Single Access Antenna Pointing Control System Design of TDRS

Single Access Antenna Pointing Control System Design of TDRS

JinpengYuan,DiYang, andXiaosongSun

Abstract-Trackingand DataRelay SatelliteSystem (TDRSS) point to the user satellite with high accuracy. In order to is one of the hot spots in the development of the aerospace satisfy the requirement for high pointing accuracy, the engineering recently. It is a challenging task to design the SA attitudestabilization control system of themain bodyandthe pointing control system with high pointing accuracyto ensure SAantennapointing controlsystem are being studied[1-4] in the communication between the Tracking and Data Relay some

countries.

Satellite(TDRS)and theusersatellites. The SApointingcontrol

system is designed in this paper in detail. Firstlythe dynamic Sun Panel modelof the TDRS is established usingtheLagrangeEquation.

Secondly the control scheme of the TDRS satellite is selected for themainbody and thesingleaccess antennae.Thetrackinglaws arederived and the antenna's azimuth and elevationanglescan bederivedby thetrackinglaws when theTDRS istrackingthe usersatellites.Thirdlytheantennapointingcontrolconceptsare

described, and the onboard autonomous control method is Single Access Antenna SingleAccessAntenna

designed. The on-board autonomous control scheme is x -I

composedofacquisition and autotrack modes.On onehand the Xa

acquisition processof the SA antenna isdesigned, On the other

+ 7 Td

hand, the antenna steplogic of the autotrack mode isproperly Z /

Bo\

^Ya

selected. The SA antenna is driven by two-phase permanent T Za

magnetic stepper motor, and the mathematical model of the steppermotoris established.Finally,themathematic simulation of theantenna pointingcontrol system designedinthis paper is

conducted in thecaseoftakingtheusersatellite and theground SunPanel station astracking objects according to tracking laws derived

before,and the SAantennapointing performance of the TDRS Fig.1. Thesimplifiedstructurediagramof the TDRS is demonstratedby theanalysisof the simulation results.

The controlsystemdesignof such flexiblespacecraftmust I. INTRODUCTION be considered

seriously

because of the severe interaction

r

'HE

Tracking and Data Relay Satellite (TDRS) is a between the

appendages

and the main

body

of the satellite

spacecraft

that is used to

provide tracking

services and

[5-6].

Onone

hand,

the

attitude

^{maneuver of the}main

body

can

impose disturbance

torque on the appendages. On the data relay services between the

ground

station and the other

hand the motions

ofthe appendages also cause

much

earth-orbiting satellites_3,10 mies.TheTrakinat altitudes from^{an Dat Reay}750atelitmilestoSytemabout

dturbanct

disturbance to^thethe

maionb

main

body.

The^theaof

design

of the SA^as

canten

antenna 3,100

miles.

The

Tracking and Data Relay

Satellite System pointing control system and the TDRS attitude control system which is normally composed of three TDRS in different is animportant part of the whole system design to ensure the orbits, is animportant

approach

to increase the information highpointing accuracy of the SA antennae.

transport capability in space,

improve

the

novelty

of the This paper describes the SA

antenna

pointing control obtainedinformation,soit have been

developed rapidly

inthe system design in detail. The tracking laws for the SA countrieskept aheadintheaerospace

technology

suchasthe

antennae

to trackthe user spacecrafts is established, then the UnitedStates,Russia, Europe and Japan. actuator for drive the SA antennae the PM stepper motor is The

configuration

of the TDRS is very complex. Each introduced and itsmathematical model is established. Finally, TDRS has many large flexible appendages such as solar thesimulation is done to verify the validity of the SA pointing panels, SA antennae and etc. The

simplified

structure of control system of the TDRS.

