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At least 271 records · Page 15

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NASA NTRS1978

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗

NASA NTRS1979

Design curves for non-linear analysis of simply-supported, uniformly-loaded rectangular plates

Design curves for the non-linear analysis of simply-supported rectangular plates subjected to uniform normal pressure loads have been developed. These curves yield the center deflection, center stress and corner stress in non-dimensionalized form plotted against a dimensionless parameter describing the load intensity. The results presented are based on extensive non-linear finite element analysis employing the ARGUS structural analysis program. Plates with length to width ratios of 1, 1.5, 2, 3 and 4 are included. The load range considered extends to 1000 times the load at which the behavior of the plate becomes significantly non-linear. Over the load range considered, the analysis shows that the ratio of center deflection to plate thickness for a square plate is less than 16 to 1, whereas linear theory would predict a center deflection 400 times the plate thickness. Likewise, the stress is markedly lower than would be predicted by linear theory. The present results are shown to be in excellent agreement with the classical linear theory up to a central deflection to plate thickness ratio of about one-half. In the non-linear regime the present results for deflection and stress are in very good agreement with the analytical and experimental work of other investigators.

Moore, D.↗

NASA NTRS1985

A sequential linear optimization approach for controller design

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Horta, L. G.↗

NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x(t)) + the sum to m terms(i=1) u sub i (t)g sub i (x(t)) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

NASA NTRS1990

On linear structure and phase rotation invariant properties of block 2(sup l)-PSK modulation codes

Two important structural properties of block 2(l)-ary PSK (phase shift keying) modulation codes, linear structure and phase symmetry, are investigated. For an additive white Gaussian noise (AWGN) channel, the error performance of a modulation code depends on its squared Euclidean distance distribution. Linear structure of a code makes the error performance analysis much easier. Phase symmetry of a code is important in resolving carrier phase ambiguity and ensuring rapid carrier phase resynchronization after temporary loss of synchronization. It is desirable for a code to have as many phase symmetries as possible. A 2(l)-ary modulation code is represented here as a code with symbols from the integer group. S sub 2(l) PSK = (0,1,2,...,2(l)-1), under the modulo-2(l) addition. The linear structure of block 2(l)-ary PSK modulation codes over S sub 2(l)-ary PSK with respect to the modulo-2(l) vector addition is defined, and conditions under which a block 2(l)-ary PSK modulation code is linear are derived. Once the linear structure is developed, phase symmetry of a block 2(l)-ary PSK modulation code is studied. It is a necessary and sufficient condition for a block 2(l)-PSK modulation code, which is linear as a binary code, to be invariant under 180 deg/2(l-h) phase rotation, for 1 is less than or equal to h is less than or equal to l. A list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant.

Lin, Shu↗

NASA NTRS1991

ALPS: A Linear Program Solver

ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

Ferencz, Donald C.↗

NASA NTRS1991

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland W.↗

NASA NTRS1994

Stars and linear dunes on Mars

A field containing 11 star and incipient star dunes occurs on Mars at 8.8 deg S, 270.9 deg W. Examples of linear dunes are found in a crater at 59.4 deg S, 343 deg W. While rare, dune varieties that form in bi- and multidirectional wind regimes are not absent from the surface of Mars. The occurence of both of these dune fields offers new insight into the nature of martian wind conditions and sand supply. The linear dunes appears to have formed through modification of a formerly transverse aeolian deposit, suggesting a relatively recent change in local wind direction. The 11 dunes in the star dune locality show a progressive change from barchan to star form as each successive dune has traveled up into a valley, into a more complex wind regime. The star dunes corroborate the model of N. Lancaster (1989), for the formation of star dunes by projection of transverse dunes into a complex, topographically influenced wind regime. The star dunes have dark streaks emanating from them, providing evidence that the dunes were active at or near the time the relevant image was obtained by the Viking 1 orbiter in 1978. The star and linear dunes described here are located in different regions on the martian surface. Unlike most star and linear dunes on Earth, both martian examples are isolated occurrences; neither is part of a major sand sea. Previously published Mars general circulation model results suggest that the region in which the linear dune field occurs should be a bimodal wind regime, while the region in which the star dunes occur should be unimodal. The star dunes are probably the result of localized complication of the wind regime owing to topographic confinement of the dunes. Local topographic influence on wind regime is also evident in the linear dune field, as there are transverse dunes in close proximity to the linear dunes, and their occurrence is best explained by funneling of wind through a topographic gap in the upwind crater wall.

