERVO AND NETWORK

Figure 12 Root Locus Plot of Nominal First-Stage System at Launch

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FREQUENCY& RADISEC

Figure 13 Bode Plot of Nominal First-Stage System at Launch

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?;OhFzNAL SERVO AND NETWORK

Figure 14 Root Locus Plot of Nominal First-Stage System 17 Seconds after Launc

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BURNOUT (FULL THRUST)XOMINAL SERVO AND NETWORK

- 3 5 -30 -25 -20 -1 5 -10 -5O- (SEC-l)

Figure 15 Root locus Plot of Nominal First- Sta ge Syste m at Burnout

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I FREQUENCY& RAD/SECFigure 16 Bode Plot of Nominal First-Stage System at Burnout

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The nominal control gains and tran sf er function we re chosen so thatreaso nable changes in such quanti ties a s se rvo r espo nse and bendingfrequency would ma intain the gain and phas e mar gin within thei r prop erl imits. Tolerances wer e establi shed for gain, gain rat io , servoresponse, and the network break frequencies . These tolerances a r equite conservat ive i n that the system wi l l perform sat i sfactori ly evenif each parameter is i n e r r o r i n its worst direct ion.

The m os t difficult requ irem ent to specify, and one which cau ses themo st c once rn about stabi l i ty, i s the frequency response of the netwo::k-servo t ransfer funct ion.th ree po les , it is unlike ly that al l of th em wil l e i ther increase orde cr ea se in frequ ency together. If one pole shifts in the lowerfrequency direct ion, the rigid-body damping wil l be decre ased , butthe system wi l l become m ore stable due to the beneficial phase shiftat the fi rs t mode. This pole can var y by mor e than a factor of th reei n frequency and still maintain a s ix db gain marg in.in the compensating-network component values tend to sep ara te thetwo brea k frequenc ies, a behavior which red uces the effect of thechange on the sy stem . Component tole ran ces a r e held to within fivepercent , so that se ve ra l combined value shifts a r e needed to significantlya l t e r the response .

Since this t ra ns fe r function is compo sed of

Most variat ions

Changes in the rate-to-posi t ion gain rat io shift the locat ions of m os t

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of the ze ro s on the complex plane.beforehand the results of a single gain variation.be s ee n f r o m the plots of "SCOUT Sy ste m Design Report, Supplemknt11, 'I inc reas ing the rate gain aids the rigid-body damping but aggr ava testhe bending modes.because of its fa r reaching effects.

There fore it is difficult t o judgeIn general , a s can

Gain ratio ha s b een held to a 10 p e r c e n t t o l e r a n c t

The behavior of the control system af ter f irs t -s tage burnout degradesrapidly a s the sensible a tmosphere is left behind.Bode plot of the no minal sy st em just after burnout (with ze ro je t vanelift).response , the damping has deter iora ted even a t this relativ ely high qcondition. In the coasting perio d bef ore second - sta ge ignition, thesy st em damping will be reduced to only a few pe rce nt of critical,and angular momentum still pre sen t will re sul t i n continued att i tudeosci l la t ions . Moreover , a s M a decreased due to the decreas ingq, the frequ ency of osc illation is reduced, causing the amplitude tobecome grea te r .switching to a. hi'gher loop gain soon after burnout, thus helping todamp any t ransi ents appl ied a t that time ( such as sudden remova l bfthr uct mis align men t) before the c ontrols becom e too ineffective.

Figure 17 shows tire

As can be se en fro m the rigid-body porti on of the amplitude

P a r t of-this effect could be compensated by

Gain switching af ter burnout, however, was not considered to offersufficient improvemen t in perform ance to justify the complexity(a t least for the e ar ly f lights) .switching is incorporated in the SCOUT ele ctr oni cs package in caseit i s deemed advisable i n the future. Eve n inc rea sed loot, gain does

A me ans of accomp lishing this

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0

- IO(

-200

-300

-4oc

10F R E Q U E N C Y Q RADJSEC

Figure 17 Bode Plot of Nominal First-S tage Sys tem after BurnoutR-ED 11117- 38 -


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N 0

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2


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Thus components such a s r ipple f i l te rs and t ra nsf orm ers must bechecked to ens ure that th eir pass bands a r e compat ible with the designdynamics.

The s erv o t rans fer funct ion, dur ing design taken to be 131S+ 1

, wat;specif ied in te rm s of i t s f requency response .we re r equ ired t o be met twice; once in a preliminary component checkto be cer tai n that a parti cula r valve-actuator combination w a s capableof responding a s a f i rs t -o rde r device , and again in a mo re completetes t in which the ser vo and network resp onses we re m easured together .In the f i r s t instance faulty valves and act uat ors w ere to be detected bythe pre sen ce of high-frequency lags o r nonlinear operation. Accordingly,frequency respo nse tolerance bands we re establishe d to exclude thepossibil i ty of significant changes in curve shape, al though they we renot adequate to specify brea k frequency.bands used to check actu ators and valves a r e shown in figu re 18.

Servo response specif icat ion

The f requency-response to lerance

These bands we re gen erated by taking a s the upper l im it the re sponseof a f i r s t - , ord er s yst em having a brea k f requency 1D bercent h igherthan that des i r ed for the servo, while the lower l imit was establ ishedby the response of a second-order syst em with one break f requency10 perc ent lower than the servo nominal and the o ther bre ak f requency at150 r a d / s e c .high-frequency lags below 300 ra d/ se c , the lower to lerance l imit shouldbe tightened somewhat.

