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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Hubble Space Telescope Fine Guidance Sensors Instrument Handbook, version 4.0

This is a revised version of the Hubble Space Telescope Fine Guidance Sensor Instrument Handbook. The main goal of this edition is to help the potential General Observer (GO) learn how to most efficiently use the Fine Guidance Sensors (FGS's). First, the actual performance of the FGS's as scientific instruments is reviewed. Next, each of the available operating modes of the FGS's are reviewed in turn. The status and findings of pertinent calibrations, including Orbital Verification, Science Verification, and Instrument Scientist Calibrations are included as well as the relevant data reduction software.

Holfeltz, S. T.↗
NASA NTRS1994

Astrometry with Hubble Space Telescope Fine Guidance Sensor number 3: Position-mode stability and precision

We report results from a test exploring the long- and short-term astrometric stability of Hubble Space Telescope Fine Guidance Sensor (FGS) #3. A test field was observed 40 times over 522 days to determine the precision and accuracy of FGS astrometry and to measure the character and magnitude of possible secular scale changes. We examine the astrometric data and the associated guide-star data to determine random errors. These data are also explored to find sources of systematic error. After correcting for some systematic effects we obtain a precision of 0.002 arcsec (2 mas) per observation (RSS of x and y). This is relative astrometry within a central 2.5 arcmin FGS field of view for any orientation. We find that the scale varies over time and confirm the sense of the trend with independent data. From the 40 observation sets we produce a catalog of an astrometry test field containing eight stars whose relative positions are known to an average 0.7 and 0.9 mas in x and y. One reference star has a relative parallax of 3.1 plus or minus 0.5 mas. Finally, we report that eleven observation sets acquired over 387 days produce parallaxes and relative positions with 1-mas precision.

Benedict, G. F.↗
NASA NTRS1994

Hubble Space Telescope Fine Guidance Sensor interferometric observations of the core of 30 doradus

We present the results of the first high angular resolution observations taken with a Fine Guidance Sensor (FGS) aboard the Hubble Space Telescope (HST) of a star cluster embedded in very bright background. The strong and complex background around the R136 cluster in the 30 Dor nebula does not prevent the FGS from achieving performance close to its angular resolution limit of approximately 0.015 sec per axis with reliable photometry. These FGS observations establish that the central object in R136a is a triple star with the third component delta V = 1.1 mag fainter than the primary star al approximately 0.08 sec way. We estimate from the grid of models of Maeder (1990) that the present mass of al is between 30 and 80 solar masses, with the main-sequence progenitor between 60 and 120 solar masses.

Lattanzi, M. G.↗
NASA NTRS2005

Hubble Space Telescope Fine Guidance Sensor and Two-Gyro Control Law Design, Implementation, and On-Orbit Performance

For fifteen years, the science mission of the Hubble Space Telescope (HST) required using at least three rate gyros for n Controlling with alternate sensors to replace failing gyros can extend the HST science mission. A two-gyro control law has been designed and implemented using magnetometers, star trackers, and Fine Guidance Sensors (FGSs) to control vehicle rate about the missing gyro axis. The three aforementioned sensors are used in succession to reduce HST boresight jitter to less than 7 milli-arcseconds rms prior to science imaging. The Magnetometer and 2-Gyro (M2G) control law is used for large angle maneuvers and attitude control during earth. occultation of star trackers and FGSs. The Tracker and 2-Gyro (T2G) control law dampens M2G rates and controls attitude in preparation for guide star acquisition with the FGSs. The Fine Guidance Sensor and 2-Gyro (F2G) control law dampens T2G rates and controls HST attitude during science imaging. This paper describes the F2G control law. Details of F2G algorithms are presented, including computation of the FGS-measured star vector using non-linear equations, optimal estimation of HST body rate, design of the F2G control laws and gyro bias observer, SISO and MIMO linear stability analyses, and design of the F2G intramode transition and guide star acquisition logic. Results from an FGS flight spare ground test are presented that define acceptable HST jitter levels for successful guide star acquisition under two-gyro control. HST-specific disturbance and noise models are described that are based upon flight telemetry; these models are used in HSTSIM, a high-fidelity non-linear time domain simulation, to predict HST on-orbit disturbance responses and FGS interferometer Loss of Lock (LOL) characteristics under F2G control. Additional HSTSIM results are presented predicting HST quiescent boresight jitter performance, science maneuver performance, and observer configuration performance during F2G operation. Simulation results are compared to on-orbit data b m F2G flight tests performed in February 2005. Science images and point spread functions from the Advanced Camera for Surveys (ACS) High Resolution Camera (HRC) are presented that compare HST science performance under F2G versus three-gyro control. Images and flight telemetry show that HST boresight jitter with the new F2G control law is usually less than jitter using the three-gyro law, and HST boresight jitter during F2G operation is dependent upon guide star magnitude.

