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NASA NTRS1976

Stability and Relative Stability of Linear Systems with Many Constant Time Delays

A method of determining the stability of linear systems with many constant time delays is developed. This technique, an extension of the tau-decomposition method, is used to examine not only the stability but also the relative stability of retarded systems with many delays and a class of neutral equations with one delay. Analytical equations are derived for partitioning the delay space of a retarded system with two time delays. The stability of the system in each of the regions defined by the partitioning curves in the parameter plane is determined using the extended tau-decomposition method. In addition, relative stability boundaries are defined using the extended tau-decompositon method in association with parameter plane techniques. Several applications of the extended tau-decomposition method are presented and compared with stability results obtained from other analyses. In all cases the results obtained using the method outlined herein coincide with and extend those of previous investigations. The extended tau-decomposition method applied to systems with time delays requires less computational effort and yields more complete stability analyses than previous techniques.

Barker, Larry Keith↗

NASA NTRS1982

The partitioning of Zr and Nb between diopside and melts in the system diopside-albite-anorthite

The crystal/liquid distribution coefficient for Zr between diopside and melt is measured for six compositions and three temperatures in the diopside field of Di-Ab-An, and the distribution coefficient for Nb is measured for three of these compositions. Nb is found to be excluded from diopside, while D(Zr), which is defined as wt % ZrO2 in crystals/wt % ZrO2 in melt, is variable and ranging from 0.05 to 0.45. D(Zr) is positively correlated with the Al content of both the melt and the pyroxene, and is negatively correlated with temperature. Both D(Zr) and D(Nb) are independent of oxygen fugacity, which implies that neither Zr nor Nb suffer valence changes over a range of oxygen fugacities spanning lunar and terrestrial conditions.

Dunn, T.↗

NASA NTRS1992

Modeling Hubble Space Telescope flight data by Q-Markov cover identification

A state space model for the Hubble Space Telescope under the influence of unknown disturbances in orbit is presented. This model was obtained from flight data by applying the Q-Markov covariance equivalent realization identification algorithm. This state space model guarantees the match of the first Q-Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high- and low-frequency components for more efficient Q-Markov cover modeling, to reduce some computational difficulties of the Q-Markov cover algorithm. This identification revealed more than 20 lightly damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

Liu, K.↗

NASA NTRS1991

IMPAC: An Integrated Methodology for Propulsion and Airframe Control

The National Aeronautics and Space Administration is actively involved in the development of enabling technologies that will lead towards aircraft with new/enhanced maneuver capabilities such as Short Take-Off Vertical Landing (STOVL) and high angle of attack performance. Because of the high degree of dynamic coupling between the airframe and propulsion systems of these types of aircraft, one key technology is the integration of the flight and propulsion control. The NASA Lewis Research Center approach to developing Integrated Flight Propulsion Control (IFPC) technologies is an in-house research program referred to as IMPAC (Integrated Methodology for Propulsion and Airframe Control). The goals of IMPAC are to develop a viable alternative to the existing integrated control design methodologies that will allow for improved system performance and simplicity of control law synthesis and implementation, and to demonstrate the applicability of the methodology to a supersonic STOVL fighter aircraft. Based on some preliminary control design studies that included evaluation of the existing methodologies, the IFPC design methodology that is emerging at the Lewis Research Center consists of considering the airframe and propulsion system as one integrated system for an initial centralized controller design and then partitioning the centralized controller into separate airframe and propulsion system subcontrollers to ease implementation and to set meaningful design requirements for detailed subsystem control design and evaluation. An overview of IMPAC is provided and detailed discussion of the various important design and evaluation steps in the methodology are included.