Becau se l at er ser vo s in good condition do not exhibit

The s er vo consist ing of the valve and actuato r to be teste d and a

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sta ge s of amplification, the compensation network, and finally, thehydraul ic servo. The se rv o shaft posit ion, corresponding to je tvane and tip deflection, w a s sensed by a dc potentiometer and theresult ing signal return ed to the com puter where i t completed thecon trol loop.could then be m eas ure d and compa red with those pre dic ted by the mo:-eexact , but less complete , d igi ta l analysis . Ph ase and gain mar ginsobtained in this way agre ed with predicted values ve ry close ly ( within1/4 db in gain).was m ea sur ed with analog simulation that would have been imp ossib leto determ ine by solving the l inearized sy ste m equations. First , thecontrol behavior was checked with the se rv o loaded with s pr in gs ,correspo nding to hinge mom ent loading expected in flight.ra te was made both positive and negative and, in addition, a l a rgestead y (inva riant with .deflection) momen t was applied.resp onse v ariat ions could be observed but they we re negligibly small.The effect of connecting a 0.5-mfd capacitor a c ro ss the s er vo valvecoil was als o copsidered, because f ie ld ope ration had shown thatele ctr ica l noise imposed on the long signal wi re s connecting the fi rs tand third stag es had caused the se rv o to chat ter.conveniently accomp lished a t a d c point, could eliminate the chat ter ,and tests showed that a capacitor connected ac ro ss the valve coilwould suffice. The add ition of the ca pa cit or , howeve r, caus ed anonlinear pe rformanc e of the serv o ampl i f ier , which al te red the se rv 3response in a manner not easi ly described in te rm s of t ransfer-func t ionpoles and zeros.by applying either simulated wind gusts (instantaneous changes inangle of at tack) o r at t i tude commands.

The t ime and frequency respo nses of the ent i re sys tem

The effect of sev era l anomal ies in cont rol componer.t s

The spring

The vehicle

Fi l ter ing, most

Time respon ses of the ai r fr am e we re determined

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I

S U R F A C E 0D E F L E C T I O N

- 2 5 O+5F I K S T

BENDINGNOR MALI ZE DD E F L E C T I O N

- 5+o. 5

S EC O N DBENDINGN OR M A LI Z EDD E F L E C T I O N

-0.5+o. 4

TH I R DBENDINGN O R M A L I Z E DD E F L E C T I O N

-0.4

F T .

0

FT.F T .

_c_ in----.0

F T .F T .

0

F T .

ANGLEO FA T T A C K

P I T C HANGLE

+ s o

0- 5 O

-5O

0

+ 5 O+25O

NOMINAL SYSTEM,S I M U LA TED C O M P O N EN TS

-d bl SEC.

Figure 20 First-Stage Pitch Time Response at Launch

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ANGLEO FATTACK

PITCHANGLE

+ O

0

- 5 O

0

+ 5 O+25O

SURFACE 0DEFLECTION

-25*+5 FT.

0IRSTBENDINGNORMALI ZEDDEFLECTION -5 FT.

+O. 5 FT.SECONDBENDINGNORMALIZEDDEFLECTION

0

-0.5 FT.+O. 4 FT.

THIRDBENDINGNOR MALI ZE DDEFLECTION

0

-0 - 4 FT.

NOMINAL SYSTEM,SIMULATED COMPONENTS

Figure 21 First-Stage Pitch Time Response at Maximum q Condition

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ANGLEO FATTACK

PITCHANGLE

SURFACEDEFLECTION

+FIRSTBENDINGNORMALIZEDDEFLECTION

+O.SECONDBENDINGDEFLECTION

-0 .+O .

NORMALIZED

THIRDBENDINGNORMALIZEDDEFLECTION-0.

+5O

0

- O- 5 O

0

+ 5 O+25O

0

-25O5 FT.

0

5 F T .5 F T .

0

5 F T .4 F T .

0

4 F T .

NOMINAL SYSTEMBURNOUT CONDITION (FULL THRUST)SIMULATED COMPONENTS

1 S E C d

Figure 22 First-Stage Pitch Time Response at Burnout

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A N G L EO FA T T A C K

P I T C HA T TI TU D EA N G L E

C O N T R O LS U R F A C ED E F L E C T I O N

F I R S TBE NDINCN O R M A L I Z E DD E F L E C T I O N

SE C O N DBENDINGN O R M A L I Z E DD E F L E C T I O N

T H I R DBENDINGNOR MALI ZE DD E F L E C T ON

MAXIMUM DYNAMICPRES SURE CONDITIONNOMINAL SYS TEM WITHA C T U A L N E T WO R K , E L E C T R O N I C ,AND SE RVO HARDWARE.

+ 5"0

- 5"+ 5'i

- 5"- 2 5 "c-y---------I

+ 25"+ 5 F T . I

*+'pc,0 - s 4 '

- 5 F T .+ 0 . 5 FT.

O--"rvc------

-0 .5 F T .+ 0.4 F T .

0LF i g u r e 23 Firs t -Stage T i m e Response of Sys tem with Actual Hardw are

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T h e r e is essentially no coupling among the torsional modes of vibra-tion and the rigid-body since all the aerodynamic t e rms a r e v e r ysmall , so tha t in p rac t ice, the above matr ix is degenerate and canbe written with only its diagonal te rm s. The mom ents applied to thebody which excite the "rigid" o r flexible modes a r e functions only ofthe cont rol su rfa ce deflection. The coefficient--I--s obviously therol l mom ent pe r unit differential deflection of the two sur fac es dividedby the ro ll m om en t of in er tia . R16 and R2b a r e given by there la t ion A . L

L 6

= i d 6I:1

where - Angular acce ler atio n of the i th tor sio n modedue to a unit cont rol deflection

- Tors ion mode shap e of the i th mode a t thecontrol surfac e s ta t ion

'i 6

moment due t o a unit contro l deflectioncharac te r i s t i c iner t ia of the ith mode

--6-Ii

The f i r s t two tors ion modes we re considered adequate to des cr ibethe ai r f rame fo r the control ana lys is; the natura l frequ encie s of thef i r s t and second modes a r e 22 an d 37 cps, respectively.

