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NASA NTRS1981

Robustness results in linear-quadratic Gaussian based multivariable control designs

The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Available and new results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, robustness results associated with multivariable control systems designed on the basis of linear-quadratic (LQ) and the linear-quadratic Gaussian (LQG) design methodologies are presented.

Lehtomaki, N. A.↗

NASA NTRS1981

PAN AIR - A higher order panel method for predicting subsonic or supersonic linear potential flows about arbitrary configurations

PAN AIR is a computer program for predicting subsonic or supersonic linear potential flow about arbitrary configurations. It uses linear source and quadratic doublet strength distributions. These higher-order distributions have been implemented in a manner that greatly reduces the numerical stability problems that have plagued earlier attempts to make surface paneling methods work successfully for supersonic flow. PAN AIR's problem-solving capability, numerical approach, modeling features, and program architecture are described. Numerical results are presented for a variety of geometries at supersonic Mach numbers.

Carmichael, R. L.↗

NASA NTRS1980

Identification of a linear model of rotor-fuselage dynamics from nonlinear simulation data

Linear regression techniques are used to obtain 9- and 12-degree-of-freedom linear rotorcraft models from the input-output data generated by a nonlinear, blade-element rotorcraft simulation in hover. The resulting models are used to evaluate the coupling of the fuselage modes with the rotor flapping and lead-lag modes at various frequencies. New techniques are proposed and evaluated to improve the identification process, including a method of verifying the assumed model structure by using data sets generated at different input frequencies.

Duval, R. W.↗

NASA NTRS1981

A model for the acoustic impedance of linear suppressor materials bonded on perforated plate

An analytical model is developed for the acoustic impedance of a composite made of a fine screen bonded to a perforated plate, the resistance having been modeled using steady flow theory and data, and including both linear and nonlinear components. The model of the screen resistance alone is derived first, and it is then extended to include a perforated plate bonded to the screen. Quantities such as effective open ratio and pressure recovery are evaluated. Conclusions are presented, including: (1) when the screen is bonded to a perforated plate, the linear resistance increases as the inverse of the perforate open area, (2) the nonlinearity in the screen resistance depends on the square of the screen wire diameter, and (3) when the resistance is considered as a function of approach velocity, the screen nonlinear term increases as the inverse of the square of the perforated plate open area ratio. The general theory can be applied to any screen structure, but final results are limited to a twilled square weave screen. Results can be applied to the study of sound absorbing materials used for lining the walls of aircraft engine duct suppressors.

Rice, E. J.↗

NASA NTRS1982

Out-of-Core Solutions of Complex Sparse Linear Equations

ETCLIB is library of subroutines for obtaining out-of-core solutions of complex sparse linear equations. Routines apply to dense and sparse matrices too large to be stored in core. Useful for solving any set of linear equations, but particularly useful in cases where coefficient matrix has no special properties that guarantee convergence with any of interative processes. The only assumption made is that coefficient matrix is not singular.

Yip, E. L.↗

NASA NTRS1982

Optimal Regulator Algorithms for the Control of Linear Systems

Control-theory design package, called Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), aids in design of controllers and optimal filters for systems modeled by linear, time invariant differential and difference equations. ORACLS is particularly attractive rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete forms.

Armstrong, E. S.↗

NASA NTRS1982

Linear magnetic motor/generator

A linear magnetic motor/generator is disclosed which uses magnetic flux to provide mechanical motion or electrical energy. The linear magnetic motor/generator includes an axially movable actuator mechanism. A permament magnet mechanism defines a first magnetic flux path which passes through a first end portion of the actuator mechanism. Another permament magnet mechanism defines a second magnetic flux path which passes through a second end portion of the actuator mechanism. A drive coil defines a third magnetic flux path passing through a third central portion of the actuator mechanism. A drive coil selectively adds magnetic flux to and subtracts magnetic flux from magnetic flux flowing in the first and second magnetic flux path.

Studer, P. A.↗

NASA NTRS1982

Thermal oxidative degradation reactions of linear perfluoroalky lethers

Thermal and thermal oxidative stability studies were performed on linear perfluoro alkyl ether fluids. The effect on degradation by metal catalysts and degradation inhibitors are reported. The liner perfluoro alkylethers are inherently unstable at 316 C in an oxidizing atmosphere. The metal catalysts greatly increased the rate of degradation in oxidizing atmospheres. In the presence of these metals in an oxidizing atmosphere, the degradation inhibitors were highly effective in arresting degradation at 288 C. However, the inhibitors had only limited effectiveness at 316 C. The metals promote degradation by chain scission. Based on elemental analysis and oxygen consumption data, the linear perfluoro alkylether fluids have a structural arrangement based on difluoroformyl and tetrafluoroethylene oxide units, with the former predominating.

