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NASA NTRS2010

A Singular Perturbation Approach for Time-Domain Assessment of Phase Margin

This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter Epsilon. First, a bijective relationship between the Singular Perturbation Margin (SPM) max and the PM of the nominal (slow) system is established with an approximation error on the order of Epsilon(exp 2). In proving this result, relationships between the singular perturbation parameter Epsilon, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time-domain for SISO LTI systems using the SPM with a standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.

Zhu, J. Jim↗

NASA NTRS2009

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

Nguyen, Nhan T.↗

NASA NTRS2011

Negative Stress Margins - Are They Real?

Advances in modeling and simulation, new finite element software, modeling engines and powerful computers are providing opportunities to interrogate designs in a very different manner and in a more detailed approach than ever before. Margins of safety are also often evaluated using local stresses for various design concepts and design parameters quickly once analysis models are defined and developed. This paper suggests that not all the negative margins of safety evaluated are real. The structural areas where negative margins are frequently encountered are often near stress concentrations, point loads and load discontinuities, near locations of stress singularities, in areas having large gradients but with insufficient mesh density, in areas with modeling issues and modeling errors, and in areas with connections and interfaces, in two-dimensional (2D) and three-dimensional (3D) transitions, bolts and bolt modeling, and boundary conditions. Now, more than ever, structural analysts need to examine and interrogate their analysis results and perform basic sanity checks to determine if these negative margins are real.

Raju, Ivatury S.↗

NASA NTRS2016

Marginalizing Instrument Systematics in HST WFC3 Transit Light Curves

Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) infrared observations at 1.1-1.7 microns probe primarily the H2O absorption band at 1.4 microns, and have provided low-resolution transmission spectra for a wide range of exoplanets. We present the application of marginalization based on Gibson to analyze exoplanet transit light curves obtained from HST WFC3 to better determine important transit parameters such as "ramp" probability (R (sub p)) divided by "ramp" total (R (sub asterisk)), which are important for accurate detections of H2O. We approximate the evidence, often referred to as the marginal likelihood, for a grid of systematic models using the Akaike Information Criterion. We then calculate the evidence-based weight assigned to each systematic model and use the information from all tested models to calculate the final marginalized transit parameters for both the band-integrated and spectroscopic light curves to construct the transmission spectrum. We find that a majority of the highest weight models contain a correction for a linear trend in time as well as corrections related to HST orbital phase. We additionally test the dependence on the shift in spectral wavelength position over the course of the observations and find that spectroscopic wavelength shifts delta (sub lambda) times lambda) best describe the associated systematic in the spectroscopic light curves for most targets while fast scan rate observations of bright targets require an additional level of processing to produce a robust transmission spectrum. The use of marginalization allows for transparent interpretation and understanding of the instrument and the impact of each systematic evaluated statistically for each data set, expanding the ability to make true and comprehensive comparisons between exoplanet atmospheres.

Wakeford, H. R.↗

NASA NTRS2011

Negative stress margins – are they real?

Raju, Ivatury S.↗

NASA NTRS2020

2020 IEEE Paper on Psyche margin management, Draft

In January 2017, the mission concept Psyche: Journey to a Metal World was one of two concepts selected by NASA for implementation as part of the 14th Discovery mission competition. Over the course of the past year, the Psyche team has actively worked to refine and mature the technical design, culminating in a successful completion of the Project Preliminary Design review and approval to proceed to Phase C in mid-2019. Psyche is a deep space mission utilizing solar electric propulsion (SEP), consisting of SPT-140 Hall thrusters which have been successfully employed on multiple commercial spacecraft. When launched, Psyche will carry over 1000 kg of Xenon, and will represent the farthest usage of electric propulsion usage from the Sun – a distance of over 3.3 AU. The use of solar electric propulsion in deep space has resulted in challenges unique to other missions. Spacecraft designs typically balance margins across two main elements – mass and power – that are independent of one another. Utilizing a low thrust trajectory through the application of electric propulsion introduces more elements - namely flight time, missed thrust percentage and thruster duty cycle. Moreover, these elements become connected, presenting additional relationships that must be considered. This paper will present an overview of the margin management process for Psyche, and how it has evolved from the early proposal stage to its current state. It will discuss the elements that are margined, their relationship with one another, and key uncertainties that must be addressed. It discusses challenges and mitigations obtained during the refinement of the Psyche project, culminating in a new margin strategy that enables optimization across many of the system elements, and will serve as a template for future deep space SEP missions.

