ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
trapezoidal commutation. This is critical for the SIM project because torque ripple induces excess  vibrations in the structure that affect other sensitive components of the interferometer. The results of this architecture were surprising! The PID control loop utilizes 4 position sensor steps to  start and stop the screw resulting in repeatable incremental step sizes of 20 nm! This means the DC brushless motor has to be capable of positioning to 100,000 distinct points around a revolution and the mechanical imperfections are beneath the control loop sensitivity. Furthermore, PLADD is able to track a prescribed profile over its entire range with a lag of approximately 16 ± 1.5 microns. However, with correct sequencing or control logic PLADD has an effective positional tracking error of ~3 microns peak to peak at a rate of approximately 3 mm/sec. Below is a short review of the results for a 10-mm move, a 1-micron move, and a 20-nm move. Also included is a discussion of the precision piezo brake effects, future work/improvements, and lessons learned.  10-mm Slew-Nominal Gains Nominal gains are the gains chosen for well-rounded performance characteristics for a given move size.  There is a nominal set of gains for both high resolution (less than 1 micron) moves and low resolution (greater than 1 micron) moves. The nominal gains were set based entirely by trial and error, and are thus not necessarily optimal in any specific sense. Encoder resolution is increased for moves larger than 1 micron, down to 80 nm due to 22-bit electronics  counting limitation. The electronics limitation is a designed in counter size on the FPGA that was not realized to be problematic until late in the build. It is in no way related to the commonly discussed 14-bit analog noise floor in most space electronics. This allows PLADD to cover the entire 120-mm range regardless of the initial zero point location chosen by the operator. PLADD is able to track a prescribed profile over its entire range with a lag of approximately 16 ± 1.5  microns. However, with correct sequencing or control logic PLADD has an effective positional tracking error of ~3 microns peak to peak at a rate of approximately 3 mm/sec. In Figure 18, the position command profile is created using constant acceleration to get up to speed,  constant velocity for the main portion of the slew, and constant deceleration to approach the command position. Figure 18: 10-mm Slew (Nominal Gains) - Entire Move  Figure 19 highlights the 16 micron lag during the constant velocity portion of the slew. It also shows the  ~3 um error, peak to peak about the 16 micron offset. The sinusoidal commutation is also clearly displayed in this view. Figure 19: 10 mm Slew (Nominal Gains) - During Slew  Figure 20 illustrates the end of the slew and the initiation of the integral gain to reduce the steady-state  error. The proportional gain primarily contributes to slew performance. However, it can only reduce the error down to ~5 um using the nominal gain value. Once within this 5-micron zone the controller’s integral term integrates the error and creates the final step to its commanded position. 380
Figure 20: 10-mm Slew (Nominal Gains) -End of Slew  Finally, Figure 21 shows the final result of the integral action. There is a small overshoot, which is then  reduced to within ±80 nm of the command position. This is the limit of the capability of low-resolution mode, since the PID controller does not see any motion less than 80 nm (due to the previously discussed 22-bit legacy hardware limitation). The actuator could now be commanded with a new set of high-resolution gains allowing the zeroing in of the actuator down to ±5 nm of the commanded position. It is important to note that for large moves, although the actuator can move to within ±5 nm of the commanded position, in reality the overall accuracy of the move is affected by many other contributors, and are not discussed in this paper. The contributors can be, but are not limited to, thermal drifts in the unmeasured structure during the move, grating accuracy of the glass scale, and inter-grating accuracy. Large move accuracies are extremely complex comprising many error sources and are beyond the scope of this paper. Figure 21: 10-mm Slew (Nominal Gains) - Steady-state Error  1-Micron Step-Nominal Gains Full encoder resolution of 5 nm can be used for small moves of less than 20 mm. However, actuator  velocity requirements generally lead to the use of high-resolution mode for moves only less than 1 micron. Using a different control resolution changes the scaling of the PID controller and thus a different set of gains are used in high-resolution mode versus the low-resolution mode used for large slews. Figure 22 shows a 1-um move using nominal gains. Figure 23 focuses in on the last part of the move to  show the steady-state error. The nominal gains provide a fast response with minimal overshoot. The steady-state error is improved over the low-resolution mode because the PID controller is able to respond to deviations from the commanded position as small as 5 nm. The background noise in the plot will be further addressed in the Noise and Vibration section of this paper. Figure 22: 1-um Step (Nominal Gains) - Entire Move  381
