Preliminary Design Review - MIT OpenCourseWare · PDF file5/24/2002 CDIO3 Class Project 12 Constraints Schedule ... moments induced by electromagnets ... 2 m zCore mass: 19.5 kg zApplied

Preliminary Design Review

May 7, 2002Space System Product Development Class

Department of Aeronautics & Astronautics, MITElectro Magnetic Formation Flight Of Rotating

Clustered Entities

5/24/2002 CDIO3 Class Project 2

Introduction

Geeta Gupta

Introduction•Mission•Background &Motivation•RequirementsSummary•Approach•PDR Purpose•Overview

SubsystemsOperationsImplementationConclusion


EMFFORCE Mission

Demonstrate the feasibility ofelectromagnetic control forformation flying satellites.




Definition of Formation Flight

A cluster of cooperating satellitesflying in a desired formation.




Applications of Formation Flight

Large sensor aperturesIncreased resolution

ServicingCan replace failed formation elementsindividually

Upgrade and MaintenanceCan work on individual componentswithout removing whole mission

Change formation geometryEvolving mission sensing requirements




Advantages of Formation Flight

Large baselines to improve angularresolutionSmaller vehicles

Ease of packaging, launch and deployment

RedundancyMission does not fail if one satellite fails

ReconfigurableReplace individual space craftCan integrate new technology during mission




Challenges of Formation Flight

Command and ControlControl multiple vehicles’ absolutepositions/motion vs.. relativepositions/motion

Propellant DrawbacksFuel limits lifetimeExhaust particulates contaminateimaging instrumentsExhaust creates haze which limitsimaging




Definition of Electromagnetic Control

Implement electromagnetic dipoles tocreate forces and torques between thevehiclesDipoles can be controlled by varying theamount of current through theelectromagnet coil.

Can provide steady forces and torques formaneuverabilityCan provide disturbance rejection for moreprecise control




Advantages of EMFF

No thrustersFewer consumables Longer life

Zero pollutionNo contact contamination

No radiative contamination

Controls relative position/motionvs.. absolute position/motion




Challenges of EMFF

Control ProblemUnstable – not unique to EMFFCoupled control

Each vehicles’ motion affects all other vehicles

Electromagnet DrawbacksFerromagnetic material is heavyElectromagnetic force is weak

Force in the far-field drops of as the 4th powerof separation distance

Electromagnetic interference with otherelectronic subsystems




Customer RequirementsMultiple VehiclesRepresentative Formation FlyingVehiclesControl to replace thrustersControl three degrees of freedom(DOF), traceable to six DOFRobust controller

Disturbance rejectionReposition vehicles




ConstraintsScheduleBudgetLimited human resources to CDIOclass and staffTesting facilityNo use of umbilical resources; power,air supply, communicationsRecorded test dataSafety of people, facility, and system




System Functional Requirements

Musts:Stability with at least three vehiclesControl in each relative DOF

Shoulds:Representative 5 rotation maneuver

One rotation spin-up, 3 rotations steady state,and one rotation spin-down

Operate in the far fieldSeparation distance at least 10x length ofelectro-magnet




System Operational Requirements

Test time 5 minutes

Identical interchangeable vehiclesSend/record test data

Respond to other satellitesRespond to user input

Demonstrate autonomyMaintain safety




EMFFORCE Testbed Development ApproachConceive and Design EMFFORCEtestbed PDR May 7, 2002Implement testbed CDR Nov.,2002

Operate completed testbed ARMarch, 2003

Operate at MITOperate at Lockheed Flat Floor Facility inDenver




PDR Purpose

To review the preliminary designand identify and resolve high riskelements of the system.Have outside expert review ofcurrent progress.




