- NASA Contractor Report 172481

Impact of Magnetic Isolation- on Pointing System Performance

in the Presence ofStructural Flexibility

J. Sellers

- Sperry CorporationPhoenix, Az 85036

'_...

Contract NAS1-16909,Task Number 2

February 1985 LI _._!_Y _PY

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LIBRARY,NASA "- - "HAML_iON_=yJRGI_NI__

, NationalAeronauticsand-- SpaceAdministration

LangleyResearchCenterHampton. Virginia 23665 .

https://ntrs.nasa.gov/search.jsp?R=19850018550 2020-03-20T19:30:09+00:00Z

SPERRY CORPORATIONAEROSPACE & MARINE GROUPP.O BOX 21111PHOENIX, ARIZONA 85036-! 111TELEPHONE (602) 869-2311

May 21, 1985

File" A0.1700

Subject: NASAContractor Report 172481

Reference" NASI-16909Task Order No. 2

NATIONALAERONAUTICSANDSPACEADMINISTRATIONLangley Research CenterHampton, Virginia 23665

Attention: Mr. Richard ShislerM/S 126

Dear Mr. Shisler"

Distribution has been completed in accordance with the enclosed distributionlist for NASAContractor Report #172481entitled "Impact of MagneticIsolation on Pointing System performance in the Presence of StructuralFlexibility".

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[hR.E.'_aqIaceContractManagementRepresentative

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DISTRIBUTIONLIST

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!i

NASA Contractor Report 172481i|!!| Impact of Magnetic Isolation

on Pointing System Performance| in the Presence of

| Structural Flexibility

J. Sellers

Sperry Corporation- Phoenix, Az 85036i

Contract NAS1-16909,

, Task Number 2February 1985

!

l IXlASAI National Aeronautics andSpace Administration

i LangleyResearchCenter• , Hampton.Virginia 23665

I SUMMARY

l The Advanced Gimbal System (AGS) is an end-mount, three-axis gimballedpointing system designed for use in the Space Shuttle, while the Annular

i Suspension and Pointing System (ASPS) is an AGSwitha six-degree-of-freedom

magnetic system incorporated at the top of the gimballed pointing system. One

major difference in the pointing performance of these two systems is that theAGSdoes not provide translational isolation; hence, at frequencies above its

control bandwidth, base translational motion couples directly into payloadpointing error. The ASPS, on the other hand, provides high-frequency attenua-

tion (isolation) that is a function of the form bandwidth of the ASPSVernier

I System (AVS) translational controllers.

I Models of these two systems were developed from NASTRANdata, stabilized,and verified. Each was excited with a unity force input at the base of the

i ointing system, and a transfer function relating the output pointing angle tothat input was developed. These two system responses were examined and their

similarity to theoretical responses was noted. This agreement provided

I confidence that the models were indeed correct. The low-frequency asymptote ofthe ASPSresponse was 60 decibels lower than that of the AGSresponse, the major

i reason being that the AVS pointing loop is closed at a higher bandwidth than isIthe AGSelevation axis controller. Structural flexibility was the determining

i factor for the AGScontroller bandwidth, while the ASPSstability was lessaffected by this flexibility. The Shuttle dynamics were then added to each

i model and the transient time response caused by a Shuttle VRCSjet firing wasobtained. The peak value ofthe AGSdisturbance response is 7.4 arc seconds,

while that of the ASPS (obtained by correlating other system performance data)

I is approximately 0.007 arc second.

I The use of magnetic suspension to separate the payload and pointing mountdynamics, as provided by the ASPS, reduces the detrimental effects of structural

i lexibility on the maximumachievable system controller bandwidth. Thus, with ahigh controller bandwidth, better disturbance rejection capability and pointing

performance is achieved.

ll

II TABLEOF CONTENTS

I Page

I LIST OF FIGURES ii

i LIST OF TABLES iiiLIST OF ACRONYMSANDSYMBOLS iv

I BSTRACT 1INTRODUCTION i

I DEVELOPMENTOF FLEXIBILITY MODELS 6

I evelopment of Flexible AGSModel 8Development of Flexible ASPSModel 14

CONTROLLAWANDSIMULATIONDEVELOPMENT 27

i, Design of AGSControl Law 28Design of ASPSControl Laws 36

! -AGS PERFORMANCEEVALUATION 42

ASPS PERFORMANCEEVALUATION 44

I CONCLUDINGREMARKS 56

i REFERENCES 57

!l!!!

I

|n LIST OF FIGURES

I Figure Page

i I Advanced Gimbal System (AGS)................................. 42 Annular Suspension and Pointing System (ASPS)................ 53 Open-Loop Transfer Function Relating Output Pointing Angle

to Applied Elevation Gimbal Torque ......................... 7

i 4 Planar Model of AGS-Payload Configuration .................... 105 Shuttle Center-of-Mass Location and Payload Bay Location ..... 116a AGSBlock Diagram............................................ 15

i _b _S BlO_d_a_a_S_ont ) ..................................... _anar Configuration ...........................8a ASPSBlock Diagram........................................... 238b ASPSBlock Diagram (cont) .................................... 24

i 9 Uncompensated AGS Plant Transfer Function .................... 29I0 AGSOpen-Loop Transfer Function .............................. 32ii Nyquist Plot of AGSOpen-Loop Transfer Function .............. 33

i 12 Phase-Stabilized AGSClosed-Loop Transfer Function ........... 3413 AGS Pointing Error for Unity Base Input ...................... 4314 AGSTime Response to 0.24 Second, Shuttle VRCSYaw Maneuver.. 4515 ASPSFrequency Response for AGSBase Input - No Error in

i CMOffset Estimate, No Payload Flexibility ................. 4816 ASPSFrequency Response for AGSBase Input - -i PercentError in CMOffset Estimate, No Payload Flexibility ........ 49

I 17 ASPSFrequency Response for AGS Base Input - +I PercentError in CMOffset Estimate, No Payload Flexibility ........ 5018 ASPSFrequency Response for AGSBase Input - No Error in

CMOffset Estimate, No Payload Flexibility ................. 51

i 19 ASPSFrequency Response for AGSBase Input - -I PercentError in CMOffset Estimate, No Payload FlexibilityIncluded ................................................... 52

i 20 ASPSFrequency Response for AGSBase Input - +I PercentError in CMOffset Estimate, Payload FlexibilityIncluded ................................................... 53

!!

i iio

!

II LIST OF TABLES

I Table Page

I Numerical Values Used in the AGSStructural Model............ 17

i II Numerical Values Used in the ASPSStructural Model........... 25III Results of ASPSCMOffset Study .............................. 54

IIIIIII!IiII!i iii

I

I LIST OF ACRONYMSANDSYMBOLS

I Coordinate Systems

. Xo,Yo,Zo Shuttle coordinate system axesX,Y,Z AGS-ASPScoordinate system axes

I Acronyms

i AGS Advanced Gimbal SystemASPS Annular Suspension and Pointing System

i AVS ASPSVernier SystemBMF Bending Mode Filter

I CDC Control Dynamics Company

CG Center of Gravity

l CM Center of Mass

I DOF Degree of FreedomGSA General Stability Analysis

I HW HardwareIRU Inertial Reference Unit

i kip kilopound

MBA Magnetic Bearing Assembly

I MJA Mountingand JettisonAssembly

J NASTRAN NASAStructural AnalysisP-I-D Proportional Plus Integral Plus Derivative

I Payload MountingPMS Structure

PPA Payload Plate Assembly

I RPS Radiansper Second

i SW SoftwareVRCS Vernier Reaction Control System

i iv

l LIST OF ACRONYMSANDSYMBOLS(cont)

I Symbols

I Bi Term proportional to damping of i th mode (rad/sec)e Natural logarithm base (dimensionless)

I ni i th modal coordinate

n i' Component of ni due to controller input

i hi" Component of ni due to disturbance input

FXT AVSforce along X-axis (pounds)

I FZT AVSforce along Z-axis (pounds)

l J Momentof inertia (slug-in 2 or slug-ft 2)KI Spring stiffness in MJAmodel (kip/in.)

D Spring stiffness in MJAmodel (kip/in.)K2

Ki Square of i th eigenvalue Xi (rad/sec) 2

l KI Integral gain in controller (rad/sec)

Kp Proportional gain in controller (units vary)

I hi Payload CMoffset in Z direction (inches)

I _2 Distance between elevation gimbal axis and AVSactuator plane(inches)

i _MA Distance between shuttle CMand AGSbase along shuttle roll axis(inches)

_i Eigenvalue of i th mode (rad/sec)

i M Mass (slugs)

l _I Break frequency of lead network (rad/sec)_2 Break frequency of lag network (rad/sec)

I _i,j jth component of i th eigenvectorQ Quality factor (dimensionless)

U R GSAsimulation data variable

I V

I

I LIST OF ACRONYMSANDSYMBOLS(cont)

I S Laplacian operator (rad/sec)

I t d System time delay (seconds)09 AGSmodel output angle (radians)

I 09C AGSmodel commandangle (radians)09A AGSoutput angle in ASPSmodel (radians)

I OCMD AVS pointing loop commandangle (radians)

0s Shuttle small angle rotation about Yo (radians)

i Oy9P AVS pointing loop output angle (radians)

I TOp AVS pointing loop torque command(in.-Ib)U Generic system input vector

I UD input (pounds)AGSbase force

UE AGSelevation gimbal torque output (in.-Ib)

I X9A AGSnode 9 X-displacement in ASPSmodel (inches)

i X9p AVS node 9 X-displacement in ASPSmodel (inches)Z9A AGSnode 9 Z-displacement in ASPSmodel (inches)

I Z9p AVS node 9 Z-displacement in ASPSmodel (inches)_i Damping factor associated with i th mode (dimensionless)

I

vi

!

