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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 1,153 records · Page 64

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NASA NTRS1984

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.↗

NASA NTRS1992

A study of the control problem of the shoot side environment delivery system of a closed crop growth research chamber

The details of our initial study of the control problem of the crop shoot environment of a hypothetical closed crop growth research chamber (CGRC) are presented in this report. The configuration of the CGRC is hypothetical because neither a physical subject nor a design existed at the time the study began, a circumstance which is typical of large scale systems control studies. The basis of the control study is a mathematical model which was judged to adequately mimic the relevant dynamics of the system components considered necessary to provide acceptable realism in the representation. Control of pressure, temperature, and flow rate of the crop shoot environment, along with its oxygen, carbon dioxide, and water concentration is addressed. To account for mass exchange, the group of plants is represented in the model by a source of oxygen, a source of water vapor, and a sink for carbon dioxide. In terms of the thermal energy exchange, the group of plants is represented by a surface with an appropriate temperature. Most of the primitive equations about an experimental operating condition and a state variable representation which was extracted from the linearized equations are presented. Next, we present the results of a real Jordan decomposition and the repositioning of an undesirable eigenvalue via full state feedback. The state variable representation of the modeling system is of the nineteenth order and reflects the eleven control variables and eight system disturbances. Five real eigenvalues are very near zero, with one at zero, three having small magnitude positive values, and one having a small magnitude negative value. A Singular Value Decomposition analysis indicates that these non-zero eigenvalues are not results of numerical error.

Blackwell, C. C.↗

NASA NTRS1986

The identification of a distributed parameter model for a flexible structure

A computational method is developed for the estimation of parameters in a distributed model for a flexible structure. The structure we consider (part of the RPL experiment) consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion effects the transverse vibration of the beam. The Euler-Bernoulli theory is used to model the vibration of the beam and treat the hose-thruster assembly as a lumped or point mass-dashpot-spring system at the tip. Using measurements of linear acceleration at the tip, it is estimated that the parameters (mass, stiffness, damping) and a Voight-Kelvin viscoelastic structural damping parameter for the beam using a least squares fit to the data. Spline based approximations to the hybrid (coupled ordinary and partial differential equations) system are considered; theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are presented and discussed.

Banks, H. T.↗

NASA NTRS1990

Frequency analysis via the method of moment functionals

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Pearson, A. E.↗

NASA NTRS1991

Frequency analysis via the method of moment functionals

Pearson, A. E.↗

NASA NTRS1990

Effect of a crystal-melt interface on Taylor-vortex flow

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal-melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n = 1; the stability of these n = 1 modes is sensitive to the latent heat of fusion.

Mcfadden, G. B.↗

DOE OSTI2021

Assessment of empirical interatomic potential to predict thermal conductivity in ThO 2 and UO 2

Computing vibrational properties of crystals in the presence of complex defects often necessitates the use of (semi-)empirical potentials, which are typically not well characterized for perfect crystals. In this study we explore the efficacy of a commonly used embedded-atomempirical interatomic potential for the U x Th 1- x O 2 system, to compute phonon dispersion, lifetime, and branch specific thermal conductivity. Our approach for ThO 2 involves using lattice dynamics and the linearized Boltzmann transport equation to calculate phonon transport properties based on second and third order force constants derived from the empirical potential and from first-principles calculations. For UO 2 , to circumvent the accuracy issues associated with first-principles treatments of strong electronic correlations, we compare results derived from the empirical interatomic potential to previous experimental results. It is found that the empirical potential can reasonably capture the dispersion of acoustic branches, but exhibits significant discrepancies for the optical branches, leading to overestimation of phonon lifetime and thermal conductivity. The branch specific conductivity also differs significantly with either first-principles based results (ThO 2 ) or experimental measurements (UO 2 ). These findings suggest that the empirical potential needs to be further optimized for robust prediction of thermal conductivity both in perfect crystals and in the presence of complex defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Probabilistic measures for biological adaptation and resilience

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed “ecological resilience through adaptation,” specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. Importantly, the resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Revisiting matrix-based inversion of scanning mobility particle sizer (SMPS) and humidified tandem differential mobility analyzer (HTDMA) data

Abstract. Tikhonov regularization is a tool for reducing noise amplification during data inversion. This work introduces RegularizationTools.jl, a general-purpose software package for applying Tikhonov regularization to data. The package implements well-established numerical algorithms and is suitable for systems of up to ∼ 1000 equations. Included is an abstraction to systematically categorize specific inversion configurations and their associated hyperparameters. A generic interface translates arbitrary linear forward models defined by a computer function into the corresponding design matrix. This obviates the need to explicitly write out and discretize the Fredholm integral equation, thus facilitating fast prototyping of new regularization schemes associated with measurement techniques. Example applications include the inversion involving data from scanning mobility particle sizers (SMPSs) and humidified tandem differential mobility analyzers (HTDMAs). Inversion of SMPS size distributions reported in this work builds upon the freely available software DifferentialMobilityAnalyzers.jl. The speed of inversion is improved by a factor of ∼ 200, now requiring between 2 and 5 ms per SMPS scan when using 120 size bins. Previously reported occasional failure to converge to a valid solution is reduced by switching from the L-curve method to generalized cross-validation as the metric to search for the optimal regularization parameter. Higher-order inversions resulting in smooth, denoised reconstructions of size distributions are now included in DifferentialMobilityAnalyzers.jl. This work also demonstrates that an SMPS-style matrix-based inversion can be applied to find the growth factor frequency distribution from raw HTDMA data while also accounting for multiply charged particles. The outcome of the aerosol-related inversion methods is showcased by inverting multi-week SMPS and HTDMA datasets from ground-based observations, including SMPS data obtained at Bodega Marine Laboratory during the CalWater 2/ACAPEX campaign and co-located SMPS and HTDMA data collected at the US Department of Energy observatory located at the Southern Great Plains site in Oklahoma, USA. Results show that the proposed approaches are suitable for unsupervised, nonparametric inversion of large-scale datasets as well as inversion in real time during data acquisition on low-cost reduced-instruction-set architectures used in single-board computers. The included software implementation of Tikhonov regularization is freely available, general, and domain-independent and thus can be applied to many other inverse problems arising in atmospheric measurement techniques and beyond.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1972

