massachusetts institute of technology - challenges and solutions for low-area-density...

Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.

A98-45965

AIAA 98-5142

Challenges and Solutions for Low-Area-Density (LAD) Spacecraft Components

Application to ultra-thin Solar Panel Technology

O. de Week, W. HollisterDepartment of Aeronautics and AstronauticsMassachusetts Institute of Technology77 Massachusetts Avenue, Cambridge, MA 02139

Defense & Civil Space ProgramsConference and Exhibit

von Braun Center, Huntsville, ALOctober 28-30, 1998

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AIAA 98-5142

CHALLENGES AND SOLUTIONS FOR LOW-AREA-DENSITY (LAD) SPACECRAFT COMPONENTSAPPLICATION TO ULTRA-THIN SOLAR PANEL TECHNOLOGY*

Olivier de Week1, Walter Hollister2

Department of Aeronautics and AstronauticsMassachusetts Institute of Technology

77 Massachusetts Avenue, Cambridge, MA 02139

Abstract

Spacecraft miniaturization is an important trend in spacecraft design and manufacturing, which has emerged over thelast decade. There is however a class of spacecraft components, which can not be scaled down arbitrarily, as theydepend on a given surface area A,, to meet their performance requirements. These components emit or receive RFenergy from the space environment and are typically classified as optical mirrors, RF antennas, thermal radiators andsolar arrays. When designed as low-area-density (LAD) components, which are thin and ultra-light, they must bestowed during launch and subsequently deployed once on orbit. There are however fundamental limitations to the LADapproach, which arise from the flexible dynamics. It is difficult for components with very low fundamental frequencyto maintain a desired surface accuracy in the presence of dynamic disturbances. Potential solutions presented hereinclude active/passive isolation from the noisy spacecraft bus, command shaping and use of embedded smart materials.A large ultra-thin solar array with single axis articulation is used as an illustrative example.

1. Introduction

Spacecraft miniaturization and distributedarchitectures are two important trends in spacecraftdesign and manufacturing, which have emerged overthe last decade. Due to advances in electronicspackaging, light-weight composite materials andmicro-mechanical device technology (MEMS), theperformance density of spacecraft (e.g. Mbps/kg) issteadily increasing. There is however a class ofspacecraft components, which cannot be scaled downaccordingly, as they depend on a given surface area A0to meet then- performance requirements. Thesecomponents emit or receive RF energy from the spaceenvironment and can be classified in the following fourcategories as: (1) optical mirrors, (2) RF antennas, (3)solar arrays and (4) thermal control system radiators. Areduction in surface area for these components has adirect impact on then1 performance, assuming constantefficiency. Thus a weight and volume reduction forthese items - assuming constant performance - has tofocus on a reduction in the third dimension (thickness).This leads to the concept of low-area-density (LAD)components, which are thin and ultra-light and must bestowed during launch and subsequently deployed onceon orbit. This paper presents an overview of thechallenges that arise from the use of low-area density

spacecraft components in the future. Figure 1 showsthe MILSTAR communications satellite, which makesuse of large, low-area density solar arrays to generatesufficient power for RF communications andspacecraft subsystems supply.

LAD solar array

Spacecraft BusFig.l: MILSTAR communications satellite [1]

In order to characterize the challenges for low-areal-density (LAD) components, it is necessary tofirst define the function and performance metrics,which govern the design of each type of LADcomponent. Secondly the disturbance environmentacting on a component must be characterized. Thedisturbance analysis propagates these physical

* Student Paper Contribution. Copyright © 1998 The American Institute of Aeronautics and Astronautics Inc. All rights reserved.1 Graduate Research Assistant, Space Systems Laboratory, M.I.T.2 Professor, Department of Aeronautics & Astronautics, M.I.T.

American Institute of Aeronautics and Astronautics


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disturbances through the component. If it isdetermined, that if the disturbance is too severe tomeet performance, corrective measures have to betaken.