I ABSTRACT

I A study has been conducted to compare the inertial pointing stability of a

gimbal pointing system, the AGS, with that of a magnetic pointing and gimbal

I follow-up system, the ASPS, under certain conditions of structuralsystem

flexibility and disturbance inputs from the gimbal support structure. Separate

I hree-degree-of-freedom (3DOF) linear models, based on NASTRANmodal flexibilitydata for the gimbal and support structures, were generated for the AGSand ASPS

configurations. Using the models, inertial pointing control loops providing

I more than 6 decibels of gain margin and more than 45 degrees of phase margin

were defined for each configuration. The pointing-loop bandwidth obtained for

I more twice the level achieved for the AGSconfiguration. Thethe ASPSis than

AGSlimit can be directly attributed to the gimbal and support structure

I lexibility. As a result of the higher ASPSpointing-loop bandwidth and thedisturbance rejection provided by the magnetic isolation, ASPSpointing

i erformance is significantly better than that of the AGSsystem. Specifically,the low-frequency (non-modal) peak of the ASPStransfer function from base

disturbance to payload angular motion is almost 60 decibels lower than the AGS

I low-frequency peak.

I INTRODUCTION

I In the last decade, firm definition has emerged for many of the payloads to

be flown on various Shuttle missions. Characteristics of several types of these

I payloads clearly dictate the need for sub-arc second pointing stability in the

presence of undesired system disturbances, such as astronaut motion and Shuttle

I VRCSjet firings. In the classical sense of control system theory, one couldsimply increase the bandwidth of the payload pointing system controller(s) until

I the desired disturbance rejection capability is achieved, while, of course,maintaining a stable system. This stipulation places an upper bound on the

disturbance rejection capability of such a system from a purely theoretical

I standpoint. Whenusing a system such as the Advanced Gimbal System (AGS), a

high controller bandwidth is desired for the purposes of disturbance rejection;

I 1

i however,no translationaldisturbancerejectioncan be achievedat frequencies

above the controllerbandwidth. One major reasonfor this lies in the fact that

I the AGS providesa solid link - a moment arm - betweenthe Shuttle-AGSbase

interfaceand the payload. Thus, high-frequencybase vibrationcan and will

i transmitdirectlyto the payload,and the controller(s) do littleinsystem can

the way of attenuatingor rejectingsuch a disturbance.

I Anothermajor systemcharacteristicthat will impactthe maximumallowable

l bandwidthof the system is the structuralflexibilityof the systemitself.This flexibilityencompassesbendingmodes whose frequenciesare a functionof

the stiffnessof the supportingstructure,the lengthsof the individual

I structuralcomponents,and the size of the supportedpayloaditself. Thesemodes presentthemselves,in the frequencydomain,as highlyunderdampedpoles

l whose amplitudedependsupon the dampingfactor (usuallyassumed)associatedwith that particularmode, and, in the time domain,as ringingeffectswhose

i frequencyof oscillationis the modal frequency. In addition,when consideringsystemstability,the peakingassociatedwith a bendingmode will usuallyforce

the reductionof the systembandwidth. This fact is due to the gain-phase

l characteristicsof the mode at frequencieswhich are very close to the modal

frequency. At these frequencies,the gain is higherthan is the rigid-body

i response;however,the phase drops off and reversesby 180 degreesas thefrequencyof interestapproachesand then exceedsthe modal frequency. In other

I words, if the open-loopcrossoverfrequencyis sufficientlyclose to the modalfrequency,the phase drop associatedwith the mode will decreasethe available

phasemargin at the crossover. This detrimentalresultforcesa decreasein the

i value of the open-loopcrossoverfrequency,which furtherreducesthe closed-

loop bandwidth.

!The payloadsize and the lengthand stiffnessof the membersof the

I supportingstructureplay a large role in determiningthe valuesof the modalfrequencies. Assuminga constantstiffnessvalue for these members,increasing

their lengthswill decreasethe modal frequencies. Furthermore,assuminga

I constantstiffnessand lengthfor each member,increasingthe payloadmass/

m 2

I inertiawill also decreasethe modal frequencies. It can, therefore,be seen

that the AGS structureand payloadcharacteristicsare importantin determining

I the modal frequenciesand, consequently,the systembandwidth.

l Severalplausiblealternativesexist which will reduce,to a certainextent,the determentaleffectsof structuralflexibilityon pointingperfor-

I mance. One solutionis to manufacturethe structurefrom a stiffermaterialwhich will tend to increasethe modal frequencies. The drawbacksassociated

with this method are the additionalexpenseand also the fact that there is

l still no translationaldisturbancerejectioncapabilityat frequenciesabove the

controllerbandwidth. Anothersolutionis to includea bendingmode filter

i as part law; however, more does not(BMF) of the control this refinedcontroller

cure all of the flexibilityproblems. The disadvantagesassociatedwith this

I method are: 1) the locationof the modal frequenciesis not preciselyknown andthe structuraldampingcan only be assumed,leavinga degreeof inaccuracyin

i the controllaw; 2) the coefficientsof the BMF are only accurateat the systemattitudesfor which structuraldata are available,forcingthe use of a

digitally-implementedtrackingalgorithmin a gimballedsystemwhere bending

I mode frequenciesand shapes vary with the gimbalangle;and 3) there will stillbe no translationaldisturbancerejectioncapabilityat frequenciesabove the

I controllerbandwidth. Anotheralternativeis to use a systemsuch as the ASPSVernierSystem(AVS) in conjunctionwith the AGS to form a pointingand

i isolationsystem,the AnnularSuspensionand pointingSystem(ASPS). Figures1and 2 illustratethe major featuresof the AGS and ASPS, respectively.

l The AVS is a six-degree-of-freedeompointingsystemcomposedof two

noncontactingsections- a statorand an armature. The statoris rigidly

I attachedto the top-mountingstructureof the AGS, and the payloadis attachedto the armature. Six magneticbearingassemblies(MBA) provideactivecontrol

l over the six degreesof freedomof the levitatedpayload. The controllawassociatedwith each axis can be independentlyimplemented. Couplingbetween

translationand rotationis significantlyreducedin the AVS througha unique

I decouplingscheme incorporatedintothe systemdesign (ref 1). The AVS, most

importantly,can attenuatehigh-frequencytranslationaleffectsdue to the soft

I interfacebetweenthe armatureand stator.

m 3

Ii ROLL GIMBAL

IELEVATION

D LATERALGIMBAL GIMBAL

g SEPARATIONMECHANISM

IIII $715-8-1

B Figure1AdvancedGimbalSystem (AGS)

ASPSVERNIERSYSTEM(AVS)

J

AGS

$715-8-2

Figure 2Annular Suspension and Pointing System (ASPS)

5

The previousdiscussionhas emphasizedthe effectsof the structural

_ flexibilityof the AGS on payloadpointingperformance. However,when the AVS

is used in conjunctionwith the AGS, the structuralflexibilityof the

armature/payloadassemblyhas to be consideredin additionto that of the AGS.

This is due to the natureof the AVS translationaland rotationalcontrollaws.

The AVS translationalcontrollersare designedto keepthe armature/payload

centeredin the magneticbearinggaps. However,if the armature/payload

assemblyflexes,this motion is also sensedby the translationcontroller.

Therefore,payloadflexibilitycouplesinto the translationalcontroland hence

into the AVS pointingsystemdynamics.

In this section,an attempthas been made to give a qualitativeexplanation

of the effectsof structuralflexibilityon the pointingperformanceof the AGS

and the ASPS. In the following sections, NASTRANdata will be used to develop

planar models of the AGSand the ASPS. These models will then be used to

evaluatethe merits and performanceof each system in the presenceof a

disturbanceenvironment.

DEVELOPMENTOF FLEXIBILITY MODELS

This sectionis concernedwith the developmentof the linear systemmodels

-- to be used in the study and analysisof the effectsof structuralflexibilityon

the pointingperformanceof the AGS and the ASPS. The approachtaken will be to

use rigid link "stick"models with compliantinterfacesto characterizethe AGS

structure. The mountingstructurebetweenthe base of the AGS and the Shuttle

is modeledby a mass-doublespringarrangementshown as Figure 6.3.14in a

ControlDynamicsCompany(CDC)study done for the NASA MarshallSpace Flight

Center and Sperry FlightSystemsin March, 1982 (ref 2). This responseis

redrawnin Figure 3 for reference. A Bode plot of the mass-doublespringmodel

responseis also shown in Figure3. A frequencydomain expressionthat can be

-- used to approximatethe mass-doublespring responseis as follows:

6

-80

-100

-120

z -140

-16o . _ _ _SPRING MODEL

-180

-200

0.1 0.5 1.0 5.0 10.0

FREQUENCY (Hz) S715-8.3

Figure3Open-LoopTransferFunctionRelatingOutput

PointingAngle to AppliedElevationGimbal Torque

8.78 x 10-6 1.316 x 10-5 1.038x 10-5

S2 S2 + 1.75S+ 6906 S2 + 5.5S + 11881

The Q of the first flexiblemode is equal to 40, while that of the secondmode

is 20. As can be seen from this expression,the two flexiblemodes are

superimposedon top of the rigid-bodyresponsewhich is 1/Js2. Also, by

comparingFigure3 of this reportwith Figure6.3.14of reference2, it can be

seen that the first two modal frequencies,as well as the peaks,are in good

agreement.

The payloadused in both systemstudiesis a flexible,20-hertzbody,

meaningthat, if such a body were to be used as a cantileveredbeam and then

struck,the frequencyof oscillationwould be 20 hertz. For the AGS model, this

payloadis rigidlyattachedto the supportingstructure(free-fixed);for the

_ ASPS, the payload/AVSarmaturebody is suspendedabove the AGS-AVSstatorbody

(free-free). Thus, for the ASPS model, two sets of modal data are required-

one for each separatebody.

The above discussionmerely providesa brief descriptionof the hardware

- and systemplants. In the next two subsections,planarmodels of each system

will be developed,structuraldata in modal form (obtainedfrom NASTRANruns)

will be used to developa plant model of each, and system blockdiagramswhich

incorporatethese plantmodels will be developed.

