An Active Composite Reflector System

for Correcting Thermal Deformations

Samuel Case Bradford�, Greg S Agnesy, Vinh M Bachz

Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA 91109

William Keats Wilkiex

NASA Langley Research Center, Hampton VA 23681

A meter-scale piezoelectrically active composite re ector has been developed and tested.The active re ector consists of a spherically curved, graphite face sheet, aluminum honey-comb core composite panel augmented with a network of distributed piezoelectric compos-ite actuators. The piezoelectric actuator system may be used for controlling the structuraldynamic response of the re ector, or for correcting low-order, thermally-induced quasi-static distortions of the panel. In this study, thermally-induced surface deformations of1 to 5 microns were deliberately introduced onto the re ector, then measured using aspeckle holography system. The re ector surface �gure was subsequently corrected to atolerance of 100 nm using a lattice of 90 piezoelectric composite actuators distributed acrossthe re ector’s back face sheet. Initial experimental investigations consisted of open-loop�gure control to determine in uence functions and control authority for each individually-addressable actuator, followed by a closed-loop �gure control implementation. This paperwill describe the design, construction, and testing of the active composite re ector systemunder thermal loads, and subsequent correction of thermal deformations via distributedpiezoelectric actuation.

Introduction

Large, precision composite re ectors for space ight can be relatively massive and expensive to fabricate.Typically, a heavy re ector structure is necessary to maintain tight re ector surface tolerances and overallshape under highly variable mission thermal orbital environments. Concepts for the Scanning MicrowaveLimb Sounder (SMLS, Figure 1) composite primary re ector, for example, are over 4 meters long, andweigh as much as the entire remainder of the instrument and spacecraft. As part of an ongoing JPLinternal R&TD activity, this report investigates active composite systems as a less costly alternative forfuture missions needing high surface precision re ectors operating in highly variable thermal environments(e.g., MEO or precessing orbits). Speci�cally, we developed an innovative active piezoelectric compositere ector system capable of autonomously reacting to variations in thermal environment of up to 100 K tomaintain precise overall closed-loop shape stability and surface tolerances to within 10 microns per meterof characteristic length. Our concept consists of a lightweight, relatively compliant, high surface precisioncomposite re ector with a latticework of at piezoelectric composite actuators (Figure 2) integrated withthe backing face sheet (Figure 3). Lightweighting the composite panel structure increases susceptibility tolow-order thermal distortion and warping, but this is compensated actively through closed loop control ofthe actuator lattice.

Background

Active composite structural concepts have been studied for more than a decade, although functional ex-amples of integrated controlled opto-mechanical systems are rare and no large space ight examples exist.

�Advanced Deployable Structures, Jet Propulsion LaboratoryyGroup Lead, Advanced Deployable Structures, Jet Propulsion LaboratoryzAdvanced Deployable Structures, Jet Propulsion LaboratoryxBranch Head, Structural Dynamics, NASA Langley Research Center

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!Figure 1. Scanning Microwave Limb Sounder instrument concept with very large space-borne compositeprimary re ector.1 The primary re ector (blue) for this SMLS concept would be approximately 4 m long andrequires operational shape tolerances of less than 40 microns. Achieving this level of surface stability currentlyrequires a comparatively heavy, and expensive, composite structure. A lighter weight, yet correctable, surface�gure re ector using the approach outlined in this report is investigated as a cheaper alternative.

Figure 2. The active composite re ector described here utilizes Macro Fiber Composite piezoelectric actuators(MFC). MFCs are a type of piezoelectric composite actuator,2 functioning much like a at, exible, piezoelec-tric stack, and ew in space in March 2008 on STS-123 as a component of the RIGEX3 ight experiment (toprow). MFC actuators have been incorporated into a testbed panel at JPL, including a measurement of surfacedeformation in uence functions as part of open-loop control of the panel atness (bottom row).

