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Produced by the NASA Center for Aerospace Information (CASI)
ENVIRONMENTAL EFFECTS ON THE DYNAMICS

AND CONTROL OF AN ORBITING LARGE

FLEXIBLE ANTENNA SYSTEM

by

R. Krishna

Senior Graduate Research Assistant

and

Peter M. Bainum

Professor of Aerospace Engineering

Department of Mechanical Engineering

Howard University

Washington, D.C. 20059, U.S.A.

Offered for presentation at the

35th International Astronautical Congress

Lausanne, Switzerland

October 7-13, 1984

(NASA-CR-175448) ENVIRONMENTAL EFFECTS ON N84-2C627

THE DYNAMICS AND CONTROL. OF AN ORBITING

LARGE FLEXIBLE ANTENNA SYSTEM (Howard Univ.)

10 p HC A02/MF A01 CSCL 22B Unclas

G3/18 18883
CONTROL OF AN ORBITING LARGE FLEXIBLE

ANTENNA SYSTEM*

by

R. Krishna and Peter M. Bainum

Howard University, Washington, D.C. 20059, USA

Large flexible orbiting systems have been proposed for possible

use in communications, electronic orbital based mail systems, detection

of earth resources, and in solar energy collection. The size and low

weight to area ratio of such systems dictate that system flexibility is

now the main consideration in the dynamics and control problem as contrasted with the inherently rigid nature of earlier spacecraft systems.

For such large flexible systems both orientation and shape control will

often be required. In order to meet the stringent pointing and shape

control requirements of some of the proposed systems the effects of the

environmental disturbances on the dynamics of such structures need to be

considered. The purpose of the present paper is to consider the shape

and orientation control of the proposed Hoop/Column antenna system l in

the presence of the environmental disturbances.

The Hoop/Column antenna system is one of the configurations under

consideration for use in the future multi-beam Land Mobile Satellite

Systeml , designed to provided point to point communications for 250,000

subscribers across the U.S. in the mid 1990's.

*Research supported by NASA Grant NSG-1414 and the NASA/Howard Univ.

Large Space Structures Institute.
-2-

The system is based on a large geosynchronous relay antenna and a number

of mobile, Earth-based receivers. in order to achieve the required RP

performance a pointing accuracy of + (0.03 - 0.10) degree RMS and a

surface (antenna) accuracy of 12 mm RMS will be required.

The Hoop/Column antenna system2 , depicted in Fig. 1, in deployed

configuration, contains the deployable (telescoping) mast system connected to the hoop by support cables under tension. The hoc.p contains

48 rigid sections, to be deployed by motor drive units. The desired

shape of the RF reflective mesh is produced by a secondary drawing

surface using surface control cables. The reflective mesh is connected

to the hoop by quartz or graphite stringers. At one end of the mast

the electronic feed assemblies are positioned, whereas at the other end

are the principal solar arrays connected to the main bus based control.

The controllability and the control law synthesis based on a finite

element model of the Hoop/Column antenna system was considered previously,

neglecting the environmental effects. 3 Graph theoretic techniques were

employed to analyze the controllability of the system for possible proposed actuator arrangements (Fig. 2) which included torquers and point

actuators along the mast and nearby feed assembly, and a single actuator

placed on the hoop assembly. After establishing controllability for

a given combination of the number and location of the actuators, the synthesis of control laws was based tm an application of the linear regulator

theory and also pole placement techniques.
. -3-

In the present work, the linear regulator theory is used again to

obtain orientation and shape control of the orbiting antenna system considering the environmental effects. The major disturbances considered are:

(i) due to the solar radiation pressure on the vibrating antenna structure,

(ii) the solar heating effect and, (iii) the gravity-gradient torques.

The effect of solar radiation pressure on the dynamics of an orbiting

flexible beam was analyzed previously4 by using the force and moment expressions developed by Karymov. 5 The work was later extended to consider the

dynamics of an orbiting flexible square plate under the solar radiation

pressure disturbance. 6 It was shown that the principal effect of the solar

radiation pressure on the vibrating beams and plates was to induce oscillations in the rigid rotational modes. The solar radiation pressure disturbance model for the antenna system is now developed by coasiderin: the

antenna to be mainly composed of a flexible beam (the mast) and the two

rectangular solar panels, as flexible thin plates. The force end moment

expressions for the solar radiation pressure acting on the mast are evaluated numerically by considering the mode shapes of the mast. The mode

shapes and the frequencies of the solar panels which are connected to the

mast are evaluated first using a finite element program. The mode shapes

of the solar panels are then used to develop the solar radiation force

and moment expressions, numerically. The effects of the solar radiation

pressure resulting from the rest of the sturctural elements such as the

mesh and its supporting structure are considered to be negligible, based

on the extremely small projected areas involved.
control system would have time constants of t

-4-

Another important source of disturbance arises from the temperature

gradient induced in the structure due to solar heating. Expressions

for deflections induced in thin beams and plates (Fig. 3) resulting from

solar radiation heating are developed. Then mathematical models for the

moments resulting from the solar radiation pressure interacting with the

thermally deflected beams and plates are also derived. After incorporating

these expressions in the models for the uncontrolled and the controlled

dynamics of the beams and the plates, it was shown that the effect of

solar radiation pressure on the thermally deflected structures is larger

than the effect of solar radiation pressure on the vibrating structures.

