Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “MATRICES”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
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 NTRS1977

Robustness in linear quadratic feedback design with application to an aircraft control problem

Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

Patel, R. V.↗
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Patel, R. V.↗
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Patel, R. V.↗
NASA NTRS1978

Analysis of complex decisionmaking processes

The analysis of corporate decisionmaking processes related to major system developments is unusually difficult because of the number of decisionmakers involved in the process and the long development cycle. A method for analyzing such decision processes is developed and illustrated through its application to the analysis of the commercial jet engine development process. The method uses interaction matrices as the key tool for structuring the problem, recording data, and analyzing the data to establish the rank order of the major factors affecting development decisions. In the example, the use of interaction matrices permitted analysts to collect and analyze approximately 50 factors that influenced decisions during the four phases of the development cycle, and to determine the key influencers of decisions at each development phase. The results of this study indicate that the cost of new technology installed on an aircraft is the prime concern of the engine manufacturer.

Hill, J. D.↗
NASA NTRS1977

Petrology of crystalline matrix breccias from Apollo 17 rake samples

The petrology, mineralogy, and composition of 13 crystalline matrix breccias from the Apollo 17 rake samples are described. The breccias have matrices of uniform modal mineralogy (plagioclase, 50-54%; olivine and pyroxene, 41-46%) but diverse textures. Clast characteristics, including the proportion of plagioclase, the composition in comparison with matrix, and the textures of different clast types, are reported. The majority of bulk matrix compositions plot on or very near the plagioclase-olivine cotectic in the system olivine-anorthite-silica. If the matrix compositions represent impact total melts, the inferred cotectic control requires that the source material was itself an igneous differentiate with compositions along the plagioclase-olivine cotectic. Alternatively, the proximity of the matrix compositions to the plagioclase-olivine cotectic could be accounted for if the breccia matrices represent a suite of impact-generated partial melts.

Warner, R. D.↗
NASA NTRS1977

NASTRAN hydroelastic modal studies. Volume 1: Introduction, theory, and results

The implementation of a general three-dimensional hydroelastic capability in the NASTRAN computer program is described. A method for analyzing the combined mode shapes of arbitrary fluid and structure finite element models was developed. The fluid was modeled with three-dimensional solid elements with options for tetrahedron, wedge, and hexahedron shapes. The elements were then connected to fluid grid points which defined the pressure in the fluid at the specified location. Matrices were formulated to provide efficient solutions for large-order problems. The structure matrices were processed separately and could be reduced using matrix condensation procedures or through a modal formulation using the normal modes of the empty structure as solution coordinates. The fluid/structure interface and the free surface were defined by the user with special NASTRAN boundary elements. A special purpose mesh generator program was provided to generate the actual NASTRAN data cards for the fluid, the structure, and the boundary elements for typical tank-type models.

Source record↗
NASA NTRS1979

Equation modifying program, L219 (EQMOD). Volume 2: Supplemental system design and maintenance document

A digital computer program, L219 (EQMOD), available for execution on the CDC 6600 is described. The program modifies matrices according to card input instructions and prepares magnetic files of matrices suitable for use in the linear systems analysis program (QR) and the random harmonic analysis program L221 (TEV156). The particular field of application of the program is the modification of the theoretical equations of motion and load equations generated in DYLOFLEX by the equation of motion program (L217) and the load equation program (L218), respectively.

Hirayama, M. Y.↗
NASA NTRS1979

Energy conserving norms for the solution of hyperbolic systems of partial differential equations

The hyperbolic system of partial differential equations with a real constant square coefficient matrix A is considered. The problem of finding an energy conserving norm for the solution of the system is reduced to the problem of characterizing those matrices appearing in the boundary conditions which satisfy two specific matrix equations. Necessary and sufficient conditions on the coefficient matrix A and the matrices appearing in boundary conditions are derived for an energy conserving norm. The conditions serve as criteria on a given system which determine whether or not the solution will have its energy conserved in some norm. Examples of specific systems and boundary conditions are also provided.

Gunzburger, M. D.↗
NASA NTRS1979

Eigenvalues and eigenvectors for hybrid coordinate equations of motion for flexible spacecraft

The eigenvalues and eigenvectors of a system of linear time-invariant equations describing the attitude motion of flexible spacecraft in terms of hybrid coordinates are characterized in terms of literal expressions by using peculiar properties of the system parameter matrices. For the undamped case the eigenvalues are localized in terms of inertial matrices and modal parameters. A procedure for calculating the eigenvectors is proposed whereby the eigenproblem associated with the original system of dimension (2N + 6) is reduced to that of a symmetric and positive definite matrix of dimension N with the zero-damping assumption. The eigenvectors for systems of large dimension are obtained explicitly in terms of a 3x1 matrix whose elements are available from a system of three algebraic equations, which is provided.

Ohkami, Y.↗
NASA NTRS1979

Optimal control of the Shuttle-Tethered-Subsatellite system

Alternate control laws based on an application of the linear regulator problem are developed for possible use in the operation of the Shuttle-Tethered-Subsatellite system. Control is assumed to be provided only by modulating the tension level in the tether as a function of the difference between actual and commanded tether line length, length rate, in (orbital) plane swing angle and swing angle rate. Necessary and sufficient conditions for stability of the (linear) system motion in the vicinity of its nominal local vertical orientation are developed. By proper selection of the state and control penalty matrices it is possible to obtain faster responses with no increase in maximum power levels for use in station keeping when compared with alternate control strategies. The weighting matrices are adjusted in a piecewise adaptive manner to provide control law gains in order to achieve a smooth deployment history. Successful retrieval is dependent mainly on the initial conditions and the rate at which the commanded length is reduced.