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!Figure 3. Active Composite Re ector Testbed. [LEFT] Low spatial frequency quasistatic thermal distortionsof a lightweight re ector panel (a) are measured using a laser metrology system (b). A lattice of piezoelectriccomposite actuators (c) embedded in the panel back facesheet, is commanded to counteract the distortion. Theactuators function much like at, exible piezoelectric stacks. Closed-loop control is accomplished throughlaser metrology feedback, or through an array of calibrated RTD sensors (d). [RIGHT] Active CompositeRe ector panel in the Precision Environmental Test Enclosure at JPL. The panel is split into three separatelywired zones (30 actuators per zone), and each actuator (90 actuators total) is individually addressable througha breakout panel or switching unit. Three kinematic magnet mounts attach the panel to the backing trussstructure, which is a carbon-�ber truss with titanium end caps bolted into titanium nodes.

Recent developments in NASA space ight capable piezoelectric composite actuators2,3 and advanced space-quali�able laser metrology systems,4 will allow practical, closed loop active composite re ector systems tobe constructed with performance characteristics superior to purely passive re ector designs. Ultimately, thiscapability can provide a low cost option for missions requiring moderate to large aperture, high precisionspaceborne re ectors, and enable science missions requiring precision large apertures with more demandingthermo-structural stability characteristics.

Approach

A preliminary trade study was performed using a Hedgepeth-based5 mathematical approach to develop ap-propriate active composite re ector scaling parameters, and to compare performance with comparable, purelypassive (non-active) structural systems. The primary performance metric is overall system mass (which, foractive re ectors, will include ancillary power electronics and metrology systems). In parallel, we devel-oped an analytical modeling framework for detailed active composite re ector design and coupled-physicssimulations incorporating structural, thermal, and electrical actuation behavior. We used the COMSOLMultiphysics6 and SIERRA Multiphysics7 tools for this task. To support the concept development the teamdesigned, constructed and tested an active composite re ector demonstration test article. This test articleused existing piezocomposite actuator and metrology systems, and an existing generic composite re ectorpanel. A cartoon and photo of this system is shown in Figure 3. Testing of the demonstration system wasperformed in the JPL Advanced Large Precision Structures Laboratory thermal enclosure.8 This testinggenerated experimental actuator in uence functions that were used to design closed-loop quasistatic thermaldistortion correction controllers. The performance and robustness of controllers using feedback from thelaser metrology system and other metrology sources were also investigated. Finally, the experimental phaseconcluded with a distortion compensation demonstration under an applied, slowly varying radiant thermalload.

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Panel Construction

The actuators were trimmed to �t into an isogrid array without overlapping with neighboring actuators orthe panel mount points. Bonding operations were split into three phases, one for each lane of actuators inthe array (i.e., the 0�, +60� and �60� lanes). A two-part epoxy was applied to each lane of actuators andthen cured overnight under pressure. Once the actuators were bonded to the panel, wire leads were solderedto the actuators and brought out to a connector cable, one for each third of the panel. Actuator power canbe applied either through a breakout box with terminal attachment points, or by wiring the panel cablesinto a switch unit or other D/A control system.

Figure 4. MFC actuators were bonded to the back facesheet of the 0.8 m honeycomb panel. Construction wascompleted in three stages, each lane of actuators (0, +60, -60) was individually bonded to the panel and thencured for 24 hours. Vacuum bagging (right) helped considerably in creating an e�ective bond.

Results

Preliminary results show very favorable actuator authority. Deformations of 10 micron (peak to valley) forthe power/focus mode, Figure 5, are obtained with an application of a common voltage in the range of[0-100 V] to all actuators. The actuators have an operating range of -500 to 1500 V and are largely linear,so these actuators are very suitable for correcting 5 microns of thermal deformation resulting from, e.g., aheat source directed at the face of the panel.

Correcting thermal deformations required in uence functions for each actuator. Actuator in uence func-tions were measured using automated switching software. The ensemble of 90 in uence functions was thenreshaped into an in uence matrix suitable for inverting into a sensitivity matrix. Multiplying a desiredsurface deformation by the sensitivity matrix gives the command voltage pro�le that will minimize (in aleast-squares sense) the residual error between the commanded and measured pro�le.

A modeled wavefront, ~w, can be expressed as the product of the sensitivity matrix,�!dw=�!du and a set

pattern of input voltages, ~u, e.g.,:

~w =

"�!dw�!du

#~u (1)

To solve for the pattern of input voltages, inverting Equation 1 gives:

~u =

"�!dw�!du

#�1

~w (2)

The deformation pro�le in Figure 7 was used as the desired deformation surface (~w) to generate thevoltage pro�le (~u) in Figure 8. The voltage pro�le roughly matches the observed deformation intensities.Figures 9 & 10 show the various command pro�les, with residuals additionally shown in Figure 11.

