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NASA NTRS1981

Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations

Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.

Beam, R. M.↗

NASA NTRS1973

Linearized stability analysis and design of a flyback dc-dc boost regulator.

Analytic expressions for the small-signal power-stage describing functions of a switched dc-dc boost regulator are derived from an approximate continuous circuit model which is developed by a time-averaging technique. Closed-loop stability is attained through the design of frequency compensation of the loop gain. Open- and closed-loop regulator output impedances are derived from the linearized models for the given configuration. The analysis and design are compared with and confirmed by breadboard measurements.

Wester, G. W.↗

NASA NTRS1975

Time domain modelling and stability analysis of an integral pulse frequency modulated dc to dc power converter

Using state variable representation a nonlinear, discrete-time system is derived that models the converter exactly. This system is linearized about its steady state solution, and converter stability, transient response and audio susceptibility are studied. The steady state solution of the converter is stable if and only if all the roots of the linearized system are absolutely less than unity. Excellent agreement with laboratory test data has been observed.

Iwens, R. P.↗

NASA NTRS1976

Stability analysis of combined continuous and discrete systems

A discrete, time-invariant system is represented by an equivalent continuous, periodic system. A combined continuous plant and discrete controller may then be formulated as a single continuous, periodic coefficient system. The exact stability solution for the combined system is obtained, as a matrix eigenvalue problem. Periodic system theory also gives some information about the type of instabilities which may be encountered in the combined plant and controller.

Johnson, W.↗

NASA NTRS1986

Stability analysis of double-peaked proton distribution functions in the solar wind

Twelve proton velocity distribution functions as measured for different solar wind speeds by the plasma analyzer at the Helios spacecraft are modeled analytically by a superposition of two bi-Maxwellians. The stability of these distributions is investigated by solving the linear dispersion equation for parallel propagation of both left- and right-hand polarized modes. Due to the temperature anisotropy of the main proton component the presence of the resonant left-hand ion cyclotron instability is found to be typical for high-speed streams and is independent of an ion beam. The results indicate that the ratio of the beam density to total particle density and the beam drift velocity are generally close to the threshold values necessary to drive a highly unstable nonresonant right-hand mode. This instability is found for one proton distribution and is a consequence of the beam particles. It is concluded that both the ion cyclotron instability and the ion beam instability act as a regulating mechanism on the shape of solar wind double humped proton distribution functions.

Leubner, Manfred P.↗

NASA NTRS1976

Elementary Applications of a Rotorcraft Dynamic Stability Analysis

A number of applications of a rotorcraft aeroelastic analysis are presented to verify that the analysis encompasses the classical solutions of rotor dynamics, and to examine the influence of certain features of the model. Results are given for the following topics: flapping frequency response to pitch control; forward flight flapping stability; pitch/flap flutter and divergence; ground resonance instability; and the flight dynamics of several representative helicopters.

Johnson, W.↗

NASA NTRS1982

Long term frequency stability analysis of the GPS NAVSTAR 6 Cesium clock

Time domain measurements, taken between the NAVSTAR 6 Spacecraft Vehicle (SV) and the Vandenberg Global Positioning System (GPS) Monitor Site, by a pseudo random noise receiver, were collected over an extended period of time and analyzed to estimate the long term frequency stability of the NAVSTAR 6 onboard frequency standard, referenced to the Vandenberg MS frequency standard. The technique employed separates the clock offset from the composite signal by first applying corrections for equipment delays, ionospheric delay, tropospheric delay, Earth rotation and the relativistic effect. The data are edited and smoothed using the predicted SV ephemeris to calculate the geometric delay. Then all available passes from each of the four GPS monitor stations, are collected at 1-week intervals and used to calculate the NAVSTAR orbital elements. The procedure is then completed by subtracting the corrections and the geometric delay, using the final orbital elements, from the composite signal, thus leaving the clock offset and random error.