Developmentof FlexibleAGS Model

The AGS utilizesthree gimbalsto providethree-degree-of-freedompayload

motion,one about each gimbalaxis. However,for the purposesof this study,

the motion will be restrictedto a single-degree-of-freedomrigid-bodyrotation

about the AGS y-axis (elevationgimbal axis) in the X-Z plane. Such a model is

simplerto analyzethan a completethree-degree-of-freedommodel,yet will

neverthelessyield useful,relevantresults.

8

!A planar model of the AGS-payload configuration is shown in Figure 4. The

i pertinent links to be used in the model are as labeled on the figure. As statedearlier, the MJA is modeled by a mass-double spring. The spring denoted by K1

has a stiffness of 40 kilopounds per inch, while the spring constant K2 of the

i second spring is 160 kilopounds per inch. The mass M is a 12-slug mass. Forfrequency responses, the system input is a force of unity value at node ii. For

I time-response runs, the input is a VRCSpulse that is applied to the Shuttle(node 12). It is desired to determine how Shuttle motion affects the motion of

I the mass M.

The first step in the solution of this problem is to determine how forces

I and torques at the Shuttle Center of Mass (CM) create AGSbase motion. A

drawing of the Shuttle, which locates its CMrelative to the envelope of the

l payload bay, is shown in 5. The Shuttle shownFigure axes are as on the figure,

with the axis Yo completing a right-hand system. It is necessary to determine

I the distance between the Shuttle CMand the AGSbase along the Shuttle roll axisXo. Assuming that the AGSis mounted 17.5 feet behind the front portion of the

i payload bay, with the elevation gimbal axis being parallel to the Shuttle rollaxis, then using the dimensions on Figure 5, the desired moment arm length is

[1147 - (682 + 17.5 x 12)] inches, or 255 inches. This distance is defined as

I _MA- recognized that, normally, the elevation axis is transverse to theIt is

Shuttle roll axis. However, since AGSNASTRANdata are available only at the

l (0,0,0) degrees gimbal attitude, a Shuttle pitch maneuver (used in otherstudies) would not produce an AGSpointing disturbance. Thus, for this study,

i the elevation gimbal axis will be considered to be parallel to the Shuttle rollaxis. Now, if a VCRSyaw maneuver (small angle rotation about Zo) is performed

and defined as 0s, the AGSbase displacement along the Shuttle Yo axis is

I I _MAOsI inches. This base displacement shoves against the 12-slug mass in

Figure 4 by compressing the spring whose stiffness is K2, in turn exciting the

l flexible AGSstructure. Since Shuttle motion in this direction would cause theAGSto tip about the elevation gimbal axis, the gimbal controller would try to

I correct this error. Thus, the dynamics of the Shuttle-pallet-AGS interfacesthat cause AGSflexible-body motion have been described and will be used in both

the AGSand ASPSmodel development. It is now necessary to describe the AGS

!I 9

!

III z

/-vPAYLOAD CG

I (10)

X

I| ..

II

I - -T (9) TOP OFPPA/PMS

/I • (8) ROLLGIMBALCG

I (7)I • (6)

qr (5) LATERALGIMBAL__

I _1_ (4) ELEVATION GIMBAL _.

(3)

I Ir (2) EXTENSIONBRACKETS

I (.__(J_t_) K1 M K2 I_(11) _ SHUTTLE

II /////////MJA MODEL

| .- $715-8-4

I Figure4PlanarHodel of AGS-PayloadConfiguration

| 1o

DYNAMIC ENVELOPEIN THE ORBITERCARGO

BAY__._" LENGTH 60 FEET

_ ..... Z 0 =

15 FEET 400 IN.

i

ZSTATION Xo = 682 IN. TATION Xo = 1302 IN.

100%= • JET FORCE TYPICAL ORBITER CENTER OF MASS=-.,P" | | AND TORQUE XO = 1147 IN. PRINCIPAL MOMENTS OF INERTIA -

._1 I Zo = 389 IN. Ix = 0.8098 x 106 SLUGoFT2

0 _ ly = 6,2869 x 106SLUG-FT 2Iz = 6.5488 x 106 SLUG-FT2BURNTIME

PEAK FORCES AND TORQUES

BURNVRCS TIME Fx Fy Fz Tx Ty TzAXIS (SEC) (LB) (LB) (LB) (FT-LB) (FT-LB) (FT-LB) MASS= 5794.1 SLUGS

ROLL 0.24 0 -41.42 44.12 504.0 0 0

PITCH 0.24 0 0 50.1 0 -1830.5 0

YAW 0.24 0 8.6 19.1 0 0 1914.7

$715-8-5

Figure5ShuttleCenter-of-HassLocationand PayloadBay Location

plant in modal coordinate form and to use the resulting model as the plant in anoverall AGS system model.

For this particularstudy,the AGS plant will be describedby one rigid-

body mode (single-degree-of-freedom)and two prominentflexible-bodymodes. The

outputsof these three modal paths are summedtogetherto form the total

r flexible-body motion. Such a representation can be viewed as being a partial

fraction expansion of the plant transfer function, which means that the fidelity

of the model can always be increasedby appendingadditionalmodal dynamicsinparallelwith the existingones. Also, an importantpointto be made is that,

due to the parallelstructure,one modal output can and will excite all other

systemmodes throughthe feedbackcontrollaw.

The modal equationsthat describethe AGS flexible-bodymotion are of theform

[S2 + Bi S + Ki] ni : [€i ]T_ (I)

where Bi is relatedto the dampingassociatedwith the ith mode, Ki is the

squareof the ith eigenvalue_i, 6i is the ith eigenvectorassociatedwith _i,

and U is the systeminput vector. The variableni is the modal coordinate

associatedwith the ith mode. The right-handside of equation(1) describeshow

the variousmodes are excitedby the input_. The ith eigenvectorcontainsN

components,where N is equal to the numberof nodes in the model multipliedby

the degreesof freedom. Since this is a planaranalysis,each node has three

degreesof freedom; X, Z, and O; NASTRANoutputsare in that order at each

node. Thus, for the AGS, the eigenvectorfor each mode has 33 elements(11

nodes times 3DOF).

For this model,the desiredsysteminput is the single-degree-of-freedom,

rigid-bodyrotationabout the elevationgimbal axis. By studyingFigure4, it

_ can be seen that this inputwould be appliedas +UE at node 4, while the

reactiontorque on the structuredue to this inputwould be appliedas -UE at

12

I node 3. Using these facts and equation(1),the equationfor the desired

I responseportion(qi') for the ith modal coordinate_i is

, (6i,26- 6i,25) UE

I qi : S2 + Bi S + Ki (2)

I To completethe structuralmodel,the of the to undesiredresponse system an

base input (UD) must be included. Again,by using Figure4 as a reference,the

i ase disturbanceinput UD will be appliedat node 11 in the X direction;thus,the equationfor the disturbanceresponseportion(hi")of the same ith modal

i coordinateis

6i 11 UD

| -- ,hi" S2 + Bi S + Ki (3)

I The ith modal coordinateni is the sum of the two componentsgiven by equations

(2) and (3) and is

II II

I ni = ni + ni (4)The rotational motion of node 9 is the output of interest (inertial reference

I unit is locatedat this point)and is given by the expression

i 09 = s6i, 9 ni ; i = 1,2,3 (5)

I This angle is sensedby the inertialreferenceunit (IRU),fed back, and iscomparedto the con_andedangle 0c. The resultingerror signalis then used by

i the systemcontrollerto producethe desiredsystemcommand. In equationform,

UE : G(s) [g9c - g9 ] (6)

!where UE is as used in equation (2); and G(s) is a cascaded combination of the

i levationgimbal controllerGE(S),a bendingmode filter (BMF),and a Pade time-delay expression(to accountfor the phase-lageffectscaused by the digital

I implementationof the controllaw). 13

l

A systemblock diagramthat incorporatesall of the previousdiscussionand

derivationsis shown in Figures6a and 6b. A listingof the numericalvalues

used in the structuralportionof this model is given in Table I. The form of

_ G(s) will not be definedhere, but will be definedin the nextmajor section.

In the followingsubsectiona similarmodel will be developedfor the ASPS. It

is worth mentioning,at this point in the discussion,that the symbologyused in

the ASPS model developmentwill be the same as that used in the AGS case;

however,the subscriptsand numericalvalues used will be different.

._= Development of Flexible ASPSModel

The model of the flexibleASPS will be developedby using the same

methodologyas that used in the formulationof the AGS model. The MJA model

(whosedynamicsare describedby the expressionon page 15) is the same, as is

the additionof the Shuttledynamics. The same 20-hertzpayloadis also used;

however,it is not physicallydetachedfrom the rest of the systemand is a

-- free-freebody (as opposedto a free-fixedbody in the AGS case).

