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The application of singular perturbation theory to problems in systems and control is addressed. The types of systems considered include linear and nonlinear, discrete and continuous, and stochastic and deterministic. Both ordinary and partial differential equations are covered.
The Multisatellite Attitude Determination/Optical Aspect Bias Determination (MSAD/OABIAS) System, designed to determine spin axis orientation and biases in the alignment or performance of optical or infrared horizon sensors and Sun sensors used for spacecraft attitude determination is described. MSAD/OABIAS uses any combination of eight observation models to process data from a single onboard horizon sensor and Sun sensor to determine simultaneously the two components of the attitude of the spacecraft, the initial phase of the Sun sensor, the spin rate, seven sensor biases, and the orbital in-track error associated with the spacecraft ephemeris information supplied to the system. In addition, the MSAD/OABIAS System provides a data simulator for system and performance testing, an independent deterministic attitude system for preprocessing and independent testing of biases determined, and a multipurpose data prediction and comparison system.
The Multisatellite Attitude Determination/Optical Aspect Bias Determination (MSAD/OABIAS) System, designed to determine spin axis orientation and biases in the alignment or performance of optical or infrared horizon sensors and Sun sensors used for spacecraft attitude determination, is described. MSAD/OABIAS uses any combination of eight observation models to process data from a single onboard horizon sensor and Sun sensor to determine simultaneously the two components of the attitude of the spacecraft, the initial phase of the Sun sensor, the spin rate, seven sensor biases, and the orbital in-track error associated with the spacecraft ephemeris information supplied to the system. In addition, the MSAD/OABIAS system provides a data simulator for system and performance testing, an independent deterministic attitude system for preprocessing and independent testing of biases determined, and a multipurpose data prediction and comparison system.
An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.
Stable crack growth and fracture at the interface of undensified LI-900 reusable surface insulation (RSI) tile and the Nomex strain isolation pad (SIP) of the Space-Shuttle thermal-protection system (TPS) were modeled by double-edged notch-tension specimens. These specimens were loaded under uniaxial tension or 50-Hz cyclic loading and the resultant stable crack growth leading to eventual fracture was monitored by a videocamera. These tests showed that successive local tear-outs due to local tensile overload in the RSI tile resulted in the interfacial fracture where the crack-tip opening angle, CTOA, of the SIP was related to initiation and intermittent stable crack propagation. Fractures in similar static and dynamic test specimens using densified LI-900 RSI tiles occurred in the undensified regions of the RSI tiles. These failures were consistent with the above failure mechanism based on the local tensile strength of the undensified LI-900 RSI tile. The intermittent stable crack growth of undensified LI-900 RSI tile was reproduced by a deterministic, two-dimensional finite-element model with SIP of variable elastic moduli.
Yule et al. (1982) have conducted a study of vaporizing sprays with the aid of laser techniques. The present investigation has the objective to supplement the measurements performed by Yule et al., by considering the limiting case of a spray in a stagnant environment. Mean and fluctuating velocities of the continuous phase are measured by means of laser Doppler anemometry (LDA) techniques, while Fraunhofer diffraction and slide impaction methods are employed to determine drop sizes. Liquid fluxes in the spray are found by making use of an isokinetic sampling probe. The obtained data are used as a basis for the evaluation of three models of the process, including a locally homogeneous flow (LHF) model, a deterministic separated flow (DSF) model, and a stochastic separated flow (SSF) model. It is found that the LHF and DSF models do not provide very satisfactory predictions for the test sprays, while the SSF model does provide reasonably good predictions of the observed structure.
The Orr et al. (OLP) stability analysis is reformulated to yield profiles from hot-wire velocity covariance data in the boundary layer of a flow over a flat plate. The proper orthogonal decomposition theorem (PODT) is used to maximize the mean square of the inner product of the velocity vector with a deterministic candidate vector function in Hilbert space. The OLP formulation couples the PODT for the eddy viscosity with a global extremum principle for the disturbance kinetic energy. Derivation of the governing equations is described analytically, as are the extraction of the mean velocity profile and the eddy viscosity. Finally, techniques for characterizing the dominant mode of the velocity field are introduced and applied to three-dimensional flow over a flat plate. Good agreement is found between the predictions, using laboratory data, and the measured energy and three-dimensional structures of the dominant eddies.
The effects of random member length errors on the surface accuracy, the defocus, and the residual, internal loads of tetrahedral truss antenna reflectors have been studied analytically. The analytical procedure involves performing multiple, deterministic finite element structural analyses for a particular truss. For each analysis, the normally distributed, random member length errors are selected by random number generator. A best fit paraboloid analysis is used to determine a root mean square error and defocus from each analysis. The statistical properties of these quantities as well as the internal loads are calculated from the results of many independent analyses. Results indicate that the number of members in a tetrahedral truss antenna of a given diameter has a significant effect on surface accuracy, defocus and internal loads. It was also found that the member axial stiffnesses and antenna focal length have a very small effect on reflector surface accuracy.
The present investigation is concerned with the presentation of a simplified model of the spatial structure of forecast error statistics, a comparison of the model with actual numerical weather prediction results, and the extent to which simplifying assumptions made in the model are justified. A stochastic-dynamic model is derived for the spatial structure of the global atmospheric mass-field forecast error. The model states that the relative potential vorticity of the forecast error is random. The covariance function of the model's solutions is found to be governed by a simple deterministic equation. The agreement between the stochastic model and actual mass-field forecast errors fields for 12-36 h periods validates the assumptions on which the model is derived. Within this period, the difference between the potential voriticity fields of the atmosphere and of the numerical forecasts used in the comparison is well represented by white noise.