Space System Product Development Class

Actuation Formation Flight SystemsJesus Bolivar Amilio Aviles Amilio AvilesWilliam Fournier Andre’ Bosch Jesus BolivarLindsey Wolf Oscar Murillo Geeta GuptaMelanie Woo Leah Soffer

Electronics Structure/PowerStephanie Slowik Geeta GuptaErik Stockham Amy SchonsheckMaggie Sullivan Timothy SutherlandJennifer Underwood


OverviewSub-System design

ActuationFormation FlightElectronicsStructure/Power

OperationsImplementation

Resource TrackingBudgetsVerification & ValidationSchedulesAction Items

Conclusion

Introduction•Mission•Background &Motivation•RequirementsSummary•Approach•Overview



Actuation

Melanie Woo

Electromagnet

Reaction Wheel

IntroductionSubsystems•Actuation

•Requirements•EM•Reaction Wheel•Issues•BudgetEstimates

•Formation Control•Electronics•Structure/Power

OperationsImplementationConclusion


ActuationEM force induces spin-up of cluster frominitial perpendicular orientationRW provides counter torque to balancemoments induced by electromagnets


•Requirements•EM•Reaction Wheel•Issues•BudgetsEstimates




Actuation Requirements

Actuate control of vehicle clusterMagnets must be controllable innecessary DOFNo thrusters may be used

Electromagnets provide forceReaction wheel provides torque

Minimize mass and powerconsumption






Trades – EM Configuration

Possible configurations:Dipole, Y-pole, L-pole, X-pole

Eliminate:L-pole: center of mass problemX-pole: mass distribution to 4 dipole legs


•Requirements•EM

•Trades•Design

•Reaction Wheel•Issues•BudgetEstimates



Minimize mass and powerconsumption


•Requirements


Dipole vs.. Y-pole

•Design•Reaction Wheel•Issues•BudgetEstimates



Introduction

Trades – EM Configuration

Considerations:Mass distribution: Force

Dipole generates greater force since itenergizes larger amount of core massY-pole can vary direction of magnetic fieldwithout being rotated by reaction wheel

TorqueY-pole generates additional torque to becountered by reaction wheel

Subsystems•Actuation


•Trades


Trades – EM Core Material

CostAvailabilityMagneticProperties

B-H curveBsaturation

Permeability

Steel vs.. Iron

EM Core MaterialInduced Field vs. Applied Field

0

0.5

1

1.5

2

2.5

0 5000 10000 15000 20000 25000 30000 35000

H [Amps/m]

B[T

esla

]

AISI 1010 steel Remko soft pure iron



•Trades•Design





ModelingEM Software:Infolytica MagNet

Input EM configuration andgeometry to obtain forcesand torques

Example:Y-pole configurationSeparation: 2 mCore mass: 19.5 kgApplied current: 10 Amps



•Trades•Design





Modeling

Results:Force on A andB equal

Magnitude:0.42 N

Torque greateron B than A

A: 0.052 N-mB: 0.848 N-m

A

B

Energized CoilsIntroductionSubsystems•Actuation


•Trades•Design





Test Run VideoIntroductionSubsystems•Actuation


•Trades•Design





EM Design

Operational SetupSeparation: 3mSpin Rate: 1 RPM



•Trades•Design





EM Design

Magnetic Force for ThreeVehicles

Set equal to centripetal force

44 )(2

3

)2

(2

3

ssF CAoBAo

mag πµµµ

π

µµµ +=

totcent ms

F )2

(2Ω=



•Trades•Design





EM Design

Substituting in the followingrelations

And solving for mcore

coreo

core

o

coreCBA

BmBV

ρµµµµµ ====

51

5sm

Bm ototcore

core

πµρΩ=



•Trades•Design





EM Design

Substituting

Where

ocoilcoretot mmmm ++=

kgm 70 =

Hm

Cm

core

core

o

coilcoil

3

22

)4

(πρα

απρ=

core

core

r

L

2=α 20

coil

max

r

iC

π=



•Trades•Design





EM DesignSubstituting

B = 2 Tesla

α = 10H = 20000

Solving numerically for mcore yieldsmcore = 6.5 kg

Solving for core dimensionsLcore = .47mrcore = .02m



•Trades•Design





EM DesignThe applied field is set by the numberof amp-turns in the coil

Current limited by the wire gaugeNumber of turns sets coil length and voltagerequirementsCoil mass proportional to NiMore analysis needs to be done to optimizenumber of turns

coreHLNi =



•Trades•Design





RW Trades

Build vs.. BuyWill build RW to specifications

CheaperCommercial RWs are spacecraft sized

Material: Steel vs.. Aluminum vs..Plastic

Use AluminumDoesn’t interfere with magnetic fieldHigher density than plastics – RW will nothave to be as large