A planarmodel of the ASPS-payloadconfigurationis shown in Figure7. As

before,the pertinentlinks and nodes are definedper the figure. Note the

magnetic interface,and note also that nodes 9P, lOP, and 10 are used in the

figure. The AGS-AVSstatormotion is constrainedto the same rigid-body

rotationaldegreeof freedomabout the elevationgimbalaxis, while the AVS

armaturemotion is constrainedto three rigid-bodydegreesof freedom:

translationalmotion along the X and Z axes and rotationalmotion (8p) about the

Y-axis. Therefore,for this model, the AGS-AVSstatorwill be describedby a

singlerigid-bodymode and two priminentflexible-bodymodes while the AVS

armaturebody will be characterizedby three rigid-bodymodes (one for each

-- degree of freedom)and two priminentflexible-bodymodes. As an aside,the

eigenvectorsand eigenvaluesassociatedwith the AGS subsystemwill differ from

those used in the AGS-payloadmodel, due to the fact that the two bodiesare not

physicallyattachedin the ASPS. The eigenvectorassociatedwith each payload

_ mode has six elements (twonodes and three degreesof freedom),while the

14

I mm

COMMAND

R(30) _ _ GElS ) BMF: BMF:_ SECTION 1 SECTION 2]

GIMBAL LOOP CONTROLLER BENDING MODE FILTER

o_o,

R(35) .H HTIME DELAY: TIME DELAY:SECTION 1 SECTION 2

PADE" APPROXIMATION OF

TIME DELAY: e-ToS

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Figure6aAGS Block Diagram

P,k

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SHUTTLE MOMENT MJA-PALLETDYNAMICS ARM STIFFNESS UD

Io,.,,ii ] o.,.,,j

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POINTING ANGLE

v S2+B3S+K 3

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STRUCTURALPLANT

I

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INERTIAL REFERENCE UNIT $7158.7

Figure 6bAGSBlock Diagram (cont)

I TABLEI

NUMERICALVALUESUSEDIN THEAGSSTRUCTURALMODEL

(Obtained from NASTRAN)

I Rigid-body mode: i = 1_I = 0.0 _i : 0.0

I BI = 0.0 KI : 0.0

_1,11 = 0.0

I 61,25 = 0.0

I 1,26 = 2.921244x 10-361,31 = 2.921244x 10-3

I First flexible-bodymode: i : 2

_2 = 0.005 _2 = 73.587

I B2 = 0.736 K2 = 5415

_2,11 = -0.1167225

I _2,25 = 0.0

I 2,26 = -3.372369x 10-3_2,31 = 4.210238x 10-3

I Secondflexible-bodymode: i = 3

3 = 0.005 _3 = 113.94

I B3 : 1.1394 K3 : 12983

63,11 = -0.2201011

I _3,25 : 0.0

I _3,26 = 8.189604x 10-363,31 = -1.795968x 10-3

i

I 17

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PAYLOAD CG

il =x

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(9P)

I 181 ROLLGIMBALCG(7)

(5)

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i 12_5" (1) K M K2 I_

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I $715-8-8

i Figure7PlanarModel of ASPS Configuration

{

eigenvectorassociatedwith each AGS-mountingstructuremode has 30 elements

(ten nodes, each with three degreesof freedom). The base disturbanceinput is

at node 10 in this model and the Shuttleis node 11.

The modal equations that describe the AVS armature/payload flexible-bodymotion are of the form

[S2 + Bi S + Ki] ni : [_i]Tu i : 1,2...5 (7)

where the modal coordinatehi, dampingBi, stiffnessKi, and eigenvector6i have

the same genericmeaningas in the AGS case and the vector U is the input vector

(controlleroutputs)to the payloadbody. This vector is of the form.

r-

• , and is appliedat the base (node 9P) of this body. As before,the right side of

equation(7) describeshow the variouspayloadmodes are excitedby this input.

For the payloadmodel,the eigenvectorfor each mode containssix elements (two

nodes and three degreesof freedom)and describesthe motion at the payloadbase

as well as its CM.

- Using these facts and equations(7) and (8),the modal equationsfor the

motion of the payloadare

[S 2 + Bi S + Ki] ni = (9)

[_i,l FXT + 6i,3 FZT + 6i,5 TOP] i = 1,2...5

19

i These equations describe how the various payload modes are excited by the AVS

i controller output commands. The total payload motion in the X, Z, and 0directions is given by the following expressions:

i X9p : s _i,1 ni i : 1,2...5 (lOa)

I Z9p = s _i,3 ni i = 1,2...5 (lOb)

i Oy9P : E _i,5 ni i : 1,2...5 (lOc)

i These quantities are the actual positions of the base of the payload (node 9P)and are compared to either an inertial commandangle (OCMD)or to the X and Z

translational motions, defined as XgA and ZgA, respectively, on the AGSside of

I the magnetic interface. The resulting error signals, defined as the difference

between respective motions, are sensed and used by dynamic controllers to

I produce the required translational and rotational motion commands. In equation

form these relationships are:

I FXT Gx(S) [XgA - X9p] (11a)

l FZT : Gz(S) [Z9A - Z9p] (llb)

l TOp : Go(S) [OcMD - Oy9P] + _1FXT (llc)

l torque _1FXT a implementation and is requiredwhere the control is control law

to counter the overturning moment produced when x-translaltional motion at the

i payload base couples into payload rotation. The distance hl is the distancebetween the plane of the magnetic actuators and the effective payload CM

i location along the Z-axis and is known as the CMoffset.

m 2o

At this point in the discussion, the entire AVS armature/payload body has

been characterized. The next task in the ASPSmodel development is to determine

the modal coordinate representation of the AGSand its interfaces to the AVS.

The approach taken will be basically the same as before (same number and types

of modes, etc), but during the ASPSoperation, the AGSis in a follow-up mode to

the AVS; and the AVSarmature/payload body will exert reaction forces and

torques on the AGS-AVSstator as it moves in the magnetic gap. All other

operations and equation forms are similar in nature to previously derived

-- relations and will just be stated.

The flexible body motions at node 9 of the AGSside of the magnetic

interface are given by

XgA : s 6i,9 ni (12a)

Z9A = E 6i,19 ni i = 1,2,3 (12b)

09A = z _i,29 ni (12c)

and are derived in a similar fashion as equations (lOa) to (10c). The modal

coordinates ni are derived like those in equations (2) to (4), but for this

model, the base disturbance input is at node I0 and the gimbal input is at nodes

3 and 4. In addition the AVSmotion exerts reaction forces and torques on the

_ AGSat node 9. Therefore, the complete expression for the i th AGSmodal

coordinate ni is

(_i,24 - _i,23 ) UE 6i,i0 UD _i,9 FXT

ni S2 + Bi S + Ki S2 + By S + Ki S2 + By S + Ki

_i,19 FZT _i,29 TOp- - (13)

S2 + Bi S + Ki S2 + Bi S + Kii : 1,2,3

21

In equation (13),the variableUE is the AGS follow-upmode controlleroutput,

UD is the AGS base motion,and FXT, FZT, and TOp are as definedby equation

(ii).

The controlleroutputUE is composedof three components: the AGS follow-

up mode controlleroutputand two feed-forwardcommandsfrom the AVS, which are

used to counterthe reactionforcesand torquecausedby the AVS shovingagainst

the AGS. The AVS pointingloop torque commandTOp, whose expressionis given by

equation (11c),is fed forwardto the AGS controller,as is the torque produced

by the AVS translationalforce FXT, given by equation(11a),actingthroughthe

moment arm 22 as definedby Figure7. Thus,the equationfor the follow-upmode

controlleroutput UE is

UE = GFuM(S) (Oy9P - 09A) + TOp + 22 FXT (14)

where GFUM(S)is the AGS follow-upmode controller(explicitlydefinedin a

later section),and the other terms are as previouslydefined.

A block diagramthat incorporatesthe previousdiscussionand equations(7)

through(14) is shown in Figures8a and 8b. As can be seen from these figures,

the payloadangle Oy9P (obtainedfrom a gap transformationmatrix)is the input

to the AGS follow-upmode controller,while the same angle is sensedby an IRU

and used as the feedbackin the AVS pointingloop. Anothervery noticeable

featureseen on this diagramis the parallelpath structureassociatedwith each

flexiblebody. As in the AGS case, each modal outputcan exciteevery other

mode in the systemthroughthe feedbackcontrollaws. A listingof the

numericalvalues used in the structuralportionsof this modal is given in TableII.

In this section,the models for the flexibleAGS and ASPS have been

derived. Thesemodels are set up for simulationpurposesas they are shown. In

the next section,controllerswill be designed,simulationsof each model will

be developed,and systemperformanceanalysesusing these models and simulations- will be conducted.

22

I

ooR(31) _

L ---Q 0-

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A

FXT - -0

..,

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--

~R(511

I,R(52)'W Uo,f ~

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--f q,81, 24 - q,81, 23

,,~

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1+_ r

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Rlnt'

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i·~•

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~

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22

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~ q, 81,19 1 -_1 -''',9 ~)--1 -

~A,

..,52 +82 5+ K2 Rl531

+jr

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R(36)_J-q, 83,19 r~ • -.-q, 82,29 r

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+ G 0--.

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+ +

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++ .., ---I

rI

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1 + °9A-. +

+rI

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II

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I Figure 8aASPS Block Diagram

I 23

I ®

SECTION1 _ @P1,3 _ S2+BIS+K1 I ,,v I '-" '1

-- . -- "_ @P1,5 I_ ¢P1,31

I TIME DELAY

I R146)_

1

G_(S) _ _ SECTION I TION 2 R(41) _ k NODE 9P

• ' 1 k , X MOTIO,_._

NODE 9P

I R(44) . 0 MOTIOI_

+ R(45) "_ _ P4, 3 S2 + B4 S + K4

Q IRU '_" "_ ¢P4,5 ,1._ _P4,3

II o_o 0_,0t --/I _p+® -_0 " 1 _t t:L _ SECTION 1 _ SECTION 2 o/c FZT _: _ I _ P5, 3 - < ¢ P5. 1'

• R(43) v S2 + B5 S + K5

• _ • ITIME DELAY _ _ P5, 5 • _ q @P5, 3'PAYLOAD MODES

i GII © °"_ ' $715-8-10

II Figure 8bASPS Block Diagram (cont)

I 24

I TABLE II

NUMBERICALVALUESUSEDIN THEASPSSTRUCTURALMODEL

I (Obtained from NASTRAN)

