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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 685 records · Page 38

Evaluating Twenty-Year Trends in Earth’s Energy Flows from Observations and Reanalyses

Satellite, reanalysis, and ocean in situ data are analyzed to evaluate regional, hemispheric and global mean trends in Earth’s energy fluxes during the first twenty years of the 21st century. Regional trends in net top-of-atmosphere (TOA) radiation from the Clouds and the Earth’s Radiant Energy System (CERES), ECMWF Reanalysis 5 (ERA5), and a model similar to ERA5 with prescribed sea surface temperature (SST) and sea ice differ markedly, particularly over the Eastern Pacific Ocean, where CERES observes large positive trends. Hemispheric and global mean net TOA flux trends for the two reanalyses are smaller than CERES, and their climatological means are half those of CERES in the southern hemisphere (SH) and more than nine times larger in the northern hemisphere (NH). The regional trend pattern of the divergence of total atmospheric energy transport (TEDIV) over ocean determined using ERA5 analyzed fields is similar to that inferred from the difference between TOA and surface fluxes from ERA5 short-term forecasts. There is also agreement in the trend pattern over ocean for surface fluxes inferred as a residual between CERES net TOA flux and ERA5 analysis TEDIV and surface fluxes obtained directly from ERA5 forecasts. Robust trends are observed over the Gulf Stream associated with enhanced surface-to-atmosphere transfer of heat. Within the ocean, larger trends in ocean heating rate are found in the NH than the SH after 2005, but the magnitude of the trend varies greatly among datasets.

Norman G Loeb↗

Understanding and improving anode performance in an alkaline membrane electrolyzer using statistical design of experiments

The behavior of the oxygen-evolving positive electrode (i.e. anode) in the anion exchange membrane water electrolyzer (AEMEL) is complex and influenced by several factors. Very few studies have been performed to understand oxygen evolution reaction (OER) behavior by optimizing the individual factors that influence performance. Here, this study highlights the effects of catalyst loading, catalyst selection, porous transport layer (PTL) type and conductive additive content. The influence of each factor is elucidated through a design of experiments (DoE) approach with a full statistical analysis. Electrochemical data, alongside Pareto charts, parametric trends and their mutual interactions are discussed. This DoE approach is also helpful in making useful predictions and discovering new combinations to be tested. The end result was a high-performance AEMEL able to operate at a current density of 1.0 A/cm 2 at 1.80 V with IrOx OER and PtNi hydrogen evolution reaction (HER) catalysts using 0.3 M KOH fed to the anode. Even lower operating voltage was observed with PbRuOx catalyst at the anode, 1.64 V @ 1.0 A/cm 2 , though the cell decay rate was higher. Lastly, a IrOx/PtNi cell was stably operated continuously for 30 days (720 h) at 1.0 A/cm 2 . This study can serve as a guide for optimal electrode design with insights into component-performance compromises, which can aid in making design choices and performing techno-economic analyses.

08 HYDROGEN↗

Self-reported health impacts of do-it-yourself air cleaner use in a smoke-impacted community

Smoke exposure from wildfires or residential wood burning for heat is a public health problem for many communities. Do-It-Yourself (DIY) portable air cleaners (PACs) are promoted as affordable alternatives to commercial PACs, but evidence of their effect on health outcomes is limited. Pilot test an evaluation of the effect of DIY PAC usage on self-reported symptoms, and investigate barriers and facilitators of PAC use, among members of a tribal community that routinely experiences elevated concentrations of fine particulate matter (PM 2.5 ) from smoke. We conducted studies in Fall 2021 (“wildfire study”; N = 10) and Winter 2022 (“wood stove study”; N = 17). Each study included four sequential one-to-two-week phases: 1) initial, 2) DIY PAC usage ≥8 h/day, 3) commercial PAC usage ≥8 h/day, and 4) air sensor with visual display and optional PAC use. We continuously monitored PAC usage and indoor/outdoor PM 2.5 concentrations in homes. Concluding each phase, we conducted phone surveys about participants’ symptoms, perceptions, and behaviors. We analyzed symptoms associated with PAC usage and conducted an analysis of indoor PM 2.5 concentrations as a mediating pathway using mixed effects multivariate linear regression. We categorized perceptions related to PACs into barriers and facilitators of use. No association was observed between PAC usage and symptoms, and the mediation analysis did not indicate that small observed trends were attributable to changes in indoor PM 2.5 concentrations. Small sample sizes hindered the ability to draw conclusions regarding the presence or absence of causal associations. DIY PAC usage was low; loud operating noise was a barrier to use. This research is novel in studying health effects of DIY PACs during wildfire and wood smoke exposures. Such research is needed to inform public health guidance. Recommendations for future studies on PAC use during smoke exposure include building flexibility of intervention timing into the study design.

