Nonlinear feedback design: Optimal responses by tensor analysis
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New design proposed for highly-efficient 34-m-diameter millimeter-wavelength antennas of NASA's Deep Space Network. Incorporates axial beam waveguide, BWG, and improved structure to maintain shape and alignment of reflecting surfaces. General approach to conceptual construction of structure to modularize overall system so critical constraint conditions pertaining to microwave optics and structural performance satisfied. Design retrofitted to existing NASA Deep Space Network 34-m antennas, or used as basis to build large ground-based steerable antennas. Engineering concepts involved in design adapted to design of other large, steerable antennas for telecommunications, radio astronomy, and military uses.
Optimal actuator placement schemes are presently studied for cases of adaptive truss precision control and prestressing control, with a view to the maximization of actuator efficiencies. In statically indeterminate truss structures, the optimal placement criteria and techniques differ, depending on whether the primary determinate structure is known. A suboptimal actuator-placement solution to the global optimization problem which combines displacement control and prestressing control is suggested, by combining the separate displacement control and prestressing control optimization results. Attention is given to the results obtained for the illustrative case of a two-bay, three-dimensional precision truss structure.
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A new telecommunications service for location determination via satellite is being proposed for the continental USA and Europe, which provides users with the capability to find the location of, and communicate from, a moving vehicle to a central hub and vice versa. This communications system is expected to operate in an extremely noisy channel in the presence of fading. In order to achieve high levels of data integrity, it is essential to employ forward error correcting (FEC) encoding and decoding techniques in such mobile satellite systems. A constraint length k = 7 FEC decoder has been implemented in a single chip for such systems. The single chip implementation of the maximum likelihood decoder helps to minimize the cost, size, and power consumption, and improves the bit error rate (BER) performance of the mobile earth terminal (MET).
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In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.
Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.
This paper presents a design methodology for a laminated composite stiffened panel, subjected to multiple in-plane loads and bending moments. Design variables include the skin and stiffener ply orientation angles and stiffener geometry variables. Optimum designs are sought which minimize structural weight and satisfy mechanical performance requirements. Two types of mechanical performance requirements are placed on the panel, maximum strain and minimum strength. Minimum weight designs are presented which document that the choice of mechanical performance requirements cause changes in the optimum design. The effects of lay-up constraints which limit the ply angles to user specified values, such as symmetric or quasi-isotropic laminates, are also investigated.
An approximate structural eigenvalue/vector analysis technique which uses eigensensitivities in a truncated Taylor series expression is presented. It is shown that this technique can provide the computational efficiency urgently needed for large scale control-structure optimization problems. In addition, a unified formulation and solution approach for calculating eigenvalue and eigenvector derivatives of the real symmetric structural eigenvalue problem is presented.
A nonlinear constrained optimization of a hydrodynamic bearing was performed yielding three main variables: radial clearance, bearing length to diameter ratio, and lubricating oil viscosity. As an objective function a combined model of temperature rise and oil supply has been adopted. The optimized model of the bearing has been simulated for population of 1000 cases using Monte Carlo statistical method. It appeared that the so called 'optimal solution' generated more than 50 percent of failed bearings, because their minimum oil film thickness violated stipulated minimum constraint value. As a remedy change of oil viscosity is suggested after several sensitivities of variables have been investigated.
This paper discusses certain connections between nonlinear programming algorithms and the formulation of optimization problems for systems governed by state constraints. The major points of this paper are the detailed calculation of the sensitivities associated with different formulations of optimization problems and the identification of some useful relationships between different formulations. These relationships have practical consequences; if one uses a reduced basis nonlinear programming algorithm, then the implementations for the different formulations need only differ in a single step.
Recently, a turbine-brush was analyzed based on the energy conservation and the force momentum equation with an empirical relationship of the drag coefficient. An equation was derived to predict the rotational speed of the turbine-brush in terms of the blade angle, number of blades, rest of geometries of the turbine-brush and the incoming velocity. Using the observed flow conditions, drag coefficients were determined. Based on the experimental values as boundary conditions, the turbine-brush flows were numerically simulated to understand first the nature of the flows, and to extend the observed drag coefficient to a flow without holding the turbine-brush.
The design criteria for an optimum prosthetic-aortic leaflet valve are a smooth washout in the valve cusps, minimal leaflet stress, minimal transmembrane pressure for the valve to open, an adequate lifetime (for a given blood-compatible leaflet material's fatigue data). A rigorous design analysis is presented to obtain the prosthetic tri-leaflet aortic valve leaflet's optimum design parameters. Four alternative optimum leaflet geometries are obtained to satisfy the criteria of a smooth washout and minimal leaflet stress. The leaflet thicknesses of these four optimum designs are determined by satisfying the two remaining design criteria for minimal transmembrane opening pressure and adequate fatigue lifetime, which are formulated in terms of the elastic and fatigue properties of the selected leaflet material - Avcothane-51 (of the Avco-Everett Co. of Massachusetts). Prosthetic valves are fabricated on the basis of the optimum analysis and the resulting detailed engineering drawings of the designs are also presented in the paper.