2. Typology of LAD Components

It can be concluded that components, which areappendages to the spacecraft, are usually directlyinteracting with the space environment. Theseappendages are clearly candidates for low-area-density components. There is one thing, which allthe types of low-area density appendages have incommon. They all receive or transmit energy in theform of electromagnetic radiation. The maindifference between them is the operating pointwavelength and subsequently the accuracyrequirements of the surface itself. It is important tonote, that the area is merely a collecting or emittingsurface, which has to be held to a certain accuracy.The physical laws governing the LAD components'performance are as follows:

Angular resolution of optical aperture (-500 nm):(2.1)

Peak gain in pattern of RF antenna (0.001-10m):

n.f!/!̂ l (2.2)

Power generated by solar array (250-2000 nm):(2.3)

Power radiated by thermal radiator (1-100 um):A (2-4)

In all four cases the surface area A or diameter of acircular aperture D, enters directly into thegoverning equation. If these appendages have madeup a significant portion of spacecraft mass andvolume in the past, it is due to the massive backframes, truss structures, deployment and actuationmechanisms, which were necessary to ensure thesurface accuracy of this class of components. Therethus is a demand for a new class of lightweightcomponents, which use active and passive isolationtechniques, as well as "smart" sandwich structureswith embedded active materials for quasi-staticshape control. A reduction in the area-density ofcomponents becomes a necessity when theperformance requirements become more stringentbut mass and volume constraints of present launchvehicles remain constant. Figure 2 shows the trend

for reduction in area density for space and land-based telescope primary mirrors and the goals,which have been set by NASA for the nextgeneration space telescope (NGST) primary mirrorin particular [2]. Current proposals for the NGSTprimary mirror range from 14.5 - 22.3 kg/m2 interms of the area density.

Primary Mirror Area Density Evolution

10'

1.0 10.0Mirror Diameter m

Fig. 2: Trend for area density reduction

3. Performance Modeling

In order for this approach to be successful it isparamount to first exactly understand the function,which each LAD component fulfills and to defineappropriate performance metrics. These can laterbe a basis for the definition of a cost function (e.g.based on H2 and H«> norms), that can be used by astructural controller.

The first step consists of creating a model of thestructure, the disturbances and performances. It hasto be determined whether the structure can meet therequired performances under the influence of thedisturbances. This process is shown schematicallyin figure 3 within the framework of controlledstructures technology (CST).

It is necessary to define relevant performancemetrics for each low-area-density component, thesemetrics are different for optical reflectors, RFantennas, thermal radiators or solar arrays, wherebythe optical surface precision requirements are themost demanding.



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Fig. 3 Analysis and CST- Methodology

In order to assess the performance of variousdesigns, a cost function must be established (e.g.cost per kWh of usable energy from solar panels =cost per unit function). These are generally relatedto the surface accuracy of the LAD component. Thefollowing is a breakdown of typical performancemetrics associated with each LAD component:

Thermal Control radiators: Heat flux radiated• Always pointing to free space• View factor to rest of spacecraft• Thermal mass and time constant

Solar Array: Power collected• Power Loss cost function• Minimize end-point displacement (bending)• Minimize torsional twist• Tracking of input from articulation

RF Antenna: Radiation Pattern• Peak Gain G, of main lobe• Side lobe levels• Beamwidth ©• RMS Surface accuracy

Optical mirrors: Image Quality• Spherical Aberration• Coma and Astigmatism• RMS Surface error **

•* RMS surface error:

This is a frequently used performance metric, as itmeasures the difference between the actual surfaceand a perfect reference surface and expresses it as asingle scalar value. While this number is simple tohandle, it does not give any information, which areaof the mirror or component surface is contributingthe most to the error.

For NGST the acceptable RMS surface error is afraction of the wavelength and is expected to bearound CRMS = X/14, which is around 157 nm forX=2.2 urn. This is a very stringent requirement. Ageneral statement to be found in the literature is:"The surface accuracy ranges from several percentof wavelength for low frequency applications to asmall fraction of wavelength for optical systems"[3]. A surface RMS accuracy of CRMS ~ 1mm isusually sufficient for applications below 15 GHzaccording to Thomas and Veal [4]. Where therequirements for the surface accuracy of a thermalradiator are not very stringent, they become a majordesign and cost driver in the case of opticalreflectors.

