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Statement of Work Deliverables Deliverable:Action: Update Ansys and Matlab code to enhance model confidence. Bugs identified and resolved. Matlab data fed back to Ansys. Model effects of temperature profile for face sheet and truss. Capability for uniform and gradient temperature loads. Evaluate the effects of actuator uncertainties. Two different uncertainty models investigated. Document model and transfer technology to UF. Documented Matlab and Ansys GT code integrated in by UF. Result: All deliverables successfully completed.

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Overview Statement of Work Deliverables Update of Previous Work – Correction of Matched CTE Cases Ansys Verification of Matlab Results –Matlab Actuator Displacements Fed Back to Ansys (closed the loop) –Thermal Aberration Reproduction vs. Correction Actuator Glitch Evaluation –Random Glitch –Discrete Glitch Actuator Forces Evaluation Concluding Remarks

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Parameters Facesheet: Diameter (tip to tip)2m F-number1.5 Thickness m Modulus of Elasticity 95 GPa Poissons ratio 0.35 CTE 13E-6 /°C Substrate data: Beam diameter 1.16 mm Modulus of elasticity 68.3 Gpa Poissons ratio 0.33 CTE 0 /°C Actuator stiffness 2N/ m Thermal loads: 1) 10°C uniform 2) 1°C/m gradient Actuators cases: 1) 15 2) 159 3) 1563

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Update of Previous Work – Correction of Matched CTE Cases Problem: Similar displacements for matched and unmatched CTEs of the facesheet and truss. Mismatched CTEs Matched CTEs (incorrect) Facesheet only 10°C uniform load – 159 actuators Solution: Bug fixed in Ansys code so correct CTEs assigned in the matched case.

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Update of Previous Work – Correction of Matched CTE Cases Problem: Similar displacements for matched and unmatched CTEs of the facesheet and truss. Mismatched CTEs Matched CTEs (incorrect) Facesheet only 10°C uniform load – 159 actuators Solution: Bug fixed in Ansys code so correct CTEs assigned in the matched case.

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Correction of Matched CTE Cases - 10ºC Uniform, 159 Actuators Updated Matched CTEs Previous Matched CTEs Matched CTE case is now similar to the facesheet only case. Previous Facesheet only

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Correction of Matched CTE Cases - 1ºC/m Gradient, 159 Actuators Matched CTE case is now similar to the facesheet only case. Updated Matched CTEs Previous Matched CTEs Previous Facesheet only

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ANSYS Verification of Matlab Results Previously, Ansys provided influence coefficients and the response to thermal loads. These were imported into Matlab to calculate actuator displacements to reproduce the aberration. Currently, the Matlab-calculated actuator displacements are fed back into Ansys to either: –Correct the thermally loaded system. –Reproduce the thermal aberrations by actuation from an initially unloaded system (similar to previous Matlab work). Results: Correct and Reproduce yield similar results.

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Summary: Reproduction vs. Correction Reproductionuniformx-graduniformx-graduniformx-grad Absolute RMS (nm) RMS (%)0.926%0.570%1.232%0.992%0.127%1.203% Correctionuniformx-graduniformx-graduniformx-grad Absolute RMS (nm) RMS (%)0.927%0.570%1.232%0.995%0.127%1.204% Results: The correction is produced with essentially the same accuracy as the reproduction.

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Ansys Plots: Reproduction vs. Correction Reproduction vs. Correction Plots: 15 actuators, 10ºC Uniform 15 actuators, 1ºC/m X-Gradient 159 actuators, 10ºC Uniform 159 actuators, 1ºC/m X-Gradient 1563 actuators, 10ºC Uniform 1563 actuators, 1ºC/m X-Gradient

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10ºC Uniform, 15 Actuators Absolute RMS 2549nm Normalized RMS0.926% Absolute RMS 2551nm Normalized RMS0.927% Reproduction Correction

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Absolute RMS 147 nm Normalized RMS % Absolute RMS 147 nm Normalized RMS % Reproduction Correction 1ºC/m X-Gradient, 15 Actuators

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10ºC Uniform, 159 Actuators Absolute RMS 2083 nm Normalized RMS % Absolute RMS 2084 nm Normalized RMS % Reproduction Correction

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Absolute RMS 93 nm Normalized RMS % Absolute RMS 93 nm Normalized RMS % Reproduction Correction 1ºC/m X-Gradient, 159 Actuators

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10ºC Uniform, 1563 Actuators Absolute RMS 341 nm Normalized RMS % Absolute RMS 342 nm Normalized RMS % Reproduction Correction

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Absolute RMS 40 nm Normalized RMS % Absolute RMS 40 nm Normalized RMS % Reproduction Correction 1ºC/m X-Gradient, 1563 Actuators

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Actuator Glitch Three cases of actuator glitch are compared: –No Glitch – actuators have infinite resolution. –Discrete Glitch – actuator displacements are multiples of 50 nm. –Random Glitch – a random glitch between +/- 50 nm is added to each actuator displacement. Results: The RMS errors are not sensitive to small glitches. (Small is relative to maximum actuator strokes).

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Glitch Summary No Glitch uniformx-graduniformx-graduniformx-grad Absolute RMS Error (nm) RMS Error (%)0.926%0.570%1.232%0.995%0.127%1.204% Glitch/Max Stroke (%)0.07%1.47%0.15%2.00%0.24%1.79% Discrete Glitch uniformx-graduniformx-graduniformx-grad Absolute RMS Error (nm) RMS Error (%)0.929%1.813%1.235%2.316%0.129%2.146% Additional RMS Error (%)0.00%1.24%0.00%1.32%0.00%0.94% Random Glitch uniformx-graduniformx-graduniformx-grad Absolute RMS Error (nm) RMS Error (%)0.942%1.366%1.236%2.871%0.129%2.629% Additional RMS Error (%)0.02%0.80%0.00%1.88%0.00%1.42% Result: Glitch Additional RMS Error % Glitch/Maximum Actuator Stroke %.