•Requirements•EM•Reaction Wheel

•Trades•Design

•Issues•BudgetEstimates




System Assumptions for RW Analysis

Cluster contains two vehiclesVehicles are modeled as uniform densitycylindersMax ΩRW = 2000 rpm ~ 210 rad/sRW is modeled as a ring with a thin platein the centerRing has square cross section withdiameter tring

rRWtring



•Trades•Design





System Dynamics

RWs provides counter torque tobalance system:

Cluster angular momentum(Hcluster):

Cluster moment of inertia (I):

Ω= IH cluster

clusterRW HH −=2

+=

2

0 22

smII tot



•Trades•Design





RW Dynamics

Moment of inertia of RW (IRW):

RW angular momentum (HRW):

RW mass (mRW):

( )22

2

1ringRWRWRWRWRW trmrmI −+=

( ) RWringRWRWRWRWRW trmrmH Ω

−+= 22

2

1

AlRWringRW rtm ρπ22=



•Trades•Design





RW Mass vs.. RW Radius

ms

mkg

sradrpm

sradrpm

kgm

Al

RW

tot

2

2700

2102000

105.01

15

3

==

==Ω==Ω

=

ρ

(kg)

(m)

ms

mkg

srad

srad

kgm

Al

RW

tot

2

2700

210

105.0

15

3

==

=Ω=Ω

=

ρ

2

2

2

21

270025.0

0077.0

−+

=

RW

RWRWRW

RW

r

mrr

m

π



•Trades•Design





RW Mass Estimate

RW has a mass of 0.16 kg givena radius of 0.2 mRW Assembly will not exceed 1kg - includes motor



•Trades•Design





RW Power Analysis

RW uses power mainly whenapplying torque – during spin up

Torque induced by dipole (τmag):

Relationship for B-field:

RWmagRWP Ω= τ

BAmag ×= µτ

30

2 xB Bµ

πµ=



•Trades•Design





RW Power EstimateMagnetic moment (µA):

Power required by RW (PRW):

RW power estimate:

RWBA

RW xP Ω=

30

2

µµπ

µ

sradrpm

mV

mr

mL

mx

RW

core

core

core

2102000

103.6

02.0

5.0

1

34

==Ω×=

==

=

−WPRW 13≅

0µµ core

A

BV=



•Trades•Design

•Issues•Budgets




Actuation Issues

System may not be able tooperate in the far fieldTotal mass is large (~15 kg)

Magnet core mass increasesrapidly with vehicle mass

Magnet temperature must bemonitored during operation






Budgets Estimates

1.550CopperWire

1331339911501150TotalTotal(vehicle)(vehicle)

1000

100

Cost($US)

131RWAssembly

>1206.5Iron Core

Power (W)Mass (kg)Part






Control

Will Fournier

Control

IntroductionSubsystems•Actuation•Formation Control

•Control•Requirements•Design•Trades•Issues•BudgetsEstimates

•Metrology•Electronics•Structure/Power



RequirementsCounteract disturbancesReposition satellites to performmaneuvers

One rotation spin-upThree rotations steady stateOne rotation spin-down

Control tolerance to 1/10separation distance






Design

Two modes:Steady state

Spin-up/De-Spin






Steady State

Must model axial dynamics






Steady State Derivation of Poles for Three VehiclesForce Balance

avgavg

avgavg

avgavg

s

cs

s

mhsm

ss

mh

ss

cssm

sms

c

s

csm

δµµ

δδ

δδδµµ

δ

µµ

40

0

40

2

30

2

40

20

0

24

20

4

20

4

)()(16

)(17)(

)2(

−=−

++

++

=+

Ω−+=

&&

&&&&

&&

avgCBA

c

µµµµπµ

===

=2

3 00

3

22

2

. s

mhsm

s

mvFcent =Ω== 4

20

4

0

)2( s

c

s

cF avgavg

EM

µ+=

Ω±=± 20s

hYieldspoles at

Perturbation Analysis






State Space Analysis

Where Rxx describes what states thecontroller penalizes. Ruu describes the“cost” of actuation.