TDRS is shown in

figure

1. The SA antenna is

required

to

II. THEDYNAMIC MODEL OF THE TDRS Manuscriptreceived November18,2005.

J. Yuan is with the Department of Astronautic Engineering, Harbin The main body of the TDRS is regarded as rigid, and the Institute and Technology, Harbin 150001, China. Phone: single pendulum model is used as the equivalent mechanical

±86-0451-86412032;fax:±86-0451-86412834;e-mail:

hitjyuan@sina.com.

model of the fuel sloshing, then the Lagrange equation D. Yang is with the Department of Astronautic Engineering, Harbin

Institute and Technology, Harbin 150001, China. Phone: tornr%bl1sh th ^ac m o T

±86-0451-86412032; fax: ±86-0451-86412834; e-mail:dyang@hit.edu.cn. The finaldynamic model of the TDRS isgiven as Eq. (1). of X. Sun was with the Department of Astronautic Engineering, Harbin its high frequency and smaller rigid-elastic coupling scalar.

Institute and Technology, Harbin 150001, China. He is now with the Beijing Institute ofControl Engineering, Beijing 100080, China.

AttitudeAngle

Fig.2.dThetiollor ^ockdia ^TDRS Ady

The top-e

MofeTdesel

ConmiRd+ +P + ritentemi

I/ba+RTdb+ ~ StpLoTto(1)sltandard appran-chi..saseorndgosfrtiue

i~27w~ +FSd)+ FO pafrmasMbdly o omlmd tiuecnrl h

Pointfing Angle

user Satellite

Fig.2. ^Thetop-levelcontrol blockdiagram^{of TDRS}

The

top-level

ofthe TDRS' control

system

^aredescribed^as Ibb+Raa)+F Q+

Pa,C

^+bX

Hb

⁼Tb

figure

2. The attitude control for the main

body adopts

the

Tat

^{l)- a7=T} standard

approach,

i.e. star sensor and gyros for attitude

*- ^{a a}

2b =T-

^T-

estimation,

and

three-axis orthogonal

reaction wheels

77+2,f

^f

77+

^f77+

F,ob

+

Fa

Coa

=°platform assembly

for normal mode attitude control. The s+ ° + w a+

Qs6)b 0

attitude controller is designed using the traditional PID WhereIbis the moment-of-inertia matrix ofthesatellite; c9b

(proportion plus integral plus derivative)

control laws.

is the angular velocityvectorof the satellite main body; c9ais In the antenna pointing control system, the antenna is the angular velocityvectorof the antenna; Hb is the angular driven by the gimbal drive assembly. The gimbal drive momentum vectorof thesatellite; qis the vibrationmodal;

4f

assembly consists of a two-phase,permanentmagnet stepper is the flexible modesdamping matrix;

ofjis

the flexible modes motor with a 1

.5°

step size and a harmonic drive speed frequency matrix;QbiS thetorqueapplied to the satellite main reducer with a reduction ratio of 200:1. The pointing body; Qa is the torque applied to the SA antenna; Ia is the

accuracy

^{of the SAantenna}must be below

0.03.

moment-of-inertia of the SA antenna; Ra is the influence

matrix ofthe main bodyonthe rotationofthe appendages;

FS IV.

TRACKING LAWS OF THETDRS is the flexible modes coupling

matrix;

Fa is the flexible

coupingmatixf te apenage; a istheslohin moal; In the process of the SA antennae pointing to the user

coupl osimng

modes

dampin

ma is the

sloshingmd satellites,

the onboard computermust calculate the desired

modeis frequeoshinc ^matrix dampisgtheasing modesi ^couping

^gimbal

^angles

^to

^point

^{theantenna attheuser} satellite. This modes

frequency matrix; Ps

iSthe

sloshfng

modes touthen ay also call the

tracking

laws.

slosing

^{of the}

liui. . ^Assuming

^{that the}

^position

^{of theuser}satellite is known in

sloshing ^{of the} liquid. theantenna

fixed

coordinates

(denote by

a, the null

position

III. CONTROL SCHEME DESIGN OF THETDRS of theZaaxis

through

main beam isasthesamedirectiontoZ axis of thebodyfixed coordinate, and the null position of xa

The

pointingcontrol systemofthe sAantennae isessential axis is the same direction as the X axis as the body

fixed

to insure

thehigh pointing accuracy because ofthe following coordinate). The body

fixed

coordinate and the antenna

fixed

three reasons.