Control Sy stem Design:a t the outse t to be a relatively smal l prob lem, the f i r s t - s ta geele ctr oni cs wer e designed with no prov ision for roll compensation.Moreove r , the ser vos dr iving the ro l l control me mb ers we re thesame a s those used in yaw, and their res po nse had been se t to meet

Because f i rs t -s t age rol l control appeared

LLa s e ieqaiycmcntz s f t he l a t t e r e y ~ t e ~ .he O ~ Yatitude left the

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designer was the s e lect ion of rol l control gains .analyzing the sy ste m using the root-locus technique to solve the totalloop equations of motion shown in the ze ro m at rix of f ig ure 24.The rol l rate and position gyros a r e separa ted jus t a s a r e those ofthe pitch and yaw channels, so that different combinations of rigidand flexible body motion a r e sen sed by each.

This wa s done by

The rate g y r o s e n s e s

while the posit ion gyro r eg is te rs= Q + ~ r t ~ r

in 1G 1 2G 2TG

The posit ion-gyro dynam ics a r e negligible, while those of the ra tegyro a r e second or de r with a nominal natura l frequency and dampingra tio of 33 cps and 0.5, respectively.

The rol l control sys tem was analyzed a t two flight conditions: a tlaunch where the loop gain i s low and the damping could be expectedto be poor, and a t a t ime when the combination of dynamic pr es su re ,vehic le iner t ia , and control surface effectiveness produced the high-e s t loop gain. The two se ts of coefficients used were:

LAUNCH PEAK GAIN%/I 2.325 deg/ sec2 /deg 12.83 deg/secZ/de g

-3370 de g/s ecZ /de g -11670 deg /se cZ /de gR16 6740 deg /se c2/ deg 23340 deg /secZ /deg26The r ol l control sy s te m must mainta in the vehic le a t t i tude withinspecified l imits in the pres ence of external d is turbance mom ents .Dis turbances in rol l can occur in a number of ways, but the more

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severe dis tu rbances a r e caused by f in misal ignment , control- surfa ceoffset, and by aer od yn am ic coupling of yaw and pitch angl es of a t-t ack th rough the C1 9 te rm .fin misalignm ent, and c an exceed 1000 f t - lbs .

The la rge s t moments a r e produced by

The change in control sy ste m res po nse with flight condition is v e r ynear ly that caused by a loop gain change, a fact which mak es it e a s yto se lec t approximate control pa ra m et er s wi thout solving a n addit ion-a l set of equations.

Root-locus plots w er e made of the rol l s ys te m using the two torsi onmodes, gyro dynamics , and a s er vo t r an sf er function ofDifferent gain ratios we re t r i ed and it was de te rmined tha t l a rgedeviations we re to lerab le without sac rif ic ing good damping andstabi l ity margin s .sys tem se lec ted a s nominal at launch and a t 32 seconds af ter launch.The damping ratio is 0 . 5 a t th e se e x t r e m e s if the contro l gain isse t a t 4.0 , and is even g rea te r ( somet im es g r ea te r than unity ) a tother flight conditions.a t 0 .4 s e c s i n ce it gave sa t is factory operat ion and a t t he s a m e t imewas compatible with the upper stage syste ms.eliminate d the need f or one gain switch.

1m*Fig ure s 25 and 26 a r e root-locus plots of the

The ra t io of ra te- to-p osi t ion gain was se t

This gain se t t ing a l so

I n s u m m a r y , t he r o l l c o n tr ol p a r a m e t e r s a r e :Att itude gain (dif ferentia l deflect ion pe r unit ro l l e r r or ) 4 .0 f 1570Rate gain (differential deflection pe r unit r oll rate) 1. 6 f 15%Rate to posit ion gain ra t io (sec) 0 . 4 f 10%servoLiLa-.+s& - - - - - S - - - c . - - -A : - - 1Irz a u a z c z A u u C I r i u u ) 31s + 1( same to le rance a s yaw servo)

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140

j,

1 3 51-10 - 5U r

Figure 25 Root Locus Plot of Nominal First-Stage Roll System at Launch

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-10 -50-

140

.w

135

35

30

25 -220 2p:-15 3.,-I

10

5-.0-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 O

Figure 26 Root Locus Plot of Nominal First-Stage Roll System at Maximum q Cond

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These con t ro l ga ins a r e suf fi ci en t t o p r e v e n t s e r i o u s r o l l e r r o r s i nthe pre sen ce of the la rg es t expected d is turbance moment .

Roll-Yaw Coupling: In pra ct i ce it is not possib le to cons ider thecon t ro l sys t em of each axis se p a r a t e ly b e c a u se t h e r e i s couplingamong axes f r o m a var ie ty of sour ces .ae rodynamic , s t ruc tu ra l , o r con t ro l t e r m s in the equat ions of motionof t h e o th e r w ise s e p a r a t e sy s t e m s .exhibit the only signif icant coupling pro ble m on SCOUT, and the irin teract ion was, accordingly , s tudied to determin e the ef fect on pe r -fo rmance and s t ab i l it y .