Clapp, Brian R.↗
NASA NTRS2010

Hybrid Architecture Active Wavefront Sensing and Control

A method was developed for performing relatively high-speed wavefront sensing and control to overcome thermal instabilities in a segmented primary mirror telescope [e.g., James Webb Space Telescope (JWST) at L2], by using the onboard fine guidance sensor (FGS) to minimize expense and complexity. This FGS performs centroiding on a bright star to feed the information to the pointing and control system. The proposed concept is to beam split the image of the guide star (or use a single defocused guide star image) to perform wavefront sensing using phase retrieval techniques. Using the fine guidance sensor star image for guiding and fine phasing eliminates the need for other, more complex ways of achieving very accurate sensing and control that is needed for UV-optical applications. The phase retrieval occurs nearly constantly, so passive thermal stability over fourteen days is not required. Using the FGS as the sensor, one can feed segment update information to actuators on the primary mirror that can update the primary mirror segment fine phasing with this frequency. Because the thermal time constants of the primary mirror are very slow compared to this duration, the mirror will appear extremely stable during observations (to the level of accuracy of the sensing and control). The sensing can use the same phase retrieval techniques as the JWST by employing an additional beam splitter, and having each channel go through a weak lens (one positive and one negative). The channels can use common or separate detectors. Phase retrieval can be performed onboard. The actuation scheme would include a coarse stage able to achieve initial alignment of several millimeters of range (similar to JWST and can use a JWST heritage sensing approach in the science camera) and a fine stage capable of continual updates.

Feinberg, Lee↗
NASA NTRS2013

Dynamic Black-Level Correction and Artifact Flagging in the Kepler Data Pipeline

Instrument-induced artifacts in the raw Kepler pixel data include time-varying crosstalk from the fine guidance sensor (FGS) clock signals, manifestations of drifting moiré pattern as locally correlated nonstationary noise and rolling bands in the images which find their way into the calibrated pixel time series and ultimately into the calibrated target flux time series. Using a combination of raw science pixel data, full frame images, reverse-clocked pixel data and ancillary temperature data the Keplerpipeline models and removes the FGS crosstalk artifacts by dynamically adjusting the black level correction. By examining the residuals to the model fits, the pipeline detects and flags spatial regions and time intervals of strong time-varying blacklevel (rolling bands ) on a per row per cadence basis. These flags are made available to downstream users of the data since the uncorrected rolling band artifacts could complicate processing or lead to misinterpretation of instrument behavior as stellar. This model fitting and artifact flagging is performed within the new stand-alone pipeline model called Dynablack. We discuss the implementation of Dynablack in the Kepler data pipeline and present results regarding the improvement in calibrated pixels and the expected improvement in cotrending performances as a result of including FGS corrections in the calibration. We also discuss the effectiveness of the rolling band flagging for downstream users and illustrate with some affected light curves.

Clarke, B. D.↗
NASA NTRS2017

Precision Pointing for the Wide-Field Infrared Survey Telescope (WFIRST)

The Wide-Field Infrared Survey Telescope (WFIRST) mission, scheduled for a mid-2020's launch, is currently in its definition phase. The mission is designed to investigate essential questions in the areas of dark energy, exoplanets, and infrared astrophysics. WFIRST will use a 2.4-meter primary telescope (same size as the Hubble Space Telescope's primary mirror) and two instruments: the Wide Field Instrument (WFI) and the Coronagraph Instrument (CGI). In order to ad-dress the critical science requirements, the WFIRST mission will conduct large-scale surveys of the infrared sky, requiring both agility and precision pointing (11.6 milli-arcsec stability, 14 milli-arcsec jitter). This paper describes some of the challenges this mission profile presents to the GNC subsystem, and some of the design elements chosen to accommodate those challenges. The high-galactic-latitude survey is characterized by 3-minute observations separated by slews ranging from 0.025 deg to 0.8 deg. The need for observation efficiency drives the slew and settle process to be as rapid as possible. A description of the shaped slew profile chosen to minimize excitation of structural oscillation, and the handoff from star tracker-gyro control to fine guidance sensor control is detailed. Also presented is the fine guidance sensor (FGS), which is integral with the primary instrument (WFI). The FGS is capable of tracking up to 18 guide stars, enabling robust FGS acquisition and precision pointing. To avoid excitation of observatory structural jitter, reaction wheel speeds are operationally maintained within set limits. In addition, the wheel balance law is designed to maintain 1-Hz separation between the wheel speeds to avoid reinforcing jitter excitation at any particular frequency. The wheel balance law and operational implications are described. Finally, the candidate GNC hardware suite needed to meet the requirements of the mission is presented.