54 ENVIRONMENTAL SCIENCES↗

The effect of ink ball milling time on interparticle interactions and ink microstructure and their influence on crack formation in rod-coated catalyst layers

This work investigates the influence of ballmilling (sometimes also referred to as jar roller milling) time on cathode catalyst layer (CL) inks and electrode properties using formulations and coating methods relevant for industrial manufacturing. Four CL inks with the same composition were milled for 24, 48, 72, or 96 h. Rheological investigation of these inks showed a reduction of elastic moduli and steady-shear viscosity with continuous ink milling, which is correlated to a decrease in particle-particle interactions as well as formation of smaller agglomerates. Optical microscopy (OM) analysis of the fabricated electrodes revealed a trend in surface crack formation; formulations milled for 24 h contained the lowest average surface crack area percentages of 0.370% at heavy-duty loadings of ~0.300 mg Pt cm -2 , compared to 2.418% for the ink milled for 96 h. Further characterization of the CL through transmission electron microscopy (TEM) imaging showed a decrease in the mean agglomerate and pore size with milling time. Furthermore, these smaller electrode features were consistent with reduced fracture resistance and, hence, development of larger stresses during drying. Our results highlight the need to consider ink processing as an important component in defect-free CL manufacturing.

30 DIRECT ENERGY CONVERSION↗

Hydration Free Energies of Polypeptides from Popular Implicit Solvent Models versus All-Atom Simulation Results Based on Molecular Quasichemical Theory

Calculating the hydration free energy of a macromolecule in all-atom simulations has long remained a challenge, necessitating the use of models wherein the effect of the solvent is captured without explicit account of solvent degrees of freedom. This situation has changed with developments in the molecular quasi-chemical theory (QCT)-an approach that enables calculation of the hydration free energy of macromolecules within all-atom simulations at the same resolution as is possible for small molecular solutes. The theory also provides a rigorous and physically transparent framework to conceptualize and model interactions in molecular solutions and thus provides a convenient framework to investigate the assumptions in implicit solvent models. In this study, we compare the results using molecular QCT versus predictions from EEF1, ABSINTH, and GB/SA implicit solvent models for polyglycine and polyalanine solutes covering a range of chain lengths and conformations. The hydration free energies or the differences in hydration free energies between conformers obtained from the implicit solvent models do not agree with explicit solvent results, with the deviations being largest for the group additive EEF1 and ABSINTH models. GB/SA does better in capturing the qualitative trends seen in explicit solvent results. Finally, analysis founded on QCT reveals the critical importance of the cooperativity of hydration that is inherent in the hydrophilic and hydrophobic contributions to hydration-physics that is not well captured in additive models but somewhat better accounted for by means of a dielectric in the GB/SA approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Rapid Polyolefin Plastic Hydrogenolysis Mediated by Single-Site Heterogeneous Electrophilic/Cationic Organo-group IV Catalysts