Coupling can occ ur through

The ro l l and yaw contro l loops

Rol l and yaw ax es a r e na tu ra l ly sub jec t to in t e r ac t ion becau se thesame con t ro l members a r e u sed i n b ot h axes. I n a d di ti on , a n a e r o -dynamic moment is introduced to rol l ( through the C1p te rm) when-ev er a p i tch and yaw angle of a t t ack occur s imult aneous ly. Becausea n unbalance i n the ro l l cont ro l s ignal to the je t vane and t ip s e rv oscan cause a res id ual yawing momen t , and s inc e vehic le yaw ca ninduce an aerody nam ic ro l ling moment , a closed loop can be forme dincluding the r ol l and yaw control chann els.

The ro l l and yaw in tera ct ion can have e i t her a s t ab i l iz ing o r d e -stabil izing effect upon ei ther con trol loop, depending upon the direc t lonof ro l l s ignal o r se rv o unbalance. Th er e is fur ther coupl ing pos-s ib le , however , through gain unbalance between the two yaw-rol lse rvos , wh ich is alw ays of a destabil izing nature. Suppose, fo rexample , t ha t t he upper con t ro l su r f ac e se r vo has 10 pe rce n t m or eclosed- loop gain than does the lowe r one. In applying a negative yaw

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mo me nt through deflect ion of the top and bottom s urf ac es , a posit iveyaw e r r o r wi l l i nduce a n ex t r aneous pos it ive ro l l moment . On theoth er hand, a pos i t ive ro l l moment soon p roduces a p o s i t i v e e r r o r , andthe con t ro l sy s t e m a t tempts to de f lec t the su r f aces to genera te anegat ive ro l l moment . S ince the upper su r f ace de f lec t s f a r the r , how-e v e r , a net posi t ive yaw moment res ul t s which c l ose s the loop andtends to continue the proc es s . The amount of equivalent def lec tioncoupled into yaw fro m the rol l channel is(K-1) KSCEf r om the yaw channel i s (K-l)(K,, ,+&), w h e r e KJ,, Kq, a r e t he ro l land yaw posi t ion control gains, +E and 14 E a r e the ro l l and yawe r r o r s , a nd K is the ra t io of upper to lower s ta t i c se rv o gain .that , in ord er to complete the coupl ing loop, the in teract ion gain(K-1) m us t be used twice, making the tota l coupling propo rt iona l to

and in to ro l l

Note

2(K-1) .The effect of ro l l -yaw in teract ion was invest igated cons ider ing thatone se rvo had a gain 10 per cen t high and the oth er 10 perce n t low,The inv est igat ion al s o included the contr ibu tion of the CC1plen gth of 8.72 ft2 and 3. 33 f t ) , assu ming tha t t he veh ic l e is operat ingat fou r deg ree s p i tch angle of a t tack .wi th such a s ign tha t it aide d the effect of s er v o unbalance.vehic le behavior in the presen ce of i n t e r ac t ion was de te rmined in tw oways: by solving the total equation of motion (s impli f ied) and bysimulat ing the pro ble m on the analog com puter .

t e r m . T h e1Pvalue used wa s t. 0143 deg-1 (b as ed on a r e f e r e n c e area and

Thi s t e r m was a lways in t roducedThe

In s impl i fy ing the s ys tem equat ions to facilitate ana lys i s , it w asdecided to dis pen se with the dynamics of the posi t ion and ra te gyros .

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This eliminates fo ur r elat ions which do not influence the contro lgrea t ly , and in any event , a r e no t requ i red to compare the per form -an ce s of the ve hic le with and without coupling of a xe s.to rs iona l mode was a l so e l imina ted s ince it does not contributeg rea t l y to the proble m, but the third bending and f i r s t t o rs ion modeswere re t a ined .

The second

The ma tr ix of equations used is given in f igure 27.

In this se t of equations, the fract ion of su rf ac e deflect ion in onechannel that i s added into the other is contained i n the terms z64JT 'Nb+ 9 Z l b p 9 z26+ 9 Z 3 6 g * L b + and R16+ *Solutions of the sy st em equations w er e obtained under var iou s condi-t ions of ro ll and yaw gain, deg ree of co ntro l coupling, and c l pA roo t-loc us plot of the sin gula ritie s of the com plete equation withvaryin g yaw gain and with ro l l gain fixed a t i ts nominal value(4. Odegrees d i ffe ren ti a l def lec tion pe r degre e ro l l e r ro r ) , is shown inf igure 28 .ae rodynam i c t e rm C and two ser vo s, one of which was 10 pe rc en thigh in gain and the othe r 10 per cen t low.change in respo nse , al though noticeable, i s not se rio us . Only a maxi-mu m q condition was studied, sinc e a t th is condi tion the cont ro ls a r eve ry e f fec tive and Clp i s l a rge .control components was used to check the re su l t s obtained by solut ionof the s im pl i f ied equat ions and to mea su re the effect of the interactionupon t ime response .we re used but the r a te gy ro dynamics wer e included in the s imulat ion.F i g u r e 29 shows the t ra nsie nt respo nse of the a i r f r ame in ro l l and yaw.

.

Here the coupling is due to the combined effects of the1P

It can be see n tha t t he

The analog computer with simulated

The same coupling terms and fl ight condit ion

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YAW AND ROLL CONTROLS COU PLE D BY20 PERCENT DIFFERENTIAL SERVO GAINAND MAXIMUM AERODYNAMIC EF FE CTTHROUGH C1MAXIMUM q CONDITIONB

ISECONDBENDINGMODE

X

J 60

55

-50

Figure 28 Root Locus Plot of the First-Stage Coupled Roll-Yaw System

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MAXIMUM q CONDITION

+2

SIDESLIPANGLE

-2+l.