Garg, Sanjay↗

NASA NTRS1988

Sensitivity of control-augmented structure obtained by a system decomposition method

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Sobieszczanskisobieski, Jaroslaw↗

NASA NTRS1991

Sensitivity of control-augmented structure obtained by a system decomposition method

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS2016

Apatite-Melt Partitioning at 1 Bar: An Assessment of Apatite-Melt Exchange Equilibria Resulting from Non-Ideal Mixing of F and Cl in Apatite

The mineral apatite [Ca5(PO4)3(F,Cl,OH)] is present in a wide range of planetary materials. Due to the presence of volatiles within its crystal structure (X-site), many recent studies have attempted to use apatite to constrain the volatile contents of planetary magmas and mantle sources. In order to use the volatile contents of apatite to precisely determine the abundances of volatiles in coexisting silicate melt or fluids, thermodynamic models for the apatite solid solution and for the apatite components in multi-component silicate melts and fluids are required. Although some thermodynamic models for apatite have been developed, they are incomplete. Furthermore, no mixing model is available for all of the apatite components in silicate melts or fluids, especially for F and Cl components. Several experimental studies have investigated the apatite-melt and apatite-fluid partitioning behavior of F, Cl, and OH in terrestrial and planetary systems, which have determined that apatite-melt partitioning of volatiles are best described as exchange equilibria similar to Fe-Mg partitioning between olivine and silicate melt. However, McCubbin et al. recently reported that the exchange coefficients may vary in portions of apatite compositional space where F, Cl, and OH do not mix ideally in apatite. In particular, solution calorimetry data of apatite compositions along the F-Cl join exhibit substantial excess enthalpies of mixing. In the present study, we conducted apatite-melt partitioning experiments in evacuated, sealed silica-glass tubes at approximately 1 bar and 950-1050 degrees Centigrade on a synthetic Martian basalt composition equivalent to the basaltic shergottite Queen Alexandria Range (QUE) 94201. These experiments were conducted dry, at low pressure, to assess the effects of temperature and apatite composition on the partitioning behavior of F and Cl between apatite and basaltic melt along the F-Cl apatite binary join, where there is non-ideal mixing of F and Cl in apatite.

McCubbin, F. M.↗

NASA NTRS2017

Partitioning of F and Cl Between Apatite and a Synthetic Shergottite Liquid (QUE 94201) at 4 Gpa from 1300 TO 1500 C

Apatite [Ca5(PO4)3(F,Cl,OH)] is present in a wide range of planetary materials. Due to the presence of volatiles within its crystal structure (Xsite), many recent studies have attempted to use apatite to constrain the volatile contents of planetary magmas and mantle sources. In order to use the volatile contents of apatite to accurately determine the abundances of volatiles in coexisting silicate melt or fluids, thermodynamic models for the apatite solid solution and for the apatite components in multicomponent silicate melts and fluids are required. Although some thermodynamic models for apatite have been developed, they are incomplete. Furthermore, no mixing model is available for all of the apatite components in silicate melts or fluids, especially for F and Cl components. Several experimental studies have investigated the apatite-melt and apatite-fluid partitioning behavior of F, Cl, and OH in terrestrial and planetary systems, which have determined that apatite-melt partitioning of volatiles are best described as exchange equilibria similar to Fe-Mg partitioning between olivine and silicate melt. However, McCubbin et al., recently reported that the exchange coefficients vary in portions of apatite compositional space where F, Cl, and OH do not mix ideally in apatite. In particular, solution calorimetry data of apatite compositions along the F-Cl join exhibit substantial excess enthalpies of mixing, and McCubbin et al. reported substantial deviations in the Cl-F exchange Kd along the F-Cl apatite join that could be explained by the preferential incorporation of F into apatite. In the present study, we assess the effect of apatite crystal chemistry on F-Cl exchange equilibria between apatite and melt at 4 GPa over the temperature range of 1300-1500 C. The goal of these experiments is to assess the variation in the Ap-melt Cl-F exchange Kd over a broad range of F:Cl ratios in apatite. The results of these experiments could be used to understand at what composition apatite shifts from a hexagonal unit cell with space group P63/m to a unit cell with monoclinic symmetry within space group P21/b. We anticipate that this transition occurs at >70% chlorapatite based on solution calorimetry data.

