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At least 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Stability margins for Hurwitz polynomials

The authors treat the robust stability issue using the characteristic polynomial, for two different cases: first in coefficient space with respect to perturbations in the coefficient of the characteristic polynomial; and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l-(squared) stability margin for both the monic and nonmonic cases. Following this, a method is given to find the l(infinity) margin, and the method is extended to reveal much larger stability regions. In parameter space the authors consider all single-input (multi-output) or single-output (multi-input) systems with a fixed controller and a plant described by a set of transfer functions which are ratios of polynomials with variable coefficients. A procedure is presented to calculate the radius of the largest stability ball in the space of these variable parameters. The calculation serves as a stability margin for the control system. The formulas that result are quasi-closed-form expressions for the stability margin and are computationally efficient.

Chapellat, Herve↗
NASA NTRS1989

False lock in quadriphase receivers with unequal I- and Q-channel data rates

Results are presented concerning the noise-free false-lock problem in quadriphase receivers with unequal I-channel and Q-channel data rates. It is shown that false lock may occur when the incoming carrier frequency and the loop VCO (voltage-controlled oscillator) frequency differ by an amount that is a linear combination of a quarter of I-channel and Q-channel data rates. General expressions for the false-lock performance of quadriphase receivers are given for random as well as periodic data patterns. Specific closed-form expressions for the false-lock margin are are derived when the arm filters of the quadriphase receivers are single-pole Butterworth filters, and the format of the random data is NRZ (nonreturn-to-zero). Numerical evaluations of false-lock margin as a function of the product of 3-dB arm-filter bandwidth and symbol duration are carried out for random data using various arm filters and for different periodic I-chanel and Q-channel data patterns.

Cideciyan, Roy D.↗
NASA NTRS1989

Theory of the optimally coupled Q-switched laser

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.

Degnan, John J.↗
NASA NTRS1989

Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other.

Kapania, Rakesh K.↗
NASA NTRS1989

Phobos and Deimos control networks

Viking Orbiter images of Phobos and Deimos have been measured to establish global control networks for 98 surface features of the former and 53 of the latter; photogrammetric triangulation has yielded body-fixed coordinates of these control-points, as well as mean triaxial radii of 13.3 x 11.1 x 9.3 km for Phobos and 7.5 x 6.2 x 5.4 for Deimos. Expressions are also obtained for the inertial orientations of these bodies' spin axes and prime meridians. While these expressions should be accurate to a few tenths of a deg for the 1971-1980 period, their accuracy will degrade with time as the orbit accuracy degrades.

Duxbury, Thomas C.↗
NASA NTRS1988

An empirical model of the earth's plasmasphere

An empirical model is developed for plasmaspheric low-energy plasma consisting of H(+). The model is developed from a data base derived from measurements taken by the Retarding Ion Mass Spectrometer on the DE-1 satellite. An analytical expression that reproduces the density profiles for moderate geomagnetic activity is given and discussed. This expression reproduces the density fall-off in the ionosphere as well as the sharp density decrease at the plasmapause.

Gallagher, D. L.↗
NASA NTRS1989

Gravitational moment exerted on a small body by an oblate body

The present demonstration of a method for obtaining vector-dyadic expressions of the gravitational moment about a body's center-of-mass proceeds through the derivation of an expression for the gravitational moment exerted by an oblate spheroid. The contribution of the earth's oblateness to the gravitational moment exerted on a body has been numerically evaluated for a greatly simplified illustrative case; this contribution is noted to be significant by comparison with such other external moments as those exerted by aerodynamic forces.

Roithmayr, Carlos M.↗
NASA NTRS1989

Computational complexities and storage requirements of some Riccati equation solvers

The linear optimal control problem of an nth-order time-invariant dynamic system with a quadratic performance functional is usually solved by the Hamilton-Jacobi approach. This leads to the solution of the differential matrix Riccati equation with a terminal condition. The bulk of the computation for the optimal control problem is related to the solution of this equation. There are various algorithms in the literature for solving the matrix Riccati equation. However, computational complexities and storage requirements as a function of numbers of state variables, control variables, and sensors are not available for all these algorithms. In this work, the computational complexities and storage requirements for some of these algorithms are given. These expressions show the immensity of the computational requirements of the algorithms in solving the Riccati equation for large-order systems such as the control of highly flexible space structures. The expressions are also needed to compute the speedup and efficiency of any implementation of these algorithms on concurrent machines.

Utku, Senol↗
NASA NTRS1989

Thrust law effects on the long-period modes of aerospace craft

An analytical study is presented of the longitudinal long-period dynamics of an aerospace craft in a nearly circular orbit, with a thrust law depending arbitrarily on the speed and altitude. A plane of engine possibilities is first defined, with points corresponding to propulsion systems having prescribed thrust slopes with respect to speed and altitude. Approximate expressions for the characteristic roots and times are obtained by first identifying a small quantity in the coefficients of the characteristic equation, and then expanding in a perturbation series about the origin of the plane of engine possibilities, for which the solution is always known. These expressions agree very well with the exact solutions over a wide range of altitudes and thrust laws. The period of the oscillatory translational mode (phugoid) is found to be independent to first order of the thrust law, generalizing results found by previous investigators for specific thrust laws. The results apply to the speed range from hypersonic to orbital.

Markopoulos, Nikos↗
NASA NTRS1989

Slow twists of solar magnetic flux tubes and the polar magnetic field of the sun

The solar wind model of Weber and Davis (1967) is generalized to compute the heliospheric magnetic field resulting from solar rotation or a steady axisymmetric twist including a geometrical expansion which is more rapid than spherical. The calculated increase in the ratio of the toroidal to poloidal field components with heliocentric radial distance r clarifies an expression derived recently by Jokipii and Kota (1989). Magnetic-field components transverse to r do not in general grow to dominate the radial component at large r. The analysis also yields expressions for the Poynting flux associated with the steady twists.