A homologous series of cationic electrophilic group IV metal hydrides (M = Ti, Zr, Hf) created by chemisorption of the corresponding MNp 4 precursors on highly Brønsted acidic sulfated alumina (AlS) to yield loosely coordinated surface AlS/MNp 2 (Np = neopentyl) species are systematically characterized by ICP, EXAFS/XANES, DRIFTS, and solid-state high-resolution multidimensional NMR spectroscopy (SSNMR), as well as by energy span DFT computation. With effective stirring, these complexes readily undergo reaction with H 2 to yield AlS/M(alkyl)H species, which are highly active for the hydrogenolysis of diverse commercial polyethylenes, α-olefin-ethylene copolymers, isotactic polypropylene, and postconsumer polyolefins including high-density polyethylenes, yielding medium and small linear and branched hydrocarbons at turnover frequencies as high as 36,300 h –1 at 200 °C/17 atm H 2 for M = Zr. For given polyolefin and reaction conditions, turnover frequencies scale approximately as M = Zr > Hf > Ti, whereas catalyst thermal stability scales approximately as M = Hf ≈ Zr > Ti, and these trends are qualitatively understandable from the DFT analysis. These catalytic results reveal that the AlS/Hf(R)H-mediated hydrogenolysis favors wax-like and liquid products, whereas the AlS/Zr(R)H-mediated hydrogenolysis can be tuned between gases and liquids. Finally, DFT analysis identifies β-alkyl elimination as the turnover-limiting C–C scission process, which is particularly facile in these cationic d 0 complexes but not so in the neutrally charged analogues.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Composition, Activity, and Stability of IrO x Oxygen Evolution Reaction Electrocatalysts

The oxygen evolution reaction (OER) is integral to several electrochemical energy conversion and storage technologies, including carbon dioxide reduction to value added fuels, nitrogen reduction to ammonia, reversible fuel cells, rechargeable metal−air batteries, and water electrolysis to produce hydrogen. Iridium oxide (IrO x ) is widely recognized as the benchmark OER catalyst for acidic environments. Despite widespread use of IrO x catalysts, most notably in proton-exchange membrane water electrolyzers (PEMWEs), a comprehensive understanding of the physicochemical properties of commercial catalysts and the impact of these properties on both the activity and stability of these catalysts is lacking. Here, we study commercial IrO x catalysts with different physicochemical properties, three nominally considered amorphous and three rutile, to elucidate how structural and compositional variations affect OER activity and stability. Utilizing standardized aqueous electrochemical protocols, time-resolved dissolution quantification using inductively-coupled plasma mass spectrometry, and physicochemical characterization, including multiple synchrotron X-ray techniques, we systematically correlate catalyst properties with OER performance and degradation behavior aided by principal component analysis (PCA). Our results demonstrate the general trend of amorphous IrO x having higher intrinsic activity but limited stability and crystalline rutile IrO 2 having lower activity but enhanced stability against dissolution. The trends within the amorphous and rutile catalyst groups correlate with inherent material properties, including phase composition and structure, crystallinity, particle size, surface area, and surface structure/chemistry. Notably, we identify a rutile catalyst with the largest crystallite/ domain sizes, moderate surface area, a small fraction of hydrous phase, and a favorable pore structure (trimodal distributions of pore sizes ranging from 2−5 nm) that exhibits the best balance between activity and stability among the six catalysts studied here. These findings illustrate a fundamental structure-governed trade-off between activity and stability and highlight the critical role of surface chemistry modification and structure engineering in IrO x catalyst optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ternary Phosphides Ba M 2 P 2 : Tailoring Crystal and Electronic Structures Enables Highly Efficient HER Electrocatalysis

Binary transition metal phosphides and their solid solutions have emerged as promising hydrogen evolution reaction (HER) catalysts. Although many research endeavors have adopted strategies to vary compositions to optimize catalytic performance, they mainly focus on binary structures, which represent only a small fraction of the abundant phase space of structure types among transition metal phosphides. Here, the largely unexplored class of ternary and multinary ordered phosphides in catalysis comprises two or more metals with quite different chemical nature, concealing the structure–property relationships essential for advancing catalyst design. Here, we explored phosphides crystallizing in one of the most abundant ordered intermetallic structure types, —the ThCr 2 Si 2 type, —where square nets of 3d transition metal M and P atoms are separated by layers of electropositive Ba cations. Four ternary BaM 2 P 2 (M = Fe, Fe/Cu, Fe/Ni, Ni) catalysts were synthesized and characterized. BaNi 2 P 2 showed high HER activity in acidic electrolyte, which required an overpotential, η 10 , of only 62 mV to drive current density j = –10 mA/cm 2 and high stability with a potential drop rate of 0.25 mV/h. BaNi 2 P 2 outperformed other Ni-based catalysts, such as Ni 2 P and Ni 5 P 4 . Notably, at current densities above –170 mA/cm 2 , BaNi 2 P 2 outperformed the standard Pt electrode measured under identical conditions. Electronic structure analysis revealed a volcano-type activity trend among the four BaM 2 P 2 catalysts based on their d-band center positions, highlighting the role of electropositive Ba cations in shifting the Ni-3d orbitals into an optimal position.

