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At least 523 records · Page 29

Design of optimal partial state feedback controllers for linear systems in stochastic environments

The problem of obtaining an optimal control law, which is constrained to be a feedback of the available measurements, is considered for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite duration cases. The feedback gain matrices are constrained to be constant for the infinite duration cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. Computational aspects are discussed via application to two continuous time processes, including a helicopter/slung load system subjected to measurement noise and random wind gust input.

Joshi, S. M.↗

Advances and trends in computational structural mechanics

Recent developments in computational structural mechanics are reviewed with reference to computational needs for future structures technology, advances in computational models for material behavior, discrete element technology, assessment and control of numerical simulations of structural response, hybrid analysis, and techniques for large-scale optimization. Research areas in computational structural mechanics which have high potential for meeting future technological needs are identified. These include prediction and analysis of the failure of structural components made of new materials, development of computational strategies and solution methodologies for large-scale structural calculations, and assessment of reliability and adaptive improvement of response predictions.

Noor, A. K.↗

Longitudinal-control design approach for high-angle-of-attack aircraft

This paper describes a control synthesis methodology that emphasizes a variable-gain output feedback technique that is applied to the longitudinal channel of a high-angle-of-attack aircraft. The aircraft is a modified F/A-18 aircraft with thrust-vectored controls. The flight regime covers a range up to a Mach number of 0.7; an altitude range from 15,000 to 35,000 ft; and an angle-of-attack (alpha) range up to 70 deg, which is deep into the poststall region. A brief overview is given of the variable-gain mathematical formulation as well as a description of the discrete control structure used for the feedback controller. This paper also presents an approximate design procedure with relationships for the optimal weights for the selected feedback control structure. These weights are selected to meet control design guidelines for high-alpha flight controls. Those guidelines that apply to the longitudinal-control design are also summarized. A unique approach is presented for the feed-forward command generator to obtain smooth transitions between load factor and alpha commands. Finally, representative linear analysis results and nonlinear batch simulation results are provided.

Ostroff, Aaron J.↗

Hybrid state-space self-tuning control of uncertain linear systems

The paper presents a hybrid state-space self-tuner using a new dual-rate sampling scheme for digital adaptive control of continuous-time uncertain linear systems. A state-space-based recursive least-squares algorithm, together with a variable forgetting factor, is used for direct estimations of both the equivalent discrete-time uncertain linear system parameters and the associated discrete-time state of a continuous-time uncertain linear system from the sampled input and output data. An analogue optimal regional pole-placement design method is used for designing an optimal observer-based analogue controller. A suboptimal observer-based digital controller is then designed from the designed analogue controller using digital redesign technique. To enhance the robustness of parameter identification and state estimation algorithms, a dynamic bound for a class of uncertain bilinear parameters and a fast-rate digital controller are developed at each fast-sampling period. Also, to accommodate computation loads and computation delay for developing the advanced hybrid self-tuner, the designed analogue controller and observer gains are both updated at each slow-sampling period. This control technique has been successfully applied to benchmark control problems.

Shieh, L. S.↗

Development of an hp-version finite element method for computational optimal control

The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element.

Hodges, Dewey H.↗

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

The Pheno-Evo Model: Evolution of Microbial Phenotypic Diversity in 2D Space

Biologists appreciate microbes for their simplicity and predictability: we assume that a population of genetically identical cells in a uniform environment will all behave the same way. While this assumption is often useful, it is also often wrong. Not only might microbes in a clonal population act differently from one another, the differences may be categorical (growing v. non-growing; toxin-sensitive v. tolerant), and this diversity might be an evolved trait conferring increased fitness on the population. How does such phenotypic heterogeneity evolve? And how does a population find the optimal distribution of phenotypes for a given environment? Efforts at modeling microbial phenotypic heterogeneity often focus on populations with two discrete phenotypic types; phenotypes in continuous distributions remain poorly explored. To address this gap and to explore the role of spatial relationships, we use agent-based modeling to simulate a phenotypically diverse population of microbial cells evolving in the presence of periodic toxic stress. Cells on patches in a 2D grid may degrade toxin, suffer damage from toxin, switch phenotype, and reproduce. An individual's phenotype its toxin degradation rate-- for which there is a tradeoff with reproduction-- and the genotype encodes the distribution of phenotypic values in the population. The rate of toxin diffusion determines how individuals influence their neighbors' environments. We examine the effects of toxin concentration, diffusion rate, and environmental predictability on the survival success of populations with different phenotype distributions, and populations' evolutionary trajectories when phenotype distribution is allowed to evolve. We conduct all simulations on the platform NetLogo, which provides a friendly interface allowing users of any experience level to tweak parameters and run their own simulations. We have also created custom tools in R for analyzing and visualizing the results of multiple runs.

microbial evolution↗

Design, Modeling and Performance Optimization of a Novel Rotary Piezoelectric Motor

This work has demonstrated a proof of concept for a torsional inchworm type motor. The prototype motor has shown that piezoelectric stack actuators can be used for rotary inchworm motor. The discrete linear motion of piezoelectric stacks can be converted into rotary stepping motion. The stacks with its high force and displacement output are suitable actuators for use in piezoelectric motor. The designed motor is capable of delivering high torque and speed. Critical issues involving the design and operation of piezoelectric motors were studied. The tolerance between the contact shoes and the rotor has proved to be very critical to the performance of the motor. Based on the prototype motor, a waveform optimization scheme was proposed and implemented to improve the performance of the motor. The motor was successfully modeled in MATLAB. The model closely represents the behavior of the prototype motor. Using the motor model, the input waveforms were successfully optimized to improve the performance of the motor in term of speed, torque, power and precision. These optimized waveforms drastically improve the speed of the motor at different frequencies and loading conditions experimentally. The optimized waveforms also increase the level of precision of the motor. The use of the optimized waveform is a break-away from the traditional use of sinusoidal and square waves as the driving signals. This waveform optimization scheme can be applied to any inchworm motors to improve their performance. The prototype motor in this dissertation as a proof of concept was designed to be robust and large. Future motor can be designed much smaller and more efficient with lessons learned from the prototype motor.