Hollweg, Joseph V.↗
NASA NTRS1989

Stability and performance tradeoffs in bi-lateral telemanipulation

Kinesthetic force feedback provides measurable increase in remote manipulation system performance. Intensive computation time requirements or operation under conditions of time delay can cause serious stability problems in control-system design. Here, a simplified linear analysis of this stability problem is presented for the forward-flow generalized architecture, applying the hybrid two-port representation to express the loop gain of the traditional master-slave architecture, which can be subjected to similar analysis. The hybrid two-port representation is also used to express the effects on the fidelity of manipulation or feel of one design approach used to stabilize the forward-flow architecture. The results suggest that, when local force feedback at the slave side is used to reduce manipulator stability problems, a price is paid in terms of telemanipulation fidelity.

Hannaford, Blake↗
NASA NTRS1989

Radiation pressure dynamics in planetary exospheres - A 'natural' framework

Exospheric theory is reformulated to provide for the analysis of dynamical underpinning of exospheric features. The formulation is based on the parabolic-cylindrical separability of the Hamiltonian that describes particle motions in the combined fields of planetary gravity and solar radiation pressure. An approximate solution for trajectory evolution in terms of orbital elements is derived and the role of the exopause in the tail phenomenon is discussed. Also, an expression is obtained for the bound constituent atom densities at outer planetocoronal positions along the planet-sun axis for the case of an evaporative, uniform exobase. This expression is used to estimate midnight density enhancements as a function of radial distance for the terrestrial planets.

Bishop, James↗
NASA NTRS1989

Approximate formulation of redistribution in the Ly-alpha, Ly-beta, H-alpha system

Simple approximate formulas are given for the coupled redistribution of Ly-alpha, Ly-beta, and H-alpha, by using well-defined approximations to an essentially exact formulation. These formulas incorporate all the essential physics including Raman scattering, lower state radiative decay, and correlated terms representing emission during a collision which must be retained in order that the emission coefficients are properly behaved in the line wings. Approximate expressions for the appropriate line broadening parameters are collected. Finally, practical expressions for the source functions are given. These are formulated through newly introduced nonimpact redistribution functions, which are shown to be reasonably approximated by existing (ordinary and generalized) redistribution functions.

Cooper, J.↗
NASA NTRS1989

Stability robustness improvement of direct eigenspace assignment based feedback systems using singular value sensitivities

A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.

Garg, Sanjay↗
NASA NTRS1989

Flexible aircraft dynamic modeling for dynamic analysis and control synthesis

The linearization and simplification of a nonlinear, literal model for flexible aircraft is highlighted. Areas of model fidelity that are critical if the model is to be used for control system synthesis are developed and several simplification techniques that can deliver the necessary model fidelity are discussed. These techniques include both numerical and analytical approaches. An analytical approach, based on first-order sensitivity theory is shown to lead not only to excellent numerical results, but also to closed-form analytical expressions for key system dynamic properties such as the pole/zero factors of the vehicle transfer-function matrix. The analytical results are expressed in terms of vehicle mass properties, vibrational characteristics, and rigid-body and aeroelastic stability derivatives, thus leading to the underlying causes for critical dynamic characteristics.

Schmidt, David K.↗
NASA NTRS1989

Parametric study of power absorption from electromagnetic waves by small ferrite spheres

Algebraic expressions in terms of elementary mathematical functions are derived for power absorption and dissipation by eddy currents and magnetic hysteresis in ferrite spheres. Skin depth is determined by using a variable inner radius in descriptive integral equations. Numerical results are presented for sphere diameters less than one wavelength. A generalized power absorption parameter for both eddy currents and hysteresis is expressed in terms of the independent parameters involving wave frequency, sphere radius, resistivity, and complex permeability. In general, the hysteresis phenomenon has a greater sensitivity to these independent parameters than do eddy currents over the ranges of independent parameters studied herein. Working curves are presented for obtaining power losses from input to the independent parameters.

Englert, Gerald W.↗
NASA NTRS1989

Analysis of radar images of the active volcanic zone at Krafla, Iceland: The effects of look azimuth biasing

The geomorphic expression of Mid-Ocean-Ridge (MOR) volcanism in a subaerial setting occurs uniquely on Earth in Iceland, and the most recent MOR eruptive activity has been concentrated in the Northeastern Volcanic Zone in an area known as Krafla. Within the Krafla region are many of the key morphologic elements of MOR-related basaltic volcanism, as well as volcanic explosion craters, subglacial lava shields, tectonic fissure swarms known as gjar, and basaltic-andesite flows with well developed ogives (pressure-ridges). The objective was to quantify the degree to which the basic volcanic and structural features can be mapped from directional SAR imagery as a function of the look azimuth. To accomplish this, the current expression of volcanic and tectonic constructs was independently mapped within the Krafla region on the E, W, and N-looking SAR images, as well as from SPOT Panchromatic imagery acquired in 1987. The initial observations of the E, W, and N images indicates that fresh a'a lava surfaces are extremely radar bright (rough at 3 cm to meter scales) independent of look direction; this suggests that these flows do not have strong flow direction related structures at meter and cm scales, which is consistent with typical Icelandic a'a lava surfaces in general. The basic impression from a preliminary analysis of the effects of look azimuth biasing on interpretation of the geology of an active MOR volcanic zone is that up to 30 percent of the diagnostic features can be missed at any given look direction, but that having two orthogonal look direction images is probably sufficient to prevent gross misinterpretation.

Garvin, J. B.↗