Stoneking, Eric↗
NASA NTRS2017

Precision Pointing for the Wide-Field Infrared Survey Telescope(WFIRST)

The Wide-Field Infrared Survey Telescope (WFIRST) mission, scheduled for a mid-2020's launch, is currently in its definition phase. The mission is designed to investigate essential questions in the areas of dark energy, exoplanets, and infrared astrophysics. WFIRST will use a 2.4-meter primary telescope (same size as the Hubble Space Telescope's primary mirror) and two instruments: the Wide Field Instrument (WFI) and the Coronagraph Instrument (CGI). In order to address the critical science requirements, the WFIRST mission will conduct large-scale surveys of the infrared sky, requiring both agility and precision pointing (11.6 milli-arcsec stability, 14 milli-arcsec jitter). This paper describes some of the challenges this mission profile presents to the Guidance, Navigation, and Control (GNC) subsystem, and some of the design elements chosen to accommodate those challenges. The high-galactic-latitude survey is characterized by 3-minute observations separated by slews ranging from 0.025 deg to 0.8 deg. The need for observation efficiency drives the slew and settle process to be as rapid as possible. A description of the shaped slew profile chosen to minimize excitation of structural oscillation, and the handoff from star tracker-gyro control to fine guidance sensor control is detailed. Also presented is the fine guidance sensor (FGS), which is integral with the primary instrument (WFI). The FGS is capable of tracking up to 18 guide stars, enabling robust FGS acquisition and precision pointing. To avoid excitation of observatory structural jitter, reaction wheel speeds are operationally maintained within set limits. In addition, the wheel balance law is designed to maintain 1-Hz separation between the wheel speeds to avoid reinforcing jitter excitation at any particular frequency. The wheel balance law and operational implications are described. Finally, the candidate GNC hardware suite needed to meet the requirements of the mission is presented.

Stoneking, Eric T.↗
DOE OSTI2014

Energetics of Defects on Graphene through Fluorination

In the present study, we used FGS[5] as the substrate and implemented low temperature (<=150 oC) direct fluorination on graphene sheets. The fluorine content has been modulated to investigate the formation mechanism of different functional groups such as C-F, CF2, O-CF2 and (C=O)F during the fluorination process. The detailed structure and chemical bonds were simulated theoretically and quantified experimentally by using density function theory (DFT) calculations and NMR techniques, respectively. The adjustable power/energy ratio from fluorinated graphene as cathode for primary lithium batteries is also discussed. From a combination of NMR spectroscopy and theoretical calculation, we conclude that the topological defects without oxygen containing groups provide most of the reactive sites to react with F. FGS also contain a small number of COOH groups which contribute for the fluorination reaction. Hydroxyl or epoxy groups contribute to another fraction of the reaction products.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2011

Hierarchically Porous Graphene as a Lithium-Air Battery Electrode

Functionalized graphene sheets (FGS) are successfully utilized as a novel air electrode for Li-O2 batteries. An extremely high capacity of 15,000 mAh/g was achieved by using the as-prepared graphene air electrode at a current density of 0.1 mA/cm2 in the pure oxygen environment. Although there is no pore in the two-dimensional FGS the as-prepared graphene air electrode consists of randomly arranged graphene nano-sheets which automatically form tunnels with different sizes. The large tunnels work as highways for the oxygen to quickly flow into the air electrode while the small pore-like tunnels can be considered as the numerous exits where the discharge products are accumulated. Combined with an appropriate electrolyte, the ideal discharge product Li2O2 is obtained without any carbonates byproducts in this system. Even when operated in ambient environment with a relative humidity of ~20% the specific capacity delivered from the pouch type cell achieves more than 5000 mAh/g making the graphene-based air electrode extremely attractive in the energy storage applications.