Firstly,

the antenna pointing accuracy is higher codnt r losoni iue1 d,ci ~ eoe

than the stabilization accuracy of the main

body,

and the ^y

antennae are embarked on the body of the TDRS, so the the

position

of the user satellite. The

position

of the user

pointing controlsystemoftheSA antennae mustbedesigned satellite and the antenna fixed coordinate are redrawn in inaddition. Secondly, there existssevereinteraction between

figure

3.aand a denote the azimuth

angle

and elevation

angle

the SA antenna and the body of the satellite; the attitude respectively. The position ofthe user satellite is denoted by u.

stabilization control error has bad effect on the pointing From the ubiety of the user satellite and the antenna fixed control accuracy of theSA antenna. Finally, the vibrations of coordinate we can get:

the boom that support the SA antennae also make the antennae deviate from the user satellites.

oc^=-arctan

(dy

^I

dz

) blindzonedue to the gimbal lock or the truncation

(2)

of the earth.

=

arcsin (dI ^/ d) c) Performing

^{the new}

acquisition

^{when the user}

satellitepasses the blind^zoneof the TDRS.

where d= +c12 +dZ2 denote the distance between Acquisitionis composed ofthree modes: slew mode, open loop tracking mode and the pull-in mode.

the usersatellite and TDRS.

Xa A. The Mathematical Model

of

the PM

Stepper

Motor

A The antenna is driven

by

^the

gimbal

^drive

assembly.

^The

gimbal drive assembly consists of a two-phase, permanent

dx

magnet steppermotor and a harmonic drive speed reducer. In order to establish the whole simulation model to test the d

validity

^{of the}

pointing

control

system,

the mathematical o , < C F model for thePM

stepper

^motoris

given

^below[

/X

Q/

^Za

d'a

⁼

[V -Ria

⁺

Kmo Sin (NrO)]

^{/ L}

B/ \/di =[Vb-=Rib-Km,W)cos(NrO)]/

^{L (3)}

dz Q dt

=L[-K,i,

= ^sin

^(Nt)

⁺

^KJbcos (NrO)-BW]/

^J

Fig. 3. The position of theusersatellite inthe antenna fixedcoordinate. dO _=co

V. THETDRS SA ANTENNA POINTINGCONTROL SYSTEM where

Va,Vb

dt ^and

i,

ib are thevoltages andcurrents in phases DESIGN A and B, respectively. Further, 0 is the rotor (angular) Theusersatellite acquisitionand tracking is a key problem

speed,

0 is the rotor (angular)

position,

^{B is the viscous}

to ensure the communication between the TDRS and user friction

coefficient,

J is the inertia of themotor and the SA satellites. Presently there are twomethods for designing the antenna,

Km

is themotortorqueconstant. Ris the resistance antennapointing control system, one is the satellite-ground of the

phase winding,

^L is the inductance of the

phase

interconnection controlmethod and the other is the onboard

winding,

and

N,

is the number ofrotorteeth.

autonomous

close-loop

control method. In the The

parameters

of the

mathematical

model are

given

ⁱⁿ

satellite-ground interconnection control method, the TDRS table

1.

needsanelaborate ground support system.The error sensors TABLE I

embarked on the satellite give the error information to the THESTEPPER MOTOR

PARAMETERS

groundsupportsystem,then the control commands generated Parameter Value by the groundsupport system aretransferredtotheTDRS. In L 0.5mH

the onboardautonomous close-loop controlmethod, there is R 2 Q

nonecessary to have a complex ground support system, all Km

0.5Nm/A

the information and control commands is processedby the B 5.0X10-3Nms/rad onboard computer embarked on the satellite. The onboard

autonomous close-loop control method can realize real-time B. Acquisition design

control, and the loop time delay is small which is criticalfor The acquisition mode is composed of slew, open loop the high-speed communication. The onboard autonomous

tracking

and

pull in[8].

