The modeling of diffuse boundaries in the 2-D digital waveguide mesh

The digital waveguide mesh can be used to simulate the propagation of sound waves in an acoustic system. The accurate simulation of the acoustic characteristics of boundaries within such a system is an important part of the model. One significant property of an acoustic boundary is its diffusivity. Previous approaches to simulating diffuse boundaries in a digital waveguide mesh are effective but exhibit limitations and have not been analyzed in detail. An improved technique is presented here that simulates diffusion at boundaries and offers a high degree of control and consistency. This technique works by rotating wavefronts as they pass through a special diffusing layer adjacent to the boundary. The waves are rotated randomly according to a chosen probability function and the model is lossless. This diffusion model is analyzed in detail, and its diffusivity is quantified in the form of frequency dependent diffusion coefficients. The approach used to measuring boundary diffusion is described here in detail for the 2-D digital waveguide mesh and can readily be extended for the 3-D case

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of MFIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included

Sliding mode and shaped input vibration control of flexible systems

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the vibration reduction problem is investigated for a flexible spacecraft during attitude maneuvering. A new control strategy is proposed, which integrates both the command input shaping and the sliding mode output feedback control (SMOFC) techniques. Specifically, the input shaper is designed for the reference model and implemented outside of the feedback loop in order to achieve the exact elimination of the residual vibration by modifying the existing command. The feedback controller, on the other hand, is designed based on the SMOFC such that the closed-loop system behaves like the reference model with input shaper, where the residual vibrations are eliminated in the presence of parametric uncertainties and external disturbances. An attractive feature of this SMOFC algorithm is that the parametric uncertainties or external disturbances of the system do not need to satisfy the so-called matching conditions or invariance conditions provided that certain bounds are known. In addition, a smoothed hyperbolic tangent function is introduced to eliminate the chattering phenomenon. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved

Adaptive cancelation of self-generated sensory signals in a whisking robot

Sensory signals are often caused by one's own active movements. This raises a problem of discriminating between self-generated sensory signals and signals generated by the external world. Such discrimination is of general importance for robotic systems, where operational robustness is dependent on the correct interpretation of sensory signals. Here, we investigate this problem in the context of a whiskered robot. The whisker sensory signal comprises two components: one due to contact with an object (externally generated) and another due to active movement of the whisker (self-generated). We propose a solution to this discrimination problem based on adaptive noise cancelation, where the robot learns to predict the sensory consequences of its own movements using an adaptive filter. The filter inputs (copy of motor commands) are transformed by Laguerre functions instead of the often-used tapped-delay line, which reduces model order and, therefore, computational complexity. Results from a contact-detection task demonstrate that false positives are significantly reduced using the proposed scheme

Transform methods for precision continuum and control models of flexible space structures

An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality

Control and dynamics of a flexible spacecraft during stationkeeping maneuvers

A case study of a spacecraft having flexible solar arrays is presented. A stationkeeping attitude control mode using both earth and rate gyro reference signals and a flexible vehicle dynamics modeling and implementation is discussed. The control system is designed to achieve both pointing accuracy and structural mode stability during stationkeeping maneuvers. Reduction of structural mode interactions over the entire mode duration is presented. The control mode using a discrete time observer structure is described to show the convergence of the spacecraft attitude transients during Delta-V thrusting maneuvers without preloading thrusting bias to the onboard control processor. The simulation performance using the three axis, body stabilized nonlinear dynamics is provided. The details of a five body dynamics model are discussed. The spacecraft is modeled as a central rigid body having cantilevered flexible antennas, a pair of flexible articulated solar arrays, and to gimballed momentum wheels. The vehicle is free to undergo unrestricted rotations and translations relative to inertial space. A direct implementation of the equations of motion is compared to an indirect implementation that uses a symbolic manipulation software to generate rigid body equations