We can model a dynamic performance bydetermining the following four items:

• Location (where measured, local, distributed)• Type (displacement, angle, power etc....)• Amplitude and frequency content

Several performances can be established for a lowarea-density component. These may then becombined in a single cost function Jz with the helpof a weighting matrix RZZ. This cost function can bedefined in the time domain or hi the frequencydomain.

4. Disturbance Modeling

An overview of internal (onboard) and externaldisturbance sources (depending on orbital altitude)acting on LAD components hi the spaceenvironment is given here. The disturbances, whichcan affect the structural performance of low-areadensity components in space, are the ones that exerttorques or forces on the LAD components and areshown hi a simplified way in Figure 4.

Torq

ue [N

mj /

For

ce [N

]

%

51

% «

GravityGadettoques

i

4AtmosphDrag

I

toques

ThrusterFit Forces

>• Thsrma

. Snapno toques ...• Magnate JgI Toques

uaiai o ———OyostatVanlirFaces

ing 9 ̂

®SEffects

0 ————————Gain Antenna

later Noise

1

*

ITIQ noiss 11.̂ . _i M.J

SecondaryChoppingToques

Internal Distuibance

Exteinal Distuibsno

®WitudeControl F«aVAieei Imbalance

5

£

N(3.1) 104 1C* 1CP 1*

Frequency [Hz]

Fig. 4 Typical disturbance characterization (LEO). [5]



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It can be seen that the external disturbances areusually quasi-static and have virtually no energy athigh frequencies, whereas internal disturbances ahave significant high frequency content.

It is now necessary to characterize thesedisturbances mathematically, in order to use themfor our analysis purposes. It is obvious that theexternal disturbances are mainly a function of theposition (altitude) and orientation of the spacecraft,whereas the internal disturbances depend on thedesign and mode of operation of an individualspacecraft. Regardless of this, the disturbance mustbe characterized as follows [9]:

• Location• Type (torque, force, pressure)• Amplitude and frequency content (PSD)

Generally we can characterize disturbances in thefrequency domain or in the time domain, with theprimary relationship between the two being theFourier transform. This has been attempted for oneexternal and one internal disturbance. These resultswill subsequently be used for the ultra-thin solararray example.

External: Solar Radiation Pressure

The sun emits a flux of electromagnetic energyover a large frequency range. According toPlanck's law the peak of the power spectral densitycorresponds to the surface temperature of theemitting black body (sol: 6000 K). The powerreceived by an area of 1m2 at a distance of 1 AU iscalled the solar constant:

P0=1358±5W/m2 (4.1)

Traditionally the effect of solar radiation pressureon the shape of a spacecraft component had notbeen considered, because the resulting deflectionswere negligible. When solar radiation impinges ona non-transmissive low-area density componentthree kinds of effects may be observed. These are

Absorption

dA

Fig. 5: Solar Radiation Absorption

total absorption, specular reflection and diffusereflection. A conservative approach is to assume100% absorption as shown in Figure 5:

-cosQ-dA (4.2)

where ccs is the absorptivity of the surface at agiven wavelength. For a 3-axis space stabilizedspacecraft the relative angle between the surfacenormal and the incident flux changes only as afunction of the mean anomaly and the other orbitalelements. An upper bound for the frequency changeof the sun incidence angle ®(t) in earth orbit is theSchuler period of 84.4 minutes [6]. This results in afrequency of 1.97x10"4 Hz. This allows us to modelthe incident disturbance as a quasi-static distributedforce. Dynamically we can model this disturbanceas a band-limited white noise with a very low cutofffrequency of- 2.0X10"4 Hz. The transfer functionbetween the filtered disturbance di and the whitenoise disturbance can be written as:

G (s\ = _^s' = ^RQ (4.3)d \ ) ~7T" , . ~~* V * /

RO

The power spectral density of the filtereddisturbance can be written as:

>2RO (4.4)

CO + CORO

where 5_ is the power spectrum of the white noisedisturbance. The solar pressure can be essentiallyviewed as a DC disturbance; this however has to berelated to the flexible modes of the structure uponwhich it impinges. An upper bound for themagnitude of the solar pressure disturbance can beassessed by assuming 100% absorption with as =1.0 and a sun incidence angle 0=0°.

dF = ̂ -dA (4.5)c

We thus obtain a maximum magnitude of solarpressure of 4.5xlO'6 N/m2.