BaNi2P2↗

A deep neural network regressor for phase constitution estimation in the high entropy alloy system Al-Co-Cr-Fe-Mn-Nb-Ni

High Entropy Alloys (HEAs) are composed of more than one principal element and constitute a major paradigm in metals research. The HEA space is vast and an exhaustive exploration is improbable. Therefore, a thorough estimation of the phases present in the HEA is of paramount importance for alloy design. Machine Learning presents a feasible and non-expensive method for predicting possible new HEAs on-the-fly. A deep neural network (DNN) model for the elemental system of: Mn, Ni, Fe, Al, Cr, Nb, and Co is developed using a dataset generated by high-throughput computational thermodynamic calculations using Thermo-Calc. The features list used for the neural network is developed based on literature and freely available databases. A feature significance analysis matches the reported HEAs phase constitution trends on elemental properties and further expands it by providing so far-overlooked features. The final regressor has a coefficient of determination ( r 2 ) greater than 0.96 for identifying the most recurrent phases and the functionality is tested by running optimization tasks that simulate those required in alloy design. The DNN developed constitutes an example of an emulator that can be used in fast, real-time materials discovery/design tasks.

36 MATERIALS SCIENCE↗

Long-term multi-wavelength study of 1ES 0647+250

The BL Lac object 1ES 0647+250 is one of the few distant γ-ray emitting blazars detected at very high energies (VHEs; &100 GeV) during a non-flaring state. It was detected with the MAGIC telescopes during a period of low activity in the years 2009-2011 as well as during three flaring activities in the years 2014, 2019, and 2020, with the highest VHE flux in the last epoch. An extensive multi-instrument data set was collected as part of several coordinated observing campaigns over these years. We aim to characterise the long-term multi-band flux variability of 1ES 0647+250, as well as its broadband spectral energy distribution (SED) during four distinct activity states selected in four different epochs, in order to constrain the physical parameters of the blazar emission region under certain assumptions. We evaluated the variability and correlation of the emission in the different energy bands with the fractional variability and the Z transformed discrete correlation function, as well as its spectral evolution in X-rays and γ rays. Owing to the controversy in the redshift measurements of 1ES 0647+250 reported in the literature, we also estimated its distance in an indirect manner through a comparison of the GeV and TeV spectra from simultaneous observations with Fermi-LAT and MAGIC during the strongest flaring activity detected to date. Moreover, we interpret the SEDs from the four distinct activity states within the framework of one-component and two-component leptonic models, proposing specific scenarios that are able to reproduce the available multi-instrument data. We find significant long-term variability, especially in X-rays and VHE γ rays. Furthermore, significant (3-4σ) correlations were found between the radio, optical, and high-energy (HE) γ-ray fluxes, with the radio emission delayed by about ~400 days with respect to the optical and γ-ray bands. The spectral analysis reveals a harder-when-brighter trend during the non-flaring state in the X-ray domain. However, no clear patterns were observed for either the enhanced states or the HE (30 MeV < E < 100 GeV) and VHE γ-ray emission of the source. The indirect estimation of the redshift yielded a value of z = 0.45 ± 0.05, which is compatible with some of the values reported in the literature. The SEDs related to the low-activity state and the three flaring states of 1ES 0647+250 can be described reasonably well with the both one-component and two-component leptonic scenarios. However, the long-term correlations indicate the need for an additional radio-producing region located about 3.6 pc downstream from the gamma-ray producing region.