Mccaskill, T. B.↗

NASA NTRS1981

Stability analysis of automobile driver steering control

In steering an automobile, the driver must basically control the direction of the car's trajectory (heading angle) and the lateral deviation of the car relative to a delineated pathway. A previously published linear control model of driver steering behavior which is analyzed from a stability point of view is considered. A simple approximate expression for a stability parameter, phase margin, is derived in terms of various driver and vehicle control parameters, and boundaries for stability are discussed. A field test study is reviewed that includes the measurement of driver steering control parameters. Phase margins derived for a range of vehicle characteristics are found to be generally consistent with known adaptive properties of the human operator. The implications of these results are discussed in terms of driver adaptive behavior.

Allen, R. W.↗

NASA NTRS1995

Non-gyrotropic proton and alpha-particle velocity distributions in the solar wind: TAUS observations and stability analysis

Ion velocity distribution functions have been measured with high time resolution by the TAUS plasma instrument on the PHOBOS mission to Mars in 1989. The unambiguous separation of protons and alpha-particles by TAUS enabled us to study the nonthermal features of their distributions separately and to analyze the stability of the distributions against excitation of waves in the cyclotron-frequency domain. Typical nonthermal features include temperature anisotropies, with T(sub perpendicular) larger than T(sub parallel), and ion beam populations drifting along the local magnetic field direction. Also, distinctly non-gyrotropic alpha-particle velocity distributions were sometimes found. Non-gyrotropy strongly changes the wave dispersion and gives rise to new growing modes, related to the coupling of the standard wave modes existing in gyrotropic plasma. It is found that for the measured non-gyrotropic ion distributions the right-hand polarized wave can also be excited by a temperature anistropy instead of the usual beam drift.

Astudillo, H. F.↗

NASA NTRS1989

Lateral stability analysis for X-29A drop model using system identification methodology

A 22-percent dynamically scaled replica of the X-29A forward-swept-wing airplane has been flown in radio-controlled drop tests at the NASA Langley Research Center. A system identification study of the recorded data was undertaken to examine the stability and control derivatives that influence the lateral behavior of this vehicle with particular emphasis on an observed wing rock phenomenon. All major lateral stability derivatives and the damping-in-roll derivative were identified for angles of attack from 5 to 80 degrees by using a data-partitioning methodology and a modified stepwise regression algorithm.

Raney, David L.↗

NASA NTRS1991

Reflectance stability analysis of Spectralon diffuse calibration panels

The Multi-angle Imaging SpectroRadiometer (MISR) plans to use deployable diffuse reflectance panels to provide periodic radiometric calibrations of its nine cameras while in-flight. Near-Lambertian reflectance characteristics are desirable to facilitate flat-field camera intercomparisons. Also required is panel spatial and spectral uniformity, and stability with time. Spectralon, a commercially available polytetrafluoroethylene (PTFE) compound, has been baselined in the MISR design. To assess the suitability of this material, a series of degradation tests were planned and implemented. These included UV vacuum exposure and proton bombardment tests which simulated the exposure levels to be encountered during the mission life. Proton levels are now considered too low to be of concern, but UV vacuum tests demonstrate sensitivity to material contamination. Material investigations have concluded that hydrocarbons are present in the bulk of the material, and that plastic packaging materials can introduce additional surface-layer contamination. It is found however, that these unwanted elements can be eliminated through vacuum pumping at elevated temperatures. Exposure to a UV source, while in vacuum, is again planned for a set of targets which have been vacuum baked. This will assess the stability of the pure PTFE form.

Bruegge, Carol J.↗

NASA NTRS1983

Stability analysis of intermediate boundary conditions in approximate factorization schemes

In many cases, approximate factorization schemes have provided a significant increase in efficiency over previously used solution methods in certain problems. The present investigation is concerned with the importance of intermediate boundary conditions in approximate factorization schemes, taking into account a specific example regarding a boundary-induced stability restriction in a scheme for the transonic full-potential equation. The considered scheme has been discussed by Holst (1979). Holst's scheme is a variation of the AF2 schemes described by Ballhaus and Steger (1975). The application of the AF2 scheme to the two-dimensional Laplace equation in a rectangle is studied giving attention to the stability of the scheme in connection with various boundary conditions for the intermediate variable.