Internal: Solar Array Actuator Noise

We assume that the solar array is controlled by aone axis actuator, which can rotate the panel aboutthe x-axis. Typically actuator noise is concentratedover a certain frequency range, i.e. it's PSD (powerspectral density) is band-limited. The spectrum ofthe disturbance rolls up at low frequency until a



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roll-up frequency eoRU. Then it rolls off again at afrequency of ORO- The filter or transfer functionbetween the filtered disturbance and white noise isgiven by:

(4.6)

Typically actuators have rotating parts and exhibitinternal resonant frequencies. These resonances andtheir higher harmonics can be identified as peaks inthe PSD's, these peaks would be contained in thenarrowband disturbance (overbound). Here thepower spectrum is the given as:

fzf> RO (4.7)

Figure 6 shows the amplitude spectrum of themodeled solar array actuator noise, as it will beused in the next section. A peak magnitude of 1 Nmwas assumed.

Solar Array Actuator No«o - AmpllHKlo Spectrum J(wj

10" ID"'Frequency [Hzl

10°

SO

' 0

-so

10" 10°

Fig. 6 Solar Array actuator disturbance spectrum

5. Static and Dynamic Analysis

Finally a static and a dynamic model of the lowarea density component needs to be established inorder to see how the disturbances propagatethrough the structure and to verify if the requiredperformance in terms of a cost function Jz(ra) canbe met.

6. Example: Ultra-Thin Solar Array

This paper uses a specific example from spacecraftsubsystem design. An ultra-lightweight rectangularsolar array, which is deployed with the help of Bi-Stem technology is shown in figure 7 (area=40m2).

We consider a planar array, which is a thin flatpanel pointed toward the sun. The pointing isachieved with a single axis articulation about the x-axis, which allows the solar array to rotate by andangle O, when the solar array actuator exerts amoment Mx(t). This paper assumes that thephotovoltaic cells can be manufactured as thinmembrane-like materials.

A 2x2cm cross bar represents the attach fitting andprovides stability; it is used for deployment of thepanel. The thickness of the solar panel has beendimensioned, so that the material is as thin aspossible, but does not deflect more than 10% of thesolar panel length 1 at the tip under the influence ofthe solar pressure (very thin plate). For a firstcalculation, the solar panel can be modeled as athin, cantilever beam under uniform loading q.Figure 8 shows the bending line w(x) andmaximum deflection f at the tip. The materialproperties of isotropic aluminum where used, i.e.density p = 2700 kg/m3, Young's Modulus E= 71GPa and Poisson's ratio v =0.33.

i i i i iw(x)

Fig. 8 Cantilever beam approximation

(6.1)

(6.2)

Based on the requirement of less than 10%deflection and a safety factor of 2 (validity of beamapproximation), a solar panel thickness of 0.0002m = 200 um was chosen. This results in a cross barmass of 21.6 kg and a solar panel mass of 21.6 kgfor a total system mass of 43.2 kg. The area densityof this solar panel is thus 1.08 kg/m2.



AIAA 98-5142

Stowed Configuration(Launch)

Bi-STEM\

Deployed Configuration(On-Orbit)

LAD Solar Array

Solar ArrayActuator

AluminumCross Bar

Fig. 7 Design of single-axis articulated LAD solar array with Bi-STEM deployment

The two disturbances which have been consideredin this problem are solar radiation pressure dlswhich acts on the entire array surface in negative zdirection and solar array actuator noise d2, which isintroduced as a torque in the attach fitting.