Hart, William↗

NASA NTRSDate not supplied

Stall Margin Improvement in a Transonic Compressor with a Casing Treatment: Flow Mechanism

Effects of casing treatments for improved stall margin in transonic compressors are investigated. Two types of compressor casing treatments, circumferential grooves and axial slots casing treatments, are studied in detail. The primary objective of the current paper is to identify the underlying fluid mechanics that change the stall margin of transonic compressors with these two casing treatments. Large eddy simulation (LES) is applied to calculate the compressor flow fields with these two types of casing treatments. Calculated flow fields are first compared with measured experimental data to validate the LES simulation. Details of the calculated unsteady flow structures are examined to unearth the underlying flow mechanism for the improved stall margin. Further possible design optimization of the casing treatment for the stall margin extension without any performance penalty near the design condition is also explored.

compressor↗

NASA NTRS2024

Sampling the Margin Unit of Jezero Crater, Mars for Future Mars Sample Return

Mars 2020 Perseverance rover is currently exploring Jezero crater, which contains an ancient lake-delta system with a high potential for past habitability. One of Perseverance’s primary science goals is to collect a set of scientifically return-worthy samples for return to Earth (Mars Sample Return; MSR). Between February 2021 and December 2023, Perseverance has sealed 23 tubes containing 20 rock cores, 2 regolith samples and one atmosphere sample. All rock and regolith samples are accompanied by a set of observations (Sample Threshold Observation Protocol, the STOP List) performed on abrasion patches or regolith near each sample collection site. These observations are documented in the Initial Reports and the Sample Dossier (https://pds-geosciences.wustl.edu/missions/mars2020/returned_sample_science.htm). Here we provide an overview of the samples collected during the Margin campaign. The Margin unit is situated interior and adjacent to the western crater rim and exhibits a strong carbonate signal from orbital reflectance spectroscopy. Stratigraphically the unit lies beneath the previously explored curvilinear and blocky units of the fan top and is therefore older than those units. Based on its position near the crater rim and the strong carbonate detections it has been proposed to be a shoreline deposit with possible lacustrine carbonates. Alternative hypotheses include pyroclastic, fluviolacustrine and aeolian deposits. Based on rover observations a lacustrine shoreline deposit seems most likely. The planning of the Margin campaign took place during the summer of 2023, and 3-5 samples were baselined to be collected. Exploration of the Margin unit began in September 2023 and so far, two samples have been collected: the Pelican Point core at the Hans Amundsen Memorial Workspace in the Mandu Wall region , and the Lefroy Bay core at Lake Newell in the Turquoise Bay region (Fig. 1). The associated abrasion patches are Amherst Point (Pelican Point) and Bills Bay (Lefroy Bay) . Mandu Wall is interpreted to be stratigraphically lower than Turquoise Bay based on topography.