Edgett, Kenneth S.↗

NASA NTRS2001

State-Dependent Pseudo-Linear Filter for Spacecraft Attitude and Rate Estimation

This paper presents the development and performance of a special algorithm for estimating the attitude and angular rate of a spacecraft. The algorithm is a pseudo-linear Kalman filter, which is an ordinary linear Kalman filter that operates on a linear model whose matrices are current state estimate dependent. The nonlinear rotational dynamics equation of the spacecraft is presented in the state space as a state-dependent linear system. Two types of measurements are considered. One type is a measurement of the quaternion of rotation, which is obtained from a newly introduced star tracker based apparatus. The other type of measurement is that of vectors, which permits the use of a variety of vector measuring sensors like sun sensors and magnetometers. While quaternion measurements are related linearly to the state vector, vector measurements constitute a nonlinear function of the state vector. Therefore, in this paper, a state-dependent linear measurement equation is developed for the vector measurement case. The state-dependent pseudo linear filter is applied to simulated spacecraft rotations and adequate estimates of the spacecraft attitude and rate are obtained for the case of quaternion measurements as well as of vector measurements.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1997

Response properties of pigeon otolith afferents to linear acceleration

In the present study, the sensitivity to sinusoidal linear accelerations in the plane of the utricular macula was tested in afferents. The head orientation relative to the translation axis was varied in order to determine the head position that elicited the maximal and minimal responses for each afferent. The response gain and phase values obtained to 0.5-Hz and 2-Hz linear acceleration stimuli were then plotted as a function of head orientation and a modified cosine function was fit to the data. From the best-fit cosine function, the predicted head orientations that would produce the maximal and minimal response gains were estimated. The estimated maximum response gains to linear acceleration in the utricular plane for the afferents varied between 75 and 1420 spikes s-1 g-1. The mean maximal gains for all afferents to 0.5-Hz and 2-Hz sinusoidal linear acceleration stimuli were 282 and 367 spikes s-1 g-1, respectively. The minimal response gains were essentially zero for most units. The response phases always led linear acceleration and remained constant for each afferent, regardless of head orientation. These response characteristics indicate that otolith afferents are cosine tuned and behave as one-dimensional linear accelerometers. The directions of maximal sensitivity to linear acceleration for the afferents varied throughout the plane of the utricle; however, most vectors were directed out of the opposite ear near the interaural axis. The response dynamics of the afferents were tested using stimulus frequencies ranging between 0.25 Hz and 10 Hz (0.1 g peak acceleration). Across stimulus frequencies, most afferents had increasing gains and constant phase values. These dynamic properties for individual afferents were fit with a simple transfer function that included three parameters: a mechanical time constant, a gain constant, and a fractional order distributed adaptation operator.

Non-NASA Center↗

NASA NTRS2002

Multidimensional indexing structure for use with linear optimization queries

Linear optimization queries, which usually arise in various decision support and resource planning applications, are queries that retrieve top N data records (where N is an integer greater than zero) which satisfy a specific optimization criterion. The optimization criterion is to either maximize or minimize a linear equation. The coefficients of the linear equation are given at query time. Methods and apparatus are disclosed for constructing, maintaining and utilizing a multidimensional indexing structure of database records to improve the execution speed of linear optimization queries. Database records with numerical attributes are organized into a number of layers and each layer represents a geometric structure called convex hull. Such linear optimization queries are processed by searching from the outer-most layer of this multi-layer indexing structure inwards. At least one record per layer will satisfy the query criterion and the number of layers needed to be searched depends on the spatial distribution of records, the query-issued linear coefficients, and N, the number of records to be returned. When N is small compared to the total size of the database, answering the query typically requires searching only a small fraction of all relevant records, resulting in a tremendous speedup as compared to linearly scanning the entire dataset.

Bergman, Lawrence David↗

NASA NTRS2010

Explosive Volcanic Eruptions from Linear Vents on Earth, Venus and Mars: Comparisons with Circular Vent Eruptions

Conditions required to support buoyant convective plumes are investigated for explosive volcanic eruptions from circular and linear vents on Earth, Venus, and Mars. Vent geometry (linear versus circular) plays a significant role in the ability of an explosive eruption to sustain a buoyant plume. On Earth, linear and circular vent eruptions are both capable of driving buoyant plumes to equivalent maximum rise heights, however, linear vent plumes are more sensitive to vent size. For analogous mass eruption rates, linear vent plumes surpass circular vent plumes in entrainment efficiency approximately when L(sub o) > 3r(sub o) owing to the larger entrainment area relative to the control volume. Relative to circular vents, linear vents on Venus favor column collapse and the formation of pyroclastic flows because the range of conditions required to establish and sustain buoyancy is narrow. When buoyancy can be sustained, however, maximum plume heights exceed those from circular vents. For current atmospheric conditions on Mars, linear vent eruptions are capable of injecting volcanic material slightly higher than analogous circular vent eruptions. However, both geometries are more likely to produce pyroclastic fountains, as opposed to convective plumes, owing to the low density atmosphere. Due to the atmospheric density profile and water content on Earth, explosive eruptions enjoy favorable conditions for producing sustained buoyant columns, while pyroclastic flows would be relatively more prevalent on Venus and Mars. These results have implications for the injection and dispersal of particulates into the planetary atmosphere and the ability to interpret the geologic record of planetary volcanism.