Acknowledgments

This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, undera contract with the National Aeronautics and Space Administration. The help and assistance provided byPhil Walkemeyer, Dan Barber, Eric Oakes, Jo Tillis, and Ari Miller is greatly appreciated.

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Figure 5. Surface deformations for range of applied voltages [50, 100, -50, 100, 0 V]. Total peak-to-valleydeformations of 10 microns were obtained with a 100 V actuator range. All actuators were connected to acommon signal, but are individually addressable through a switch unit or D/A controller for full surface control

Surface Temperature under Thermal Load [K]

295

295.5

296

296.5

297

297.5

298

298.5

299

299.5

300

Surface Deformation under Thermal Load [micron]

−3

−2.5

−2

−1.5

−1

−0.5

0

Figure 6. Surface deformations from applied thermal load. A heat lamp (left) created a thermal pro�lemeasured with a FLIR system (center) and corresponding displacement pro�le measured with the speckleholography system (right). The shadow of the supporting truss on the back of the panel is visible in both thedisplacement and temperature pro�les on the front of the panel.

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Figure 7. Surface deformations [microns], out-of-plane, induced by a thermal gradient of 1 C.

References

1Co�eld, R. and Kasl, E., \Thermal stability of a 4 meter primary re ector for the Scanning Microwave Limb Sounder,"2010.

2Wilkie, W. K., Inman, D., High, J., and Williams, R., \Recent Developments in NASA Piezocomposite Actuator Tech-nology," 2008.

3Cooper, B., Black, J., Swenson, E., and Cobb, R., \Rigidizable In atable Get-Away-Special Experiment (RIGEX) SpaceFlight Data Analysis," AIAA 2009-2157, 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Mate-rials Conference, 4-7 May 2009, Palm Springs, California, 2009.

4Zhao, F., Ksendrov, A., Rao, S., and Kadogawa, H., \Swept-Frequency Laser Ranging Using a Calibrated Common-PathHeterodyne Interferometer," ODIMAP V, 5th Topical Meeting on Optoelectronic Distance/Displacement Measurements andApplications, Aula de Grados, Escuela Politecnica Superior Universidad Carlos III, Madrid, Spain, October 2006 , 2006.

5Hedgepeth, J., \Critical Requirements for the Design of Large Space Structures," NASA CR 3484, 1981.6COMSOL, COMSOL Multiphysics: User’s Guide, Version 3.5a, 2008.7Sandia, SIERRA Mechanics, sandia.gov, 2011.8Bradford, S. C., Agnes, G. S., and Wilkie, W. K., \Active Thermal Distortion Compensation for Lightweight Composite

Re ectors," R&TD Year 1 Report, JPL, 2010.

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10 20 30 40 50 60 70 80 900

10

20

30

Actuator Number

Co

mm

and V

olta

ge

Commanded Voltages to Null Thermal Deformations

Actuator X Position

Actu

ato

r Y

Positio

n

0

5

10

15

20

25

30

35

Figure 8. Commanded voltage pro�le for a given thermal load condition. The top plot shows actuator numbervs. voltage. In the bottom plot, actuator voltages are plotted at their approximate position in the ACR. Thegeneral voltage pattern reproduces the shape of the thermal pro�le (Figure 7).

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Figure 9. Thermal pro�le distortion, compared to measured surface under an applied voltage pro�le intendedto reproduce the thermal distortion. Print through features of high spatial frequency dominate the residual(see Figure 11).

Figure 10. Thermal pro�le distortion, compared to predicted surface under the same voltage pro�le as inFigure 9. The residual has similar print through features, but there is also a drift term that adds to the errorbetween the measured and theoretical pro�les (see Figure 11).

Figure 11. Residual maps [microns] between voltage cases. Obvious print through e�ects are visible in bothresidual plots. Left: Residual between measured thermal pro�le and measured command pro�le (Figure 10).The residual is dominated by a linear drift term. Right: Residual between the measured thermal pro�le andthe predicted surface based on an optimal command pro�le (Figure 9).

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