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NASA NTRS1983

Analysis of structural perturbations in systems via cost decomposition methods

It has long been common practice to analyze linear dynamic systems by decomposing the total response in terms of individual contributions which are easier to analyze. Examples of this philosophy include the expansion of transfer functions using: (1) the superposition principle, (2) residue theory and partial fraction expansions, (3) Markov parameters, Hankel matrices, and (4) regular and singular perturbations. This paper summarizes a new and different kind of expansion designed to decompose the norm of the response vector rather than the response vector itself. This is referred to as "cost-decomposition' of the system. The notable advantages of this type of decomposition are: (a) easy application to multi-input, multi-output systems, (b) natural compatibility with Linear Quadratic Gaussian Theory, (c) applicability to the analysis of more general types of structural perturbations involving inputs, outputs, states, parameters. Property (c) makes the method suitable for problems in model reduction, measurement/actuator selections, and sensitivity analysis.

Skelton, R. E.↗

NASA NTRS1981

Geological terrain models

The initial phase of a program to determine the best interpretation strategy and sensor configuration for a radar remote sensing system for geologic applications is discussed. In this phase, terrain modeling and radar image simulation were used to perform parametric sensitivity studies. A relatively simple computer-generated terrain model is presented, and the data base, backscatter file, and transfer function for digital image simulation are described. Sets of images are presented that simulate the results obtained with an X-band radar from an altitude of 800 km and at three different terrain-illumination angles. The simulations include power maps, slant-range images, ground-range images, and ground-range images with statistical noise incorporated. It is concluded that digital image simulation and computer modeling provide cost-effective methods for evaluating terrain variations and sensor parameter changes, for predicting results, and for defining optimum sensor parameters.

Kaupp, V. H.↗

NASA NTRS1982

Further efforts to limit lunar internal temperatures from electrical conductivity determinations

A representative set of 18 electrical conductivity profiles consistent with lunar transfer function data in the 0.00001 to 0.001 Hz range is generated by means of a Monte Carlo procedure. Laboratory electrical conductivity vs temperature data extrapolated to lower and higher temperatures are used to convert the 18 profiles into temperature profiles for a series of radially homogeneous olivine-pyroxene mixtures ranging from 100% olivine to 100% aluminous orthopyroxene. The former yields selenotherms approaching the Ringwood-Essene solidus at depths near 500 km, while additions of the latter in concentrations greater than 15-30 vol% leads to cooler selenotherms which approach the solidus only at depths greater than about 1000 km. On the basis of independent geophysical constraints, the profile envelopes for compositions containing more than 15-30 vol% aluminous orthopyroxene are considered to be the most probable.

Hood, L. L.↗

NASA NTRS1983

An exploratory study of finite difference grids for transonic unsteady aerodynamics

A pulse-transfer function technique for calculating unsteady aerodynamic forces for a wide range of reduced frequencies is implemented in a finite difference program solving the complete unsteady transonic small perturbation equation. Forces are calculated for a two-dimensional linear flat plate case utilizing the default grids from several currently used finite difference programs. The forces are compared to exact theoretical values and grid generated boundary and internal reflections are demonstrated. Grids designed to alleviate the reflections are presented and forces for a 6% thick parabolic arc airfoil are calculated to investigate non-linear transonic effects.

Seidel, D. A.↗

NASA NTRS1983

Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

Frequency domain methods are developed to obtain explicit equations for the angles of arrival and departure for multivariable root loci. The techniques involve an evaluation of polynomials formulated within the transfer function matrix. The equations defined require simpler computations than the state-space results of Shaked (1976). A class of higher order poles and zeros is formulated in terms of simpler equations than Shaked's, and the equations are shown to be generalizations of the single-input-single-output root locus equations.

Yagle, A. E.↗

NASA NTRS1981

Stability of magnetically suspended optics in a vibration environment

The improving resolution capabilities of large spaceborne optical experiments are placing ever-increasing demands on platform stability in a vibration environment. The present paper discusses the principles of magnetic suspension systems as a promising alternative to conventional methods. The disadvantages of various conventional pointing mount geometrics are discussed, including the CG-mount approach and end-mount pointing, and advantages of a system whereby the payload has a high degree of isolation from the carrier in translation are pointed out. The Annular Suspension and Pointing System Vernier System is then presented as a hardware realization of a complete magnetic suspension system consisting of six magnetic bearing assemblies controlling six degrees of freedom of payload motion in a standardized end-mount configuration. A model of a simplified two-degrees-of-freedom isolation and pointing unit is considered and the transfer function from carrier translation to payload pointing is derived. The function is evaluated for several degenerate cases corresponding to conventional mounting techniques and magnetic suspension. Analytical performance predictions show a stability of better than 0.01 arcsec for a wide range of payloads in the worst-case shuttle disturbance environment.