YAWANGLE

. 5 "

0

. 5 O25 '

0

6 = 6 + . 2 6 a B 0 * 2 "6at= ba + . 2 6

b e t a 6e - . 2 66at= 6a - . 2 bee t e

-1.25"+25O-

YAW - '.'*+r- ~.>CONTROLSURFACEDEFLECTION

FIRSTBENDINGNORMALIZEDDEFLECTION -5 F T . -

+12.5"- -

ROLLANGLE

ROLLCONTROL 0 -SURFACE

Figure 29 First-Sta ge Time Response with Roll-Y aw Coupling

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M or e plots of coupled resp ons es may be found in Supplement 11.deg ree of in teract ion used in the analysis was considerably gre aterthan that to be exp ected in practice.w r i t t e n s o that the roll-yaw serv os would not differ in gain by mor ethan 10 pe rce nt, thus reducing the loop coupling coefficient by a fac to rof four.they could otherw ise introduce disturb ance mo men ts into the ro lla x i s . A pit ch -ro ll loop, however, cannot be fo rmed .

The

Servo specif ica tions we re

The p i tch se rvos a r e subject to the same spec i fica tion fo r

T h e r e i s a difficulty connected with s haring contro l su rfa ce s whichi s not evident fro m a l ine ar analysis . If no me asu res a r e taken topreven t it, a larg e e r r o r in one channel could dr ive the s urfa ces tothei r s tops , leaving no control for the other axis .possibil i ty h as been pa rti all y eliminated by l imiting the magnitude ofthe yaw e r r o r s ignal before i t i s mixed with rol l e r r o r and appl ied tothe servo.g rea te r than a f 17. 5 degree surface deflection.two deg rees of deflection rem ains before a m echan ical stop i sencou ntered . If a max imum yaw signa l has been commanded and ar o l l deflection of g re at er than two deg ree s is required immediate lythereaf ter , only one surface wi l l be f re e to deflect the require damount. Deflection of the other surf ac e will be re str ict ed by theproxim ity of a mecha nical stop. Yaw limiting is not abrup t ; the e r ro rs ignal is linear only up to 2 . 5 de gre es , beyond which i t asym ptoticallyapproaches a max imum of 3.5 d e g r e e s .r o l l channel.

On SCOUT thi s

With this limiting, a maximum y a w signal will produce noThus a maximum of

There i s no l imi t ing in the

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81 I

'-IN 1s

EQ)c,m

cIdaF:0VQ)rn

0m

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The nitrogen pr es su re for ces the fuel out of the bladders to the valves.The second-stage c ar ri es six peroxide and si x nitrogen tanks, whilethe third-stage has only two of each type.

The design of th e SCOUT upper-stage control sys tem involved theselect ion of react ion- je t thrust levels and perm iss ib le response t im es,the deadbands, degre e of damping, and othe r pa ram ete rs. The sys temdesign thus determin ed w a s to consume no more than a specified amountof fuel while m aintaining the vehicle attitude in eac h axis w ithintolera nces , counteracting external disturbance mom ents and holdingt rans ien t e r r o rs to a min imum.and low fuel consumption a r e contradictory objectives, the ref orecom pro mi ses had to be rea ched which gaveperformance.thr ust m isalignmen t during boost perio ds, and to the additionalinfluences of in it ial angular rat es and att i tude e r ro r s a t ignition.

The requirements of precise contro'l

sa t is factory overal lBoth s tag es ar e subject to d is turba nces due to engine

Moreo ver the second- stage , which is ignited at a condition of consider-ab le dynamic p ressur e , i s aerodyna mically unstable and can be expectedto produce a disturbing moment.mu st be capable of res t r ic t ing the igni tion t ransien t err o rs to lessthan eight degr ees ( le ss than the na rro we st of the gy ro l imits) underthe simultaneous action of the maxim um thr ust misalignment, thr eed e g r e e s of in i t ia l a t ti tude e rr or , and three degr ees per second ofangula r ra te . A l l these distu rban ces we-re to be combined i n themos t adverse manner.was specified to be 0.25 degree for the second-s tage and 0.10 d e g r e efor the th i rd-s tage. Fo r purposes of analysis , th is thru st misal ignment

It was decided that each stag e sys tem

The maximum engine thrust misalignment

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w a s a s s u m e d t o a c t a t the s ta t ion of the nozzle throa t . The dynam icp r e s s u r e at which the second -s tage could be safe ly ignited was to bedetermin ed. Unti l second- s tage ignit ion, ove ra l l s tabi l i ty would bemainta ined by re ta ining the burned out f i r s t - s ta ge (with its cont ro l sstil l opera t ive ) .

The second and th i rd- s tag es ca r r y 16.6 and 1.66 gallons of hydrogenp e r oxide, re spec t ive ly .Accordingly, a l lowing fo r expuls ion efficiencyand a reasonab le sp ec if ic impulse , the tota l contro l impu lse had tobe r e s t r i c t e d t o l e s s than 25 ,560 lb- s ec on the second-s tage and2556 lb-s ec on the thi rd-s tag e .w a s t o be 45 second s , about for t y seconds of which is spent dur ingengine thru s t and the rema in ing t ime during coas t ing.

The second-s tage ope ra t ing t ime

The sh or t coas t pe r iod be tween expec ted second-s tage burnout andth i rd- s tage ign it ion was incorpo ra ted to reduce the poss ib i l i ty of as low-burning second - s tag e having suff ic ient thr us t left t o ove r t a keand ram the th i rd- s tage a f te r sepa ra t ion .approxima te ly 40 seconds and then coas t s unde r cont ro l fo r a maximyJmof 600 seconds .

