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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 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

True covariance simulation of the EUVE update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the real behavior of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗
NASA NTRS1991

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Mercadal, Mathieu↗
DOE OSTI2022

Verification of a fully kinetic ion model for electromagnetic simulations of high-frequency waves in toroidal geometry

For the research of high-frequency electromagnetic waves in tokamaks, an electromagnetic simulation model, in which the ion dynamics is described by a six-dimensional Vlasov equation and the electron dynamics is described by a drift kinetic equation, is formulated and implemented in the global gyrokinetic toroidal code (GTC). Analytic dispersion relations are derived in reduced systems and compared with various theories to verify the model. Linear simulations of a generalized ion Bernstein wave and ion cyclotron emission are verified by comparing the GTC simulation results with analytic dispersion relation theory and magnetoacoustic cyclotron instability theory, respectively, in cylindrical geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

Multigrid properties of upwind-biased data reconstructions

The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.

Warren, Gary P.↗
NASA NTRS1973

A guidance and navigation system for continuous low-thrust vehicles

A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.

Jack-Chingtse, C.↗
DOE OSTI2020

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Linear stability analysis via simulated annealing and accelerated relaxation

Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. In conclusion, since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Warming, Robert F.↗
DOE OSTI2024

A Simple Comparison of Biochemical Systems Theory and Metabolic Control Analysis

This paper explores some basic concepts of Biochemical Systems Theory (BST) and Metabolic Control Analysis (MCA), two frameworks developed to understand the behavior of biochemical networks. Initially introduced by Savageau, BST focuses on system stability and employs power laws in modeling biochemical systems. On the other hand, MCA, pioneered by authors such as Kacser and Burns and Heinrich and Rapoport, emphasizes linearization of the governing equations and describes relationships (known as theorems) between different measures. Despite apparent differences, both frameworks are shown to be equivalent in many respects. Through a simple example of a linear chain, the paper demonstrates how BST and MCA yield identical results when analyzing steady-state behavior and logarithmic gains within biochemical pathways. This comparative analysis highlights the interchangeability of concepts such as kinetic orders, elasticities and other logarithmic gains.

FOS: Biological sciences↗
NASA NTRS1974

Buckling of cylindrical shells with random imperfections

Buckling of long cylindrical shells with random imperfections subjected to axial loads is treated using the method of truncated hierarchy. A system of homogeneous variational equations is set up to examine the existence of bifurcation in the neighborhood of the equilibrium state. These equations are linear and involve stationary random coefficients. The truncated-hierarchy method is applied, and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively, the results obtained are as anticipated.

Fersht, R. S.↗
NASA NTRS1981

Symbolic Solution of Linear Differential Equations

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Feinberg, R. B.↗
NASA NTRS1981

Research on numerical algorithms for large space structures

Numerical algorithms for analysis and design of large space structures are investigated. The sign algorithm and its application to decoupling of differential equations are presented. The generalized sign algorithm is given and its application to several problems discussed. The Laplace transforms of matrix functions and the diagonalization procedure for a finite element equation are discussed. The diagonalization of matrix polynomials is considered. The quadrature method and Laplace transforms is discussed and the identification of linear systems by the quadrature method investigated.

Denman, E. D.↗
NASA NTRS1987

A new state space model for the NASA/JPL 70-meter antenna servo controls

A control axis referenced model of the NASA/JPL 70-m antenna structure is combined with the dynamic equations of servo components to produce a comprehansive state variable (matrix) model of the coupled system. An interactive Fortran program for generating the linear system model and computing its salient parameters is described. Results are produced in a state variable, block diagram, and in factored transfer function forms to facilitate design and analysis by classical as well as modern control methods.

Hill, R. E.↗
NASA NTRS1987

Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics

The recursive difference equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing, arising in the state estimation theory for linear state space systems, are used here to solve problems of serial manipulator inverse and forward dynamics. The configuration analyzed is that of a joint connected N-link serial manipulator attached to an immobile base. The equivalence between the filtering and smoothing techniques from state estimation theory and recursive robot dynamics methods is demonstrated. Several areas for future research are suggested.

Rodriguez, Guillermo↗
NASA NTRS1991

Computing the Lyapunov spectrum of a dynamical system from an observed time series

The paper examines the problem of accurately determining, from an observed time series, the Liapunov exponents for the dynamical system generating the data. It is shown that, even with very large data sets, it is clearly advantageous to utilize local neighborhood-to-neighborhood mappings with higher-order Taylor series rather than just local linear maps. This procedure is demonstrated on the Henon and Ikeda maps of the plane itself, the Lorenz system of three ordinary differential equations, and the Mackey-Glass delay differential equation.

Brown, Reggie↗
NASA NTRS1992

Dynamic modeling and control of multibody mechanical systems which are structurally flexible

This paper concerns the dynamic modeling and control of multibody, open-chained, structurally flexible, mechanical systems where the bodies are connected by revolute joints. The equations of motion are formulated based on a matrix form of Lagrange's equations for inertial quasi-coordinates. Each body is treated as a substructure of the system. For the purposes of simulation and control, the equations of motion are separated into two sets of equations using a perturbation approach: one to describe large rigid-body motions of the articulated system and the other to describe small linear motions of the bodies about the large motions. A biologically natural control strategy is used for vibration suppression and tracking the prescribed motion.

Quinn, R. D.↗
NASA NTRS1992

Active structural control for the mini-MAST and ACES structures

Two experiments based on the maximum entropy/optimal projection design approach are discussed which were conducted by Harris Corporation as part of the NASA Controls Structures Interaction Guest Investigator program. The design equations consist of four coupled matrix equations which specialize to the standard linear-quadratic Guassian Riccati equations, when the plant is known perfectly and a full order controller is desired. These experiments demonstrate successful control system design and implementation for flexible structures.

Collins, E. G., Jr.↗
NASA NTRS2001

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Tessler, A.↗