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Mechanical Engineering

1998

Brigham Young University

Articles 1 - 8 of 8

Full-Text Articles in Engineering

The Evolution Of Probability Functions In An Inelasticly Deforming Two-Phase Medium, Brent L. Adams, H. Garmestani, S. Lin Dec 1998

The Evolution Of Probability Functions In An Inelasticly Deforming Two-Phase Medium, Brent L. Adams, H. Garmestani, S. Lin

Faculty Publications

A formulation is introduced here for the evolution of correlation functions in an inelastically deforming two phase medium. Probability functions play a major role in describing the statistical distribution of different phases in a heterogeneous medium in the development of statistical continuum theory. Proper formulation of statistical continuum model for inelastic deformation requires better understanding of the evolution of the corresponding probability functions. A two point probability function representation is used to approximate the statistical correlation functions. The evolution of these functions requires the information from higher order probability functions, in this case, a three point probability function. A decomposition …

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Successive Galerkin Approximation Algorithms For Nonlinear Optimal And Robust Control, Timothy Mclain, Randal W. Beard Nov 1998

Successive Galerkin Approximation Algorithms For Nonlinear Optimal And Robust Control, Timothy Mclain, Randal W. Beard

Faculty Publications

Nonlinear optimal control and nonlinear H infinity control are two of the most significant paradigms in nonlinear systems theory. Unfortunately, these problems require the solution of Hamilton-Jacobi equations, which are extremely difficult to solve in practice. To make matters worse, approximation techniques for these equations are inherently prone to the so-called 'curse of dimensionality'. While there have been many attempts to approximate these equations, solutions resulting in closed-loop control with well-defined stability and robustness have remained elusive. This paper describes a recent breakthrough in approximating the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations. Successive approximation and Galerkin approximation methods are combined to derive …

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Nonlinear Optimal Control Design Of A Missile Autopilot, Tim Mclain, Randal W. Beard Aug 1998

Nonlinear Optimal Control Design Of A Missile Autopilot, Tim Mclain, Randal W. Beard

Faculty Publications

The application of a new nonlinear optimal control strategy to the design of missile autopilots is presented. The control approach described and demonstrated here is based upon the numerical solution of the Hamilton-Jacobi-Bellman equation by Successive Galerkin Approximation. Using this approach, feedback controllers are computed by an iterative application of a numerical Galerkin-type PDE solver. Simulation results demonstrating the application of this approach to the design of a missile autopilot are presented.

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Successive Galerkin Approximations To The Nonlinear Optimal Control Of An Underwater Robotic Vehicle, Timothy Mclain, Randal W. Beard Jul 1998

Successive Galerkin Approximations To The Nonlinear Optimal Control Of An Underwater Robotic Vehicle, Timothy Mclain, Randal W. Beard

Faculty Publications

The application of a new nonlinear optimal control strategy to the station-keeping control of an underwater robotic vehicle is considered. The control approach described and demonstrated here is based upon the numerical approximation of solutions to the Hamilton-Jacobi-Bellman equation. These solutions are computed by an iterative application of Galerkin's method. Preliminary simulation results demonstrating the application of this approach to the control of an underwater vehicle in the horizontal plane are presented.

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Development And Experimental Validation Of An Underwater Manipulator Hydrodynamic Model, Timothy W. Mclain, Stephen M. Rock Jul 1998

Development And Experimental Validation Of An Underwater Manipulator Hydrodynamic Model, Timothy W. Mclain, Stephen M. Rock

Faculty Publications

Hydrodynamic forces can be large and hence have a significant effect on the dynamic performance of underwater manipulation systems. this paper investigates these forces for a cylindrical single-link arm undergoing motions that are characteristics of a robotic manipulator. Based on flow visualization, theoretical analysis, and experimental measurements, a new model is developed that describes these forces. This model differs from previous models in that the drag and added-mass coefficients are state-dependent functions that depend on the distance traveled by the arm. A factor of four improvement in accuracy is demonstrated over standard constant-coefficient models.

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Fuel Equalized Retargeting For Separated Spacecraft Interferometry, Timothy Mclain, Randal W. Beard, Fred Y. Hadaegh Jun 1998

Fuel Equalized Retargeting For Separated Spacecraft Interferometry, Timothy Mclain, Randal W. Beard, Fred Y. Hadaegh

Faculty Publications

Motivated by NASA's proposed Deep Space 3 interferometer mission, the paper considers the problem of reorienting a constellation of spacecraft such that the total fuel distributed across the constellation is both conserved and expended uniformly. The spacecraft constellation is controlled to reorient as if it were a rigid body. Two approaches to fuel equalization are investigated. The first approach picks a point of rotation a priori that optimizes an objective function that trades off minimum-fuel maneuvers and maneuvers that equalize the fuel. Since the point of rotation is selected a priori and is fixed during the rotation, this approach is …

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A Practical Algorithm For Designing H∞ Control Laws, Timothy Mclain, Randal W. Beard Jun 1998

A Practical Algorithm For Designing H∞ Control Laws, Timothy Mclain, Randal W. Beard

Faculty Publications

We describe an approximation method for the Hamilton-Jacobi-Isaacs (HJI) equation that results in feedback control. The approximation is accomplished via a two-step successive Galerkin approximation scheme. An application of the technique to the control of the forward motion of an underwater vehicle is described.

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Determination Of The Asymmetry Parameter And Scattering Coefficient Of Turbid Media From Spatially Resolved Reflectance Measurments, Matthew R. Jones, Yukio Yamada Mar 1998

Determination Of The Asymmetry Parameter And Scattering Coefficient Of Turbid Media From Spatially Resolved Reflectance Measurments, Matthew R. Jones, Yukio Yamada

Faculty Publications

We present a technique for determining the asymmetry parameter and scattering coefficient of turbid media from spatially resolved reflectance measurements. This technique will contribute to the development of medical applications in which it is necessary to predict the distribution and propagation of light in tissue. Based on Monte Carlo simulations, we derived correlations which relate the reduced scattering coefficient and the asymmetry parameter to the relative reflectance curve. Initial estimates of the optical properties are obtained from these correlations. Final values are obtained by adjusting the optical parameters and repeating the Monte Carlo simulations until the simulated reflectance pattern matches …

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