The t h i r d - s t a ge bu r ns f o r

Because of the ve r y d i ffe ren t r equ i rem ents of counte ract ing la r gedis turb ing mome nts dur ing boos t and conse rv ing fue l for a prolongedcoas t , d i f f e r e n t sets of reac t ion je t s a r e used fo r boos t and coas topera t io n on the thi rd-s tag e . At the end of the thi r d-s t age coas tper iod, the con trol sys te m is turned off and the igni tion s ignal iss e n t t o t he f ow th - s t a g e . The fou r th- s tag e , which is mounted on asp in bea r ing a t the upper end of the thi r d-s t age , i s given a r o l l

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angular veloci ty by three sm al l spin-up roc kets , and is then ignited.Com prom ises we re continually requir ed in the se lection of contro ls y s t e m p a r a m e te r s s uc h a s reac tion je t th rus t , j e t r esponse t ime ,and deadband.large , but a s la t er informat ion bgcame avai lable f ro m tes ts , theest im ate was revis ed, and eventually specif ica t ions were w ri t tendef ining the maximu m tolerable t im e delays f ro m valve s ignal to thedifferent portion s of ful l thrust .charac ter ized by a cer t a in deadt ime af te r the valve command duringwhich no thru st oc cu rs, and then a r ise t ime dur ing which the thru str i s e s f r o m z e r o to fu l l value. When the je t is turned off, a s im i l a rsequence occurs . Frequent ly for convenience, the te rm s turn-onor turn-off t im e a r e used to mean deadt imes equivalent to the actualresponse . Once je t response specif icat ions we re wri t ten , sys temperf orm anc e was calcula ted using the specified values . Since i t wasrecognized that to leranc es would be appl ied to each para me ter valueselected , perform ance calcula t ions were a lways made with je tthr us ts, deadbands, etc . , differing fr om nominal by the expectedtoleranc e and in the most detr imental d i rect ion.

At f i r s t , j e t r esponse t ime was assumed to be ra the r

In genera l the responses a r e

In the in ter es t of im proving the per form anc e and relia bil i t y of theSCOUT syst em , and fo r the purpose of cor rect ing unavoidable o runsuspected condi tions , sev eral changes were made in the controlsy ste m s of the la te r vehicles. Accordingly, the design des crib edhere i s d i f fe ren t fo r each of the f ir st thr ee SCOUTS, and each hasbeen considered separa tely. The fourth vehicle has not been launcheda t the t ime of this writ ing, s o that only estimated final data can begiven.

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SECOND STAGE CONTROL SYSTEM

Air f r am e Descr ip t ion

The second SCOUT s te p i s composed of the C as tor , A n t a r e s , a n dAlta i r roc ket mo tors and assoc ia ted equipment. Dynamical ly itbehaves as a f r e e body exhibit ing ine rt ia effects and -a n aerodynamicmom ent due to angle of at tack.f lexible, and if d e s i r e d , the ef fects of body bending and t or si on c an betaken in to account. Except for cer ta i n speci f ic t es t s , body flexibilityhas been ignored in the design of SCOUT upp er-s tage sy ste ms .

In addit ion , the s t ru ctu re itself is

In pi tch and yaw during burning the secon d-stage i s charac te r i zed by2a mom ent of ine r t i a vary ing between 35,952 and 24,026 slug-f tabout a cen ter of mass moving f ro m body s tat ion 298.1 to 236.2.ro l l , the moment of in er t ia about the vehic le center l ine de cre as efr o m 370.2 slug-f t a t secon d-stage ignition to 185. 3 s lug- f t a tburnout. The react ion je t s were speci f ica l ly p laced to provide thela r ge s t p r ac t i ca l moment a r m fo r con t ro l . The pi t ch and yaw je t sa c t a t body sta tion 467.68, a nd t he ro l l - j e t e f fec tive d i s t ance f ro mthe vehic le center l ine i s 16.02 inches . The aero dyn am ic ce nte r ofp r e s s u r e n e a r i gn it io n is taken t o be at stat ion 220 and th e l i f tcoefficient is 0.072 deg ree based on a 5.25- f t reference area .

Ink2

- 1 2

SalectIo'~f Pi tc h and Yaw Cont ro l Pa ra m et e r s - for Fi r s t Two Vehicles

When the second-stage i s ignited, the pi tch and yaw co ntro l sy st emcan be subjected to d i s t u r h a n r e s diie to engine thrust misal ignment ,

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ini t ial att i tudes and ra te s, and to ang les of attack.mu st be suffic ient ly counterac ted by the co ntrol je ts to i nsu re tha t thein i t i a l t r ans ie n t e r r o r does not exceed e ight degrees .t h r us t l e ve l ne c e s s a ry t o r e s t r i c t t he e r r o r to e igh t de g r e e s w a sdeterm ined by s imula t ing the ent i re dynamic s i tua t ion on an analogcomputer and varying the per t inent parameters .

These d i s turbances

The reac t ion- jz t

The magni tude of the ini t ia l t rans ient e r r o r depends upon the je tre sponse t ime a s we l l a s upon the thrus t , a s i s also affected bythe deadband and the d egr ee of damping. The res po nse of peroxideje ts and valves capable of d elivering m o re than 500 pounds of thrustwas a t f i r s t found to be of the or d e r of 100 m s turn- on and turn-offt ime. Accordingly, the je t response t im es used in the analys is of thef i r s t sy s te ms and specif ied as a req ui rement to the j e t suppl ie r were110 m s deadt ime and a ota l of 130 m s fo r th rus t to r each 90 pe rcentof f ina l value fo r both turn -on and turn-off .with valu es of deadband and rat e gain which would give re aso na bleaccura cy, the minimum al lowable reac t ion je t thru s t w as de te rminedto be ju st ove r 500 pounds. It wa s found, how ever, that when thesy st em of pitch, yaw, and rol l je ts we re plumbed, some supplypr es su re in te rac t ion ex is ted and that any s ingle j e t th rus t %vasl ow e r if othe r j e t s were turned on.ment ioned d i s turbances to occur at ignit ion in all a xe s .t ion could requ ire many jets to f i re s imultaneously and thus momentar i lyreduce th e th rus t capabi li ty of individual je ts .it was de termined tha t the thrus t leve l of ea ch je t was to be at l e a s t510 pounds and that th e th ru st lev el of a je t acting individually wa s tobe 570 pounds.