I AGS/AVSStator: Rigid-body mode: i : 1_1 = 0.0 _1 = 0.0

I BI = 0.0 KI = 0.0

61,10 = 0.0

I 61,23 = 0.0

I 61,24 = 2.954426 x 10-261,29 = 2.954426 x 10-2

I First flexible-body mode: i : 2_2 : 0.005 _2 = 97.64

I B2 = 0.976 K2 : 9533

62,10 = 0.2429462

I 62,23 = 0.0

I 62,24 = -8.124529x 10-361,29 = -8.715468x 10-3

I Second flexible-body mode: i = 3

_3 : 0.005 _3 = 243.3

I B3 = 2.433 K3 = 59198

63,10 = -5.874251x 10-2

I 63,23 = 0.0

I 3,24 = -2.388733x 10_263,29 = -4.071004x 10-2

I

I 25

l TABLE II (cont)

NUMBERICALVALUES USED IN THE ASPS STRUCTURALMODEL

(Obtainedfrom NASTRAN)

AVS Armature/Payload:First rigid-bodymode (z): i = 1

l _1 = 0.0 _1 = 0.0B1 = 0.0 K1 = 0.0

_1,1 = 0.0

61,3 = -0.277196

l _1,5 = 0.0

Secondrigid-bodymode

(X and 0): i : 2_2 : 0.0 _2 : 0.0

B2 : 0.0 K2 : 0.0

62,1 = -0.3030391

62,3 = 0.0

_2,5 = 6.554324 x 10-3Third rigid-body mode(X and 0): i = 3

_3 = 0.0 _3 = 0.0

B3 = 0.0 K3 = 0.063,1 = -0.3203905

= 0.063,3

_3,5 : 8.807127 x 10-4

26

D TABLE II (cont)

i NUMBERICALVALUESUSED IN THE ASPS STRUCTURALMODEL(Obtainedfrom NASTRAN)

D First flexible-body mode: i = 4_4 = 0.0 _4 : 564.5

H B4 = 5.65 K4 = 318655

64,1 = 0.6053111

H 64,3 : 0

H 64,5 = -2.02517x 10-2Secondflexible-bodymode: i = 5

g _5 = 0.005 _5 = 2739.4

B5 = 27.4 K5 = 7504413

H _5,1 = -0.258577

i _5,3 = 0.065,5 = -5.618044x 10-2

H CONTROLLAWANDSIMULATIONDEVELOPMENT

D In the previoussection,the flexibilitymodels of the AGS and the ASPS

were developedand a qualitativedescriptionof the operationof each was given.

H In this section,the controllaws for each model will be developedand verified,as will be a quantitativeexpressionfor the time delay associatedwith the

D digitalimplementationof these controllers. Once all of the systemblocksassociatedwith each model have been defined,a GeneralStabilityAnalysis (GSA)

H programfile will be generatedfor each and will be used to predictsystemperformancein the presenceof unwanteddisturbanceinputs.

I

D 27

i

I Design of AGSControl Law

I The first step in the design of the AGScontrol law is to determine the

plant characteristics as a function of frequency. This is done by using the

l structural data in Table I and the form of the shown in 6.given plant as Figure

A plot of this uncompensated plant transfer frunction is shown in Figure 9. As

l the figure shows, two prominent flexible modes are superimposed on top of therigid-body response. In order to provide good disturbance rejection, a

i bandwidth of approximately 1.0 Hz is desired. However, this will cause thepeaking of the two bending modes to exceed 0 decibel, possibly resulting in

instability. Several methods could be used to compensate such a response, the

I simplest of which would be pole-zero cancellation to eliminate the flelxibilityeffects. However, this method would run the risk of creating a system instabil-

l ity, due to the location of such poles. On a root-locus plot, these roots wouldappear as highly underdamped poles which are located very close to the imaginary

i axis. The intent of pole-zero cancellation would be to place a zero exactly ontop of the pole, thereby removing this particular response from the overall

system response. However, since the damping associated with modal roots can

I only be estimated and the modal frequency is not precisely known, the polelocation associated with the mode is uncertain to a degree. Thus, if it were

I desired to place a zero directly on top of such a pole, it is quite possible andmost probable that you would "miss". The danger associated with this occurrence

I is that the locus shape, for certain ranges of system gains, could possibly bedriven into the right half-plane, thus creating an instability. Pole-zero

cancellation is therefore to be avoided due to its high sensitivity to knowledge

I of the plant dynamics.

l Another commonly used method of flexible structure withcompensating a

prominent modes is to phase-stabilize the open-loop response. The basic

l advantage of such an approach is that it will force any modal peaking (if modalfrequency values are fairly accurate) to occur in the right-half plane of the

i Nyquist plane, away from the -I point, no matter what the actual values of modaldamping happen to be. This procedure will yeild a more robust design, meaning

that even if modal peaks were to rise above 0 decibel, the resulting ringing

I be damped out due to the location of the modal peaks in the Nyquist plane.would

m 28

10

0 150

PHASE _

00 ill 00GAIN _ _%_ 50-3o

_ Z L _- j "'(9 -40 0 €_

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FREQUENCY (Hz) S715-8 12

Figure9UncompensatedAGS Plant TransferFunction

I The majority of the compensation design for the AGScontrol law was done on

a Hewlett-Packard 5423 Structural Dynamics Analyzer, due to the speed and ease

I with which a design could be implemented, checked, and iterated to achieve the

"best" open-loop margins and closed-loop performance. The analyzer designs were

I buffered with as much gain and phase margin as possible, so that when thecomplete AGSmodel (including the time-delay effects and IRU) was implemented on

I GSA, the resulting open-loop margins would be acceptable.

The initial step in the overall controller design was simply to use the

I plant shown in Figure 9 and, in an iterative fashion, to derive a P-I-D

controller that would properly compensate the rigid-body portion of the transfer

I function. Once this task was completed, the resulting response was studied, and

a bending mode filter (BMF) that would phase stabilize the flexible-body effects

I as developed. The two were "fine-tuned" in an iterative fashion and the finalresults are:

I P-I-D Controller:

I P-I-D : 117183 [1.0098 + 0.4488 + 0.561s] (15)s

I Bendin9 Mode Filter:

( 1+ 4s 1+ 0.0064s1( 2(0.5)s s2 )BMF= I + 0.5s I + 0.0266s I + 50.3 + _ (16)50.32

. It can be seen from equation (16) that the bending mode filter is composed of alead-lag network, a lag-lead network, and a complex pole pair. The purpose of

the lead-lag is to add positive phase in the vicinity of the O-decibel cross-over, while the lag-lead attenuates gain in the frequency band containing the

modes. The complex pole pair gradually reverses the phase by 180 degrees

(without adding peaking in the gain characteristic) such that the modes peak in

the right half-plane of the Nyquist plane, away from the -1 + Jo point. The

resulting open-loop plot, the corresponding Nyquist plot, and the closed-loop

3O

response are shown in Figures 10 through 12, respectively. The open-loop

-- characteristics of this response are:

crossover frequency (fco) = 0.56 hertz

gain margin = 20 decibels

phase margin = 60 degrees

while the closed-loop performance values are:

closed-loop bandwidth (fBW) = 0.9 hertz

closed-loop peak = 1.0 decibel

highest modal peak : -4 decibels

The above system performance parameters were obtained under the assumption

of an "ideal" system; i.e., no feedback dynamics and no digital affects. For

- completeness, these effects should be included and are now quantitativelydefined.

The inertial reference unit (IRU) is used to provide feedback information

for an inertial pointing system such as the AGS; its dynamic effects have been

widely documented (ref 3) and are

IRU : 12 s2 (17)

(1.6s s )( 1.2s )I +--gT-+-- I + +- (942) _ (3242 )

_ At the previously-defined crossover frequency (fco), the additional phase lag

caused by these dynamics is approximately 3.5 degrees, leaving a net phase

margin of 56.5 degrees.

31

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Figure10AGS Open-LoopTransferFunction

600.00m

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$715-8-14

Figure 11NyquistPlot of AGS Open-LoopTransferFunction

10

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,_z -30 /-40 I-50

-60

-70

0.1 0.5 1.0 5.0 10.0FREQUENCY (Hz) $715-8-15

Figure 12Phase-StabilizedAGS Closed-LoopTransferFunction

I Digitaleffectscan have significantimpacton the phasemarginsof a

I controlsystem and, hence, on the achievablebandwidthof the controlloops. Inthis study, two sourcesof digitalphase lag are considered;sampleand hold,

and transportdelay. The sample-and-hold(S-H)effect actuallyinvolvesa gain

I roll-off,as well as a phase lag. However,if the samplefrequencyis signifi-cantly higherthan the control-loopbandwidth,then the S-H can be approximated

I as a pure phase lag of the form

e-j_/_s

!where us is the sample frequency,assumedto be I00 hertz for both the AGS and

I ASPS configurations. Similarlythe transportdelay is modelledby a phasepure

lag

I e_JTd_

I where Td is the transportdelay time. As shown,the phase lag expressioncannotbe includedin the linearAGS and ASPS models. However,a Pade approximationof

I the complexexponential,consistingOf a polynomialquotientwith approximateunity gain and linearphase characteristics,can be includedin the models. A

third-orderapproximationwas determinedto be adequate. A combinedeffective

I delay, (x_/ms+ Td), of 0.01 secondbased on a Td of 0.05 secondhas beenassumed.

!It is recognizedthat a stabilityanalysisof a sampledata System

I performedby addinga time delay to the continuousplant will not give the sameresultsachievedby performinga sampledata stabilityanalysis. However,in

i this study,the continuoussystemstabilitymargins shouldbe close to thesampledata values,since the ratiosof half-samplefrequencyto open-loop

crossoverfrequenciesare large.

!The time-delayexponentialtakes the form

1 e-O'Ols : _-_ (18)

!I 35

I

I where D(s), for a third-order approximation, is

I D(s) = I + O.005s + 1.0714 x 10-5s2 + 1.1905 x lO-8s 3 (19)

I Substitutingequation (18) into (19) and simplifyingyields the expression

e-O.Ols: (377- s) (s2 - 530s + 222846) (20)

I (377+ s) (s2 + 530s + 222846)

l This expressionwas synthesizedon the analyzerand was found to have a unitygain, linear-phasedropoffrelationat frequenciesup to 25 hertz. However,the

i phase of a second-orderapproximation,obtainedin a similarfashion,began todistortat the higherfrequencies. Thus, since unity gain and linearphase

dropoffis desired,the third-orderapproximationcan be used in good faith and

l will yield good resultsover the frequencyrange of interest. At the previouslystatedcrossoverfrequency,the additionalphase lag createdby the time delay

i is approximately2 degrees,leavinga net phase marginof 54.5 degreesafter theIRU and time delay have been considered.