[ ]∫∞

+=0

dtRRJ uuT

xxT uuxx

xxu FPBR Tuu −=−= −1

PBPBRPAPAR Tuu

Txx

10 −−++=

uxx BA +=&

Using the Cost Function:

And knowing that cost, J, is minimized when

avg

avg

s

ss

s

s

ss

s

µδµ

δ

δ

δ

δ

Ω

+

Ω

=

2

0

02

0

0

2

0

0

10&&&

&IntroductionSubsystems•Actuation•Formation Control





State Space Analysis Continued

Choosing:ρ=uuR

=

00

0αxxR

And using:

=

2212

1211

PP

PPP

Feedback is then:

[ ] [ ]2212

2

2212

121121 220

1PP

PP

PPPBRF T

uu ρρΩ=

Ω== −






Now solve for the closed loop matrixwhere

Evaluate as increases from 0

State Space Analysis Continued

[ ] xxuxx CLABFABA =−=+=&xu F−=

ρα ∞

Therefore the closedloop poles for the mostefficient controller lie alongthis curve






Steady State Stable Test Setup

imx

avg

0

206

πµµ

±

Stable mode poles at:






16.62X Uncontrolled System

Step responseof plant

Negligibledamping






16.62x Controlled System

Phase leadcontrollerDamping ratio:0.11 ± 0.01

Error causedby distancesensor noise






Steady State Unstable Test Setup

mxavg

0

206

πµµ

±

Unstable mode poles at:






Controller forUnstable Test Setup

Phase Lead Controller

p = -20, z = -3, k = 30

Damping = 0.68






Spin-up/De-spin Modes

MorecomplexNeed tomodeltranslationalforces andtorques






Initial Spin-up Forces

Results in a force and a torque on eachmagnet

S NS

N

s






Response to Translational Forces

Three regimes ofmotion

Two equilibriumpoints






Due to the configuration,when α + β = 0, thus when d = s

Response to Translational Forces

( )[ ]βαπµµ

+= Sins

F avgtrans 4

20

4

3

±0=transF






Spin-up Configuration Trade

A closer look at the resultant forceson the two dipole configuration

S NS

N

s







α=0, β=90

[ ])(3)(8

20 βαβα

πµµ

τ ++−= SinavgA

[ ])(3)(8

20 αβαβ

πµµ

τ ++−= SinavgB

[ ]

[ ] 2

1

4

2

)(3)(8

)(3)(8

20

20

==++−

++−=

αβαβπµµ

βαβαπµµ

ττ

Sin

Sin

avg

avg

B

A

S NS

NA

B

s







Configuration options:

• Favors a largercenter vehicle

• Favors equallysized vehicles






Control Location Trade

CentralizedAll information communicated to a hubwhich calculates a control solution

Independent ControlVehicles collect and process their owninformation and derive a control solutionfor their own vehicle

Hybrid controlCertain systems are controlledindependently while other systems arecontrolled by the hub’s control solution






Hysteresis and Saturation

HysteresisExperimental data

for curve

Saturation of electromagnets andtorque wheels






Budget Estimates

No massNo powerCost for maintenance of labequipment






Metrology

Metrology

Oscar Murillo


•Control•Metrology

•Requirements•Trades•Design•Issues•BudgetEstimates

•Electronics•Structure/Power


Documents

Preliminary Design Review - MIT OpenCourseWare · PDF file5/24/2002 CDIO3 Class Project 12 Constraints Schedule ... moments induced by electromagnets ... 2 m zCore mass: 19.5 kg zApplied