South, J. C., Jr.↗

NASA NTRS1977

Stability analysis for linear systems with time delays

Time delays in the mathematical description of a physical system occur whenever the system is affected not only by conditions at the present time, but also by conditions which have occurred in the past. The tau-decomposition method, as refined by Lee and Hsu, is a method for studying the effects of time delay on the stability of retarded dynamical systems. In this paper, the method is extended to examine the stability and relative stability of: (1) retarded systems with many time delays; and (2) a class of neutral systems with one delay. Applications are included which illustrate the power of the technique.

Barker, L. K.↗

NASA NTRS1995

A parametric study of supersonic laminar flow for swept wings using linear stability analysis

A parametric study to predict the extent of laminar flow on the upper surface of a generic swept-back wing (NACA 64A010 airfoil section) at supersonic speeds was conducted. The results were obtained by using surface pressure predictions from an Euler/Navier-Stokes computational fluid dynamics code coupled with a boundary layer code, which predicts detailed boundary layer profiles, and finally with a linear stability code to determine the extent of laminar flow. The parameters addressed are Reynolds number, angle of attack, and leading-edge wing sweep. The results of this study show that an increase in angle of attack, for specific Reynolds numbers, can actually delay transition. Therefore, higher lift capability, caused by the increased angle of attack, as well as a reduction in viscous drag due to the delay in transition is possible for certain flight conditions.

Cummings, Russell M.↗

NASA NTRS1994

Thermal Stability Analysis for a Heliocentric Gravitational Radiation Detection Mission

The Laser Interferometer Space Antenna (LISA) mission is designed for detailed studies of low-frequency gravitational radiation. The mission is currently a candidate for ESA's post-Horizon 2000 program. Thermal noise affects the measurement in at least two ways. Thermal variation of the length of the optical cavity to which the lasers are stabilized introduces phase variations in the interferometer signal, which have to be corrected for by using data from the two arms separately.

Laser Interferometer Space Antenna LISA gravitatio↗

NASA NTRS2014

Vertical Spin Tunnel Testing and Stability Analysis of Multi-Mission Earth Entry Vehicles

Multi-Mission Earth Entry Vehicles (MMEEVs) are blunt-body vehicles designed with the purpose of transporting payloads from space to the surface of the Earth. To achieve high reliability and minimum weight, MMEEVs avoid using limited-reliability systems, such as parachutes, retro-rockets, and reaction control systems and rely on the natural aerodynamic stability of the vehicle throughout the Entry, Descent, and Landing phases of flight. Testing in NASA Langley's 20-FT Vertical Spin Tunnel (20-FT VST), dynamically-scaled MMEEV models was conducted to improve subsonic aerodynamic models and validate stability criteria for this class of vehicle. This report documents the resulting data from VST testing for an array of 60-deg sphere-cone MMEEVs. Model configurations included were 1.2 meter, and 1.8 meter designs. The addition of a backshell extender, which provided a 150% increase in backshell diameter for the 1.2 meter design, provided a third test configuration. Center of Gravity limits were established for all MMEEV configurations. An application of System Identification (SID) techniques was performed to determine the aerodynamic coefficients in order to provide databases for subsequent 6-degree-of-freedom simulations.

Glaab, Louis J.↗

NASA NTRS1996

Stability Analysis for Constrained Principal Axis Slew Maneuvers

This paper addresses the problem of reorienting a rigid spacecraft from arbitrary initial conditions to prescribed final conditions with zero angular velocity. The control law analyzed is based on quaternion feedback and leaves the user to choose two gains as functions of position, angular rate, and time. For arbitrary initial states, conditions on the controller gains are identified that guarantee global asymptotic stability. For the special case of rest-to-rest reorientations, the control law reduces to earlier results involving a principal axis rotation. The paper also addresses slew rate constraints, both, in terms of the two and infinity norms.

Seywald, Hans↗

NASA NTRS1986

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Gottlieb, D.↗