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292 records · Page 17

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NASA NTRS1996

Optimal Output Trajectory Redesign for Invertible Systems

Given a desired output trajectory, inversion-based techniques find input-state trajectories required to exactly track the output. These inversion-based techniques have been successfully applied to the endpoint tracking control of multijoint flexible manipulators and to aircraft control. The specified output trajectory uniquely determines the required input and state trajectories that are found through inversion. These input-state trajectories exactly track the desired output; however, they might not meet acceptable performance requirements. For example, during slewing maneuvers of flexible structures, the structural deformations, which depend on the required state trajectories, may be unacceptably large. Further, the required inputs might cause actuator saturation during an exact tracking maneuver, for example, in the flight control of conventional takeoff and landing aircraft. In such situations, a compromise is desired between the tracking requirement and other goals such as reduction of internal vibrations and prevention of actuator saturation; the desired output trajectory needs to redesigned. Here, we pose the trajectory redesign problem as an optimization of a general quadratic cost function and solve it in the context of linear systems. The solution is obtained as an off-line prefilter of the desired output trajectory. An advantage of our technique is that the prefilter is independent of the particular trajectory. The prefilter can therefore be precomputed, which is a major advantage over other optimization approaches. Previous works have addressed the issue of preshaping inputs to minimize residual and in-maneuver vibrations for flexible structures; Since the command preshaping is computed off-line. Further minimization of optimal quadratic cost functions has also been previously use to preshape command inputs for disturbance rejection. All of these approaches are applicable when the inputs to the system are known a priori. Typically, outputs (not inputs) are specified in tracking problems, and hence the input trajectories have to be computed. The inputs to the system are however, difficult to determine for non-minimum phase systems like flexible structures. One approach to solve this problem is to (1) choose a tracking controller (the desired output trajectory is now an input to the closed-loop system and (2) redesign this input to the closed-loop system. Thus we effectively perform output redesign. These redesigns are however, dependent on the choice of the tracking controllers. Thus the controller optimization and trajectory redesign problems become coupled; this coupled optimization is still an open problem. In contrast, we decouple the trajectory redesign problem from the choice of feedback-based tracking controller. It is noted that our approach remains valid when a particular tracking controller is chosen. In addition, the formulation of our problem not only allows for the minimization of residual vibration as in available techniques but also allows for the optimal reduction fo vibrations during the maneuver, e.g., the altitude control of flexible spacecraft. We begin by formulating the optimal output trajectory redesign problem and then solve it in the context of general linear systems. This theory is then applied to an example flexible structure, and simulation results are provided.