Glaze, Lori S.↗

NASA NTRS2015

Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.

4DVAR↗

NASA NTRS2017

Linearity Analysis and Efficiency Testing of The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) Science Cameras for Flight

To unveil the complexity of the solar atmosphere, measurement of the magnetic field in the upper chromosphere and transition region is fundamentally important, as this is where the forces transition from plasma to magnetic field dominated. Measurements of the field are also needed to elucidate the energy transport from the lower atmospheric regions to the corona beyond. Such an advance in heliospheric knowledge became possible with the first flight of the international solar sounding rocket mission, CLASP. For the first time, linear polarization was measured in Hydrogen Lyman-Alpha at 121.60 nm in September 2015. For linear polarization measurements in this emission line, high sensitivity is required due to the relatively weak polarization signal compared to the intensity. To achieve this high sensitivity, a low-noise sensor is required with good knowledge of its characterization, including linearity. This work presents further refinement of the linearity characterization of the cameras flown in 2015. We compared the current from a photodiode in the light path to the digital response of the detectors. Pre-flight CCD linearity measurements were taken for all three flight cameras and calculations of the linear fits and residuals were performed. However, the previous calculations included a smearing pattern and a digital saturation region on the detectors which were not properly taken into account. The calculations have been adjusted and were repeated for manually chosen sub-regions on the detectors that were found not to be affected. We present a brief overview of the instrument, the calibration data and procedures, and a comparison of the old and new linearity results. The CLASP cameras will be reused for the successor mission, CLASP2, which will measure the Magnesium II h & k emission lines between 279.45 nm and 280.35 nm. The new approach will help to better prepare for and to improve the camera characterization for CLASP2.

linearit↗

NASA NTRS2018

Linearity Analysis and Efficiency Testing of The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) Science Cameras for Flight

detector↗

DOE OSTI2015

Calibrating Nonlinear Soil Material Properties for Seismic Analysis Using Soil Material Properties Intended for Linear Analysis

Seismic analysis of nuclear structures is routinely performed using guidance provided in “Seismic Analysis of Safety-Related Nuclear Structures and Commentary (ASCE 4, 1998).” This document, which is currently under revision, provides detailed guidance on linear seismic soil-structure-interaction (SSI) analysis of nuclear structures. To accommodate the linear analysis, soil material properties are typically developed as shear modulus and damping ratio versus cyclic shear strain amplitude. A new Appendix in ASCE 4-2014 (draft) is being added to provide guidance for nonlinear time domain SSI analysis. To accommodate the nonlinear analysis, a more appropriate form of the soil material properties includes shear stress and energy absorbed per cycle versus shear strain. Ideally, nonlinear soil model material properties would be established with soil testing appropriate for the nonlinear constitutive model being used. However, much of the soil testing done for SSI analysis is performed for use with linear analysis techniques. Consequently, a method is described in this paper that uses soil test data intended for linear analysis to develop nonlinear soil material properties. To produce nonlinear material properties that are equivalent to the linear material properties, the linear and nonlinear model hysteresis loops are considered. For equivalent material properties, the shear stress at peak shear strain and energy absorbed per cycle should match when comparing the linear and nonlinear model hysteresis loops. Consequently, nonlinear material properties are selected based on these criteria.

nonlinear↗

DOE OSTI2020

Method and precision nanopositioning apparatus with compact vertical and horizontal linear nanopositioning flexure stages for implementing enhanced nanopositioning performance

An enhanced method and precision nanopositioning apparatus for implementing enhanced nanopositioning performance is provided. The nanopositioning apparatus includes a vertical linear nanopositioning flexure stage and a horizontal linear nanopositioning flexure stage. The vertical linear nanopositioning flexure stage includes a stage base, a symmetrically configured flexure linear guiding mechanism with precision motion enhancement structure, and a stage carriage. The horizontal linear nanopositioning flexure stage is mounted on the stage carriage of the vertical linear nanopositioning flexure stage, and includes a middle-bar relative position control mechanism to enhance the stiffness of a flexure linear guiding mechanism.

77 NANOSCIENCE AND NANOTECHNOLOGY↗