Hamilton, B. J.↗

NASA NTRS1983

Model reference adaptive control of large structural systems

Attention is given to model reference adaptive control procedures that do not require explicit parameter identification for large structural systems. Even though such applications have been shown to be feasible for multivariable systems, provided there exists a feedback gain matrix that makes the resulting input/output transfer function strictly positive real, it is shown here that this constraint is overly restrictive and that only positive realness is required. Subsequent consideration of a simply supported beam reveals that if actuators and sensors are collocated, then the positive realness constraint will be satisfied and the model reference adaptive control will then indeed be suitable for velocity following when only velocity sensors are available and for both position and velocity following when velocity plus scaled position outputs are measured. For both cases, all states are guaranteed to be stable, regardless of system dimension.

Bar-Kana, I.↗

NASA NTRS1983

Sound radiation from annular ducts/nozzles using modal decomposition of in-duct acoustic power

Using a refined acoustic impulse technique, an experimental program was carried out to determine the proper procedure for measuring the acoustic power for both incident and reflected sound fields for annular ducts with and without nozzles at various flow conditions. Several radial and azimuthal pressure measurements were made, and using these complex pressure data, the modal content of the pressure field was determined. A mathematical approach for the modal decomposition of annular duct acoustic power was developed. The acoustic power due to each individual mode and also their total sum were derived. The acoustic characteristics of annular duct-nozzle systems were studied at various flow conditions. The results derived from the experiments include the termination reflection coefficient, the normalized transmission coefficients, the power transfer functions and the power imbalance.

Salikuddin, M.↗

NASA NTRS1982

Gravito-inertial sensitivity of the spider - Araneus sericatus

The gravito-inertial transfer function of the orb-weaving spider was evaluated by changes in the cardiac reflex. A non-intrusive method, using a laser system recorded the cardiac pulse. Between 1.001 and 1.5 Gz the data are 'best-fit' by a log function (r-squared 0.92). The response of the neurogenic heart is seen to be a good dependent variable for invetebrate research. The arachnid lyriform organ has those qualities which complement the obtained gravity function. It is hypothesized that the cardiac pump maintains the spiders equilibrium in the gravito-inertial field.

Finck, A.↗

NASA NTRS1982

Different atmospheric effects in remote sensing of uniform and nonuniform surfaces

The atmospheric effect on the radiance of sunlight scattered from the earth-atmosphere system is greatly dependent on the surface reflectance pattern, the contrast between adjacent fields, and the optical properties of the atmosphere. In addition, the atmospheric effect is described by the range and magnitude of the adjacency effects, the atmospheric modulation transfer function, and the apparent spatial resolution of remotely sensed imagery. This paper discusses the atmospheric effect on classification of surface features and shows that surface nonuniformity can be used for developing procedures to remove the atmospheric effect from the satellite imagery.

Kaufman, Y. J.↗

NASA NTRS1983

Diagnostic analysis of vibration signals using adaptive digital filtering techniques

Signal enhancement techniques are described using recently developed digital adaptive filtering equipment. Adaptive filtering concepts are not new; however, as a result of recent advances in microprocessor-based electronics, hardware has been developed that has stable characteristics and of a size exceeding 1000th order. Selected data processing examples are presented illustrating spectral line enhancement, adaptive noise cancellation, and transfer function estimation in the presence of corrupting noise.

Jewell, R. E.↗

NASA NTRS1983

Asymptotic unbounded root loci - Formulas and computation

A new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.

Sastry, S. S.↗

NASA NTRS1983

Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation

The 'simultaneous stabilization problem' is defined and theorems are proposed for its solution. The problem consists in answering the question: given an r-tuple G sub 1(s), G sub r(s) of p x m proper transfer functions, does there exist a compensator K(s) such that the closed loop systems G sub 1(s) (I+K(s)G sub 1(s)) (-1), G sub r(s) (I+K(s) G sub r(s)) (-1) are (internally) stable. This question arises in reliability theory, where G sub 2(s), G sub r(s) represents a plant G sub 1(s) operating in various modes of failure and K(s) is a nonswitching stabilizing compensator. It is important in the stability analysis and design of a plant which can be switched into various operating modes. The simultaneous stabilization problem can also apply to the stabilization of a nonlinear system which is linearized at several equilibria. Conditions are defined for pole placement and the generalized Sylvestor matrix is discussed. Previously announced in STAR as N82-31031