So the detailed design procedure is close-loop control method is the major control methodinthe givenbelow.

next generation advanced TDRS(ATDRS), and the

1)

Slew mode

design

satellite-ground interconnection control method will be When thepointingerrorisgreater than 1 degree,then the adopted in the emergency case. Only the onboard SA antenna is controlledby slew mode. The slew mode is autonomous close-loop control method is considered inthis made up of three segments:

acceleration,

constant rate, and

paper. deceleration. The acceleration time is

5s,

and the desired

The onboard autonomous close-loop control method is maximum slewrateis 30 stepsper

minute,

that istosay, the composed oftwomajor modes. One is theacquisition mode desired constant rate of the SA antenna is 0.225 degree per in which the onboard computer generates gimbal angle minute. The start time of the deceleration depend on the commands based on the computed location of the user pointing error. When the pointing error is less than 1.17 satellites. The acquisition mode is used to: degree, the motion of the SA antenna must be slow down to

a) Slew from one usersatellite to the other. ensure the success of the acquisition.

b) Generate the pointing controlcommand to the SA 2) Open-looptracking modedesign

antenna when the user satellite is located in the When the pointing error is less than 1 degree, the pointing

controlsystemisintheopenlooptracking mode. According coordinate system, d denote the distance between the ground to the physical characteristics of the SA antenna and the station and TDRS. According to the previous proposed stepper motor, the desired pointing rate is 0.03 degree per tracking law we can get the initial error angles of azimuth axis

minute. is -30 degree and that of elevation axis is 45 degree

3) Pull-in mode design respectively. SA antenna 2 is in tracking a normal user When theusersatellite entered the field of view of theRF satellite in the sun synchronous orbit with the altitude of sensor,then the SA antenna can lock the user satellite. So the 1000km without initial pointing error. The simulation results pointing control system is in the pull-inmode. The field of are shown in followingfigures.

view of the RFsensoris 0.4 degree, and the diagram of the , pull-in mode is showninfigure4.

0 0.06 0.22 0.4 2-30.1

) 0 50 100 150 200 250 300 350 400

PointingError(deg) 50

Fig. 4. Diagram of the pull-in mode

0

Suppose lineAO in figure 4 describes thepointing error ^E

trajectory of the SA antenna. The design procedure is as < -50c 50 100 150 200 250 300 350 40

follows. When thepointingerrorisinthezoneI, the desired 05

tracking rate of the SA antenna is 0.03 degree per minute. a Slew 0-P Autotrack When the pointingerrorisinthezoneIT, the desired tracking ^ry ° _

rateoftheSAantenna is0.0225degreeperminute. When the E

pointing erroriserrorinthezoneIII, the desired trackingrateofthe < 0 50 100 150

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t(s)

200 250 300 350 400 SA antenna is 0.00375 degree per minute.

Fig. 5. The azimuth tracking performance of antenna1

C. Autotrack modedesign

The autotrackuses RF sensor to measurethe pointingerror O ____

andpoint theusersatellite withhighaccuracy.Only when the ^.2 acquisition mode achieves certain accuracy,the SA antenna 45

canbe switchedtothe autotrack mode. ll

a)c44.9

The step logic of the autotrack mode generates step ⁾ 0 50 100 150 200 250 300 350 400 commands in responseto the estimated trackingrate of the 5C

antenna and the autotrack error. The stepping period

Ts

is L 0 determined according to the estimated tracking rate of the ^>

antenna Ca The required stepping periodcanbe determined 0 0 50 100 150 200 250 300 350 400

by _

Aa/Ts

^{> )} (4) ^{C Slew}

m-p

^Autotrack

After the selection ofthestepping period, then the role of the ^> -0 50 100 150 200 250 300 350 400 step command generationmust be confirmed. In this paper t(s)

weconsiderasimplecase--ineachstepping period onlyone step command is generated. If the tracking error of the

antenna exceeds the antenna step size

Aa

in a certain

Figure

5 and

figure

6 shows the simulation results of the stepping period, then a step command is generated in that firstSA antenna. Where O-P is the abbreviation of the open stepping periodinthesamedirection oftheantenna'smotion.

loop tracking

mode and

pull

in mode. From

Figure

5 and Otherwise,nostepcommand isgenerated.

figure

6 we can see that the antennal

experienced

all the modes, from slew mode to autotrack mode, and realized VI. SIMULATION AND ANALYSIS

tracking

and

pointing

the desired

target successfully.

The In orderto verify the validity of the SA antennapointing slew mode costs about 200s, and the slew rate is up to 0.225 control system and the attitude stabilization control

system,

degree per

minute.

the simulation is conducted using

Matlab/Simulink<.