Mars sample return↗

NASA NTRS2020

Unexpected Source and Transport of Iron from the Deep Peru Margin

Iron is the most important micronutrient in the ocean, but the nature and magnitude of its sources and sinks to the ocean are poorly constrained. Here we assess our understanding of the sources and sinks of iron in margin environments by synthesizing observations from the U.S. GEOTRACES GP16 Eastern Tropical Pacific Zonal Transect (EPZT) cruise near the Peru margin. GP16 observations showed elevated dissolved iron (dFe) concentrations along the margin, but a larger westward plume of dFe at slope depths (1000-3000 m) in oxygenated waters, rather than at shelf depths (100-300 m) in oxygen deficient waters. We examine the potential explanations for this unexpected observation. Multiple tracers from GP16 suggest that sediment resuspension was important at slope depths, which would lead to enhanced benthic flux of dFe above what was previously measured. The difference in the apparent persistence and penetration of shelf vs slope plumes of dFe into the interior of the ocean likely results from faster removal rates of the shelf dFe compared to slope dFe. DFe sourced from the shelf was almost entirely in the dFe(II) form, whereas dFe sourced from the slope was almost entirely in the dFe(III) form. Although benthic dFe(II) diffuses into oxygen deficient overlying waters, there is still oxidation of dFe(II), which precipitates to particulate Fe(III). In contrast, the slope plume appears to persist in a stabilized dFe(III) form. We hypothesize that sediment porewaters with moderate organic carbon delivery to sediments and shallow oxygen penetration are especially good sources of persistent dFe to the water column.

iron↗

NASA NTRS2022

Treatment of Launch Vehicle Flight Control Stability Margin Reductions for Crewed Missions with Emphasis on Slosh Dynamics

NESC’s perspective for crewed spaceflight: Acceptance of flight control gain/phase stability margin reductions from industry standards should be accompanied by an adequately extensive technical treatment, including: •Analyzing the fundamental physics involved, with applicable simulation tool verification (particularly if results are dissimilar among rules of thumb, linear tools, nonlinear analysis, and flight data) •Conducting sensitivity studies in time and frequency domains to analyze effects of possible parameter and system variations •Studying the effects of the consequence of instability associated with offending modes by running stressing cases in time domain •Assessing alternative flight control designs to demonstrate that present design appropriately balances overall vehicle risk (i.e., quantitatively delineate chosen tradeoffs between various stability margins and vehicle performance in the context of risk/consequence) Work presented here represents an example summary of expected engineering work to flight-certify crewed missions with unstable slosh modes and reduced stability margins

Launch Vehicle Flight Control↗

NASA NTRS2022

NASA Engineering and Safety Center Technical Bulletin No. 22-05: Launch Vehicle Flight Control Stability Margin Reduction Considerations

Launch vehicle ascent stability analyses typically rely on a combination of frequency and time domain analyses. Frequency domain analysis uses a sequence of high-fidelity linear models with constant parameters spanning the ascent trajectory. Complementary time domain analysis is performed using high-fidelity, nonlinear 6-DOF simulations. Analyses are typically dispersed to verify robustness to parameter variations by showing the vehicle meets frequency domain stability margin requirements and time domain performance metrics. This Technical Bulletin outlines standard stability margin best practices and provides recommendations for treatment of deviations from industry-standard launch vehicle stability margins due to vehicle flexibility, slosh dynamics, aerodynamics, other offending dynamics, or coupling thereof.

Launch Vehicle↗

NASA NTRSDate not supplied

Probabilistic Approach to Assessing CCRS Capture System Performance Margin

In the aerospace industry, there are standard design principles and/or rule-of-thumb targets that define healthy levels of margins required at each developmental milestone for traditional metrics, such as mass, thermal, and power margins. When the technical resource is “non-traditional” in the sense that guiding margin principles are non-existent, systems engineering judgment is required to internally generate performance targets and methodologies to assess the system against the derived targets. This paper presents a probabilistic approach for assessing complex time-critical operations in order to apply global sensitivity analyses to identify input parameters that should (or should not) serve as design drivers.

Performance Margins↗

NASA NTRSDate not supplied

Probabilistic Approach to Assessing Capture System Performance Margin in Mars Sample Return's Capture, Containment, and Return System

In the aerospace industry, there are standard design principles and/or rule-of-thumb targets that define healthy levels of margins required at each developmental milestone for traditional metrics, such as mass, thermal, and power margins. When the technical resource is “non-traditional,” in the sense that guiding margin principles are non-existent, systems engineering processes are required to internally generate performance targets and methodologies to assess the system against the derived targets. This paper presents a probabilistic approach for assessing complex time-critical operations which applies global sensitivity analyses to identify input parameters that should drive the design. This approach is used to design a critical payload required for the Mars Sample Return campaign aiming at bringing back rock and atmospheric samples from Mars.