The first performance z\ is the rotation angle 6X atthe tip; this represents a tracking metric, as the tipshould track the commanded angle at the inputpoint with a minimal error. The second metric z2 isrelated to disturbance rejection. The actuator noiseand impulsive inputs are likely to excite the flexiblemodes of the solar panel, which will cause a powerloss as the thin flexible panel starts to oscillate andthe projected area Ap is reduced.

We know that the total power collected by the solarpanel at the beginning of life (BOL) is given by

P — PrBOL ~ ro TJ-A0-COS® (6.3)

This assumes that the panel is a rigid surface. Apower loss due to the flexible dynamics can becalculated with the help of a finite element model.The Power loss coefficient 22 is defined as thefraction of total power lost due to reductions in theprojected area. It is always a value between 0 and 1and can be calculated as:

The power loss function Jz2((n) is defined, to reflectthe power which is lost when disturbances (solararray actuator noise, solar pressure) excite theflexible modes of the array.

The deflection angles in the above equation can beobtained from the mode shapes O; of a dynamicmodel of the array. A performance requirementcould be that the cost J^co) has to be lower than0.5 over the entire frequency range. Figure 9 showsthe definition of the geometry, which defines thepower loss coefficient definition.

Node i on surface

Fig. 9 Power loss function definitionDistorted Panel Surface

In order to asses if the performance metric is met,static and structural dynamic models of the solarpanel were created. First the dynamic model wascreated and a modal analysis for the first 10flexible modes of the solar panel was conducted.This was done with the help of the ANSYS finiteelement solver. The solar panel was modeled with160 4-node bilinear shell elements and a total of205 nodes.

The basic equation solved in this undamped modalanalysis is the classical eigenvalue problem [8]:

(6.5)

where K and M are the stiffness and mass matricesrespectively, fy is the mode shape vector of mode iand QI is the natural circular frequency of mode i.



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This resulted in a single rigid body mode, which isthe rotation about the x-axis. Table 1 gives anoverview of the modes and natural frequenciesfrom the modal analysis:

1011

Rigid Body Rotation ©xFirst Bending y-axisSecond Bending y-axisThird Bending y-axisFirst Torsion x-axisFourth Bending y-axisFifth Bending y-axisSecond Torsion x-axisSixth Bending y-axisThird Torsion x-axisSeventh Bending y-axis

0.0000600.00041810.0026170.0073350.0097710.0143940.0238420.0239620.0356780.0394440.049945

Table 1: Structural Modes of Solar Panel

It can be seen that the fundamental frequency of thepanel is 0.0004 Hz, which is extremely low. Thisfrequency is low due to the small bending stiffness.It is however still higher than the rolloff frequencyof the solar pressure disturbance di. Thus it can beconcluded that the solar pressure acts like a staticdisturbance and will be included only in the staticanalysis. Figure 10 shows the second torsionalmode of the solar panel.

BMWS S.3NCW 30 1»0720U6I43WWL 90UITUII51EP.1sue «r

Fig.10 Modeshape for 2nd torsional mode

We are now primarily interested in the transferfunction from moment input Mx at the attach pointto <|>x at the tip point. In order to compute thistransfer function a state space representation of thesystem in second order modal and orthonormalform was obtained. The system in state spacerepresentation can be written as follows:

(6.6)

where x are the modal orthonormal coordinates, Bdare the disturbance influence coefficients and C^are the performance influence coefficients.Proportional damping £=0.005 was assumed. Thedisturbance d2 is the band-limited white noisemoment Mx defined in equation (4.6). Theperformance z\ is the angle <j>x at the tip node. Thedisturbance to performance transfer functionGzid^oo) is shown in figure 11 and is obtained asfollows:

(6.7)

dzw from Attach Point Mclo MM Point Robt

Fig.ll Actuator noise to tip angle transfer function

As expected we only observe the three torsionalmodes of our model hi Gzld2(ca), the dominantmode being mode 5 just below 0.01 Hz. Thebending modes are not observable. Above 0.05 Hzthe transfer function rolls off with -40dB/decade.This means that we can not drive the system withfast, impulse-like commands as they will not betransmitted, or alternatively we will excite theflexible modes of the solar panel. The transferfunction is typical of non-collocated transferfunctions with missing zeros hi the pole-zero-pattern. It would be very difficult to close a controlloop in this situation due to the large phase losses.This means that for ultra-flexible panels like thisone, we have to consider local control, where thesensors and actuators are nearly collocated.

