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At least 523 records · Page 29
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NASA NTRS1978

DYGABCD: A program for calculating linear A, B, C, and D matrices from a nonlinear dynamic engine simulation

A digital computer program, DYGABCD, was developed that generates linearized, dynamic models of simulated turbofan and turbojet engines. DYGABCD is based on an earlier computer program, DYNGEN, that is capable of calculating simulated nonlinear steady-state and transient performance of one- and two-spool turbojet engines or two- and three-spool turbofan engines. Most control design techniques require linear system descriptions. For multiple-input/multiple-output systems such as turbine engines, state space matrix descriptions of the system are often desirable. DYGABCD computes the state space matrices commonly referred to as the A, B, C, and D matrices required for a linear system description. The report discusses the analytical approach and provides a users manual, FORTRAN listings, and a sample case.

Geyser, L. C.↗
NASA NTRS1977

Computation of output feedback gains for linear stochastic systems using the Zangwill-Powell method

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell.

Kaufman, H.↗
NASA NTRS1977

Non-linear duct acoustics and its application to fan noise

Quite often the scalar Helmholtz equation is assumed to be the fundamental equation of duct acoustics and various relations are derived from it. An investigation is, therefore, conducted regarding the underlying assumptions leading to the Helmholtz equation. It is found that serious errors, even well below 186 dB, are possible if the assumption of linearity were to be made. In duct acoustics these errors are highest near the cutoff points and in the case of ducts with transonic flow. It is pointed out that serious errors could arise if a nonlinear problem is analyzed by linear methods. At times, an entire phenomenon remains unpredictable by linear methods. Attention is given to the characteristics of nonlinear systems, the phenomenon of multiple pure tones in the case of noise from the aircraft engine fans, the limitations of the conventional acoustics equation, duct shape and nonlinearity, and the numerical simulation of a fan with 8 blades.

Vaidya, P. G.↗
NASA NTRS1978

A temporary threshold shift for self-motion detection following sustained, oscillating linear acceleration

Thresholds for detecting linear motion (self-motion) increased following exposure of human observers to sustained linear oscillation (fatiguing stimulus) at 0.26 Hz and approximately 0.5 G peak-to-peak for durations up to 30 min. Recovery to preexposure levels took place over a period of 10 to 15 min following the sustained oscillation termination. Differences in threshold shift magnitudes following sustained oscillation in various orientations support the interpretation that the observed threshold shifts resulted from fatigue of the utricular otolith receptors. Threshold shifts were not obtained following exposure of the human observers to sustained, unidirectional linear acceleration (2G) for durations up to 10 min with a centrifuge. The results of this study suggest a previously unobserved response property of the otolith organs, namely, that these organs can be fatigued in a manner analogous to other receptor systems.

Parker, D. E.↗
NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗
NASA NTRS1979

A modification to linearized theory for prediction of pressure loadings on lifting surfaces at high supersonic Mach numbers and large angles of attack

A new linearized-theory pressure-coefficient formulation was studied. The new formulation is intended to provide more accurate estimates of detailed pressure loadings for improved stability analysis and for analysis of critical structural design conditions. The approach is based on the use of oblique-shock and Prandtl-Meyer expansion relationships for accurate representation of the variation of pressures with surface slopes in two-dimensional flow and linearized-theory perturbation velocities for evaluation of local three-dimensional aerodynamic interference effects. The applicability and limitations of the modification to linearized theory are illustrated through comparisons with experimental pressure distributions for delta wings covering a Mach number range from 1.45 to 4.60 and angles of attack from 0 to 25 degrees.

Carlson, H. W.↗
NASA NTRS1979

Differences between measured and linearly interpolated synoptic variables over a 12-h period during AVE 4

Results of analyses revealed that nonlinear changes or differences formed centers or systems, that were mesosynoptic in nature. These systems correlated well in space with upper level short waves, frontal zones, and radar observed convection, and were very systematic in time and space. Many of the centers of differences were well established in the vertical, extending up to the tropopause. Statistical analysis showed that on the average nonlinear changes were larger in convective areas than nonconvective regions. Errors often exceeding 100 percent were made by assuming variables to change linearly through a 12-h period in areas of thunderstorms, indicating that these nonlinear changes are important in the development of severe weather. Linear changes, however, accounted for more and more of an observed change as the time interval (within the 12-h interpolation period) increased, implying that the accuracy of linear interpolation increased over larger time intervals.

Dupuis, L. R.↗
NASA NTRS1979

Linear state feedback, quadratic weights, and closed loop eigenstructures

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. 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 for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, 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.

Thompson, P. M.↗
NASA NTRS1979

Linear Approximation SAR Azimuth Processing Study

A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

Lindquist, R. B.↗
NASA NTRS1979

Red and photographic infrared linear combinations for monitoring vegetation

The relationships between various linear combinations of red and photographic infrared radiances and vegetation parameters are investigated. In situ spectrometers are used to measure the relationships between linear combinations of red and IR radiances, their ratios and square roots, and biomass, leaf water content and chlorophyll content of a grass canopy in June, September and October. Regression analysis shows red-IR combinations to be more significant than green-red combinations. The IR/red ratio, the square root of the IR/red ratio, the vegetation index (IR-red difference divided by their sum) and the transformed vegetation index (the square root of the vegetation index + 0.5) are found to be sensitive to the amount of photosynthetically active vegetation. The accumulation of dead vegetation over the year is found to have a linearizing effect on the various vegetation measures.