Devasia, S.↗

NASA NTRSDate not supplied

Inferred Sea Level Prediction in the NASA GMAO Seasonal Forecasting System

Reliable predictions of sea level anomalies on seasonal timescales with lead times of 1 to 9 months may have relevance to stakeholders – for example, in the advance deployment of resources for coastal flood mitigation. Routine prediction and analysis may also highlight physical processes associated with sea level change and modeling capabilities on seasonal and other timescales. These forecasts may represent interannual changes in the seasonal slope of the ocean surface, teleconnection effects such as the El Niño/Southern Oscillation phenomenon, and variations in seasonal hydrology including precipitation and coastal runoff. Coupled atmosphere/ocean models are routinely used in the seasonal prediction of temperature anomalies, precipitation anomalies, sea ice cover, and climate indices such as the Niño3.4 predictions under the North American Multi-Model Ensemble (NMME) protocol. Within the limits of their configuration, these complex Earth-system models have a potential for depicting regional changes in oceanic column properties, including the sea surface height. Seasonal prediction models generally have no representation of long-term mass contributions from melting land ice, or changes in vertical land motion; their output may be more specifically characterized as predictions of the ocean dynamic sea level. In practice however, the sea surface height prognostic variable is substantially compromised by the forecast model response to initial conditions. Imbalances between the initial, observed hydrologic cycle and the forecast model state produce abrupt adjustments in the model sea surface height. As a result, most seasonal prediction systems employ a constraint on the globally-averaged sea surface height that is applied at each time step. This essentially renders the prognostic sea surface height variable as unserviceable. Several approaches have previously been used to retrieve sea level information from seasonal forecasts beyond the use of the sea surface height variable. Here, we extend a method of relating other prognostic values, including ocean circulation and climate indices, to observed sea level variations. We use the merged altimetry record of the NASA MEaSUREs Gridded Sea Surface Height Anomalies data set and monthly revised local reference gauge observations from the National Oceanography Centre Permanent Service for Mean Sea Level (PSMSL) to evaluate derived prognostic variables from the NASA Global Modeling and Assimilation Office subseasonal-to-seasonal system version 2.1 (GMAO S2S v2.1). We focus on results for the midlatitudes with particular emphasis on US gauge locations. As shown in previous studies, prognostic ENSO-related indices in boreal winter are well correlated with gauge observations for the US west coast, but also for other locations in the southeastern US. Other forecast climate indices such as the North Atlantic Oscillation have relations to sea level that are limited both seasonally and spatially. As expected, surface atmospheric pressure (e.g., inverse barometer effect) is found to be particularly well correlated with observed sea level. We provide a characterization of forecast skill for seasonal sea level with this method.

Richard I Cullather↗

NASA NTRS2000

Dynamics in Layer Models of Solid Flame Propagation

Self-propagating high-temperature synthesis (SHS) is a process in which combustion waves, e.g., "solid flames", which are considered here, are employed to synthesize desired materials. Like many other systems, SHS is a pattern forming system. The problem of describing experimentally observed patterns and of predicting new, as yet unobserved, patterns continues to attract the attention of scientists and mathematicians due to the fundamental significance of the phenomena in combustion in particular, and in nonlinear science in general. Here, we analyze the dynamics of solid flame propagation in a 2D region by considering the region to be composed of parallel, identical layers aligned along the direction of propagation and having thermal contact. Each layer is then described by wave propagation in 1D, with the transverse Laplacian replaced by a term describing heat exchange between neighboring layers. This configuration is the simplest model of a 2D system because it accounts, in a simple way, for the principal feature of the problem, i.e., heat exchange between neighbors in the transverse direction. For simplicity, we describe the situation for two layers. Because the layers are identical, uniformly propagating waves in each layer must be identical, independent of the heat exchange rate alpha. When the Zeldovich number Z exceeds a critical value Z(sub c), which depends on alpha, uniformly propagating waves become unstable. The stability diagram for the two coupled layers reproduces that for the full 2D problem after appropriate identification of parameters in the two problems. Depending on parameter values, we determine three different steady-state dynamical behaviors (though additional behaviors are also expected to occur). The three behaviors are: (i) waves in each layer which pulsate in phase as they propagate, so that together they form a single pulsating propagating wave; (ii) the waves in each layer are no longer identical, and antiphase pulsations occur, with the two waves alternately advancing and receding as they propagate. This wave is the analog of the spinning wave on the surface of a circular cylinder; (iii) finally, there is a region of bistability between the in phase and antiphase waves. with each having its own domain of attraction, so that which of the two behaviors occur depends on the condition of initiation of the wave. The results of our computations indicate a qualitative similarity in the behavior of combustion waves in the layer model and in the full 2D model. Specifically, due to the similarity between the small alpha wave behavior in the layer model and the large diameter behavior in the model of waves on the surface of a cylinder, we are able to predict the behavior of the mean velocity for the waves on the cylinder, where computations of the full problem can be rather difficult. We also compute solutions for three or more layers. The results of our computations prompt us to predict that, while planar uniformly propagating waves are unstable, the wave will be quasiplanar, i.e., the resulting spinning waves have very low amplitude hot spots, and travel with the velocity close to that of the uniformly propagating wave. Such waves may be difficult to distinguish from uniformly propagating waves in experiments. We also find that for both the layer model and full 2D problem, steady-state time-dependent waves, e.g., pulsating and spinning wave, have a conserved quantity H which characterizes the excess energy in the wave, just as in the case of uniformly propagating waves. The quantity H, which is generated by dissipation, does not vary in time and is proportional to the diffusivity and caloricity of the system, and inversely proportional to the mean wave velocity.