The effect of the disturbance d2 on the performancez2 is computed as well. The cost function J^co) waspreviously defined and the transfer functions fromd2 to 0X and 0y for each node are calculated.



AIAA 98-5142

Subsequently the cost function J^cfl) is evaluatedas defined in equation (6.4). This function is ameasure of the power loss due to flexible dynamics.Figure 12 contains the function J^o) evaluated ateach frequency with and without isolation.

FHnibtt Solar Pan* Powr Loa Cost Function Jz(«)

10*

Fig. 12: Power loss coefficient J^

We can see that the system does not meet therequired performance level, which is that J^ra) hasto remain below 0.5 at all frequencies. Below 10"4

Hz the cost is zero because we are at the lower endof the disturbance spectrum, above 10"1 Hz we arealso at zero, because the Gzd transfer functions rollsoff rapidly. The range between 10"3 and 10"1 Hzcharacterizes a regime, where the disturbancemoment is able to excite the flexible modes of thesystem and a power loss is experienced.

The ultra-thin solar panel basically acts as aflexible sheet that the solar radiation pressure isable to deflect enough to reduce the collectedpower. It would be very challenging to control theangular position of the solar panel with theactuator, without exiting the flexible modes of thepanel.

7. Potential Solutions for LAD Solar Array

The use of passive isolation between the array andthe noisy satellite structure, input shaping for theone-axis articulation input commands andembedded active materials (SMA's) for shapecontrol are investigated as potential solutions.

Isolation from Spacecraft Bus

The disturbance rejection can be accomplished bypassively isolating the solar panel from the rest ofthe spacecraft at higher frequencies. This can beachieved with a passive/active isolator, which is

characterized by its transmissibility transferfunction T^,(<a). The isolator can be modeled as atorsional spring and dashpot as shown in figure 13.

S/C Solar 2-ParameterStructure Array Isolator

ActuatorFlexible Solar Panel

Fig.13: Passive Isolator model for solar array

We choose a 2-parameter passive isolator forsimplicity, which meets the following performancerequirements:

• Allow Rigid body control (rotation about x-axis) below 0.00055 Hz (T=1800 sec)

• No amplification above 0.001 Hz• Attenuation of at least 20 dB for the first

torsional mode at 0.00977 Hz

We assume that the base (spacecraft structure) isrigid compared to the solar panel. We will firstdevelop the fundamental equations of the 2-parameter isolator and then determine the isolatorparameters in order to meet the specification. Themoment of inertia of the solar panel about the x-axis can be calculated as:

(6.8)

where Is is the moment of inertia of the panel and Ibis the moment of inertia of the attach fitting. Weobtain a value of 14.4 kgm2 for the entireconfiguration. The input u is the angle <j)u at theactuator end., whereas the output y is the angle <j>yat the solar panel end. We can now write themoment equilibrium for the isolator as follows:

(6.9)

Taking the Laplace transform and solving for thetransmissibility we obtain

cs + kItols2+cs + k

(6.10)

where co0 is the natural frequency of the oscillatorand £ is the damping ratio of the oscillator. Thetransmissibility transfer function crosses the 0 dBline at a frequency of V2co0. Assuming a 2.5%

8American Institute of Aeronautics and Astronautics


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damping in the dashpot, we obtain the followingvalues:

Natural frequency of isolator:k In

1800--N/2 = 0.00247

Damping ratio of isolator:c 0.025 = 1.563

(6.11)

(6.12)

The torsional spring to be used in the isolator has avalue of k=1.421xlO"4 Nm, which is very soft. Thisresult suggests that active isolation with a controllermight me necessary. Theoretically we haveachieved attenuation of 24 dB for the first torsionalmode. Figure 12 shows the effect of the 2-parameter isolator on the power loss coefficient

Isolation can be effective in increasing theperformance of low-area density appendages,which are attached to noisy spacecraft structures byacting as a low-pass filter. More advanced isolationschemes with 3-parameter isolators (noamplification) and active isolation with controllersare recommended.