Figure 23: 1-um Step (Nominal Gains) - Steady-state Error  20-Nanometer Step-Nominal Gains Due to a 4X minimum encoder resolution command limitation within the control system (a legacy piece of  hardware originally intended for another use) 20 nm is the smallest incremental step that can be taken.  The following series of plots will show 20-nm steps using the same nominal gains as the 1-um steps.  Figure 24 displays a 20-nm move. Overshoot is non-existent, with a move time of roughly one second. At  this nanometer level of position control, the noise of the encoder position signal is significant. It has a noise of approximately ±5 to ±10 nm, with occasional spikes of ±20 nm. The nature of this noise is not fully understood, but is conjectured to be from a combination of mechanical (background vibration) and electrical (sensor and wiring noise) sources. Environmental noise and its potential elimination are discussed in the Noise and Vibration, Future Work, and Lessons Learned sections of this paper.  Figure 24: 20-nm Step (nominal Gains)  Noise and Vibration Nanometer level work requires an extremely quite environment. Vibration and external noise sources can  greatly affect test results. All test data was taken in Bldg 318 (Space Interferometry Test Lab), which is specifically designed to be a low noise test facility. The test was performed on an air table separated from the building via an isolation pad. In order to better understand the test noise environment, we sampled 1 second of high rate position data (approx. 1240 samples/second) with no power applied to the actuator. The measurement below is unfiltered data. It is clear that there is a noise disturbance identical to the noise seen when the actuator reaches its commanded position at steady state. This suggests that the noise seen in our position graphs is either environmental mechanical or the electrical noise of the sensor.  382
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4985-4980-4975-4970-4965-4960-4955POSITION TIME (s)POSITION (nm) Figure 25: Vibration Measurement - Test Environment and Sensor Noise  Figure 26 shows a 30-point moving average of the steady state error of the actuator with the actuator  powered on and attempting to hold a position. Averaging decreases the steady-state error down to ±4nm. The average position is -0.2 nm with a standard deviation of 1.14 nm.  Figure 26: Steady State Error, 30-Point Moving Average Piezo-Brake Effect Creating a brake for an actuator performing nanometer size moves is not an easy job. In order to achieve  high braking forces, PLADD is equipped with a piezo-actuated brake mechanism. This is required in a coarse stage/fine stage configuration where the coarse stage is turned off and locked while the fine stage operates. A brake is also a necessity when the actuator moves periodically. Through the use of a custom piezo brake and correct power shut off sequencing, the SID team was able to brake the actuator with minimum disturbance. The correct sequencing of the brake and actuator control power off must be performed in order to achieve the best results.  Figure 27 shows a 200-nm step at one second with the brake engaged at the third second. Since the PID  controller remains on during the slow braking, it recognizes and corrects for the brake-induced drift, bringing the actuator back to its commanded position. At the ninth second, the power is removed from the motor. The current brake design degrades the relative accuracy of the move and also requires much longer  times to reach a position and stop. The SID team believes that some design alterations could create a brake with much less induced drift. Also, if the actuator were to be used as a fine actuator it could potentially always be powered on, thus requiring no brake. 383