Performance Margins↗

NASA NTRSDate not supplied

Chemistry and Mineralogy of the Margin Unit, Jezero Crater, Mars, Observed By M2020 / Supercam

The Margin Unit of Jezero crater, Mars, was identified from orbit as one of the most carbonate-rich regions of the planet [e.g., 1,2]. Its presence, along with the adjacent fluvial delta [e.g., 3] made Jezero crater the most compelling landing site for the Mars 2020 mission. Investigation of Jezero’s Margin-Unit carbonates provides a unique opportunity to address the formation of carbonates in sedimentary deposits, possibly under a CO 2 -rich martian atmosphere. Here we report on chemistry and mineralogy of 55 targets observed by the multi-technique SuperCam instrument during Perseverance’s crater-margin campaign.

Mars 2020↗

NASA NTRS1978

Strobe-margin test for plated memory systems

Technique measures performance of plated-wire memories. Strobe-margin test (SMT) utilizes worst-case testing and automatically gives exact strobe margin. Test is automatic; thus, memory system-level test is superior to tests at component level that use artificial test conditions. Test is significant tool in design and test of plated-wire memory systems. It can rapidly quantify memory-system margin on each production unit and impact of any design changes.

Anspach, T. E.↗

NASA NTRS1979

A multiloop generalization of the circle criterion for stability margin analysis

In order to provide a theoretical tool suited for characterizing the stability margins of multiloop feedback systems, multiloop input-output stability results generalizing the circle stability criterion are considered. Generalized conic sectors with 'centers' and 'radii' determined by linear dynamical operators are employed to specify the stability margins as a frequency dependent convex set of modeling errors (including nonlinearities, gain variations and phase variations) which the system must be able to tolerate in each feedback loop without instability. The resulting stability criterion gives sufficient conditions for closed loop stability in the presence of frequency dependent modeling errors, even when the modeling errors occur simultaneously in all loops. The stability conditions yield an easily interpreted scalar measure of the amount by which a multiloop system exceeds, or falls short of, its stability margin specifications.

Safonov, M. G.↗

NASA NTRS1981

A multiloop generalization of the circle criterion for stability margin analysis

In order to provide a theoretical tool well suited for use in characterizing the stability margins (e.g., gain and phase margins) of multiloop feedback systems, multiloop input-output stability results generalizing the circle stability criterion are considered. Generalized conic sectors with 'centers' and 'radii' determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency-dependent convex set of modeling errors (including nonlinearities, gain variations, and phase variations) which the system must be able to tolerate in each feedback loop without instability. The resulting stability criterion gives sufficient conditions for closed-loop stability in the presence of such frequency-dependent modeling errors, even when the modeling errors occur simultaneously in all loops.

Safonov, M. G.↗

NASA NTRS1986

Satellite microwave and in situ observations of the Weddell Sea ice cover and its marginal ice zone

The radiative and physical characteristics of the Weddell Sea ice cover and its marginal ice zone are analyzed using multichannel satellite passive microwave data and ship and helicopter observations obtained during the 1983 Antarctic Marine Ecosystem Research. Winter and spring brightness temperatures are examined; spatial variability in the brightness temperatures of consolidated ice in winter and spring cyclic increases and decrease in brightness temperatures of consolidated ice with an amplitude of 50 K at 37 GHz and 20 K at 18 GHz are observed. The roles of variations in air temperature and surface characteristics in the variability of spring brightness temperatures are investigated. Ice concentrations are derived using the frequency and polarization techniques, and the data are compared with the helicopter and ship observations. Temporal changes in the ice margin structure and the mass balance of fresh water and of biological features of the marginal ice zone are studied.

Comiso, J. C.↗