Input Shaping for solar array control

The previous section has raised some validconcerns about the feasibility of rigid body controlfor the ultra-thin flexible solar panel. We need torotate the panel fast enough in order to track thesun, which is difficult with an isolator cutofffrequency of SxlO"4 Hz, which corresponds to aperiod of 30 min. An alternative would be to use atechnique for rigid body control called inputshaping. Input shaping convolves the defaultmoment input with an impulse sequence, so that thepanel can be rotated fast, without exciting the firsttorsional mode of the system [7].

In order to demonstrate the benefits of inputshaping, a commanded rigid body rotation of 20° ofthe solar panel was analyzed. First we create thedefault moment input M0(t), secondly we calculatethe impulse sequence and convolve the two tocreate the shaped input and thirdly we analyze theresulting rise time and settling time of the solarpanel. The default input u(t)=M0(t) for a 20°rotation for the rigid body panel can be obtained asfollows:

M0 2 (, ,„—r-r+c, (6.13)

(6.14)

with the initial angle Ci=0, we can solve for thecommand time T of a square pulse. The panel isaccelerated for 50% of the command anddecelerated for 50% of the time until it comes torest at the desired position <(>0. In order to shape theinput, a three impulse sequence is computed, whichis tuned to the first torsional mode o5. Assuming a0.005 damping ratio we can calculate themagnitudes A and the time space AT of the threepulses as follows [7]:

(6.15)

(6.16)

(6.17)

where the factor k and the spacing AT can becompletely determined from the followingequations:

(6.18)(6.19)

The effects of input shaping are best seen in figure14. While the unshaped command leads to largeoscillations, the shaped input leads to a muchshorter settling time.

5 J j J f. j i, , '. :•J »YT y4i!-?i-[>• "T-S i-t~}"if<"l y-iI !i !|!i!iii! ! i!;!! '•', i; M :i!ii'

'i i' I! i1! ii y !j jl ii •,! I' i; y-^•l-trfv-r-f*-"

500 1000 1500 2000 2500 3XWfime[a«oj

Fig.14: System response for 20° rotation of solar panel



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It can be seen that there is a tradeoff between riseand settling times. We sacrifice a small amount ofrise time for much shorter settling times with inputshaping. With shaping the solar panel has settleddown after 275 seconds with the shaped input,when it is still oscillating outside of the ±2% bandafter 45 minutes, when driven with the unshapedinput. It was thus demonstrated, that input shapingis another beneficial way of controlling largeflexible space structures. Table 2 summarizes theresults for this test case.

Table 2: Improvement in settling time with shaping

Embedded Shape Memory Alloy actuators for quasi-static shape control

The idea presented in this subsection employsSMA actuators hi order to correct for the solarpanel surface aberration, which is caused by thesolar radiation pressure. This technology could alsobe used to control solar sails and other thinmembrane devices hi the future. Figure 15 showsthe concept of a "smart solar panel" which hasembedded SMA actuators to provide quasi-staticshape correction. The working principle of the"smart solar cell" idea is as follows:

SMA wire

Kapton-Copper layer

Mylar substrate

Fig.15: Solar Panel with embedded SMA's

The solar array has a tendency to naturally orientitself toward a light source with this solution. Asthe angle ® between the solar cell normal vectorand the incident flux becomes smaller, the power,which is generated by the solar cell, increases. Thispower from a few dedicated cells is directly fed to aSMA actuator, which is embedded above theneutral axis. As the temperature exceeds the phasetransformation starts and the actuator contracts.This decreases the curvature even further and againincreases the power received by the SMA. Thus the

solar panel will be held at a stable equilibrium withall SMA actuators in the fully contracted position.

