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The authors present a novel method called time-varying transfer function estimation (TTFE) in which time-domain parameters are computed through identification in the frequency domain. The method is particularly well suited for flexible structure control problems. An example of a flexible manipulator system is presented for which a self-tuning control law with frequency shaping is derived and demonstrated.
A detailed derivation of a finite-time arbitrary-motion incompressible cascade theory is presented for both Laplace and frequency domains. The generalized cascade lift deficiency function is shown to be consistent with the generalized Theodorsen's lift deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity; it also yields a correct value for the zero reduced frequency limit. Efficient numerical procedures are presented for the evaluation of the cascade lift deficiency function. Numerical examples comparing the cascade lift deficiency function with Loewy's (1957) rotary-wing lift deficiency function in frequency domain are presented. Pade approximants of the cascade lift deficiency function are constructed using a Bode plot approach that allows for complex poles. A general-purpose optimization program is used to determine the coefficients of the approximant.
A method is presented for the analysis of damped structural systems in which the structural components are represented by impedance models and analyzed in the frequency domain. Methods are presented to assemble and condense system impedance matrices, and then to identify approximate mass, stiffness, and damping matrices for systems whose impedances are complicated functions of frequency. Formulas are derived for determination of approximate values for system natural frequencies and damping using frequency domain quantities. The sensitivities of these approximate values to system parameter changes are analyzed. The implementation of these analysis tools is discussed and applied to a simple mechanical system.
A prototype multi-channel laser Doppler anemometry (LDA) processor was assembled using a wideband transient recorder and a microcomputer with an array processor for fast Fourier transform (FFT) computations. The prototype instrument was used to acquire, process, and record signals from a three-component wind tunnel LDA system subject to various conditions of noise and flow turbulence. The recorded data was used to evaluate the effectiveness of burst acceptance criteria, processing algorithms, and selection of processing parameters such as record length. The recorded signals were also used to obtain comparative estimates of signal-to-noise ratio between time-domain and frequency-domain signal detection schemes. These comparisons show that the FFT processing scheme allows accurate processing of signals for which the signal-to-noise ratio is 10 to 15 dB less than is practical using counter processors.
The evolution of domain walls in the early universe is studied via 2-D computer simulation. The walls are initially configured on a triangular lattice and then released from the lattice, their evolution driven by wall curvature and by the universal expansion. The walls attain an average velocity of about 0.3c and their surface area per volume (as measured in comoving coordinates) goes down with a slope of -1 with respect to conformal time, regardless of whether the universe is matter or radiation dominated. The additional influence of vacuum pressure causes the energy density to fall away from this slope and steepen, thus allowing a situation in which domain walls can constitute a significant portion of the energy density of the universe without provoking an unacceptably large perturbation upon the microwave background.
Mathematical models for the dynamics of the DLR BO 105 helicopter are extracted from flight test data using two different approaches: frequency-domain and time-domain identification. Both approaches are reviewed. Results from an extensive data consistency analysis are given. Identifications for 6 degrees of freedom (DOF) rigid body models are presented and compared in detail. The extracted models compare favorably and their prediction capability is demonstrated in verification results. Approaches to extend the 6 DOF models are addressed and first results are presented. System identification is broadly defined as the deduction of system characteristics from measured data. It provides the only possibility to extract both non-parametric (e.g., frequency responses) and parametric (e.g., state space matrices) aircraft models from flight test data and therefore gives a reliable characterization of the dynamics of the actually existing aircraft. Main applications of system identification are seen in areas where higher accuracies of the mathematical models are required: Simulation validation, control system design (in particular model-following control system design for in-flight simulation), and handling qualities.
The evolution of domain walls generated in the early Universe is discussed considering an interaction between the walls and a major gaseous component of the dark matter. The walls are supposed able to reflect the particles elastically and with a reflection coefficient of unity. A toy Lagrangian that could give rise to such a phenomenon is discussed. In the simple model studied, highly non-relativistic and slowly varying speeds are obtained for the domain walls (approximately 10 (exp -2)(1+z)(exp -1)) and negligible distortions of the microwave background. In addition, these topological defects may provide a mechanism of forming the large scale structure of the Universe, by creating fluctuations in the dark matter (delta rho/rho approximately O(1)) on a scale comparable with the distance the walls move from the formation (in the model d less than 20 h(exp -1) Mpc). The characteristic scale of the wall separation can be easily chosen to be of the order of 100 Mpc instead of being restricted to the horizon scale, as usually obtained.
The magnitude and angular pattern of distortions of the microwave background are analyzed by collapsing spherical domain walls. A characteristic pattern of redshift distortions of red or blue spikes surrounded by blue discs was found. The width and height of a spike is related to the diameter and magnitude of the disc. A measurement of the relations between these quantities thus can serve as an unambiguous indicator for a collapsing spherical domain wall. From the redshift distortion in the blue discs an upper bound was found on the surface energy density of the walls sigma is less than or approximately 8 MeV cubed.
A new method for frequency-domain identification of rotorcraft dynamics is presented. Nonparametric frequency-response identification and parametric transfer-function modeling methods are extended to allow the extraction of state-space (stability and control derivative) representations. An interactive computer program DERIVID is described for the iterative solution of the multi-input/multi-output frequency-response matching approach used in the identification. Theoretical accuracy methods are used to determine the appropriate model structure and degree-of-confidence in the identified parameters. The method is applied to XV-15 tilt-rotor aircraft data in hover. Bare-airframe stability and control derivatives for the lateral/directional dynamics are shown to compare favorably with models previously obtained using time-domain identification methods and the XV-15 simulation program.