A theory is developed which describes intensity moments for wave propagation through random media. It is shown using the path integral technique that these moments are significantly different from those of a Rayleigh distribution in certain asymptotic regions. The path integral approach is extended to inhomogeneous, anisotropic media possessing a strong deterministic velocity profile. The behavior of the corrections to Rayleigh statistics is examined, and it is shown that the important characteristics can be attributed to a local micropath focusing function. The correction factor gamma is a micropath focusing parameter defined in terms of medium fluctuations. The value of gamma is calculated for three ocean acoustic experiments, using internal waves as the medium fluctuations. It is found that all three experiments show excellent agreement as to the relative values of the intensity moments. The full curved ray is found to yield results that are significantly different from the straight-line approximations. It is noted that these methods are applicable to a variety of experimental situations, including atmospheric optics and radio waves through plasmas.
A computer aided design method for multiobjective parameter-insensitive design of airplane control systems is described. Methods are presented for trading off nominal values of design objectives against sensitivities of the design objectives to parameter uncertainties, together with guidelines for designer utilization of the methods. The methods are illustrated by application to the design of a lateral stability augmentation system for two supersonic flight conditions of the Shuttle Orbiter. Objective functions are conventional handling quality measures and peak magnitudes of control deflections and rates. The uncertain parameters are assumed Gaussian, and numerical approximations of the stochastic behavior of the objectives are described. Results of applying the tradeoff methods to this example show that stochastic-insensitive designs are distinctly different from deterministic multiobjective designs. The main penalty for achieving significant decrease in sensitivity is decreased speed of response for the nominal system.
The present general purpose automated planner/scheduler generates parallel plans aimed at the achievement of goals having imposed time constraints, with both durations and start time windows being specifiable for sets of goal conditions. Deterministic durations of such parallel plan activities as actions, events triggered by circumstances, inferences, and scheduled events entirely outside the actor's control, are explicitly modeled and may be any computable function of the activity variables. The final plan network resembles a PERT chart. Examples are given from the traditional 'blocksworld', and from a realistic 'Spaceworld' in which an autonomous spacecraft photographs objects in deep space and transmits the information to earth.
The history of distortion analysis is traced back to its origin in parallel compressor theory which was initially proposed in the late fifties. The development of this theory is reviewed up to its inclusion in the complex computer codes of today. It is found to be a very useful tool to guide development but not quantitative enough to predict compatibility. Dynamic or instantaneous distortion methodology is also reviewed from its origins in the sixties, to its current application in the eighties. Many of the requirements for interpreting instantaneous distortion are considered and illustrated. Statistical methods for predicting the peak distortion are described, and their limitations and advantages discussed. Finally, some Reynolds number and scaling considerations for inlet testing are considered. It is concluded that the deterministic instantaneous distortion methodology combined with distortion testing of engines with screens will remain the primary method of predicting compatibility for the near future. However, parallel compressor analysis and statistical peak distortion prediction will be important tools employed during the development of inlet/engine compatibility. Previously announced in STAR as N83-27991
Probability density function of the surface elevation of a nonlinear random wave field is obtained. The wave model is based on the Stokes expansion carried to the third order for both deep water waves and waves in finite depth. The amplitude and phase of the first-order component of the Stokes wave are assumed to be Rayleigh and uniformly distributed and slowly varying, respectively. The probability density function for the deep water case was found to depend on two parameters: the root-mean-square surface elevation and the significant slope. For water of finite depth, an additional parameter, the nondimensional depth, is also required. An important difference between the present result and the Gram-Charlier representation is that the present probability density functions are always nonnegative. It is also found that the 'constant' term in the Stokes expansion, usually neglected in deterministic studies, plays an important role in determining the details of the density function. The results compare well with laboratory and field experiment data.
Two time periods are studied for which comprehensive data coverage is available at both 1 AU using IMP-8 and ISEE-3 and beyond using Voyager 1. One of these periods is characterized by the predominance of corotating stream interactions. Relatively small scale transient flows characterize the second period. The evolution of these flows with heliocentric distance is studied using power spectral techniques. The evolution of the transient dominated period is consistent with the hypothesis of turbulent evolution including an inverse cascade of large scales. The evolution of the corotating period is consistent with the entrainment of slow streams by faster streams in a deterministic model.
Mean and fluctuating velocities of both phases, particle mass fluxes, particle size distributions in turbulent particle-laden jets were measured. The following models are considered: (1) a locally homogeneous flow (LHF) model, where slip between the phases was neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of particle dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model. The SSF model performed reasonably well with no modifications in the prescriptions for eddy properties from its original calibration. A modified k- model, incorporating direct contributions of interphase transport on turbulence properties (turbulence modulation), was developed within the framework of the SSF model.
Nonlinear mappings that exhibit chaotic, seemingly random, evolution have appeal as models of dynamic systems. Their deterministic evolution, vis-a-vis Markov evolutions, results in much simpler optimal detection and estimation algorithms. The variation of a chaotic parameter (mu) results in diverse evolutions, suggesting a simple but rich source of model variations. For the specific mapping examined, this latter possibility is problematic due to the extreme sensitivity on mu of the evolution in the chaotic regime.
Mean and fluctuating phase velocities; mean particle mass flux; particle size; and mean gas-phase Reynolds stress, composition and temperature were measured in stationary, turbulent, axisymmetric, and flows which conform to the boundary layer approximations while having well-defined initial and boundary conditions in dilute particle-laden jets, nonevaporating sprays, and evaporating sprays injected into a still air environment. Three models of the processes, typical of current practice, were evaluated. The local homogeneous flow and deterministic separated flow models did not provide very satisfactory predictions over the present data base. In contrast, the stochastic separated flow model generally provided good predictions and appears to be an attractive approach for treating nonlinear interphase transport processes in turbulent flows containing particles (drops).