!l Designof ASPS ControlLaws

This subsectionaddressesthe developmentof the controllaws associated

I with the ASPS model. The approachtaken is similarto that used on the AGSmodel; i.e., the preliminarydesignsare done on the analyzeras single-input/

I single-outputloops. These designsare bufferedwith as much gain and phasemargin as possible,for the same reasonsgiven in the AGS designsection. The

I three AVS loops are independently designed, and then included as the control lawin the dynamic, cross-coupled AVSmodel to be implemented on GSA. The stability

of each of the three AVS loops is then verified with the other AVS loops closed,

l performance for each of these loops is obtained by successiveand the "best"

iterations on GSA. Once the AVSloops have been adequately stabilized, the AGS

I follow-upmode controlleris designed.

m 36

There are three main objectivesin definingthe variousmagneticand gimbal

_ control-loopbandwidthsfor the ASPS configuration. Firstof all, the distur-

bance rejectioncapabilityof the inertialpointingloop shouldbe maximizedby

definingas large a pointing-loopbandwidthas possible. Secondly,the level of

disturbanceseen by the pointingloop shouldbe minimizedby minimizingthe

translationsand follow-uploop bandwidths. Finally,the first two objectives

must be satisfiedwhile maintainingadequatestabilitymargins and reasonable

magneticactuatorgaps. In general,the stabilitymargin requirementimposesan

-- upper limit on all of the loop bandwidths,while the gap requirementdefinesa

lower bound to the follow-upand translation-loopbandwidths. Becauseof the

gap requirement,it is considereddesirableto close the follow-upand transla-

tion loops at roughlythe same bandwidthsthat have been used in past ASPS

studies. Thus, a O.2-hertztranslation-loopbandwidthand a O.5-hertzgimbal-

- loop bandwidthwere establishedas goals for the compensatordesigns.

-- The first step in the design of the AVS translationalloops is to identify

the struturalplant that each compensatorcontrols. This task was done with the

aid of Figure8 and the data in Table II. These transferfunctionswere

synthesizedon the analyzerand shown to be essentiallyrigid-bodyresponses

over the frequencyrange of interest(highestmodal peak is -70 decibelsand

occurs at 89.9 hertz). Thus, the designof a P-I plus lead-lagcontrollerto

stabilizesuch a responseis a relativelystraightforwardprocedure. The P-I

plus lead-lagcompensationwas chosen becauseit is the simplestcompensator

form that zeros a bias error while stabilizinga 1/S2 plant and producinga S-2

high frequencyrolloff.

These controllersare, after rearrangingthe classicalexpression,of theform

(1 + s/Ki) (1 + s/m1)

-- Gx(S) = Gz(S) = KpKI S (i + s/_2) (21)

37

l Equation (21)is used in conjunctionwith the rigid-bodyresponseof l/Ms2to

obtainthe desiredopen-looptransferfunction. This open-loopresponsewas

I synthesizedon the analyzerand, after itertation,a controllerthat yielded

good open-loopmarginsand closed-loopresponsecharacteristicswas found and is

I Gx(S) = Gz(S) = 0.04113(1 + 15.92s)(1 + 15.92s)s (1 + 0.592s) (22)

I This controllerin cascadewith the rigid-bodyplant (1/13.016s2) yields the

i followingopen-loopvalues:Crossoverfrequency(fco)= 0.12 hertz

I Gain margin =Phasemargin = 56.5 degrees

l The correspondingclosed loop characteristicsare:

i Closed-loopbandwidth(fBW) = 0.19 hertzClosed-looppeaking= 1.35decibels

!At the crossoverfrequency,the additionalphase lag causedby the systemtime

l delay is calculatedfrom equation(20) and is approximately0.4 degree.

The AVS pointingloop controlleris designedin basicallythe same manner

J as were the translationalcontrollers;however,due to the non-unityfeedback

(IRU is used in AVS pointingloop) and the presenceof modal peakingin the

I open-loopresponse,care has to be taken to ensurethat such peakingdoes notoccur in the closed-loopresponse. The reason for this can be seen if one

l envisionsthe form of a genericclosed-loopcontrolsystem. In other words, ifR is the system input,C is the output,G is the forwardpath transferfunction,

H is the feedbackpath transferfunction,and E is the error signal,then the

I followingstatementscan be made:

I a. The stabilityof the open-looptransferfunctionis found by studyingthe frequencyresponseof the productGH. From an input/output

relationship,the stabilityis determinedby the gain-phase

!I 38

• characteristicof the productGH operatingon the error E. The

cumulativeproductis then comparedto the input R at the summing

junction.

b. The output responseC is equal to the open-looptransferfunctionG

operatingon the same error signal E.

iIt can be seen from statementsa and b that, if G has modal peakingin its

frequency-responsecharacteristicand H is sufficientlylow pass in nature (in

the frequencyrangecontainingthis peaking),then it is possiblethat the

peakingwould not affectsystem stabilityat all, but would show up in the

closed-loopresponseas lightlydamped "spikes". It should be emphasizedthat

these spikesdo not create a systeminstability,but would cause ringingin the

-- time responseif they were not attenuated. Such a situationwas encountered

when stabilizingthe AVS pointingloop. A P-I-D controllerwas used to

-- stabilizethe pointingloop, and no problemswere anticipateddue to the shape

of the open-loopplant transferfunction. A P-I-D designwas used that yielded

a 16-decibelgain marginof 50 degreesof phase margin;yet when the loopwas

closed,a stablemodal peak of 24 decibelsoccurredat 89.9 hertz (firstpayload

mode). To reducethis closed-looppeaking,a bendingmode filterwas added as

part of the pointingloop controller. The frequencyresponsedictatedthat the

bendingmode filter shouldhave a lightlydamped zero at 700 radiansper second

- and a heavilydamped (Q=I) pole at 100 radiansper second. In equationform

this bendingmode filteris

- 1 + (0.1/700)s+ s2/7002BMF- (23)I + (i/lO0)s + s2/1002

This filterwas added to the GSA simulation,and a P-I-D controllerwas then

designedthat would compensatethis "new" plant. After severaliterations,one

was determinedthat gave good open-loopmarginsas well as closed-loopperfor-

mance. Its equationis

P-I-D = 22865 (21 + 18/s + 8.8s) (24)

39

l The controller,in conjunctionwith the bendingmode filter in equation(23),

i gives the followingsystemperformance:Open loop: crossoverfrequency(fco)= 1.4 hertz

I gain margin= 13 decibelsphasemargin = 54 degrees

I loop: (fBW) = 2.8 hertzClosed bandwidth

peak = 2.3 decibels

I highestmodal peak is -16 decibelsat 89.9 hertz

I As can be seen from these results,the bendingmode filterdid successfully

attenuatethe modal peakingwithoutany detrimentaleffectson pointing

I performancestability.

I As a last check to verifythese loops, each loop in the AVS portionof theGSA model was opened in successionwhile the other two loops were left closed.

The input of the open loop was then excited,and its open-looptransferfunction

l was determinedand checkedfor stability. Each of the three loops showedmore

than adequateopen-loopmargins (at least 10 decibelsgain margin and 40 degrees

I phasemargin). Thus, it is assuredthat the AVS model is stableand willoperateproperly.

l The last step in the completionof the ASPS model is to determinethe

controllerfor the elevationgimbalaxis, as the AGS operatesin the follow-up

l mode. In this particularmode, the input to the AGS controllaw is the payload

tilt angle (obtainedfrom a gap transformationmatrix),while the feedback

I is the inertial the AGS side of the interface.signal angle on magnetic The

purposeof this mode is to keep the AGS alignedwith and followingthe motion of

l the payloadbody as it moves in the gap, such as during a trackingmaneuver.The natureof this particularoperationdictatesthat the elevationgimbal

I follow-upmode controller"sees"the entiresystemdynamics- the AGS, AVS, andthe uncancelledreactionforcesand torquesexertedby the AVS on the AGS.

Keepingthese facts in mind, the completeopen-looptransferfunction,from the

!I 40

II follow-up mode input to the AGSinertial angle output, was run on GSAand was

found to be a rigid-body response of 1/1146s 2 out to at least I0 hertz. Since

I t was desired to close this loop at a bandwidth of approximately 0.5 hertz, noproblems were anticipated.

I The type controller to be used for this mode is a P-I plus lead/lag of the

I ame generic form as that given by equation (21). The design was done on theanalyzer and the resulting controller is

I GFuM(s) : 254 (I + 6.37s) (1 + 1.54s) (25)s (1 + 0.172s)

I hen using this controller, the open-loop characteristics for the follow-up modeare :

I rossover frequency (fco) : 0.34 hertzgain margin = =

I phase margin = 49 degrees

I The corresponding closed loop response is:

bandwidth (fBW) : 0.58 hertz

I closed-loop peaking : 2.9 decibels

I uch a closed-loop response should be more than adequate for this particular AGSapplication.

IIII

| 41

I

f

i

I

1 AGSPERFORMANCEEVALUATION

I System performance for both the AGSand ASPSconfigurations is defined by

the inertial pointing stability achieved in the presence of shuttle disturbancesr; (as defined in the above section on model development). Using the GSAmodels

developed for the study, performance stability is experssed most conveniently by

i- the frequency transformation from disturbance input to inertial payload angular

motion. On option, a time history of the system response to a step disturbance

input can be generated.