79 ASTRONOMY AND ASTROPHYSICS↗

Spread Spectrum Time Domain Reflectometry (SSTDR) and Frequency Domain Reflectometry (FDR) for Detection of Cable Anomalies Using Machine Learning

Cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation Inc. that is designed to operate on live cables up to 1000 volts. One of the main conclusions of a previous effort was that cable reflectometry plots can be difficult for humans to analyze due to baseline noise, low or noisy anomaly response peaks, or large responses from cable ends. Detection of cable anomalies for many of these frequencies and test conditions was challenging for manual analysis. This presented an ideal opportunity for ML analysis to distinguish undamaged cable indications from anomalous cable indications. This research discusses application of machine learning (ML) to reflectometry cable test methods. The goal was to assess feasibility to distinguish undamaged cable reflectometry responses from damaged or anomalous cable reflectometry responses. The assessment considered the 3 instruments, multiple frequency bandwidths from each instrument, multiple cable anomalies and test conditions, and both supervised and unsupervised ML approaches. Although approaches and analysis methods were not identical or directly comparable, both outputs were encouraging. The unsupervised prediction weighted accuracy was assessed by instrument and by frequency. It performed better at high frequencies with the highest prediction accuracy of 0.84 for the higher frequency FDR, 0.79 for the 48-MHz LiveWire SSTDR, and 0.77 for 300-MHz PNNL SSTDR. The initial weighted accuracy average across all frequencies for using supervised ML was 0.56 to 0.68. The supervised analysis was repeated with noisier training data removed resulting in weighted accuracies of 0.69 to 0.87. These weighted accuracies are not directly comparable due to differences in the supervised and unsupervised analysis details but do indicate an encouraging trend. Even with limited and unbalanced data, strong prediction accuracies seem encouraging for further work including more data under a wider range of conditions.

42 ENGINEERING↗

Experimental Fuel Consumption Results from a Heterogeneous Four-Truck Platoon

Platooning has the potential to reduce greenhouse gas missions of heavy-duty vehicles. Prior platooning studies have chiefly focused on the fuel economy characteristics and three-truck platoons, and most have investigated aerodynamically homogeneous platoons with trucks of the same trim. For real world application and accurate return on investment for potential adopters, non-uniform platoons and the impacts of grade and disturbances on a platoon’s fuel economy must also be characterized. This study investigates the fuel economy of a heterogeneous four-truck platoon on a closed test track. Tests were run for one hour at a speed of 45 mph. The trucks used for this study are two 2015 Peterbilt 579’s with a Cummins ISX15 and a Paccar MX-13, and two 2009 Freightliner M915A5’s, one armored and the other unarmored. Many analysis methodologies were leveraged to describe and compare the fuel data, including lap-wise and track-segment analysis. The methodology for dividing the data into laps is described in detail. The influence of other factors beyond the aerodynamics of platooning is discussed. CAN fuel rate analysis showed excellent agreement with previous experimental trends for two and three-truck platoons. In general, the indicated fuel economy benefits in this study were 5-11% for following vehicles and 0-4% for the lead vehicle in platoon relative to their baseline fuel consumption. On a cumulative basis, all platoons saved fuel, ranging from 6% to 8% versus the sum of the standalone trucks’ fuel consumption. The practical implications of the fuel economy results are discussed, as well as avenues for future research. Introduction and Motivation platooning is controlled coordination of two or more vehicles in a convoy, sometimes called CACC (Coordinated or Cooperative Adaptive Cruise Control). The distance between vehicles in a platoon can be controlled tightly at no additional fatigue to the driver. Platooning vehicles can also respond quickly to braking events of the leader, much more quickly than the typical human driver’s reaction time of 1-1.5 s. Therefore, vehicles in a platoon can follow each other much more closely than would usually be considered a safe following distance under human operation. It is implied that under very close following conditions, platooning technology must be extremely robust before it is safe for wide-scale implementation. Platooning is under investigation as a fuel-saving technology. Close-following significantly reduces aerodynamic drag for both leading and trailing vehicles. According to the NRC in 2010, aerodynamic drag represents roughly half of a Class-8 truck’s on-highway fuel usage, meaning a 20% reduction in drag roughly equals a 10% reduction in fuel usage, if all other sources of energy loss remain equal (i.e. accessory, rolling resistance, drivetrain, braking). It is by aerodynamics that platooning saves fuel. At risk of oversimplifying the aerodynamics, following (or trailing) vehicles experience reduced wind velocity due to shielding, and the leading vehicles experience an increased aft pressure, especially at distances closer than 75’ (23 m).