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Ansys Plots: Actuator Glitch No Glitch vs. Discrete Glitch vs. Random Glitch: 15 actuators, 10ºC Uniform 159 actuators, 10ºC Uniform 1563 actuators, 10ºC Uniform 15 actuators, 1ºC/m X-Gradient 159 actuators, 1ºC/m X-Gradient 1563 actuators, 1ºC/m X-Gradient

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10ºC Uniform, 15 Actuators No Glitch Discrete Glitch Random Glitch Abs RMS 2551 nm % RMS % Abs RMS 2556 nm % RMS % Abs RMS 2593 nm % RMS %

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10ºC Uniform, 159 Actuators No Glitch Discrete Glitch Random Glitch Abs RMS 2084 nm % RMS % Abs RMS 2089 nm % RMS % Abs RMS 2089 nm % RMS %

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10ºC Uniform, 1563 Actuators No Glitch Discrete Glitch Random Glitch Abs RMS 342 nm % RMS % Abs RMS 347 nm % RMS % Abs RMS 346 nm % RMS %

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1ºC/m X-Gradient, 15 Actuators No Glitch Discrete Glitch Random Glitch Abs RMS 147 nm % RMS 0.570% Abs RMS 468 nm % RMS % Abs RMS 353 nm % RMS %

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1ºC/m X-Gradient, 159 Actuators No Glitch Discrete Glitch Random Glitch Abs RMS 93 % RMS 0.995% Abs RMS 216 nm % RMS % Abs RMS 268 nm % RMS %

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1ºC/m X-Gradient, 1563 Actuators No Glitch Discrete Glitch Random Glitch Abs RMS 40 % RMS 1.204% Abs RMS 72 nm % RMS % Abs RMS 88 nm % RMS %

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Actuator Forces Force Evaluation –Increasing numbers of actuators, increases required actuator forces. –15 actuators case met force specifications (< 0.1N) for both 10ºC Uniform and 1ºC/m X-Gradient loads. –159 and 1563 actuators cases exceed force specifications for both loadings. –(Note: will add 45 and 93 actuator cases.)

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Ansys Plots: Actuator Forces Force Plots 15 actuators, 10ºC Uniform 45 actuators, 10°C Uniform 93 actuators, 10°C Uniform 159 actuators, 10ºC Uniform 1563 actuators, 10ºC Uniform 15 actuators, 1ºC/m X-Gradient 45 actuators, 1°C/m X-Gradient 93 actuators, 1°C/m X-Gradient 159 actuators, 1ºC/m X-Gradient 1563 actuators, 1ºC/m X-Gradient

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10ºC Uniform, 15 Actuators Maximum actuator force within limit (< 0.1N). aberration actuator forces P2V1419 m Absolute RMS2550nm Normalized RMS0.926% Maximum Force0.026N Maximum Stroke68.4 m

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10ºC Uniform, 45 Actuators Maximum actuator force is exceeded (> 0.1N). aberration actuator forces P2V592 m Absolute RMS2,482nm Normalized RMS4.72% Maximum Force3.09N Maximum Stroke49.3 m

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10ºC Uniform, 93 Actuators Maximum actuator force is exceeded (> 0.1N). aberration actuator forces P2V651 m Absolute RMS2,329nm Normalized RMS2.03% Maximum Force6.92N Maximum Stroke38.8 m

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10ºC Uniform, 159 Actuators Maximum actuator force is exceeded (> 0.1N) aberration P2V661 m Absolute RMS2085nm Normalized RMS1.23% Maximum Force10.0N Maximum Stroke32.9 m actuator forces

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10ºC Uniform, 1563 Actuators Maximum actuator force is exceeded (> 0.1N) aberration P2V654 m Absolute RMS342nm Normalized RMS0.127% Maximum Force23.0N Maximum Stroke20.8 m actuator forces

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1ºC/m X-Gradient, 15 Actuators Maximum actuator force is within limit (< 0.1N). aberration P2V254 m Absolute RMS147nm Normalized RMS0.570% Maximum Force0.0006N Maximum Stroke3.4 m actuator forces

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1ºC/m X-Gradient, 45 Actuators aberration P2V283 m Absolute RMS121nm Normalized RMS0.635% Maximum Force0.347N Maximum Stroke3.45 m actuator forces Maximum actuator force is exceeded (> 0.1N).

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1ºC/m X-Gradient, 93 Actuators aberration P2V170.7 m Absolute RMS106nm Normalized RMS0.763% Maximum Force0.469N Maximum Stroke2.98 m actuator forces Maximum actuator force is exceeded (> 0.1N).

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1ºC/m X-Gradient, 159 Actuators Maximum actuator force is exceeded (> 0.1N) aberration P2V88.1 m Absolute RMS93nm Normalized RMS0.995% Maximum Force0.58N Maximum Stroke2.5 m actuator forces

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1ºC/m X-Gradient, 1563 Actuators Maximum actuator force is exceeded (> 0.1N) aberration P2V 16.1 m Absolute RMS 40nm Normalized RMS1.204% Maximum Force4.9N Maximum Stroke2.8 m actuator forces

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Concluding Remarks Only the 15 actuator case satisfied all specified criteria –RMS errors for the two thermal loads were low, less than 1%. –Maximum force levels required only 25% of the holding force. –Maximum stroke was about 50% of maximum. –Large P2V amplitudes corrected (1419 m and 254 m). Increasing actuators increased actuator forces to unacceptable levels.

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