McCubbin, F. M.↗

NASA NTRS1993

The Fe/Mn constraint on precursors of basaltic achondrites

Most achondritic meteorites have Fe/Mn ratios that are lower than those of carbonaceous chondrites and of course are lower than the solar system abundance ratio of these elements. Models of the origin of achondritic assemblages must, therefore, account for these ratios. Fe/Mn ratios are suggested to be distinctive for samples from each achondrite parent body and for the Earth and Moon, but the correspondence between the Fe/Mn systematics of achondrites and chondritic precursors is unclear. Most models of achondrite genesis involve magmatic differentiation of chondritic precursors. The Fe/Mn difference between achondrites and chondrites is particularly significant since Fe and Mn are geochemically similar elements with similar partitioning behavior in familiar magmatic systems and are generally coupled during crystal-liquid fractionation. In contrast, however, Mn is more volatile than Fe in a nebular setting. Variation of Fe/Mn ratios based on the relative volatility of these elements in the early nebula provides a constraint for models by which the basaltic achondrites (with Fe/Mn ratios approximately = 25-50) are derived from mixtures of nebular components that were enriched in volatile components such as Mn. However, such volatile enriched components have not been identified in chondrites. When the abundance in achondrites of elements of similar volatility is examined, anomalies appear. For example, Na is massively depleted in basaltic achondrites when compared to Mn. These anomalies might be explained using current models but the alternative hypothesis, that Fe/Mn ratio is controlled not by nebular volatility constraints, but by planetary differentiation should be explored.

Delaney, Jeremy S.↗

NASA NTRS2001

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

Aftosmis, M. J.↗

NASA NTRS1975

Time domain desensitized specific optimal system design

A digital computer algorithm for desensitized specific optimal system design for general time-invariant nonlinear systems is presented. The algorithm utilizes a technique of partitioning and uncoupling of the original specific closed-loop system state and sensitivity equations into linear, nonlinear, and control subsystems. Results of the application of the algorithm in the design of a Saturn V Launch Vehicle analog attitude control system and an LST image motion compensation digital controller are given.

Henson, T. F.↗

NASA NTRS1989

'Virtual triple Schmidt' - Wide field two-stage optics

The design concept of an unobscured-wide-field two-stage optical system based on a virtual triple Schmidt (VTS) configuration is presented. It is pointed out that the single large aperture and field-partitioning capability of two-stage systems can lower material and fabrication costs, making the VTS optics suitable for ground-based and space telescopes. The VTS design combines a Schmidt-camera first stage and a second stage comprising two back-to-back Schmidt systems as a 1:1 relay. Aspheric Schmidt correction is achieved at the relayed pupil location for all three systems. The effects of the separation between the error-producing surface and the aperture stop are discussed; the performance of the wavefront-correction system is analyzed; and extensive diagrams, drawings, and graphs of projected performance data are provided.

Manhart, Paul K.↗

NASA NTRS1984

The problem of iron partition between Earth and Moon during simultaneous formation as a double planet system

A planetary model is described which requires fractional vapor/liquid condensation, planet accumulation during condensation, a late start for accumulation of the Moon, and volatile accretion to the surfaces of each planet only near the end of the accumulation process. In the model, initial accumulation of small objects is helped if the agglomerating particles are somewhat sticky. Assuming that growth proceeds through this range, agglomeration continues. If the reservoir of vapor is being preferentially depleted in iron by fractional condensation, an iron-rich planetary core forms. As the temperature decreases, condensing material becomes progressively richer in silicates and poorer in iron, forming the silicate-rich mantle of an already differentiated Earth. A second center of agglomeration successfully forms near the growing Earth after most of the iron in the reservoir has been used up. The bulk composition of the Moon then is similar to the outer mantle of the accumulating Earth.

Cassidy, W. A.↗

NASA NTRS1990

Automation of Space Station module power management and distribution system

Viewgraphs on automation of space station module (SSM) power management and distribution (PMAD) system are presented. Topics covered include: reasons for power system automation; SSM/PMAD approach to automation; SSM/PMAD test bed; SSM/PMAD topology; functional partitioning; SSM/PMAD control; rack level autonomy; FRAMES AI system; and future technology needs for power system automation.