noise sensor can help in this process greatly. This is something we did not foresee, and thus we are still  uncertain as to the root of our environmental noises.  8. Be aware that bellows buckle in proportion to their linear stiffness. Be cautious when using  them to react torque over a large stroke.  PLADD’s design uses titanium bellows to react out the rotational torque in the screw. Our bellows are  extremely soft as they must travel 120 mm full stroke. The first buckling mode of the bellows occurs when a torque is applied. The bellows collapse down as it buckles. The torque required to induce buckling is directly related to the linear stiffness of the bellows. This phenomenon was ignored during design. Fortunately our actuator works at the bitter edge of buckling, but does not buckle. Rotational alignment of the bellows is also critical to buckling, as a misalignment, or initial rotational load lowers the buckling torque drastically.  Conclusion The SIM Siderostat team successfully outperformed our initial goal of less than 1-micron repeatable  incremental step size by a factor of 50. We strongly believe we will attain incremental step sizes of 2-5 nm for large ranges given the current sensor technology. Through the elimination of gears and their inherent backlash we have been able to show that the mechanical system is not the limiting factor in fine positioning applications, if appropriate design considerations are taken into account. We have realized that sensor technology more than any other factor is the limiter with regards to fine positioning over large ranges. We hope to be able to further develop this novel linear actuator concept and to eventually use it on SIM in our PLANETQUEST, and many other future projects. Acknowledgements  The research described in this (publication or paper) was carried out at the Jet Propulsion Laboratory,  California Institute of Technology, under a contract with the National Aeronautics and Space Administration. I would like to thank all involved with this effort for their hard work and dedication towards achieving our goals. Those involved beyond the authors were Rob Calvet, Yutao He, Bruce Scardina and Don Benson. I would finally like to thank Caltech and NASA for providing the great freedom to explore the unknown. References [1] Edberg, Stephen J, “SIM PlanetQuest: A Mission for Astrophysics and Planet Finding”, NASA/JPL  White Paper, May 2005  [2] Koenig, John, “SIM Siderostat Ballscrew Testbed Electronics Report”, JPL, Feb 2007 [3]  Moore, Don, “Actuator Logs and Assembly Notes”, JPL, 1999  386
Development of a Low-Cost Fine Steering Mirror  Steven R. Wassom and Morgan Davidson* Abstract  The Space Dynamics Laboratory has used intern al funds to develop a prototype low-cost two-axis fine  steering mirror (FSM) for space-based and airborne applications. The FSM has a lightweight 75 mm-by-150-mm high-reflectance mirror, high angular deflection capability for along-track ground motion  compensation and cros s-track pointing, and a 70-Hertz bandwid th for small amplitudes to help cancel  unwanted jitter. It makes use of off-the-shelf components as much as possible. Key performance  parameters are: Clear aperture, 75 mm; elevation angle, ±15 deg (mechanical); azimuth angle, ±60 deg  (mechanical); slew rate, greater than 75 deg/sec; bandwidth, 70 Hz; steady-state average error, about 1 arcsec; average power dissipation, 0.4 Watts; mirror surface, figure, <0.1 waves RMS; and total  mechanical mass, 1 kg. Key components for the elevation axis include a rotary voice coil and a unique  patent-pending non-contact feedback sensor. The azimuth axis features a brushless DC motor and a high-resolution optical encoder. Rapid prototyping, autocoding, and real-time hardware-in-t he-loop (HIL)  testing were used to develop the control algorithms. Additional accomplishments include temperature  mapping of the feedback sensor, inventing a successful passive launch lock, launch vibration testing, and  subjecting the system to a space-like environment at pressures down to 1e-7 torr and temperatures down  to 164 K.  Introduction  Over the past two years, Space Dynamics Laboratory (SDL) has used  internal funds to develop a prototype low-cost two-axis fine steering mirror  (FSM). This mechanism is intended to have a broad flexibility for both spacebased and airborne applications.  Figure 1. Prototype FSMThe main purpose of this effort was to reduce the cost of a normally  expensive technology while maintainin g performance, thus enabling this  capability for more applications. A $2 million price tag has not been  uncommon. The first year’s development effort required about $200,000 and  resulted in a successful working prototype (Ref. 1).   This report will review the accomplishments of the first year and describe the  additional progress of the second year that includes:  /g120 Subjecting the system to a space-like environment at pressures down to  1e-7 torr and temperatures down to 164 K  /g120 Verifying that the system will survive a typical launch vibration test profile  /g120 Performing temperature mapping of the patent-pending feedback sensor  /g120 Inventing a successful passive launch lock   /g120 Mounting the system on a portable cart for demonstrations                                                        * Space Dynamics Laboratory / Utah State University Research Foundation, North Logan, Utah  Proceedings of the 39th Aerospace Mechanisms Symposium, NASA Marshall Space Flight Center, May 7-9, 2008  387