In this section, the block diagram shown in Figures 6a and 6b were used toI

obtain a frequency response of the transfer function, relating an AGSbase force

disturbance input to the payload pointing angle output. This was done by

setting the GSAvariable R(32) (shown in Figure 6b) to unity and monitoring the

output angle 0o. A Bode plot of this response is given as Figure 13. As this

figure shows, the low-frequency asymptote has a +3 slope and there is no high-

frequency rolloff. The theory which supports these findings has been described

in detail in reference 5 and so will be covered only briefly in this report.

The low-frequency asymptote of slope +3 is due to the -3 slope in the open-loop

response characteristic. The lack of a high-frequency rolloff is caused by the

fact that an end-mount pointing system such as the AGSprovides a rigid-link

path for translational motion between its base and the supported payload. For

this reason, high-frequency vibration can and will transmit directly to the

payload, and the elevation gimbal controller can do little in the way of

rejecting such a disturbance at frequencies above its bandwidth. The value of

the peaking at the high frequency will be greater if the mass/inertia ratio of

_ the portion of the system above the controlled axis is increased and will be

less if this ratio is decreased. The peak value of the response occurs at the

first AGSflexible mode, while the smaller peak is possibly due to the 20-hertzpayload.

42

-IO0

I lltil i ' [I;;;;; I• IIIII ,,

-120 i ::::: : !!I I

I-14o ,::;,,',i i i" • _

-160 ." .":.'." :

1//_ I Im

Z -180 : : ::: : !

< _%4_

-200 : : ::: :

• 1, ' I-220 I# : : ::: :

/I

-240 I ...... J-260 ' I i i , , ,,, , II

10-2 10-1 100 101 102 103

FREQUENCY (RAD/SEC) s715-8-16

Figure 13AGS PointingError for Unity Base Input

I The AGStime response was done on GSAin basically the samemanner as was

I he frequency response; however, the system input for this portion of the studyis a VRCStorque pulse applied about the shuttle Z0 (yaw) axis. In Figure 5,

the magnitude of this pulse is given as 22937 inch-pounds. This input is

I applied by setting R(31) of Figure 6b in the simulation to this value. The GSAo.

program, for the time-response option, interprets this input as being a step

I occurring at time zero. This input is assumed to last for 0.24 second. Thesystem angular time response then will decay to zero in the manner dictated by

its dynamic characteristics. This particular response was obtained from GSAin| a piecewise linear fashion by exciting R(31) with the VRCStorque value

mentioned above and running a O.24-second time response for every system

I variable. For the next portion of the run, this input was removed, and eachdynamic state input and output was initialized with its position and velocity

i (initialized as required by the corresponding differential equations) at0.24 second. The model was then run again with these initial conditions being

I the system drivers, and the output angle was monitored for 5 seconds. Theresulting response is shown in Figure 14. The peak pointing error due to the

i RCSdisturbance input is 7.4 arc seconds, while the negative swing peaks at 1.5arc seconds. It can also be seen that the response begins to decay toward zero

error at 5 seconds and that modal peaks (which could have caused system ringing)

I have been adequately and successfully attenuated.

I ASPSPERFORMANCEEVALUATION

I The model shown in Figures 8a and 8b was used in this section to perform a

detailed analysis of the effects of payload structural flexibility and misknowl-

I edge of the payload's effective CMlocation on the pointing performance of theASPS. A parametric study of the predicted CMlocation (implemented as part of

I he control law) versus the actual CMlocation, with and without the effects ofpayload flexibility, was done; and the results are included and discussed in

i this section.

I44

POINTING ERROR (SEC

f

4

VRCS PULSE

REMOVED

-2

-4

1.0 2.0 3.0 4.0 5.0TIME (SEC)

$715.8-17

Figure14AGS Time Responseto 0.24 Second,ShuttleVRCS Yaw Maneuver

The first step taken in this study was to determinethe actuallocationof

the payloadCM. Figure7 shows that the distancebetweenthe magneticactuator

plane and the payloadCG is 59.1 inches. In the NASTRANformulation,however,

11.4mass units are placedat node lOP and 1.6mass units at node 9P. This

procedureyields an "effective"CM locationof [11.4/(11.4+1.6)](59.1"),or

51.83 inchesabove the actuatorplane. Thus, if it were desiredto decouple

translationaland rotationalmotioncompletely,the value of the moment arm _1

shown in Figure8b would be set to 51.83 in the appropriatecontrollaw.

_- However,it would be unrealisticto assumethat one could preciselylocatethe

effectiveCM of a payload;thus a worst case ±1 percentuncertainty(both high

and low extremes)is used in the study. As an exampleof this decouplinglaw

error, considerthe case of 99 percentpayloadCM knowledge. This terminology

means that, since the actual effectiveCM locationis 51.83 inches,but the

value of _1 used in the decouplinglaw is only 51.31 inches,perfectdecoupling

is not achieved. In the case of 101 percentknowledge,the value of _1 to be

used in the decouplinglaw is 52.35 inches,againmeaningthat perfectdecoupl-

ing would not occur.

The responsestudiedin this sectionis, as in the AGS case, the transfer

functionrelatingan AGS base unity inputto the payloadpointingangle.

However,in the ASPS phase of the study,this responsewas done as a payloadCM

offset study with both a rigid and a flexiblepayload. From a simulation

standpoint,the Bode plots were obtainedby settingthe GSA variableR(33)

(shownin Figure8a) to unity and monitoringthe output angle Oy9P. Payload

flexibilitywas removedby insertinga logic switchin serieswith each flexible

payloadmode and settingthe values to zero. The units of each plot are radians

r_ per pound,expressedin decibels. Thus, if it were desiredto convertto arc

secondsper pound (in decibels),an additionof 106.3decibelswould have to be

made to each point on the curve.

P

46

I The results of thd CMoffset-payload flexibility study are shown in

Figures 15 through 20. As the figures show, these responses have the same Iow-

I frequency asymptote (+3 slope) as does the AGSresponse; however, as a worst

case, the ASPSresponse is approximately 60 decibels down when compared to the

I case. greater low-frequency attenuation is due to the fact that theAGS This

AVS pointing loop could be closed at a higher bandwidth than could the AGS

I pointing loop. This illustrates one advantage of magnetic suspension whenconsidering system flexibility effects. Structural flexibility was the major

I system aspect that determined the AGSpointing-loop bandwidth, whereas it is nota factor when stabilizing the AVS loops. This is due to the physical separation

of the AGSand the payload at the magnetic interface. The modal frequencies

I ssociated with each body are now sufficiently high that they do not affectsystem stability in the range of bandwidths associated with the AVS loops.

I Another major advantage of magnetic suspension is the presence of a high-

i frequency rolloff that the AGSresponse does not have. This rolloff is causedby the slope of the high-frequency portion of the AVStranslational-loop/open-

loop transfer function [ref 5] and could be even more pronounced if a higher

I controller/filter were to be used. This rolloff illustrates the conceptorder

of isolation; at high frequency, it is possible for the payload to remain

I essentially motionless and allow the base to move around it. Thus, from thestandpoint of isolation capability, a very low translational bandwidth would be

i esirable. However, the lower limit on this bandwidth is usually dictated bythe maximumavailable gap in the MBAs. Since this gap size determines to a

great extent the system power and weight requirements, the "optimal" setting of

I the translational-loop bandwidth would involve a tradeoff study of the amount of

isolation capability desired versus the power and weight requirements needed to

ii ensure system operation under these conditions.proper

I The effectsof payloadflexibilityare also evidentfrom the high-frequencycharacteristicsof Figures9 through15. With payloadflexibilityincludedin

i he model and simulation, the translational controllers sense the motion causedby payload flexibility effects and interpret it as being rigid-body motion. The

resulting controller action creates a high-frequency rolloff that is not as

!I 47

m I__ m

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-:°,,'" IIIIIIIII IHl tIII_;17ILI IllllIlll Illl " t,JlI

10-2 10-1 100 101 102 103 104

FREQUENCY IRAD/SEC) $715-8.1B

Figure15ASPS FrequencyResponsefor AGS Base Input

No Error in Cr.IOffset Estimate,No PayloadFlexibility

2O

+o JlllIF_+ IIIIIII_+o IIIIIJ I- Imm

_z -18o

€

/ \ I -" IIII1",

_+o I!11'+4,-380

10 -2 10-1 100 1; 1 102 103 104

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Figure 16ASPS FrequencyResponsefor AGS Base Input

-I PercentError in CH OffsetEstimate,No PayloadFlexibility

Figure17

ASPS FrequencyResponsefor AGS Base Input+I PercentError in CM Offset Estimate,No PayloadFlexibility

_,90inilnniiillIL I'IILLII!1 1_2,0fillI 111 -,, I,llll I_:::lin, iii AiIInllI, III,j IIIIIIIIII II"'tll/"I

! IIIIILIIII II 7 11IIiiii , JillIrlfIII/rll

il]bl iiiiIiirlllfpJ' IJltJIpl2222.olrlllIr i,iIollIl

10-2 10-1 100 101 102 103 104

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Figure 18ASPSFrequency Response for AGSBase Input

No Error in CMOffset Estimate, No Payload Flexibility

Ill

10-2 10-1 100 101 102 103 104

FREQUENCY (RAD/SEC) $715-8-22

Figure19ASPS FrequencyResponsefor AGS Base Input

-1 PercentError in Ci'lOffsetEstimate,No PayloadF|exibilityIncluded

11 __J

_19o I !

-210

/

-230 /

-250

/ma -27oz

r._ o

-290 /

/-310

-330

-35O

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Figure 20ASPSFrequency Response for AGSBase Input

+I Percent Error in CFIOffset Estimate, Payload Flexibility Included

pronouncedas those obtainedfrom the rigid-bodypayloadsimulation. The

results of the payload CFIoffset/flexibility study are summarized in Table III.