Bechtel, Robert↗

NASA NTRS2007

Simple, Script-Based Science Processing Archive

The Simple, Scalable, Script-based Science Processing (S4P) Archive (S4PA) is a disk-based archival system for remote sensing data. It is based on the data-driven framework of S4P and is used for data transfer, data preprocessing, metadata generation, data archive, and data distribution. New data are automatically detected by the system. S4P provides services such as data access control, data subscription, metadata publication, data replication, and data recovery. It comprises scripts that control the data flow. The system detects the availability of data on an FTP (file transfer protocol) server, initiates data transfer, preprocesses data if necessary, and archives it on readily available disk drives with FTP and HTTP (Hypertext Transfer Protocol) access, allowing instantaneous data access. There are options for plug-ins for data preprocessing before storage. Publication of metadata to external applications such as the Earth Observing System Clearinghouse (ECHO) is also supported. S4PA includes a graphical user interface for monitoring the system operation and a tool for deploying the system. To ensure reliability, S4P continuously checks stored data for integrity, Further reliability is provided by tape backups of disks made once a disk partition is full and closed. The system is designed for low maintenance, requiring minimal operator oversight.

Lynnes, Christopher↗

NASA NTRS2000

Efficient Use of Distributed Systems for Scientific Applications

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

Taylor, Valerie↗

NASA NTRS2016

Carbon Solubility in Silicon-Iron-Bearing Metals during Core Formation on Mercury

Recent results obtained from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft showed the surface of Mercury has high S abundances (approximately 4 wt%) and low Iron(II) Oxide abundances (less than 2 wt%). Based on these extreme values, the oxygen fugacity of Mercury's surface materials was estimated to be approximately 3 to 7 log(sub 10) units below the IW buffer (Delta IW-3 to Delta IW-7). This highly reducing nature of the planet has resulted in a large core and relatively thin mantle, extending to only approximately 420 km depth (corresponding to a core-mantle boundary pressure of approximately 4-7 GPa) within the planet. Furthermore, MESSENGER results have suggested the presence of carbon on the surface of the planet. Previous experimental results from have also suggested the possibility of a primary floatation crust on Mercury composed of graphite, produced after a global magma ocean event. With these exotic conditions of this compositional end-member planet, it begs the question, what is the core composition of Mercury? Although no definitive conclusion has been reached, previous studies have made advances towards answering this question. Riner et al. and Chen et al. looked at iron sulfide systems and implemented various crystallization and layered core scenarios to try and determine the composition and structure of Mercury's core. Malavergne et al. examined core crystallization scenarios in the presence of sulfur and silicon. Hauck et al. used the most recent geophysical constraints from the MESSENGER spacecraft to model the internal structure of Mercury, including the core, in a iron-sulfur-silicon system. More recently, Chabot et al. conducted a series of metal-silicate partitioning experiments in a iron-sulfur-silicon system. These results showed the core of Mercury has the potential to contain more than 15 wt% silicon. However, with the newest results from MESSENGER's low altitude campaign, carbon is another potential light element that could be incorporated into Mercury's core. The goal of this study is to determine the carbon concentration at graphite saturation in various silicon-iron bearing metals relevant to possible mercurian core compositions. Future experiments will include the addition of sulfur into these metals.

Vander Kaaden, Kathleen E.↗

NASA NTRS1998

Stable Inversion for Nonlinear Nonminimum-Phase Time Varying Systems

In this paper, we extend stable inversion to nonlinear time-varying systems and study computational issues; the technique is applicable to minimum-phase as well as nonminimum-phase systems. The inversion technique is new, even in the linear time-varying case, and relies on partitioning (the dichotomic split of) the linearized system dynamics into time-varying, stable, and unstable, submanifolds. This dichotomic split is used to build time-varying filters which are, in turn, the basis of a contraction used to find a bounded inverse input-state trajectory. Finding the inverse input-state trajectory allows the development or exact-output tracking controllers. The method is local to the time-varying trajectory and requires that the internal dynamics vary slowly; however, the method represents a significant advance relative to presently available tracking controllers. Present techniques are restricted to time-invariant nonlinear systems and, in the general case, track only asymptotically.

Devasia, S.↗