Contour Dynamics Methods

In an early paper on the stability of fluid layers with uniform vorticity Rayleigh (1880) remarks: "... In such cases, the velocity curve is composed of portions of straight lines which meet each other at finite angles. This state of things may be supposed to be slightly disturbed by bending the surfaces of transition, and the determination of the subsequent motion depends upon that of the form of these surfaces. For co retains its constant value throughout each layer unchanged in the absence of friction, and by a well-known theorem the whole motion depends upon [omega]." We can now recognize this as essentially the principal of contour dynamics (CD), where [omega] is the uniform vorticity. The theorem referred to is the Biot-Savart law. Nearly a century later Zabusky et al (1979) presented numerical CD calculations of nonlinear vortex patch evolution. Subsequently, owing to its compact form conferring a deceptive simplicity, CD has become a widely used method for the investigation of two-dimensional rotational flow of an incompressible inviscid fluid. The aim of this article is to survey the development, technical details, and vortex-dynamic applications of the CD method in an effort to assess its impact on our understanding of the mechanics of rotational flow in two dimensions at ultrahigh Reynolds numbers. The study of the dynamics of two- and three-dimensional vortex mechanics by computational methods has been an active research area for more than two decades. Quite apart from many practical applications in the aerodynamics of separated flows, the theoretical and numerical study of vortices in incompressible fluids has been stimulated by the idea that turbulent fluid motion may be viewed as comprising ensembles of more or less coherent laminar vortex structures that interact via relatively simple dynamics and by the appeal of the vorticity equation, which does not contain the fluid pressure. Two-dimensional vortex interactions have been perceived as supposedly relevant to the origins of coherent structures observed experimentally in mixing layers, jets, and wakes, and for models of large-scale atmospheric and oceanic turbulence. Interest has often focused on the limit of infinite Reynolds number, where in the absence of boundaries, the inviscid Euler equations are assumed to properly describe the flow dynamics. The numerous surveys of progress in the study of vorticity and the use of numerical methods applied to vortex mechanics include articles by Saffman & Baker (1979) and Saffman (1981) on inviscid vortex interactions and Aref (1983) on two-dimensional flows. Numerical methods have been surveyed by Chorin (1980), and Leonard (1980, 1985). Caflisch (1988) describes work on the mathematical aspects of the subject. Zabusky (1981), Aref (1983), and Melander et al (1987b) discuss various aspects of CD. The review of Dritschel (1989) gives emphasis to numerical issues in CD and to recent computations with contour surgery. This article is confined to a discussion of vortices on a two-dimensional surface. We generally follow Saffman & Baker (1979) in matters of definition. In two dimensions a vortex sheet is a line of discontinuity in velocity while a vortex jump is a line of discontinuity in vorticity. We shall, however, use filament to denote a two-dimensional ribbon of vorticity surrounded by fluid with vorticity of different magnitude (which may be zero), rather than the more usual three-dimensional idea of a vortex tube. The ambiguity is unfortunate but is already in the literature. Additionally, a vortex patch is a finite, singly connected area of uniform vorticity while a vortex strip is an infinite strip of uniform vorticity with finite thickness, or equivalently, an infinite filament. Contour Dynamics will refer to the numerical solution of initial value problems for piecewise constant vorticity distributions by the Lagrangian method of calculating the evolution of the vorticity jumps. Such flows are often related to corresponding solutions of the Euler equations that are steady in some translating or rotating frame of reference. These solutions will be called vortex equilibria, and the numerical technique for computing their shapes based on CD is often referred to as contour statics. The mathematical foundation for the study of vorticity was laid primarily by the well-known investigations of Helmholtz, Kelvin, J. J. Thomson, Love, and others. In our century, efforts to produce numerical simulations of flows governed by the Euler equations have utilized a variety of Eulerian, Lagrangian, and hybrid methods. Among the former are the class of spectral methods that now comprise the prevailing tool for large-scale two- and three-dimensional calculations (see Hussaini & Zang 1987). The Lagrangian methods for two-dimensional flows have been predominantly vortex tracking techniques based on the Helmholtz vorticity laws. The first initial value calculations were those of Rosenhead (193l) and Westwater (1935) who attempted to calculate vortex sheet evolution by the motion of O(10) point vortices. Subsequent efforts by Moore (1974) (see also Moore 1983, 1985) and others to produce more refined computations for vortex sheets have failed for reasons related to the tendency for initially smooth vortex sheet data to produce singularities (Moore 1979). Discrete vortex methods used to study the nonlinear dynamics of vortex patches and layers have included the evolution of assemblies of point vortices by direct summation (e.g. Acton 1976) and the cloud in cell method (Roberts & Christiansen 1972, Christiansen & Zabusky 1973, Aref & Siggia 1980, 1981). For reviews see Leonard (1980) and Aref (1983). These techniques have often been criticized for their lack of accuracy and numerical convergence and because they may be subject to grid scale dispersion. However, many qualitative vortex phenomena observed in nature and in experiments, such as amalgamation events and others still under active investigation (e.g. filamentation) were first simulated numerically with discrete vortices. The contour dynamics approach is attractive because it appears to allow direct access, at least for small times, to the inviscid dynamics for vorticity distributions smoother than those of either point vortices or vortex sheets, while at the same time enabling the mapping of the two-dimensional Euler equations to a one-dimensional Lagrangian form. In Section 2 we discuss the formulation and numerical implementation of contour dynamics for the Euler equations in two dimensions. Section 3 is concerned with applications to isolated and multiple vortex systems and to vortex layers. An attempt is made to relate this work to calculations of the relevant vortex equilibria and to results obtained with other methods. Axisymmetric contour dynamics and the treatment of the multi-layer model of quasigeostrophic flows are described in Section 4 while Section 5 is devoted to a discussion of the tendency shown by vorticity jumps to undergo the strange and subtle phenomenon of filamentation

A review of gear housing dynamics and acoustics literature

A review of the available literature on gear housing vibration and noise reduction is presented. Analytical and experimental methodologies used for bearing dynamics, housing vibration and noise, mounts and suspensions, and the overall geared and housing system are discussed. Typical design guidelines as outlined by various investigators are given

Integrated control-structure design

A new approach for the design and control of flexible space structures is described. The approach integrates the structure and controller design processes thereby providing extra opportunities for avoiding some of the disastrous effects of control-structures interaction and for discovering new, unexpected avenues of future structural design. A control formulation based on Boyd's implementation of Youla parameterization is employed. Control design parameters are coupled with structural design variables to produce a set of integrated-design variables which are selected through optimization-based methodology. A performance index reflecting spacecraft mission goals and constraints is formulated and optimized with respect to the integrated design variables. Initial studies have been concerned with achieving mission requirements with a lighter, more flexible space structure. Details of the formulation of the integrated-design approach are presented and results are given from a study involving the integrated redesign of a flexible geostationary platform