TABLE Ill

! RESULTSOF ASPS CI,1OFFSETSTUDY

r LF Gain (dB) IsolatorPeak HF Gain (dB)• (0.01RPS) Value (dB) (1000RPS)

__ No PayloadFlexibility:

100% CM Knowledge -343 -219 <-400

_- 99% CM Knowledge -319 -195 -373

101% CM Knowledge -320 -196 -374

i PayloadFlexibilityIncluded:

100% CM Knowledge -343 -218 -315

; 99% CM Knowledge -319 -195 -315

- 101% CM Knowledge -320 -196 -315

_- Anotherinterestingpoint to be made concerningFigures9 through15 is the

• occurrenceof zeroswhose dampingcoefficientsvary over a wide range of values.

This fact is most likelycausedby the parallelstructurethat exists betweena7-

given AVS controlleroutputcommandand the payloadpointingangle. In other

words, one could representsuch a parallelstructureas a singleinput/single

: outputtransferfunctionblock throughthe use of simplealgebraicmanipula-

tions. By studyingthe ASPS NASTRANdata given in Table II, notingboth

magnitudeas well as sign, it shouldbe evidentthat odd-lookingzeros would

i appear.

7

• An attemptwas made at obtaininga time responsefor the ASPS model but

unfortunately,numerousproblemsoccurredwith the time-responseoption

i availableon GSA which could not be resolvedin a timely manner.i

54

I However,even thoughthe ASPS time responsewas not obtained,a fairly

accurateestimateof its maximumvalue can be made by using the results

I presentedin this report. By comparingthe data shown in Figures9 and 14, itcan be seen that the low-frequencyresponseof the AGS and ASPS have the same

i generalshape up to approximatelytwo RPS. Reference5 has shownthat thisportionof such responsesis due to the pointing-loopdynamics. Thus, if it can

be shown that the majorityof the energycontainedin the AGS base force inputcausedby Shuttlemotion is at frequenciesbelow 2 RPS, then the peak value of

the ASPS time responsecan be determinedby simplymultiplyingthe AGS peak

I response(7.4arc seconds)by the directmagnituderatioof the 2 frequency

responsesbelow 2 RPS. Such an analysiswas performedand discussionof the

I procedureand resultsfollow.

l The first step in the procedureis to determinethe Fouriertransformofthe O.24-secondVRCS torque pulse shown in Figure6. The resultingexpression

is given asi

i F(j_) = 5505 sin (0.12_)0.12_ (25)

!This Shuttle torque disturbance input is then applied to the AGS base as a force

l throughthe Shuttle-palletdynamicsas shown in Figure8a; thus, it is desiredto show that most of the energycontainedin the resultingfrequencydomain

i transferfunctionis at frequenciesbelow 2 RPS. Such a procedurewas pro-grammed,and the resultsclearlyindicatedthat essentiallyall energywas below

0.1RPS. As an example,the followingthree pointsdenotedby _ (gain in dB),

I illustratethe concept: (0.01,148),(0.1,108),and (2.0,58). Note that thedifferencein gain from 0.01RPS to 2.0 RPS is a decreaseof over four ordersof

i magnitude. Therefore,the direct ratio method for determiningthe ASPS peakerror can be used with a high degree of confidence.

!

I 55

I The data given in Figures9 and 15 show that there is a low-frequencygain

attenuationassociatedwith the ASPS responseof 60 decibels (factorof 0.001).

I Thus, the peak pointingerror associatedwith the ASPS disturbanceresponseis(0.001)x (7.4arc seconds),or 0.007 arc seconds. Such an estimateis "in the

I ballpark,"so to speak,of valuesobtainedin previousstudy phasesassociatedwith the ASPS program. Lastly,due to the fact that the ASPS pointingloop is

i losed at a higherbandwidththan is that of the AGS, it can also be statedthatthe time responsecharacteristicsassociatedwith the ASPS disturbanceresponse

will be much fasterthan that of the AGS (see Figure9).

!I CONCLUDINGREMARKS

I In this report,the impactof structuralflexibilityon the pointingperformanceof the AGS and the ASPS has been assessed. It was found that the

AGS requireda phase-stabilizeddesignto eliminatethe possibilityof modal

I peakingaffectingsystemstability. In addition,the bendingmode filter

implementationfor wide-angleoperationof the AGS will requirethe use of a

I trackingalgorithmto compensatefor the modal variancesover the entirerange

of systemattitudes. In the ASPS case, the threat of systeminstabilitydue to

I odal peakingwas never an issue;however,a bendingmode filterwas requiredtoattenuatea stablemodal peak in the AVS pointing-loop/closed-loopresponse.

Due to the small angle motion of the AVS, a trackingalgorithmwould not be

I neededwith this filter,however.

I The frequencyresponsecharacteristicsof the AGS and ASPS disturbanceresponsesdo indeedassumethe theoreticalshapesof an end-mountpointing

I ystem and an end-mountpointingand isolationsystem,respectively. The AGSresponsedoes not have a high-frequencyrolloffto translationalbase distur-

i ances, due to the fact that a directmechanicallinkageexistsbetweenthe baseand payload. The ASPS, on the other hand, has a very pronouncedhigh-frequency

rolloffdue to the "soft"AVS translationalloops. This attenuationillustrates

I the conceptof isolation. The low-frequencyresponsecharacteristicsof both

systemshave the same shape;however,the ASPS responseis 60 decibelsbetter in

Im 56

i this regionthan is the AGS response. This remarkableimprovementin error

peakingcan be attributedto three sources: the significantincreasein

I pointing-loopbandwidthachievedwith the ASPS, the attenuatedlevel ofdisturbanceseen by the magneticpointingloop at the peak frequency,and the

i se of feed-forwardcommandsin the ASPS configurationto compensatedisturbanceinducedpayloadtorques. Of course,the relativelylow bandwidthof the

i ranslationloops which attenuatethe disturbancelevels alsomake it possibleto increasethe pointing-loopbandwidth. Thus, the two effects (attenuated

disturbanceand largerbandwidths)have to be viewedtogether. The componentof

i pointing-errorimprovementdue to these effectscan be regardedas a direct

benefitof addinga magneticpointinginterfaceto the flexiblegimbal

I configuration.

I REFERENCES

I 1. Anderson,W.W.; and Joshi,S.M.: The AnnularSuspensionand Pointing(ASP)

Systemfor Space Experimentsand PredictedPointingAccuracies. NASA TR-

i 448, December1975.

I 2. FlexibilityEffectsAnalysis. ControlDynamicsCorporation,Huntsville,Alabama. Sperry PublicationNo. 71-1747-48-00,March 1982.

I 3. AGS ControlSystemDesignand PointingPerformanceReport. SperryPublica-

tion No. 71-1741-00-01,December1982.

l4. Kochenburger,Ralph J.: ComputerSimulationof DynamicSystems. Prentice-

I Hall, Inc, 1972.

i 5. Hamilton,BrianJ.: Stabilityof MagneticallySuspendedOptics in aVibrationEnvironment. Sperry PublicationNo. 69-1554-02-00,June 1981.

I

i 57

i . . - .......

i 1. Report No. 2. Government Accession No. 3. Recipient's Catalo<j No.172481

i 4.TitleandSubtitleImpact of Magnetic Isolation on s.ReportDatePointing System Performance in the Presence of _ February 1985Structural Flexibility 6.Pe_ormlngOrganizationCode

07187

i 7. Author(s) 8. Perform;rig Organ;zation Report No.J. Sellers

10. Work Unit No.

9. Performing OrganizationName end AddressSperry Corporation 11. Contractor Grant No.

Space Systems Division

I Phoenix Arizona 85036 NASI-16909' 13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address

I N_tional Aeronautics and Space Administration 14. Sponsoring Agency Code

I Langley Research Center, Virginia15. Supl_ementary Notes

!16. AbstractA study has been conductedto comparethe inertialpointingstabilityof agimbal pointingsystem, (AGS),with that of a magneticpointing/gimbalfollowupsystem, (ASPS), under certainconditionsofsystem structuralflexibilityand

disturbanceinputsfrom the gimbal supportstructure. Separate3 degree-of-freedom (3DOF)linearmodelsbased on NASTRANmodal flexibilitydata for the gimbaland supportstructureswere generatedfor the AGS and ASPS configurations. Using

l the models inertialpointingcontrolloops providing6dB of gain margin and 45°of phase marginwere definedfor each configuration. The pointingloop bandwidthobtainedfor the ASPSis more than twice the level achievedfor the AGS configura-tion. The AGS limit can be directlyattributedto the gimbal and supportstructure

flexibility.As a resultof the higher ASPS pointingloop bandwidthand the disturbancere-

l ectionprovidedby the magneticisolationASPS pointingperformanceis signifi-cantly better than that of the AGS system. Specifically,the low frequency (nonmodal)peak of the ASPS transferfunctionfrom base disturbanceto payloadangularmotion is almost60dB lower than AGS low frequencypeak.!

I I"

17. Key Words (Suggestedby Authoris)) 18. Distribution Statement

l AGS, Gimbal,MagneticPointing,ASPS,Flexibility,Modal Data

i19. Security Qa_tif. (of this reportl 20. Security Clatsif. (of this page) 21. No. of Pages 22. Price

I.-3os Fu salebytheNationalTechnicalInfumationService.Sprinp.field.V,rginia22161

I

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I NASAAmes Research CenterMoffett Field, CA 94035

I Attn: Library, Mail Stop 202-3 INASADryden Flight Research FacilityP.O. Box 273

I Edwards CA 93523Attn: Library i

I NASALyndon B. Johnson Space Center2101 Webster Seabrook RoadHouston, TX 77058

i Attn: JM2/Technical Library INASALewis Research Center21000 Brookpark Road

I Cleveland, OH 44135Attn: 60-3/Library I

i NASAJohn F. Kennedy Space CenterKennedy Space Center, FL 32899Attn: NWSl-D/Library I

I NASAScientific and Technical Information Facility6571 Elkridge Landing RoadLinthicum Heights, MD 21090 15 plus original

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