Tucker, C. J.↗
NASA NTRS1979

Acceleration of linear and logarithmic convergence

Eleven different methods for accelerating convergence of sequences and series have been tested and compared on a wide range of test problems, including both linearly and logarithmically convergent series, monotone and alternating series. All but one of these methods are already in the literature, and they include both linear and nonlinear methods. The only methods found to accelerate convergence across the board were the u and v transforms of Levin and the theta algorithm of Brezinski. The paper gives detailed comparisons of all the tested methods on the basis of number of correct digits in the answer as a function of number of terms of the series used. A theorem of Germain-Bonne states that methods of a certain form which are exact on geometric series will accelerate linear convergence. The theorem applies to theta sub 2, and we have extended it to apply to Levin's transforms. No corresponding theorem is known for logarithmic convergence, but u, v, and theta are exact on certain large classes of logarithmic series, and all tested methods lacking this property failed to accelerate some logarithmically convergent series.

Smith, D. A.↗
NASA NTRS1979

Linearization of the boundary-layer equations of the minimum time-to-climb problem

Ardema (1974) has formally linearized the two-point boundary value problem arising from a general optimal control problem, and has reviewed the known stability properties of such a linear system. In the present paper, Ardema's results are applied to the minimum time-to-climb problem. The linearized zeroth-order boundary layer equations of the problem are derived and solved.

Ardema, M. D.↗
NASA NTRS1979

Application of supersonic linear theory and hypersonic impact methods to three nonslender hypersonic airplane concepts at Mach numbers from 1.10 to 2.86

Aerodynamic predictions from supersonic linear theory and hypersonic impact theory were compared with experimental data for three hypersonic research airplane concepts over a Mach number range from 1.10 to 2.86. The linear theory gave good lift prediction and fair to good pitching-moment prediction over the Mach number (M) range. The tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone/tangent-wedge method gave the least accurate prediction of lift and pitching moment. The zero-lift drag was overestimated, especially for M less than 2.0. The linear theory drag prediction was generally poor, with areas of good agreement only for M less than or equal to 1.2. For M more than or equal to 2.), the tangent-cone method predicted the zero-lift drag most accurately.

Pittman, J. L.↗
NASA NTRS1979

Linear feature selection with applications

Several ways in which feature selection techniques were used in LACIE are discussed. In all cases, the methods require some a priori information and assumptions; in most, the classification procedure (Bayes optimal) was chosen in advance. The transformations used for dimensionality reduction are linear, that is, the variables in feature space are always linear combinations of the original measurements. Several numerically tractable criteria developed for LACIE, which provide information about the probability of misclassification, are discussed. Recent results on linear feature selection techniques are included. Their use in LACIE is discussed. Related open questions are mentioned.

Decell, H. P., Jr.↗
NASA NTRS1978

Characterization of acoustic disturbances in linearly sheared flows

The equation describing the plane wave propagation, the stability, or the rectangular duct mode characteristics in a compressible inviscid linearly sheared parallel, but otherwise homogeneous flow, is shown to be reducible to Whittaker's equation. The resulting solutions, which are real, viewed as functions of two variables, depend on a parameter and an argument, the values of which have precise physical meanings depending on the problem. The exact solutions in terms of Whittaker functions are used to obtain a number of known results of plane wave propagation and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). The usefulness of the exact solutions is then discussed in connection with the problems of plane wave propagation and the stability of a finite thickness layer with a linear velocity profile.

Koutsoyannis, S. P.↗
NASA NTRS1980

Combined linear theory/impact theory method for analysis and design of high speed configurations

Pressure distributions on a wing body at Mach 4.63 are calculated. The combined theory is shown to give improved predictions over either linear theory or impact theory alone. The combined theory is also applied in the inverse design mode to calculate optimum camber slopes at Mach 4.63. Comparisons with optimum camber slopes obtained from unmodified linear theory show large differences. Analysis of the results indicate that the combined theory correctly predicts the effect of thickness on the loading distributions at high Mach numbers, and that finite thickness wings optimized at high Mach numbers using unmodified linear theory will not achieve the minimum drag characteristics for which they are designed.

Brooke, D.↗
NASA NTRS1979

Self-motion magnitude estimation during linear oscillation - Changes with head orientation and following fatigue

Two types of experiments concerning the estimated magnitude of self-motion during exposure to linear oscillation on a parallel swing are described in this paper. Experiment I examined changes in magnitude estimation as a function of variation of the subject's head orientation, and Experiments II a, II b, and II c assessed changes in magnitude estimation performance following exposure to sustained, 'intense' linear oscillation (fatigue-inducting stimulation). The subjects' performance was summarized employing Stevens' power law R = k x S to the nth, where R is perceived self-motion magnitude, k is a constant, S is amplitude of linear oscillation, and n is an exponent). The results of Experiment I indicated that the exponents, n, for the magnitude estimation functions varied with head orientation and were greatest when the head was oriented 135 deg off the vertical. In Experiments II a-c, the magnitude estimation function exponents were increased following fatigue. Both types of experiments suggest ways in which the vestibular system's contribution to a spatial orientation perceptual system may vary. This variability may be a contributing factor to the development of pilot/astronaut disorientation and may also be implicated in the occurrence of motion sickness.

Parker, D. E.↗
NASA NTRS1980

Characterization of acoustic disturbances in linearly sheared flows

Inviscid fluctuations in a compressible linearly sheared, but otherwise homogeneous, parallel two-dimensional flow are considered. The equation describing the plane wave propagation (PWP), the stability, or the rectangular duct mode characteristics in such a flow is shown to be reducible to Whittaker's equation. The exact solutions are applied to problems of PWP and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). With respect to the PWP it is shown that the shear layer possesses no resonances and no Brewster angles, while with regard to the problem of the stability of a finite thickness shear layer with a linear velocity profile, it is shown that the thin layer is unstable to long wavelength disturbances for all Mach numbers.

Koutsoyannis, S. P.↗