Bainum, P. M.↗
NASA NTRS1979

FORTRAN subroutines for out-of-core solutions of large complex linear systems

The design and usage of two main subprograms using direct methods to solve large linear complex systems, of the form Ax = b, whose coeffficient matrices are too large to be stored in core are described. The first main subprogram is for systems whose coefficient matrices are of a particular sparse structure, namely, the matrix A can be written in the form B + D, where B is a block-banded system, and D has only a few columns of nonzeros. Key elements of the algorithms used in the subprograms include: the data structure, the strategy for preserving numerical stability, the adaptability of the algorithms for dense systems as well as for block-profile systems.

Yip, E. L.↗
NASA NTRS1979

Synthesis of improved phenolic resins

Twenty seven addition cured phenolic resin compositions were prepared and tested for their ability to give char residues comparable to state-of-the-art phenolic resins. Cyanate, epoxy, allyl, acrylate, methacrylate and ethynyl derivatized phenolic oligomers were investigated. The novolac-cyanate and propargyl-novolac resins provided anaerobic char yields at 800 C of 58 percent. A 59 percent char yield was obtained from modified epoxy novolacs. A phosphonitrilic derivative was found to be effective as an additive for increasing char yields. The novolac-cyanate, epoxy-novolac and methacrylate-epoxy-novolac systems were investigated as composite matrices with Thornel 300 graphite fiber. All three resins showed good potential as composite matrices. The free radical cured methacrylate-epoxy-novolac graphite composite provided short beam shear strengths at room temperature of 93.3 MPa (13.5 ksi). The novolac-cyanate graphite composite produced a short beam shear strength of 74 MPa (10.7 ksi) and flexural strength of 1302 MPa (189 ksi) at 177 C. Air heat aging of the novolac-cyanate and epoxy novolac based composites for 12 weeks at 204 C showed good property retention.

Delano, C. B.↗
NASA NTRS1980

Spectral analysis of GEOS-3 altimeter data and frequency domain collocation

The mathematical background in spectral analysis as applied to geodetic applications is summarized. The resolution (cut-off frequency) of the GEOS 3 altimeter data is examined by determining the shortest wavelength (corresponding to the cut-off frequency) recoverable. The data from some 18 profiles are used. The total power (variance) in the sea surface topography with respect to the reference ellipsoid as well as with respect to the GEM-9 surface is computed. A fast inversion algorithm for matrices of simple and block Toeplitz matrices and its application to least squares collocation is explained. This algorithm yields a considerable gain in computer time and storage in comparison with conventional least squares collocation. Frequency domain least squares collocation techniques are also introduced and applied to estimating gravity anomalies from GEOS 3 altimeter data. These techniques substantially reduce the computer time and requirements in storage associated with the conventional least squares collocation. Numerical examples given demonstrate the efficiency and speed of these techniques.

Eren, K.↗
NASA NTRS1980

Eigenvector analysis of some observed and model-generated Climatological fields

An empirical orthogonal function analysis of monthly mean synoptic fields computed with a general circulation model and the corresponding observed climatological patterns is presented. A computer program was used to compute the principal components of the data matrices representing global maps of various observed and model-generated climatological fields. The variables analyzed were: 500mb geopotential height, 850 mb temperature, and sea level pressure. It is concluded that eigenvector analysis of observed and model-generated synoptic climatological fields is a useful diagnostic aid in the evaluation of global model simulation. The maps of any climatological variables are readily decomposed into a few orthogonal components which account for a large fraction of the total spatial variance, and the observed and model-generated patterns may then be compared in terms of these principal components of the original data matrices.

Dennis, M.↗
NASA NTRS1980

The infrared spectrum of matrix isolated hydrogen and deuterium

The induced infrared spectra of H2 and D2, trapped in matrices of Ar, Kr, N2, CO, have been investigated. It is found that in Ar and Kr, the pure rotation spectrum is always readily observable. Portions of the fundamental region, however, are induced by impurities, while the entire spectrum is impurity induced in N2 matrices. These results are discussed in light of a recent Raman study of this system, and in comparison with several single crystal studies. Effective rotational and vibrational constants for matrix isolated H2 are also given.

Warren, J. A.↗
NASA NTRS1980

Propagation directions of hydromagnetic waves in interplanetary space - Pioneer 10 and 11

The real and imaginary parts of spectral matrices of magnetic field fluctuations near 4 and 5 AU are used separately to generate estimates of hydromagnetic wave normal directions over the frequency range 0.00001 to 0.01 Hz in the spacecraft frame. Both procedures suggest the predominance of the Alfven mode over the fast and slow MHD modes among transverse magnetic field perturbations. Both procedures also show that the Alfven mode is more common among transverse perturbations at 4 AU than at 5 AU. Statistical techniques are for estimating uncertainties in computed wave normal directions and it is concluded that the real parts of the spectral matrices are more useful than the imaginary parts in specifying wave normals at times of magnetic quiet in the solar wind near 4 and 5 AU.

Parker, G. D.↗