25 ENERGY STORAGE↗
DOE OSTI2017

Magnetic microscopic imaging with an optically pumped magnetometer and flux guides

Here, by combining an optically pumped magnetometer (OPM) with flux guides (FGs) and by installing a sample platform on automated translation stages, we have implemented an ultra-sensitive FG-OPM scanning magnetic imaging system that is capable of detecting magnetic fields of ~20 pT with spatial resolution better than 300 μm (expected to reach ~10 pT sensitivity and ~100 μm spatial resolution with optimized FGs). As a demonstration of one possible application of the FG-OPM device, we conducted magnetic imaging of micron-size magnetic particles. Magnetic imaging of such particles, including nano-particles and clusters, is very important for many fields, especially for medical cancer diagnostics and biophysics applications. For rapid, precise magnetic imaging, we constructed an automatic scanning system, which holds and moves a target sample containing magnetic particles at a given stand-off distance from the FG tips. We show that the device was able to produce clear microscopic magnetic images of 10 μm-size magnetic particles. In addition, we also numerically investigated how the magnetic flux from a target sample at a given stand-off distance is transmitted to the OPM vapor cell.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

An Optimal Pufferfish Privacy Mechanism for Temporally Correlated Trajectories

Temporally correlated trajectories are ubiquitous, and it has been a challenging problem to protect the temporal correlation from being used against users’ privacy. In this work, we propose an optimal Pufferfish privacy mechanism to achieve better data utility while providing guaranteed privacy of temporally correlated daily trajectories. First, a Laplace noise mechanism is realized through geometric sum of noisy Fourier coefficients of temporally correlated daily trajectories. Then, we prove that the proposed noisy Fourier coefficients’ geometric sum satisfies Pufferfish privacy, i.e. , the so-called FGS-Pufferfish privacy mechanism. Furthermore, we achieve better data utility for a given privacy budget by solving a constrained optimization problem of the noisy Fourier coefficients via the Lagrange multiplier method. What is more, a rigorous mathematical formula has been obtained for the Fourier coefficients’ Laplace noise scale parameters. At last, we evaluate our FGS-Pufferfish privacy mechanism on both simulated and real-life data and find that our proposed mechanism achieves better data utility and privacy compared with the other state-of-the-art existing approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An Integrated Supercritical System for Efficient Produced Water Treatment and Power Generation