Structural/Thermal Analysis  Mirror Modal Analysis Finite Element Analysis (FEA) was used to predict the  modes of the mirror. The high control system bandwidth near 70 Hz required the mirror modes to  be considerably higher.  Figure 4.  Mirror Mode 1, Torsional about ZAxis, 270 Hz A normal modes analysis was run. Table 2 lists the  mode shape descriptions. Figure 4 depicts the first  mode: a torsional mode about the Z-axis at 270 Hz.  The majority of the deformation and strain energy is in the flexure mount.   Mirror Mounting Distortion Predictions Some wave-front error (WFE) is caused when non-flat  surfaces are mated to gether with a bolt preload,  producing strain in the mated parts. FEA was again used to predict optical surface displacement.   The analysis assumed that the combined  worst-case flatness tolerance of the two mating surfaces produces a Z-axis forced  displacement of the mounting surface. The  mounting pads on the mirror have a coplanarity requirement of 2 μm. The mating  surface is assumed to have a coplanarity or  flatness of 12.7 μm. Conventional machining can get surfaces as good as 7.6 μm in  flatness. This approach conservatively  assumes that all the strain occurs in the mirror as if it were mated to an infinitely stiff  part.Table 2. Mirror Modes Summary  Mode Shape Number/Description Frequency (Hz)  1 Mirror torsional, about Z-axis 270 2 Mirror rocking, about Y-axis 390 3 Mirror vertical or Z-direction translation, with  mirror bending (saddle mode) 1230 4 Complex X-direction side to side translation  with mirror surface bending/waves 2700 5 Complex Y-direction side-to-side translation  with mirror surface bending/waves 2900 6 Second saddle mode 3100 Optical surface deformations from each of the enforced displacements are then transformed into surface  normal interferometric space using Zernike polyn omial fitting. Piston and tilt can then be subtracted,  resulting in WFE due to mounting distortion. The results show that distortion in the mirror is dominated by  astigmatism and tetrafoil. Predicted surface normal displacements are shown in Figure 5 with the  dominant aberrations identified in Table 3.  Mirror Thermal Elastic Predictions Thermal simulation of the FSM in a representative orbit was used to evaluate expected performance. For  the simulation, the representative orbit was a nadir-pointing low-Earth orbit. A typical baffle geometry was  assumed. Standard minimum and maximum values were used for long-wave infrared heat from the earth and for reflected sunshine. Diurnal temperature profiles for the system as well as a detailed mapping of  temperature variation across the face of the mirror  were the principle outputs from the thermal simulation. Table 3. Zernike Polynomial Coefficients  Ordered by Highest Contributor  Standard Zernike No. Zernike Description RMS WFE  (waves  HeNe) 14 Second order Astigmatism y 0.018 6 First order Astigmatism y 0.017 27 Second order Tetrafoil y 0.005 26 Third order Astigmatism y 0.005 390
Table 4. Results of Thermal Analysis  Units Case 1 Case 2 Case 3  Azimuth motor /  yoke isolation W/K 0.019 0.007 0.007 Baffle temperature K 160 160 180 Average mirror  temperature K 210 201 210 Mirror face  gradientK 0.11 0.08 0.07 Mirror face  distortion Z-dir*nm 43 27 22 Figure 5. Predicted Surface Normal  Deformations  Thermal analysis results showed the two most sensitive elements of the thermal design were the level of  thermal isolation between the yoke and the azimuth motor and the baffle temperature. These parameters  were the principle drivers in determining the operational temperature of the mirror. Because the gradients across the mirror are affected by the overall mirror temperature, the optical distortion was weakly coupled  to the same parameters, showing small changes as the mirror temperature and baffle temperature varied.  Table 4 shows various amounts of isolation and baffle temperatures and the resulting mirror temperature and optical distortion. A typical diurnal temperature profile during one orbit and the resulting thermal  gradients across the mirror face are shown in Figure 6.  Mirror Temperature Diurnal Variation - One Orbit 209.6209.8210.0210.2210.4210.6 0 1 02 03 04 05 06 07 08 09 0 Time (minutes)Temperature (K) Figure 6. Typical diurnal temperature profile (left) and thermal gradients across mirror face (right)  FEA was again used to predict elastic distortion caused by thermal gradients across the mirror during  operation in space. Coefficient of thermal expansion (CTE) mismatch at the mounting interfaces has no  impact given that the mating materials are aluminum.  The thermal elastic analysis predicts a peak-to-valley sag (Z axis on a flat mirror) of 22 nm or 0.034-wave  HeNe (see Figure 7). This distortion is very small an d should not be a factor in maintaining a good optical  figure in operation.  391