Jones, W. R., Jr.↗

NASA NTRS1981

Theoretical quasar emission line ratios. IV - General asymptotic escape probabilities and the effects of linear Stark broadening

Established techniques permitting the evaluation of exact asymptotic forms of photon escape probabilities for a wide range of absorption coefficient profile types are used for QSO radiative transfer effect studies, and it is shown that the exact formulae are easily evaluated. It is found that some of the commonly used expressions overestimate the true value by a factor of about two, and a computationally expedient approximate expression is derived for the asymptotic form of the photon escape probability when linear Stark broadening contributes to the line absorption coefficient profile in hydrogenic lines. Attention is given to Lyman-alpha, for the case in which partial redistribution, over the linear Stark component of the line absorption coefficient profile, dominates single-flight photon escape.

Puetter, R. C.↗

NASA NTRS1982

High-accuracy linear and circular polarization measurements at 21 cm

New high-accuracy linear and circular polarization measurements have been obtained for 27 small-diameter radio sources, using the Westerbork Synthesis Radio Telescope at 21 cm (1415 MHz). From these and other observed properties of the sources, estimates of the average internal magnetic field strengths in the sources are made by applying the uniform synchrotron emission model to the measured circular polarization and by using equipartition arguments. These two values are compared and found to be in agreement to within an order of magnitude, as was previously found by Weiler and de Pater (1980). Also, the magnetic fields estimated from circular polarization measurements at two different wavelengths (49 and 21 cm) are compared and found to be in rough agreement, but with indications of differences between variable and nonvariable sources. A comparison of the magnitudes of linear and circular polarization in sources shows no correlations.

De Pater, I.↗

NASA NTRS1981

The response of a linear baroclinic equatorial ocean to periodic forcing

An investigation is conducted regarding the periodic response of the linear inviscid shallow water equations in a meridionally unbounded basin to zonal forcings at a single low frequency omega. A general solution in the long wave approximation and on an equatorial beta-plane is obtained by summing the Kelvin mode and the finite sum of Rossby modes whose turning points lie equatorward of the turning latitude at frequency omega. The results of the investigation suggest that even if the low frequency forcing has a simple structure, considerable spatial inhomogeneity in the deep ocean response would have to be expected. On the basis of linear inviscid theory, some conclusions are drawn about the causes of the differences between equatorial thermocline response in the Atlantic and Pacific.

Cane, M. A.↗

NASA NTRS1982

Non-linear inplane vibrations of wrinkling films

This paper presents analytical investigations of non-linear effects caused by wrinkling of films in the course of contraction and shearing. As shown, such non-linearities are important even for very small amplitudes of vibrations. Approximate analytical solutions for inplane vibrations are derived.

Zak, M.↗

NASA NTRS1982

ORACLS - A linear-quadratic-Gaussian computer-aided design package

ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.

Armstrong, E. S.↗

NASA NTRS1981

Theory and implementation of a fast algorithm linear equalizer

The theory and implementation of a multiplication-free linear mean-square error criterion equalizer for data transmission are considered. For many real-time signal processing situations, a large number of multiplications is objectionable. The linear estimation problem on a binary computer is considered where the estimation parameters are constrained to be powers of two and thus all multiplications are replaced by shifts. The optimal solution is obtained from an integer-programming-like problem except that the allowable discrete points are non-integers. The branch-and-bound algorithm is used to obtain the coefficients of the equalization TDL. Specific experimental performance results are given for an equalizer implemented with a 12 bit A/D device and a 8080 microprocessor.

Yan, T. Y.↗

NASA NTRS1982

Iterative algorithms for large sparse linear systems on parallel computers

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Adams, L. M.↗

NASA NTRS1982

Linear discriminant analysis with misallocation in training samples

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

Chhikara, R.↗

NASA NTRS1983

Longitudinal aerodynamic characteristics of a wing-winglet model designed at M = 0.8, C sub L = 0.4 using linear aerodynamic theory

Wind tunnel test results have been presented herein for a subsonic transport type wing fitted with winglets. Wind planform was chosen to be representative of wings used on current jet transport aircraft, while wing and winglet camber surfaces were designed using two different linear aerodynamic design methods. The purpose of the wind tunnel investigation was to determine the effectiveness of these linear aerodynamic design computer codes in designing a non-planar transport configuration which would cruise efficiently. The design lift coefficient was chosen to be 0.4, at a design Mach number of 0.8. Force and limited pressure data were obtained for the basic wing, and for the wing fitted with the two different winglet designs, at Mach numbers of 0.60, 0.70, 0.75 and 0.80 over an angle of attack range of -2 to +6 degrees, at zero sideslip. The data have been presented without analysis to expedite publication.

Kuhlman, J. M.↗

NASA NTRS1981

An empirical investigation of methods for nonsymmetric linear systems

The present investigation is concerned with a comparison of methods for solving linear algebraic systems which arise from finite difference discretizations of the elliptic convection-diffusion equation in a planar region Omega with Dirichlet boundary conditions. Such linear systems are typically of the form Ax = b where A is an N x N sparse nonsymmetric matrix. In a discussion of discretizations, it is assumed that a regular rectilinear mesh of width h has been imposed on Omega. The discretizations considered include central differences, upstream differences, and modified upstream differences. Six methods for solving Ax = b are considered. Three variants of Gaussian elimination have been chosen as representatives of state-of-the-art software for direct methods under different assumptions about pivoting. Three iterative methods are also included.

Sherman, A. H.↗