A further step after using SMA wire actuators,would be an active sandwich membrane structure.An active sandwich structure can meet therequirements for low-area density structures byactuating inside the membrane and thus creatingdifferential strain, which results in a change ofcurvature. Thus the negative effects of thedistributed forces acting as a disturbance in thespace environment could be counteracted. Figure16 shows what the basic layers of such an activesandwich structure for an optical reflector couldlook like. It will be the subject of future research toshow what curvatures and bandwidth can beobtained for different configurations and thermalboundary conditions.

+ 5VDCGND

Electric

ThermalLayer

Optical Coating

Copper (PCS etched)

SMA

Kapton Substrate

Fig.16: Active membrane sandwich with embeddedSMA material

8. Conclusions

It was shown that Low-Area Density (LAD)components offer great opportunities for spacecraftappendages, which depend on a given surface areato meet their performance requirements. There arefour types of devices, which are candidates forultra-thin low-area-density (LAD) components hispacecraft: (1) optical mirrors, (2) RF antennas, (3)solar arrays and (4) thermal control systemradiators. The performance of these components ismost often related to their surface shape accuracy.The challenge is that ultra-thin components areparticularly susceptible to dynamic disturbances.

It was found that disturbances acting on a LADcomponent can be characterized by type, location,magnitude and frequency content.



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In order to successfully implement LADtechnology on spacecraft, the following aspectshave to be closely examined at the time ofspacecraft design and development.

It was shown that it is often necessary tostructurally decouple the LAD component from themain spacecraft bus. This can be achieved withpassive or active isolators, which act like a lowpass filter. The rolloff frequency of the isolator cannot be chosen too low or rigid body control will nolonger be possible on reasonable time scales. It wasshown that input shaping can provide a largeimprovement, when the shaper is targeted at thedominant flexible modes of the component. Finallyactive sandwich materials seem promising forcontrolling low-area density components in thefuture. This will require a decentralized controlarchitecture, as the pole-zero-patterns of LADcomponents are not conducive for controlling thestructure if the sensors and actuators are non-collocated.

Furthermore the deployment aspect of low-areadensity structures represents a challenge, which wasnot addressed in this research.

9. References

[1] Hughes Space and Communications," ProductOverview", Space Clip Art, 1996

[2] NGST Preliminary Design, Presentation to ProjectOffice, NASA Goddard Space Flight Center, 1996

[3] Hedgepeth, J.M., "Accuracy potentials for largespace antenna reflectors with passive structures",Journal of Spacecraft, 19 (3), pages 211-217,1982

[4] Thomas, M., Veal G.," Highly accurate inflatablereflectors", AFRPL, TR-84-021, 1984

[5] Source: Zeiders, Ultima, Symposium on OpticalSystems Concepts and Technology for NGST,MSFC, 1996

[6] Larson, Wertz, "Space Mission Analysis andDesign", Second Edition, Microcosm Inc. 1992

[7] Campbell M., Input Shaping, Course notes 16.243[8] ANSYS, Version 5.3 User Manual, Chapter

Structural Analyses, 3.3. Modal Analysis[9] Crawley E., Campbell M., Chapter 7, "Performance

and Disturbance Modeling", Draft, 4/2/1997

Nomenclature

A surface area [m2]A, nominal surface area [m2]c speed of light [m/sec]di solar pressure disturbance [N/Hz]dj actuator noise disturbance [Nm/Hz]D diameter [m]dF differential Force exerted [N]E Young's Modulus [Pa]f frequency [Hz]Ib area moment of inertia [m4]Jz performance cost function [-]K global stiffness matrix [N/m]L length of solar array [m]M global mass matrix [kg]Mx actuator control torque [Nm]N number of surface measurements [-]P0 solar constant at 1AU [W/m2]q uniform pressure loading [N/m]RO reference surface [m]RJ actual surface [m]RZZ performance weighting matrix [-]T surface temperature [K]

a, absorptivity [-]A. wavelength [m]sx emissivity at wavelength [-]t) efficiency [-](|> solar array rotation angle [rad]0 angle between surface normal and flux [rad]a Stefan-Boltzmann constant [W/m2K4]WRO rolloff frequency [rad/sec]«RU rollup frequency [rad/sec]


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