Design of minimax output feedback controller for system with parameter uncertainty

The problem of controlling a time-invariant system with parameter uncertainty is considered with incomplete state feedback. The controller is designed by minimaximizing a quadratic performance criterion and a sensitivity (or loss) criterion, involving the state of the system, the control, and the uncertainty vector. The resulting optimal controller is linear and optimal feedback gain matrix must satisfy a set of nonlinear algebraic equations. some algorithms for algebraic minimax problems are presented.

Basuthakur, S.↗

NASA NTRS1973

A new approach to the design of time varying control systems with application to the space shuttle booster

A general approach toward the analysis and design of closed loop control for slowly time-varying linear systems was investigated. The approach is by the method of generalized multiple scales, in which slow and fast dynamics are systematically separated by employing different clocks which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, so that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock functions are shown to satisfy an algebraic characteristic equation and can be determined in general in terms of the coefficients.

Ramnath, R. V.↗

NASA NTRS1978

Direct numerical solution of the transonic perturbation integral equation for lifting and nonlifting airfoils

The linear transonic perturbation integral equation previously derived for nonlifting airfoils is formulated for lifting cases. In order to treat shock wave motions, a strained coordinate system is used in which the shock location is invariant. The tangency boundary conditions are either formulated using the thin airfoil approximation or by using the analytic continuation concept. A direct numerical solution to this equation is derived in contrast to the iterative scheme initially used, and results of both lifting and nonlifting examples indicate that the method is satisfactory.

Nixon, D.↗

NASA NTRS1980

Control of a large flexible platform in orbit

The dynamics and attitude and shape control of a large thin flexible platform in orbit are studied. Attitude and shape control is assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about nominal orientations where the undeformed plate follows either the local vertical or local horizontal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on pole placement, decoupling, and linear optimal control theory.

Reddy, A. S. S. R.↗

NASA NTRS1980

Singular perturbation equations for flexible satellites

Force equations of motion of the individual flexible elements of a satellite were obtained in a previous paper. Moment equations of motion of the composite bodies of a flexible satellite are to be developed using two sets of equations which form the basic system for any dynamic model of flexible satellites. This basic system consists of a set of N-coupled, nonlinear, ordinary, or partial differential equations, for a flexible satellite with n generalized, structural position coordinates. For single composite body satellites, N is equal to (n + 3); for dual-spin systems, N is equal to (n + 9). These equations involve time derivatives up to the second order. The study shows a method of avoiding this linearization by reducing the N equations to 3 or 9 nonlinear, coupled, first order, ordinary, differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can be solved by known methods.

Huang, T. C.↗

NASA NTRS1985

Midlatitude tropical interactions during winter

Pre-FGGE and FGGE/MONEX data are used to identify short term midlatitude tropical and longitudinal interactions during the winter monsoon. These interactions occur as cold surges, which develop over the East Asian continent and penetrate deep into the tropics with fast gravity wave speed. The observed interactions that occur after a surge include cyclogenesis and enhanced convection in the equatorial region, feedback from equatorial convection to midlatitude circulation systems, tropical east-west (Walker) circulations, and cross-equatorial influence. These interactions are also studied theoretically by analytical solutions of linearized shallow water equations. Response to transient forcing (monsoon surges) are mainly in Rossby and Kelvin modes. When the forcing time scale is short, significant gravity modes are also excited. The responses closely resemble observed winter monsoon flow. Responses to stationary forcing show that deep (barotropic) motions propagate energy away into high latitudes and that shallow (baroclinic) motions are trapped around the equator. It is shown that the barotropic teleconnection-type response to tropical sources found in previous numerical studies was due to the specified vertical wind shear and surface friction.

Chang, C. P.↗

NASA NTRS1988

Three-dimensional adaptive grid generation for body-fitted coordinate system

This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.

Chen, S. C.↗

NASA NTRS1988

A novel approach to the modelling and control of flexible robot arms

A general dynamic model of a two-link Euler-Bernoulli beam flexible robot arm is presented in the form of partial-differential-integral equations. Observations are made on important properties of the dynamic model. The resulting infinite-dimensional system is then input-output decoupled and partially linearized by a diffeomorphic state transformation and nonlinear state feedback. The local stability issue is addressed for a one-link flexible robot arm.

Ding, Xuru↗

NASA NTRS1988

Three-dimensional adaptive grid generation for body-fitted coordinate system

Chen, S. C.↗