The main goal of this project was to evaluate the feasibility of an integrated supercritical (SC) water desalination and power generation system for treatment of produced waters from CO 2 sequestration, oil production, and coal-bed methane recovery. This system may offer a transformative approach to generating power from coal or natural gas (NG) and purifying saline water or produced water with high total dissolved solids (TDS) in a zero-liquid discharge plant. The closed-loop steam cycle of conventional power plants was replaced with an open-loop steam cycle that heated the pretreated produced water above the SC point of water (374 °C and 221 bar) to precipitate and separate the salts dissolved in the water. After separation of the precipitated salt, the SC steam required further treatment to reduce the salt content from ~100 mg/L (ppm) to <1 ppm to make it suitable for use in turbines for power generation. A SC membrane distillation unit was used to polish the SC steam, which could be sent through a series of turbines for power generation, and the steam exiting the low-pressure turbine could be condensed by cooling water to produce pure water. Project tasks included a process simulation and a techno-economic evaluation of the integrated system; design and assembly of SC salt precipitation and membrane distillation systems; development and characterization of advanced carbon membranes for SC membrane distillation; and pretreatment, desalination, and purification of different produced water samples with salt concentrations of 30,000–200,000 ppm to a high-purity (<1 ppm) level. Process simulations were performed for 550 MW SC coal-fired or NG baseline cases and various scenarios for the proposed integrated SC system using produced water as the water source and coal or NG as the fuel source. Simulation results indicated that the net plant efficiency loss of the proposed SC cogeneration process would be in the range of <1% to ~4%, in which NG and lower TDS produced water cases would have higher efficiencies. The proposed process for coal-fired cases could provide all water needs for the power generation process and generate additional pure water for beneficial use. A techno-economic analysis was performed to estimate the cost of produced water treatment (dollars /kgal of treated water) by conventional treatment processes compared with the proposed cogeneration process. The cost estimation for the proposed cogeneration system included the cost of pretreatment, the cost of power loss to integrate the water desalination process into the power generation system, and the cost of plant modification or retrofitting. The cost of produced water treatment was calculated by assuming three different scenarios in which converting a baseline power plant to the proposed cogeneration plant would increase the cost of the boiler and feed water system by 10%, 50%, and 100%. Results indicated that the cost of produced water treatment, even with a 100% cost increase, was in the range of $8.6–11.6 dollars per kgal, which is about half of the treatment cost by conventional methods. The cost of produced water treatment by the proposed cogeneration system could be further reduced or a considerable income could be generated if the values of saltwater and freshwater products are considered. Overall, the techno-economic analysis results indicated that the proposed integrated SC system could potentially treat produced water at a cost significantly lower than the cost of produced water treatment by conventional technologies. To evaluate the feasibility of the proposed treatment system at a laboratory scale, a SC salt precipitation and membrane distillation system was designed and fabricated to treat a simulated brine or pretreated produced water by precipitating salts and further polishing the SC steam containing ~100 ppm salts to a high-purity steam. Through baseline tests with NaCl solutions, with concentrations ranging from 30,000 to 200,000 ppm, it was demonstrated that concentrated feed solutions could be treated by precipitating salt at SC conditions to a TDS level of 130 ppm. Produced water samples were collected from a potential CO 2 sequestration site, a coal-bed methane site, and an oilfield in Illinois. Representative samples were characterized for various water quality parameters, including pH; turbidity; conductivity; and concentrations of selected anions, cations, alkalinity, dissolved organic carbon, total suspended solids, TDS, and total petroleum hydrocarbons. The produced water samples were first treated by conventional pretreatment methods to remove residual oil, dissolved organic matter, and scale-forming species. Pretreatment methods included coagulation, sedimentation, filtration, activated carbon adsorption, and ion-exchange adsorption. Pretreated produced waters were treated at SC conditions in which salts were precipitated. Analysis of treated samples revealed that the concentration of Na (the main cation) in produced waters was reduced dramatically from 14,000–47,400 ppm in the feed to 21–80 ppm in treated waters. Concentrations of other main cations (Ca, Mg, Sr, K) also decreased significantly from initial values of ~1,000–22,000 ppm to ~1 ppm or less. However, a significant increase in the concentrations of Fe, Ni, Cu, and Co was observed, mainly caused by leaching of these elements from the system (vessels, filters, tubing), which is manufactured from alloys containing Fe, Ni, Cu, and Co. To polish the SC steam containing a salt content of ~100 ppm to a high-purity level of <1 ppm, a SC membrane distillation treatment using carbon membranes was employed. Different types of self-standing or supported carbon membranes were developed from graphite, graphene, carbon nanotubes, carbon nanofibers, and pyrolytic carbon. Screening tests revealed that only a limited number of developed carbon membranes were suitable for the purification of steam at SC conditions. Membranes that were either fragile and lacked mechanical strength or had large pores and showed limited salt rejection (<20%) were found to be unsuitable for the purification of SC steam. Promising carbon membranes that were successfully tested for purifying SC steam included two graphite membranes (i.e., AF-5, a porous graphite material, and FGS, a flexible graphite sheet) and a carbon nanotube membrane grown on a Hastelloy substrate and then further modified using a proprietary method (i.e., membrane C). The AF-5 membrane exhibited a stable water flux of ~50 kg/m 2 ∙h and ~40% salt rejection. The FGS membrane had a high salt rejection of 95%–98% but a lower water flux of ~15 kg/m 2 ∙h. Membrane C showed an extremely high flux of 200-800 kg/m 2 ∙h, which is one order of magnitude higher than the water flux of conventional membranes. Membrane C also exhibited 87%–93% salt rejection. Overall, a two-stage or multistage polishing treatment by these membranes could lower the salt content of the SC steam from initial values of ~100–200 ppm to the steam quality of <1 ppm or to parts per billion levels required for the power cycle.

20 FOSSIL-FUELED POWER PLANTS↗
NASA NTRS1982

Astrometric observations with the Space Telescope

Astrometry with the Space Telescope (ST) is performed using one of the fine guidance sensors (FGS). The FGS, which is based on a pair of Koester's prism interferometers, one for each axis, is capable of measuring the position of one object relative to another with an accuracy of 0.002 arcseconds. Astrometric Data Reduction Software (ADRS) available to the astrometric user of ST is described. The kinds of problems the space telescope astrometry team plans to investigate using ST are discussed.