Figure 7. Sag (meters) of Optical Surface due to Thermal Elastic Deformation  Control System Development  Instead of following a traditional waterfall or serial development process for the elevation and azimuth  closed-loop control algorith ms, SDL used the Rapid Prototyping Methodology (RPM) spiral development  process shown in Figure 8. This process can be quickly iterated due to its software-driven nature.  Customized features for line-of-sight (LOS) optical pointing systems include: integrated end-to-end modeling, co-simulation, and 3-D visualization of structural and system dynamics, controls, and optics;  automatic C-code synthesis from block diagrams; real-time hardware-in-the-loop (HIL) testing; dynamic  automated ray tracing, and a customizable GUI to monitor testing and change control parameters “on the fly.” Eventually, the block diagram transforms from a virtual model of the system to the complete  integrated assembly. The control algorithm is then  embedded in the actual computer.   The advantages of RPM include:   /g120 virtually no software written by hand (except for  occasional device drivers)   /g120 substantial savings of time and money in code  generation   /g120 short iteration cycles that result in early problem  identification and solution   /g120 changes can be made early in the design cycle at the  component level  The left side of Figure 9 shows the multi-body dynamic  model of the FSM. This high-fidelity model includes  flexible- and rigid-body representations of all major components (mirror, mirror flexure, flex pivots, actuators,  etc.). The right side of Figure 9 shows the top-level  hierarchy of the block diagram simulation of the FSM control system with the dynamic model embedded for co-6.  Full  System  Verification  via  Embedded  Code Testing5.  Subsystem  Verification via  Hardware-in-the-Loop Simulation/Testing4.  Automatic  Code Generation,  Real-Time  Simulation &  Visualization1.  LOS Control Problem &  Requirements  Definition2.  Physical &  Empirical  Plant  Modeling & Visualization3.  Control Algorithm  Design,  Analysis,  Simulation &  Visualization ITERATIONS &  REFINEMENTS 6.  Full  System  Verification  via  Embedded  Code Testing5.  Subsystem  Verification via  Hardware-in-the-Loop Simulation/Testing4.  Automatic  Code Generation,  Real-Time  Simulation &  Visualization1.  LOS Control Problem &  Requirements  Definition2.  Physical &  Empirical  Plant  Modeling & Visualization3.  Control Algorithm  Design,  Analysis,  Simulation &  Visualization ITERATIONS &  REFINEMENTS Figure 8. SDL’s RPM for Control Systems 392
simulation. Each of the blocks shown has detailed algorithms and calculations within it. Analytical tools in  the software were used to determine the control gains, shape the open- and closed-loop responses, and  simulate the step response and frequency response.   Figure 9. FSM Dynamic Model  Test Results and Model Validation  Mirror Surface Figure Testing Surface figure tests were performed on the mirror  to better understand the optical performance and  validate the predictions. Mounting distortion and thermal elastic distortion at cryogenic temperatures were  tested using a commercial Zygo Fizeau interferometer.  The test setup (see Figure 10) consisted of mounting the mirror in a bell jar test chamber on an optical  bench. The mirror is insulated and baffled to reduce thermal gradients during testing. The mirror looks out  the bell jar window. The interferometer is set up to view the test mirror through a fold mirror. The fold  mirror is necessary to adjust tilt on the mirror, as it is very difficult to move  the large bell jar or the  interferometer in fine increments.  It should be noted when viewing the test results  that the interferometer only spans 100 mm of the 150 mm elliptical test mirro r aperture. The test  mirror aperture outside the 100-mm center was  tested separately with the results showing a more  behaved WFE. Also, WFE from the fold mirror was  not removed from any of the results.  Room temperature tests were performed with  various mounting torques applied to the mirror.  The interferometric results show very little distortion from mounting. Figure 11 shows the  WFE after applying 0.68 N·m to the number 4  screws. The RMS WFE error is essentially 0.025 waves HeNe with or with out the applied torque.  The circular grooves noticeable in the  interferogram are residual SPDT marks in the  Figure 10. Mirror Surface Figure Test Setup  393