Ghosh, B. K.↗

NASA NTRS1983

LANDSAT-4 sensor performance

Preflight and in-orbit sensor and data measurements indicate that TM meets or exceeds most specifications. Measured spectral band edges meet instrument specifications in 12 out of 14 cases; there is ample dynamic range. The signal-to-noise ratio exceeds specifications, except for band 3, channel 4; and band 7 channel 7 is very noisy but still meets specifications. The modulation transfer function of channel 4, band 2, is smaller than specified. Registration errors between the primary focal plane (PFP) and the cold focal plane (CFP) are about 0.75 pixels along-scan and 0.2 pixels across scan. Forward and reverse scan discontinuities, are well within ground-processing capabilities to rectify. Instrument gain variability, up to 7% for band 5, requires use of the internal calibration (IC) system to assure radiometric accuracy. Preliminary applications evaluation of image contents indicates that TM provides much better definition of edges than MSS.

Barker, J. L.↗

NASA NTRS1984

Breadboard stellar tracker system test report

BASD has, in the past, developed several unique position tracking algorithms for charge transfer device (CTD) sensors. These algorithms provide an interpixel transfer function with the following characteristics: (1) high linearity; (2) simplified track logic; (3) high gain; and (4) high noise rejection. A previous test program using the GE charge injection device (CID) showed that accuracy for BASD's breadboard was limited to approximately 2% of a pixel (1 sigma) whereas analysis and simulation indicated the limit should be less than 0.5% of a pixel, assuming the limit to be detector response and dark current noise. The test program was conducted under NASA contract No. NAS8-34263. The test approach for that program did not provide sufficient data to identify the sources of error and left open the amount of contribution from parameters such as image distribution, geometric distortion and system alignment errors.

Kollodge, J. C.↗

NASA NTRS1984

An on-line equivalent system identification scheme for adaptive control

A prime obstacle to the widespread use of adaptive control is the degradation of performance and possible instability resulting from the presence of unmodeled dynamics. The approach taken is to explicitly include the unstructured model uncertainty in the output error identification algorithm. The order of the compensator is successively increased by including identified modes. During this model building stage, heuristic rules are used to test for convergence prior to designing compensators. Additionally, the recursive identification algorithm as extended to multi-input, multi-output systems. Enhancements were also made to reduce the computational burden of an algorithm for obtaining minimal state space realizations from the inexact, multivariate transfer functions which result from the identification process. A number of potential adaptive control applications for this approach are illustrated using computer simulations. Results indicated that when speed of adaptation and plant stability are not critical, the proposed schemes converge to enhance system performance.

Sliwa, S. M.↗

NASA NTRS1984

New Short Constraint Length, Rate 1/N Convolutional Codes which Minimize Required E Sub B/n Sub o for Given Bit Error Rate

Instead of using the criterion of maximum free distance, (df) or the maximum (df) with minimizing a few first distance profiles, short constraint length rate 1/N convolution codes were searched using a criterion of minimizing required bit energy-to-noise density ratio, E(b)/N(o), for a given value of desired bit error rate (BER), for the goodness of a code. The considered channel was binary antipodal signaling over additive white Gaussian noise and no quantization at the channel output. For the BER calculations, the transfer function bounding technique was used. Partial searches were performed using some known facts and a very useful idea that "good codes generate good codes.'' That is, for a given constraint length K, good rate 1/(N + 1) codes can be found by extending the code generator matrices of good rate 1/N codes. The code search results are tabulated for 3 or = K or = 7 and 2 or = N or = 8. For many pairs of K and N, the new codes are shown to save 0.1 to 0.4 dB in the required E(b)/N(o) compared to previously reported codes. Additionally, the benefits of coding bandwidth expansion are confirmed with the new codes.

Lee, P. J.↗

NASA NTRS1984

LANDSAT 4 investigations of Thematic Mapper and Multispectral Scanner applications

Interband detector noise was suppressed in the TIPS TM North Dakota data by median filtering. Procedures were developed to optimize the visual information content of thematic mapper data and evaluate the resulting photographic products by visual interpretation. A digital to analog TM transfer function was developed which properly placed the digital values on the most useable portion of film response curve. Utilizing the calculated minimum, mean, and maximum and the respective standard deviations of the bands from 50 sample scenes of TM data, look up tables were designed which resulted in acceptable photographic products. These products were evaluated by generation of color composites of selected band combinations using standard photo production procedures, and visual interpretation of scene features.

Lauer, D. T.↗