Duncombe, R. L.↗
NASA NTRS1992

Acquisition, pointing and tracking performance of the Hubble Space Telescope fine guidance sensors

The three fine guidance sensors (FGSs) on board the HST have been operated extensively since the observatory was launched in April, 1990. The FGSs, each capable of measuring angles as small as 0.003 arcsec, provide required fine pointing information to the HST's pointing control system and are intended to serve as astrometry instruments. On-orbit data have shown that the acquisition, pointing and tracking performance of the FGSs in most cases meets, and of these sometimes exceeds, requirements. The versatility of the FGS digital control electronics to adapt to the unexpected conditions imposed on the sensors by the telescope spherical aberration and by solar panel jitter is discussed. There is encouragement from both on-orbit tests and analytical studies that the FGSs can accommodate the current telescope characteristics. Improvements to guide star acquisitions within the FGSs and to target acquisitions within science instruments have been accomplished with the internal distortion calibration of each FGS and with the alignment calibration between sensors. Techniques used in the calibration process and the resulting improvements in acquisitions are presented.

Eaton, David J.↗
NASA NTRS1994

The photometric properties of the HST astrometer Fine Guidance Sensor

This paper presents the results of the photometric calibration of the F583W filter in the astrometer Fine Guidance Sensor on the Hubble Space Telescope. Dozens of observations of the 9.58 mag Fine Guidance Sensor (FGS) transfer mode reference star Upgren 69 (in the cluster NGC 188) have been utilized to verify the consistency and demonstrate the temporal stability of the photomultipliers. The measurements which provided the material for a transformation from the FGS instrumental system to the Johnson V magnitude consisted of the extensive position mode observations performed during the Optical Field Angle Distortion calibration. A total of 588 measurements of 92 stars in the galactic cluster M35 were performed. Johnson V band photometry with a precision (i.e., random errors) of plus or minus 0.05 mag is available with an accuracy (i.e., systematic errors) of 0.05 mag over 2 yr.

Bucciarelli, B.↗
NASA NTRS2000

STS-103 Mission Highlights Resource Tape (1 of 2)

The STS-103 flight crew, Commander Curtis L. Brown, Pilot Scott J. Kelly, Mission Specialists Steven L. Smith, C. Michael Foale, John M. Grunsfeld, Claude Nicollier, and Jean-Francois Clervoy, are seen performing pre-launch activities such as crew suit-up, and ride out to the launch pad for a night launch. Also, included are various panoramic views of the shuttle on the pad. The crew is readied in the White Room for their mission. After the closing of the hatch and arm retraction, launch activities are shown including countdown, engine ignition, launch, and the separation of the Solid Rocket Boosters. Once on-orbit the primary objective is to capture and service the Hubble Space Telescope. Included are various live shots of the payload bay showing the flight support system, the orbiter replacement unit carrier and the forward fixture that house the new Fine Guidance System (FGS). Smith and Grunsfeld replaces and changes the sensor units during the first space walk of this mission. The second space walk by Nicollier and Foale includes the changing of the computer and installation of the FGS. This is tape 1 of 2, tape 2 has a report number of NONP-NASA-VT-2000036031.

Source record↗
NASA NTRS2004

Software Safety Analysis of a Flight Guidance System

This document summarizes the safety analysis performed on a Flight Guidance System (FGS) requirements model. In particular, the safety properties desired of the FGS model are identified and the presence of the safety properties in the model is formally verified. Chapter 1 provides an introduction to the entire project, while Chapter 2 gives a brief overview of the problem domain, the nature of accidents, model based development, and the four-variable model. Chapter 3 outlines the approach. Chapter 4 presents the results of the traditional safety analysis techniques and illustrates how the hazardous conditions associated with the system trace into specific safety properties. Chapter 5 presents the results of the formal methods analysis technique model checking that was used to verify the presence of the safety properties in the requirements model. Finally, Chapter 6 summarizes the main conclusions of the study, first and foremost that model checking is a very effective verification technique to use on discrete models with reasonable state spaces. Additional supporting details are provided in the appendices.

Butler, Ricky W.↗