With thi s respo nse , and

It is poss ib le fo r the a fore -Such a condi-

Under thes e condit ions ,


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The dynamic p r es su re under cons idera tion at th is t ime was equivalen?:to a n ignit ion alt i tude between 100,000 and 130,000 feet .t r a j ec t o ry in format ion fo r d i f fe ren t l aunch ang les ind ica ted tha t thed y n a m ic p r e s s u r e s o m e t im e s r e m a in e d c o n s ta n t o r e v e n i n c r e a s e dslightly after ignition at the p roposed a lt i tudes, the dynamic p r es su re ,q , was held constant in the analog s imulat ion fo r 10 seconds af te rignition.

Since the

It was found that a q of 40 psf could be allowed a t ignition.

Once the je t s ize was determined, the combined pi tch and yaw fuelconsumption was co nsid ered. With pr op er choice of deadband andrate gain, the fuel consumption during burning could be made depend-ent only upon the dis t urba nce moment , thus minimizing the requiredimpulse . During the pe r iod a f te r the engine th r us t has decayed to alow value ( 8 t o 10 second s), the fuel consumption rate depends uponma ny things, chief amon g which a r e t he j e t t h r u s t an d t ime response .It was found that unless t h e sys te m deadband was in c reas ed to a nundes i rab ly la rge va lue , the je ts se lec ted to prop er ly con t ro l thein i t i a l t r ans i en t consumed m ore fuel dur ing the s hor t coas t pe r iodthan could be allowed.hys te r es i s in the switch ing c i rcu i t , and the va r ious l a gs assoc ia tedwith the gyros and e lectro nics a l so contr ibuted to the impulse consump-t ion rate.

The amount of ra te gain employed, the

The conf lic t in req u i rem ents fo r the in i t ia l "capture" and fo r economyin fue l made it n e c e s s a r y t o c o n sid e r c ha ng in g th e s y s t e m th r u s tlev els between ignit ion and the c oas t perio d.employed was to use h igh je t th rus t fo r a few seconds af ter ignition

The solution finally

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to m i n i m ize i n i t ia l tr ans i en t e r ro r s and t hen t o r educe t he t h ru s t fo rthe rema ind er of the second- stage operat ion.l eve l was accompl i shed by using two n it rogen pr es su re reg ula tors se ta t di f fe ren t l eve l s s o t ha t each would f orce hydrogen peroxide to thej e t s a t a di f fe ren t rate.a v e r y smal l ni t rogen tank which would be depleted rapidly.of its shape, th is tank is called a "toroid". When the toro id tank ischarged , the perox ide tanks a re pres su r i zed t o t he con tro l l eve l ofi ts r egu l a t o r because it has the highest set t ing.second regula tor , which i s connected to the norm al l a r ge n i t rogentanks , acts as a check valve and does not supply gas.p r e s s u r e d e ca y s to a leve l which would cau se t he output of its r egu l a t o rto fall below the pr es su re se t t ing of the o ther regula tor , gas is sup-p l ied f ro m t he m a i n tanks a t the l ower pr ess ur e . The to ro id wi th ano rm al c harg e expels a n amount of fuel equivalent to 3080 lb -sec ofi m pu l se .personnel ) i s t ha t i t is pas sive and no swi tching i s n e c e s s a r y .

The change in th rus t

The h igher p r es su re dev ice was connec ted toB ecause

In this condit ion the

When the toroid

The advan tage of this sch em e ( f i r s t suggested by NASA

Thi s sc he me provided two single je t thr us t leve ls of 570poundsminimu m and 475 pounds nominal.deadbands of 14 m r , posi t ion-to -rate gain rat io of 2 .5 , and a l a gne twork , the t rans ie n t behavior and fue l consumpt ion we re sa t i s fac tor y .The pos i t ion- to- ra te ga in ra t io i s oft en r e f e r r ed t o a s the "switchingl ine s lope", bec aus e of i t s s igni f icance when the cont rol pe rfo rm an cei s analyze d on the phase plane.incorpo ra ted jus t p r io r to l aunching the f i r s t vehicle .was not in tended to improve the cont ro l s ys t em ( in fac t it had a dele -ter iou s effect) , but it was r equi red to reduce the expec ted effect of

In conjunction with pi tch and yaw

The lag network ment ioned wasThe ne twork

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harmfu l noise p ickup in the ra te gyro channe l dur ing th i rd- s tageburning.

