Optimal controllers for finite wordlength implementation

When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exists realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the Linear Quadratic Gaussian (LQG) theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision the separation principle does not hold

Sensor/Actuator Selection for the Constrained Variance Control Problem

The problem of designing a linear controller for systems subject to inequality variance constraints is considered. A quadratic penalty function approach is used to yield a linear controller. Both the weights in the quadratic penalty function and the locations of sensors and actuators are selected by successive approximations to obtain an optimal design which satisfies the input/output variance constraints. The method is applied to NASA's 64 meter Hoop-Column Space Antenna for satellite communications. In addition the solution for the control law, the main feature of these results is the systematic determination of actuator design requirements which allow the given input/output performance constraints to be satisfied

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist

Control by model error estimation

Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST)

Linearized dynamical model for the NASA/IEEE SCOLE configuration

The linearized equation of motion for the NASA/IEEE SCOLE configuration are developed. The derivation is based on the method of Lagrange and the equations are assembled into matrix second order form

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.Comment: 13 pages, 10 figure

The effect of cation order on the elasticity of omphacite from atomistic calculations

Omphacite, a clinopyroxene mineral with two distinct crystallographic sites, M1 and M2, and composition intermediate between diopside and jadeite, is abundant throughout the Earth's upper mantle, and is the dominant mineral in subducted oceanic crust. Unlike the end-members, omphacite exists in two distinct phases, a P2/n ordered phase at low temperature and a high-temperature C2/c disordered phase. The crystal structure and full elastic constants tensor of ordered P2/n omphacite have been calculated to 15 GPa using plane-wave density functional theory. Our results show that several of the elastic constants, notably C11, C12, and C13 deviate from linear- mixing between diopside and jadeite. The anisotropy of omphacite decreases with increasing pressure and, at 10 GPa, is lower than that of either diopside or jadeite. The effect of cation disorder is investigated through force-field calculations of the elastic constants of Special Quasirandom Structures supercells with simulated disorder over the M2 sites only, and over both cation sites. These show that cation order influences the elasticity, with some components displaying particular sensitivity to order on a specific cation site. C11, C12, and C66 are sensitive to disorder on M1, while C22 is softened substantially by disorder on M2, but insensitive to disorder on M1. This shows that the elasticity of omphacite is sensitive to the degree of disorder, and hence the temperature. We expect these results to be relevant to other minerals with order-disorder phase transitions, implying that care must be taken when considering the effects of composition on seismic anisotropy

Testing and evaluation of Dacron parachute elements after exposure to ethylene oxide and simulated package loading and heat cycle

Testing Dacron parachute components and assemblies by exposure to ethylene oxide sterilization, simulated package loading, and heat cycl

Childhood and the politics of scale: Descaling children's geographies?

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2008 SAGE Publications.The past decade has witnessed a resurgence of interest in the geographies of children's lives, and particularly in engaging the voices and activities of young people in geographical research. Much of this growing body of scholarship is characterized by a very parochial locus of interest — the neighbourhood, playground, shopping mall or journey to school. In this paper I explore some of the roots of children's geographies' preoccupation with the micro-scale and argue that it limits the relevance of research, both politically and to other areas of geography. In order to widen the scope of children's geographies, some scholars have engaged with developments in the theorization of scale. I present these arguments but also point to their limitations. As an alternative, I propose that the notion of a flat ontology might help overcome some difficulties around scalar thinking, and provide a useful means of conceptualizing sociospatiality in material and non-hierarchical terms. Bringing together flat ontology and work in children's geographies on embodied subjectivity, I argue that it is important to examine the nature and limits of children's spaces of perception and action. While these spaces are not simply `local', they seldom afford children opportunities to comment on, or intervene in, the events, processes and decisions that shape their own lives. The implications for the substance and method of children's geographies and for geographical work on scale are considered