The first applications of a spectral multidomain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high-order continuity of the solution is preserved. The global flux balance is imposed in terms of a spectral integral of the discrete equations across adjoining domains. Since the discretized equations interior to each domain solved are uncoupled from each other, and since the interface relation has a block structure, the solution scheme can be adapted to the particular requirements of each subdomain. The spectral multidomain technique presented is well-suited for the multiple scales associated with the chemically reacting and transition flows in hypersonic research. A nonstaggered multidomain discretization is used for the chemically reacting flow calculation, and the first implementation of a staggered multidomain mesh is presented for accurately solving the stability equation for a viscous compressible fluid.
Tensile tests on splat-quenched Ni3Al-Cr alloys showed a sharp decrease in ductility with long-time annealing. The growth of the initially very-fine-size anti-phase domains showed a tenuous correlation with ductility up to a critical size, where ductility was lost. The grain size was relatively unaffected by these annealing treatments, but the grain-boundary curvature decreased, implying less toughness. An important observation was that, for the longest annealing time, a chromium-rich precipitate formed, which the data indicate could be a boride. Miniaturized tensile tests were performed on samples which were all obtained from the same splat-quenched foil, and the various domain sizes were controlled by subsequent annealing treatments.
Whenever the potential of a scalar field has two or more separated, degenerate minima, domain walls form as the universe cools. The evolution of the resulting network of domain walls is calculated for the case of two potential minima in two and three dimensions, including wall annihilation, crossing, and reconnection effects. The nature of the evolution is found to be largely independent of the rate at which the universe expands. Wall annihilation and reconnection occur almost as fast as causality allows, so that the horizon volume is 'swept clean' and contains, at any time, only about one, fairly smooth, wall. Quantitative statistics are given. The total area of wall per volume decreases as the first power of time. The relative slowness of the decrease and the smoothness of the wall on the horizon scale make it impossible for walls to both generate large-scale structure and be consistent with quadrupole microwave background anisotropy limits.
This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.
The unsteady aerodynamic coupling between the front and rear rotors in a counter-rotating propeller system is analyzed using a frequency-domain panel method based on linear compressible aerodynamic theory. The periodic loads are decomposed into harmonics, and the harmonic amplitudes are found iteratively. Each stage of the interation involves the solution of an isolated propeller problem, the interaction being done through the Fourier transform of the induced velocity field. The method was validated by comparing mean performance parameters with measured data and by comparing the predicted velocity field with detailed laser Doppler velocimeter measurements. Comparisons have also been made between the fluctuating loads predicted by the present method and a time-domain panel method.
FREQ (Multivariable Frequency Domain Singular Value Analysis Package) software package of subroutines performing frequency-domain analysis of: continuous- or discrete-multivariable linear systems; any continuous system for which one calculates transfer matrix at points on imaginary axis; or any discrete system for which one calculates transfer matrix at points on unit circle. Four different versions available. Single-precision brief version LAR-14119, single-precision complete version LAR-14120, double-precision brief version LAR-14121, and double-precision complete version LAR-14122. Written in ANSI standard FORTRAN 77.
The work presented here is the first part of a continuing effort to expand existing capabilities in aeroelasticity by developing the methodology which is necessary to utilize unsteady time-domain aerodynamics directly in aeroservoelastic design and analysis. The ultimate objective is to define a fully integrated state-space model of an aeroelastic vehicle's aerodynamics, structure and controls which may be used to efficiently determine the vehicle's aeroservoelastic stability. Here, the current status of developing a state-space model for linear or near-linear time-domain indicial aerodynamic forces is presented.
Simoncelli and Adelson have extended the one dimensional Quadrature Mirror Filter (QMF) to two dimensions with hexagon symmetry and three dimensional spatio-temporal extensions with rhombic-duodecahedray symmetry. Jain and Crochiere presented an excellent QMF design technique in the time domain. It is proposed to extend the design of a two dimensional QMF over a rectangular lattice in the spatial domain based primarily on the extension of the idea of Jain and Crochiere. In addition, the design will investigate the use of two dimensional Z-transformations. Since this proposed QMF is intended for the applications in image processing, all the important and interesting engineering issues will be addressed throughout the development phase. The design of a two dimensional QMF is discussed. The motivation is to achieve an extremely high data compression ratio. It is entirely possible to achieve dramatic results when pattern recognition techniques are employed. The final goal is the demonstration of extremely high data compression ratios using NASA pictures.
The feasibility of a general theory for the time-domain unsteady aerodynamics of helicopter rotors is investigated. The wake theory gives a linearized relation between the downwash and the wing bound circulation, in terms of the impulse response obtained directly in the time domain. This approach makes it possible to treat general wake configurations, including discrete wake vorticity with rolled-up and distorted geometry. The investigation establishes the approach for model order reduction; determines when a constrained identification method is needed; verifies the formulation of the theory for rolled-up, distorted trim wake geometry; and verifies the formulation of the theory for wake geometry perturbations. The basic soundness of the approach is demonstrated by the results presented. A research program to complete the development of the method is outlined. The result of this activity will be an approach for analyzing the aeroelastic stability and response of helicopter rotors, while retaining the important influence of the complicated rotor wake configuration.