On the f i r s t flight,pre sen t dur ing second-s tage ope ra t ion; on l a ter f l ights it was switchedin to the c i rcu i t a t thi rd - s tage igni t ion.

th i s l ag , a s i m p l e t ime constant of 17 m s, w as

The calculated behav ior of the seco nd- stag e pitch and yaw contro lsys tem used on the f i r s t SCOUT f l ight can be s ee n f ro m the t imeresp ons e and fue l consumption shown in f igures 32 and 33.SCOUT f l ight di f fered somewhat in tha t it had no lag network ands l ight ly fas ter j e t r e s p o n s e s , so t ha t its pe r f o r m a nc e w as better thanthat shown.tha t f o r a t t i t ude t ime re spon ses in which the in i t i a l t r an s ien t is ofp r im a r y im por t a nc e , t he s ys t e m dea dband is mad e 10 pe rce ntg r e a t e r t ha n nom ina l and t he r e a c t i on j e t t h r us t u s e d is the minimumvalue allowed by the specif ications. When fuel consumption is cal-culated, the deadband is made 10 pe rc ent too na r row and the thr us tis inc rea sed to the high s ide of the tole rance .soon af ter igni tion becau se it t ends to de c re ase fue l consumption .Note tha t in both f igures the j e t s begin s teadi ly puls ing immedia te lyaf te r engine burnout occurs .typ ical of the behav ior i n actual f l ight, but ra th er it r e p r e s e n t s t hemos t se ve re condit ion poss ib le.plot ted, one each fo r condi tions of fu l l engine th rus t misa l ignment ,f o r 1 /2 G i m e s maxim um thru s t misa l ignment , and for nomisa l ignment .tota l pi tch and yaw impulse can be shown to be e i the r the s u m of the

The second

The per t inent condi t ions a r e marked on the grap hs . Note

Also q is r e mo v e d v e r y

This s i tua t ion is not intended to be

In f igure 33 thr ee curves have been

The reason for making thre e cur ves is t ha t m a x im um

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I

maxim um and the ze ro misa l ignment cu rv es o r doub le the 1 /2misa l ignment cu rve .t h e i n i t i a l t r a n s i e n t i s tha t of the s tee p p a r t of the cu rves .eng ine th ru s t ( and , hence , misa l ignment magn i tude) de c r ea se s nea rburnout , the impu l se r a t e is at tenuated s l ight ly and then cont inues a t an ew r a t e d e t e r m i n e d by t h e c o n tr o l p a r a m e t e r s a b ov e .is conse rva t ive if t he max imum impul se consumed is double thatg iven by the 1 /2mo s t s ev ere d i s tu rb ing e f fec ts o ccur when the eng ine th ru s t mis-a l ignment is maxim um and l i e s d i r ec ted hal f way be tween the p i t chand yaw planes .t imes a s m u c h i m p u l se a s does the d i s tu rbance .misa l ignment in one p lane and ze ro in the o the r used the g re a t e rquan ti ty of fuel it would indicate that the deadband had been se t toonar row.e f f ect of gy ro dynamics , e l ec t ron ic l ags , and swit ching hy s te r es i sequa l to f ive pe rc en t of t he deadband.

EThe amoun t of impu l se r equ i r ed to ov ercom e

As the

Th e sy s t e m

=misal ignment curve . T h e r e a so n in g is tha t the

In th is condit ion each je t m us t produ ce 1/2 fiIf the case of full

The s imula t ions which genera ted the se cu rves inc luded the

Although it was apprec ia t ed tha t s t ruc tu r a l f l ex ib i li t y wou ld no t p r e -s e n t a s t ab i l i t y p rob lem on the upper s t age s as i t had on the f i r s t , i t se f f ec t s on fue l consumpt ion were cons ide red b r i e f ly .p i t ch o r yaw j e t is f ir ed , the body bending mode is exci ted whicht r a n s m i t s a h igh f r equency s e r i e s of loca l a t t i t ude changes to the gyrosIf t h e s y s t e m is c lose to the edge of the deadband ( a s i t a l w a y s i s whena j e t is f i r ed ) , t he r esu l t ing gyro pickup ma y su f f i ce to keep the je tt u rned on fo r a sh or t add it iona l t ime o r ma y tu r n i t o ff.t he f eedback f ro m f lex ib le mot ion c aus es the oppos ing j e t t o be tu rnedon br ief ly .

When a l a r g e

In s o m e c a s e s

Such ef fects do not s igni f icant ly a l te r the no rm al fuel

R - E D 11117- 76 -


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consumption calculat ions.

Se lec t ion of Ro l l Con t ro l Pa ram ete r s fo r Fi r s t Two Vehicles

The second- s t age ro l l con tro l sys t em was the same fo r the f i r s t twof l ights. The ro l l axis pose s much l e s s a des ign p rob lem than do theother two beca use the je ts can be made sm al l enough to ren der fu elconsumption almost negligible.a r e those caused by misal ignment of the lar ge r p i tch and yaw je ts .Th e se d i s t u r ba n c e s can introduce a ro l l moment i f t he i r l i ne of act iondoes not pa ss through the vehicle cente r of m a s s .the cen te r of m as s was assum ed to be a t m o s t 0.25 i nch f r om thecenter l ine .to be compatible with the center of mass uncer t a in ty wer e t aken tobe 0.125 inch.lay within 0.125 inch of the vehicle cen ter l ine , and in addit ion, a0.10-degree a ngula r to lerance was a llowed. S ince a t mo st one yawand one p i tch je t can f i r e a t one t ime, the maxim um rol l ing momentinduced was calc ulated by considering that both of thes e je ts w er ef i r ing and that the cen ter of m a s s l ay 0.25 i nches f ro m the cen te r l inein a dir ect ion half way between the pi tch and yaw planes .each j e t a n e f fec t ive mom ent a r m of 0.330 inch , and consider ing thatthe i r t h ru s t was 10 pe rcen t greater t han nomina l , t he max imum ro l lmoment was de te rmined to be 38. 3 f t - lbs .nec ess a ry to overcome th i s moment and hold the t r ans ien t e r ro rwithin l imits was found to be 24 pounds if a 14 m r deadband was used .The t ime r e sp o n se s f o r t h e se s m a l l e r j e t s w e r e c o n s id e r ab l y lessthan those fo r the p i tch and yaw m otors .

The only s igni f icant ro l l d is turbances

The location of

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