The Figure 7and figure 8is the simulation results ofthe second simuatin dagrmo th whle sste isdesribd i fiure SA antenna. This antenna is in the autotrack mode.

2. SA Antenna 1 will communicate with a

fixed

ground station that locates in (li lid ad in the antenna

2i

^'

4')

6 _____________________________________

antenna pointing

control

system

from another

point

of

view,

the attitudeerrorofTDRSisgivenas figure9. Asshowedin

S:4 X figure

9,

the pointing error of main body is less than 0.01

EN

degree. This results show that the couplingtorqueintroduced

2 bySA antenna'smotion is sustainable.

o

0 50 100 150 200 250 300 350 400 VII. CONCLUSIONS

0.04 The

pointing

control

system

of the SAantennais

designed

r- ^0.02

U M I i h

for theTDRSinthispaper.

w o The steppermotoris selectedtodrive theSAantenna.The

E0.02

i.I.I

2~~Fr ,Irti

ll'IF. I'ITIPIII!I~!lIii

~use

of ^a

stepper

motor is ^a definite

advantage

since the

< _ _ _ _ _ _ stepper motor responds to commands in a predictable,

-0.040 50 100 150 200 250 300 350 400 quantized manner. The mathematical model of the stepper t(s) motoris introduced. At the same time, the pointing control Fig. 7. The azimuth tracking performance of antenna 2 system ofthe SAantennais designed in detail. As a challenge to control the SA antenna with high accuracy to trackuser

o

satellite,

the

step logic

of the

stepper

motorwas

designed

and

C _0.5

-osaccuracy

the whole simulation ofthe TDRS is conducted. The^{of 0.03}

^degree

is achieved and this satisfies the

pointing

w -1 specification of theSApointing controlsystem.

U) -1.5

D 0 50 100 150 200 250 300 350 400 REFERENCES

________________________________________ [1] Y. Kawakami, H. Hojo,M. Ueba, "Design ofanOn-board Antenna

U,

0.01Pointing

^{Control System} for Communication Satellites," AIAA,

0.005 88-4306-CP, pp.689-694.

[2] H. Dodel, D. Fasold, E. Frisch and M. Lieke, "Antenna System

C , AlternativesforDataRelaySatellites withMultiple^SteerableBeams,"

(U-005

IAF-86-349.

t(s) AIAA-96-3787, pp.1-8.

[4] C. Catallo, "Italsat Spacecraft Multibeam Payload Antenna Closed Fig.8. Theelevationtracking performance of antenna 2 Loop Fine Pointing System," IAF-91-509.

[5] Q.Tham,F.Lee, J.H. LyandR.Y.Chiang, "Robust Pointing Control of

As canbe seen from Figure 7 and figure 8, the pointing Spacecraft with Large Appendages," Proceeding of IEEETransactions

controlaccuracyof azimuth axis and elevation axis are0.03 onAC, (1997),pp.369-375.

degree

and 0.01

degree respectively.

The simulation results [6] _d^Q.Robust Antenna Pointing Control for TDRS Spacecraft, ProceedingsTham,F. Lee,J.H.Ly, R.Y.Chiang,D. Bender and B. N.

Eyerly, satisfy

the antenna pointing accuracy of TDRS (0.01 - ofthe 36th Conference on Decision & Control," San Diego, California,

0.05degree). The simulation results show that the antenna USA, (1997),pp.4938-4942

pointing controlsystem is valid

andproper.[7]

^T.Kenjo, SteppingMotorsand theirMicroprocessor Controls, Oxford,

pointing control systemiS valid andproper. U.K.: Clarendon, 1984.

_____________________________________________ [8] H.Control system," AAS 80-007, pp. 115-146.Schmeichel, T. T. McElroy, " TDRSS Single-Access Antenna 0

-0.01_{0 50 100 150 200 250 300 350 400}

0.01

L~

^{0~ 0}

-0.01

0 50 100 150 200 250 300 350 400

0.01 0 0

-0.01_{0 50 100 150 200 250 300 350 400}

t(s)

Fig. 9. The attitude error of main body

In order to demonstrate the feasibility of the designed