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NASA NTRS1980

Linear state feedback, quadratic weights, and closed loop eigenstructures

Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

Thompson, P. M.↗

NASA NTRS1979

Non-linear wave interaction in a magnetoplasma column. I - Theory. II Experiment

The paper presents an analysis of non-linear three-wave interaction for propagation along a cylindrical plasma column surrounded either by a metallic boundary, or by an infinite dielectric, and immersed in an infinite, static, axial magnetic field. An averaged Lagrangian method is used and the results are specialized to parametric amplification and mode conversion, assuming an undepleted pump wave. Computations are presented for a magneto-plasma column surrounded by free space, indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma parameters. In addition, experiments on non-linear mode conversion in a cylindrical magnetoplasma column are described. The results are compared with the theoretical predictions and good qualitative agreement is demonstrated.

Larsen, J.-M.↗

NASA NTRS1980

Linear modes of convection in the solar envelope

The structure of the solar convective envelope calculated according to mixing-length theory is not consistent with the transport of the convective heat flux by any superposition of the fundamental linear convective modes. If the amplitudes of these modes can be estimated by consideration of the most important nonlinear terms in the equations of motion, it becomes possible to find solar models which are consistent with mode transport of the heat through the convective zone. These models may be characterized by a mixing length which varies from point to point through the envelope. The linear modes in such models show peaks in velocity at certain preferred length scales, but these scales do not necessarily correspond to those of the solar motions, such as the supergranulation.

Bogart, R. S.↗

NASA NTRS1982

Two-Stage Linearization Circuit

High accuracy is obtained by combining analog and digital corrections. Proximity-sensor linearization circuit has two stages. First-stage linearization is accurate to about 3 percent; accuracy of final output is better than 0.5 percent. By modifying contents of the Programable Read-Only Memory (PROM), circuit can also be used to derive a nonlinear output.

Waldeck, G. C.↗

NASA NTRS1980

Motion about the stable libration points in the linearized, restricted three-body problem

The motion of a point particle in the neighborhood of a triangular libration point (L sub 4 or L sub 5) in the linearized, restricted problem of three bodies in the plane is described. The derivation of the equations of motion is standard. From these equations, three invariants of the motion are obtained; the Jacobi integral is expressed linearly in terms of two of these. The trajectories for varied initial conditions are drawn, and a complete geometric description of the particle motion is given in elementary terms. Each trajectory has an exterior boundary curve; its equation is found. An approximation to this boundary curve was known; the two curves are compared graphically. For certain initial conditions, there is an interior region from which the trajectory is excluded; the equation of the boundary of this region is given.

Mittleman, D.↗

NASA NTRS1979

A higher order panel method for linearized supersonic flow

The basic integral equations of linearized supersonic theory for an advanced supersonic panel method are derived. Methods using only linear varying source strength over each panel or only quadratic doublet strength over each panel gave good agreement with analytic solutions over cones and zero thickness cambered wings. For three dimensional bodies and wings of general shape, combined source and doublet panels with interior boundary conditions to eliminate the internal perturbations lead to a stable method providing good agreement experiment. A panel system with all edges contiguous resulted from dividing the basic four point non-planar panel into eight triangular subpanels, and the doublet strength was made continuous at all edges by a quadratic distribution over each subpanel. Superinclined panels were developed and tested on s simple nacelle and on an airplane model having engine inlets, with excellent results.

Ehlers, F. E.↗

NASA NTRS1980

Discovery of intrinsic linear polarization in SS433

Observations of variable linear polarization in the optical range in the unique radio and X-ray source SS 433, which is characterized by moving emission lines in its visible and near-IR spectra, are reported. The observations were made with an unfiltered GaAs photocathode covering the spectral region 3000-9000 A, with a passband characteristic wavelength near 7000 A. Measurements reveal the presence of both a long-term and a very short time-scale variation in linear polarization in the continuum and in H-alpha, which indicate that a substantial fraction of the polarization is intrinsic to SS 433 and not produced in the interstellar medium. It is suggested that the most likely source of polarization in the optical continuum is electron scattering, and constraints on models of SS 433 implied by the discovery of intrinsic polarization are considered.

Mclean, I. S.↗

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.↗