The results of Ref. 6 are now applied to the Hoop/Column antenna, assuming

a nominal maximum thermal deflection of lm in 100m length of mast and

0.03 meters in 3m long solar panels.

The finite element model of the antenna system considered hcre does

not include the gravity effects of the structure in the orbit. Therefore,

the stabilizing gravity-gradient torques are modelled here as an external

disturbance. The effect of the solar radiation pressure interacting with

the vibrating as well as thermally deformed structure together with the

gravity-gradient torques are incorporated into the finite element model

of the antenna system.

A finite element model of the Hoop/Column antenna system which includes

all six rigid modes and seven flexible modes is considered. Only seven

actuators are selected (Nos. 1,5,6,8-11) so that the resulting closed-loop
-5-

With this choice of time constants, the environmental disturbance effects

on the transient responses of the antenna system can be visualized more

distinctly. The optimal feedback gain values are obtained using a split

weighting fuction for the matrices Q - 1000 I (except Q(4) - Q(5)- Q(6)-

1.0) and R - 100 I contained in a qiu dratic cost functional. The controlled

transient response of the antenna system lr. the pitch, roll and yaw rotational modes are shown in Fig. 4., with and-without the effect of the

environmental disturbances. The effect of disturbance is more pronounced

in the roll mode than in the pitch and yaw modes. A steat'v state biased

t

error of 0.001 radians is seen in all three modes which is recognized as

due to the interaction of solar radiation pressure on the thermally deflected structure. The effects of the disturbances on the flexible modes

of the system are found to be less than 1 percent of the peak flexural

amplitudes. The maximum control force required in actuator No. 6 increased

from 1x10

-4

 lbf to 3x10-4 lbf as a result of the disturbances induced

in the model. The total control effort required in the absence of the disturbances was about 1 lbf-sec. The control effort is increased to 400 lbfsecs in 4000 secs, when the environmental disturbance effects were induced

in the dynamic model of the system.

'In conclusion, the environmental disturbances predominantly affect

only the rigid modes of the system. The effect of solar radiation pressure interacting with the vibrating structure is seen to be much smaller

than the solar radiation pressure acting on the thermally deformed structure.

In order to reduce the control effort to maintain the shape r d orientation,

the thermal deformations will have to be minimized in the preliminary design of the system.
References

1. Golden, C.T., Lackey, J.A., and Spear, E.E., "Configuration Development of the Land Mobile Satellite System (LMSS) Spacecraft," Large

Space Systems Technology - 1981, Third Annual Technical Review,

NASA Langley Research Center, Nov. 16-19, 1981, NASA Conference

Publication 2215, Part 2, pp. 711-766.

2. Sullivan, M.R., "Maypole (Hoop/Column) Concept Development Program,"

Large Space Systems Technology - 1981, Third Annual Technical Review,

NASA Langley Research Center, Nov. 16-19, 1981, NASA Conference

Publication 2215, Part 2, pp. 503-550.

3. Bainum, P.M., Reddy, A.S.S.R. and Krishna, R., "On the Controllability

and Control Law Design for an Orbiting Large Flexible Antenna System,"

34th Congress of the International Astronautical Federation, Oct. 10-15,

1983, Budapest, Hungary, Paper No., IAF-83-340.

4. Krishna, R. and Bainia, P.M., "Effect of Solar Radiation Disturbance

on a Flexible Beam in Orbit," AL" 21st Aerospace Sciences Meeting,

Reno, Jan. 10-13, 1983, Paper No. 83-0431; to appear in AIAA Journal.

5. Karymov, A.A., "Determination of Forces and Moments Due to Light Pressure Acting on a Body in Motion in Cosmic Space," P.M.M., No. 5,

Vol. 26, 1962, pp. 867-876.

6. Bainum, P.M. and Krishna, R., "Control of an Orbiting Flexible Square

Platform in the Presence of Solar Radiation," Fourteenth International

Symposium on Space Technology and Science, Tokyo, 1984; (accepted for

presentation).
port

p section

pport

es

^viar pau^s.s

Fig. 1 The Hoop/Column Antenna System
^^, "'e, 0

•

ORIGINAL PAGE 18

OF POOR QUALITY

Lae .0 Ins

lal •

1 ,

1 ^

twat tendsas --+^ 11>) / Y

dO

tOt1

^

1

I+s-- Seen 1

I

loo ^^ © lo/

Fij. 2. lropesed arrangement of utuacors Roop/colusn systm.

(uncireled nuabers identify grid points frm finite element analysis)

Z

8i

n+A2

b Undeflected Beam

T

2 T _ AT Deflected Beam

n 2

Fig. .3. Beam Bending Due to Solar Radiation Seating

X

_.
ORIGINAL PANE 19

OF POOR QUALITY

0.0

^o

v

T+

-0.01

..-r..W.. Uia6Uavali4C wiLn alscuroance

0.0

t^

^ J

tPl

v

-0.01

0.0

v i

^+ 11

-0.01

1000 2000 3000 4000 se-:s.

I.C.'s: y(1) - y(2) - ... y(6) - 0.0

y(7) - y(8) - ... y(13) - 0.01

Q - 1000I, R - 100I, Except Q(4) - Q(5) • Q(6) • 1.0

Fig. 4. Controlled Transient Response of the Hoop / Column

Antenna System. Control Based on LQG.

- - -_ - --^ -- --- 

L-