Aldushin, A. P.↗

NASA NTRS2005

The nakhlite meteorites: Augite-rich igneous rocks from Mars

The seven nakhlite meteorites are augite-rich igneous rocks that formed in flows or shallow intrusions of basaltic magma on Mars. They consist of euhedral to subhedral crystals of augite and olivine (to 1 cm long) in fine-grained mesostases. The augite crystals have homogeneous cores of Mg' = 63% and rims that are normally zoned to iron enrichment. The core-rim zoning is cut by iron-enriched zones along fractures and is replaced locally by ferroan low-Ca pyroxene. The core compositions of the olivines vary inversely with the steepness of their rim zoning - sharp rim zoning goes with the most magnesian cores (Mg' = 42%), homogeneous olivines are the most ferroan. The olivine and augite crystals contain multiphase inclusions representing trapped magma. Among the olivine and augite crystals is mesostasis, composed principally of plagioclase and/or glass, with euhedra of titanomagnetite and many minor minerals. Olivine and mesostasis glass are partially replaced by veinlets and patches of iddingsite, a mixture of smectite clays, iron oxy-hydroxides and carbonate minerals. In the mesostasis are rare patches of a salt alteration assemblage: halite, siderite, and anhydrite/ gypsum. The nakhlites are little shocked, but have been affected chemically and biologically by their residence on Earth. Differences among the chemical compositions of the nakhlites can be ascribed mostly to different proportions of augite, olivine, and mesostasis. Compared to common basalts, they are rich in Ca, strongly depleted in Al, and enriched in magmaphile (incompatible) elements, including the LREE. Nakhlites contain little pre-terrestrial organic matter. Oxygen isotope ratios are not terrestrial, and are different in anhydrous silicates and in iddingsite. The alteration assemblages all have heavy oxygen and heavy carbon, while D/H values are extreme and scattered. Igneous sulfur had a solar-system isotopic ratio, but in most minerals was altered to higher and lower values. High precision analyses show mass-independent fractionations of S isotopes. Nitrogen and noble gases are complex and represent three components: two mantle sources (Chas-E and Chas-S), and fractionated Martian atmosphere. The nakhlites are igneous cumulate rocks, formed from basaltic magma at approx.1.3 Ga, containing excess crystals over what would form from pure magma. After accumulation of their augite and olivine crystals, they were affected (to various degrees) by crystallization of the magma, element diffusion among minerals and magma, chemical reactions among minerals and magma, magma movement among the crystals, and post-igneous chemical equilibration. The extent of these modifications varies, from least to greatest, in the order: MIL03346, NWA817, Y000593, Nakhla = Governador Valadares, Lafayette, and NWA998. Chemical, isotopic, and chronologic data confirm that the nakhlites formed on Mars, most likely in thick lava flows or shallow intrusions. Their crystallization ages, referenced to crater count chronologies for Mars, suggest that the nakhlites formed on the large volcanic constructs of Tharsis, Elysium, or Syrtis Major. The nakhlites were suffused with liquid water, probably at approx.620 ma. This water dissolved olivine and mesostasis glass, and deposited iddingsite and salt minerals in their places. The nakhlites were ejected from Mars at approx.10.75Ma by an asteroid impact and fell to Earth within the last 10,000 years. Although the nakhlites are enriched in incompatible elements, their source mantle was strongly depleted. This depletion event was ancient, as the nakhlites source mantle was fractionated while short-lived radionuclides (e.g., t(sub 1/2 = 9 my) were still active. This differentiation event may have been core formation coupled with a magma ocean, as is inferred for the moon.

Treiman, Allan H.↗