greenhouse gas emissions, truck platoon, heavy-dut↗

The impact of aerosol mixing state on immersion freezing: insights from classical nucleation theory and particle-resolved simulations

Immersion freezing, initiated by ice-nucleating particles (INPs) in supercooled aqueous droplets, plays an important role in the formation of ice crystals within clouds. The efficiency of immersion freezing depends strongly on INP composition and, crucially, on the mixing state – how chemical species are distributed across the particle population. Here, we quantify the impact of aerosol mixing state on immersion freezing using a combined theoretical and particle-resolved modeling approach. We derive analytical expressions for the frozen fraction of internally and externally mixed INP populations based on classical nucleation theory, showing that the frozen fraction is sensitive to whether ice-active species are present in all particles or only in a subset of the population. We introduce a multi-species immersion freezing scheme into the particle-resolved model PartMC, using the water activity-based immersion freezing model (ABIFM) to compute freezing probabilities for mixed-composition particles. To improve computational efficiency, we implement a Binned Tau-Leaping algorithm and demonstrate an order-of-magnitude speedup with minimal accuracy loss. Simulations reproduce the analytical trends in limiting cases and extend the analysis to more general aerosol populations, where mixing state continues to exert a substantial control on frozen fraction. Sensitivity analyses across particle size, species type, and cooling condition reveal that the mixing state effect is most pronounced when small amounts of highly efficient INPs are mixed with less efficient materials. These findings underscore the need to represent aerosol mixing state explicitly in models of heterogeneous ice nucleation to reduce uncertainty in cloud-phase partitioning.

54 ENVIRONMENTAL SCIENCES↗

Flight-determined lag of angle-of-attack and angle-of-sideslip sensors in the YF-12A airplane from analysis of dynamic maneuvers

Magnitudes of lags in the pneumatic angle-of-attack and angle-of-sideslip sensor systems of the YF-12A airplane were determined for a variety of flight conditions by analyzing stability and control data. The three analysis techniques used are described. An apparent trend with Mach number for measurements from both of the differential-pressure sensors showed that the lag ranged from approximately 0.15 second at subsonic speed to 0.4 second at Mach 3. Because Mach number was closely related to altitude for the available flight data, the individual effects of Mach number and altitude on the lag could not be separated clearly. However, the results indicated the influence of factors other than simple pneumatic lag.

Gilyard, G. B.↗

Phase equilibria in molecular hydrogen-helium mixtures at high pressures

Experiments on phase behavior in hydrogen-helium mixtures have been carried out at pressures up to 9.3 kilobars, at temperatures from 26 to 100 K. Two distinct fluid phases are shown to exist at supercritical temperatures and high pressures. Both the trend of the experimental results and an analysis based on the van der Waals theory of mixtures suggest that this fluid-fluid phase separation persists at temperatures and pressures beyond the range of these experiments, perhaps even to the limits of stability of the molecular phases. The results confirm earlier predictions concerning the form of the hydrogen-helium phase diagram in the region of pressure-induced solidification of the molecular phases at supercritical temperatures. The implications of this phase diagram for planetary interiors are discussed.

Streett, W. B.↗

Trends in Materials' Outgassing Technology

Test sample acquisition and chemical analysis techniques for outgassing products from spacecraft, experiment modules, and support equipment is described. The reduction of test data to a computer compatible format to implement materials selection policies is described. A list of the most troublesome outgassing species is given and several materials correlations are discussed. Outgassing from solar panels, thermal blankets, and wire insulation are examined individually.

Colony, J. A.↗

Robustness studies in adaptive control

It has been shown that several similar Model Reference Adaptive Controllers (MRAC's) are globally stable under certain restrictive assumptions, including the assumption that the order and relative degree of the plant are exactly known, and that no disturbances are present. Under certain 'sufficiently rich' excitation conditions, the origin is globally asymptotically stable for the adaptive controller parameter error. The time-evolution of the parameter error vector represents the key factor to the stability of the adaptive controller. This time-evolution is described by a complicated set of time-varying nonlinear differential equations. The present investigation is concerned with an approximate analysis technique for studying the long term trends of the parameter error vector trajectory for an adaptive controller under periodic excitation.

Krause, J.↗