Duong, Khanh A.↗

A Discrete Component Low-Noise Preamplifier Readout for a Linear (1x16) SiC Photodiode Array

A compact, low-noise and inexpensive preamplifier circuit has been designed and fabricated to optimally readout a common cathode (1x16) channel 4H-SiC Schottky photodiode array for use in ultraviolet experiments. The readout uses an operational amplifier with 10 pF capacitor in the feedback loop in parallel with a low leakage switch for each of the channels. This circuit configuration allows for reiterative sample, integrate and reset. A sampling technique is given to remove Johnson noise, enabling a femtoampere level readout noise performance. Commercial-off-the-shelf acquisition electronics are used to digitize the preamplifier analogue signals. The data logging acquisition electronics has a different integration circuit, which allows the bandwidth and gain to be independently adjusted. Using this readout, photoresponse measurements across the array between spectral wavelengths 200 nm and 370 nm are made to establish the array pixels external quantum efficiency, current responsivity and noise equivalent power.

low-noise preamplifier↗

Localized Evaluation for Constructing Discrete Vector Fields

Topological abstractions offer a method to summarize the behavior of vector fields, but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach, which constructs a collection of pairs of simplices in the input mesh that satisfies criteria introduced by Forman's discrete Morse theory. While numerous approaches exist to compute pairs in the restricted case of the gradient of a scalar field, state-of-the-art algorithms for the general case of vector fields require expensive optimization procedures. This paper introduces a fast, novel approach for pairing simplices of two-dimensional, triangulated vector fields that do not vary in time. The key insight of our approach is that we can employ a local evaluation, inspired by the approach used to construct a discrete gradient field, where every simplex in a mesh is considered by no more than one of its vertices. Specifically, we observe that for any edge in the input mesh, we can uniquely assign an outward direction of flow. We can further expand this consistent notion of outward flow at each vertex, which corresponds to the concept of a downhill flow in the case of scalar fields. Working with outward flow enables a linear-time algorithm that processes the (outward) neighborhoods of each vertex one-by-one, similar to the approach used for scalar fields. Here, we couple our approach to constructing discrete vector fields with a method to extract, simplify, and visualize topological features. Empirical results on analytic and simulation data demonstrate drastic improvements in running time, produce features similar to the current state-of-the-art, and show the application of simplification to large, complex flows.

97 MATHEMATICS AND COMPUTING↗

Advances and trends in computational structural mechanics

The development status and applicational range of techniques in computational structural mechanics (CSM) are evaluated with a view to advances in computational models for material behavior, discrete-element technology, quality assessment, the control of numerical simulations of structural response, hybrid analysis techniques, techniques for large-scale optimization, and the impact of new computing systems on CSM. Primary pacers of CSM development encompass prediction and analysis of novel materials for structural components, computational strategies for large-scale structural calculations, and the assessment of response prediction reliability together with its adaptive improvement.

Noor, Ahmed K.↗

Linear quadratic stationkeeping on travelling ellipses

An automatic controller for Space Shuttle stationkeeping or formationkeeping is presented. The controller, which is a candidate for future on-orbit autopilot enhancement, uses a fuel 'optimized' limit cycle trajectory in a feedforward loop for precise control at nonequilibrium set points. Disturbance rejection is accomplished by a discrete time, linear quadratic regulator, which is employed for tracking of the feedforward model. Feedback gain selection is done to provide good limit cycling performance and low fuel consumption. Velocity correlations are carried out by use of a pseudo 6 degree-of-freedom jet selection scheme. Results indicate that 20 ft precision can be achieved using current sensors.

Adams, Neil J.↗

Implementation of adaptive proximate time-optimal controllers

Following a review of the Proximate Time-Optimal Servomechanism (PTOS) and the adaptive version of PTOS (APTOS), implementation techniques are described which make both algorithms practical for discrete-time control of second-order plants with real roots. The double integrator plant and the real pole plus an integrator plant are both used as examples. The effects of unmodeled dynamics on the algorithms are discussed and illustrated by simulation and experiment.

Workman, M. L.↗

Applications of wavelet-based compression to multidimensional Earth science data

A data compression algorithm involving vector quantization (VQ) and the discrete wavelet transform (DWT) is applied to two different types of multidimensional digital earth-science data. The algorithms (WVQ) is optimized for each particular application through an optimization procedure that assigns VQ parameters to the wavelet transform subbands subject to constraints on compression ratio and encoding complexity. Preliminary results of compressing global ocean model data generated on a Thinking Machines CM-200 supercomputer are presented. The WVQ scheme is used in both a predictive and nonpredictive mode. Parameters generated by the optimization algorithm are reported, as are signal-to-noise (SNR) measurements of actual quantized data. The problem of extrapolating hydrodynamic variables across the continental landmasses in order to compute the DWT on a rectangular grid is discussed. Results are also presented for compressing Landsat TM 7-band data using the WVQ scheme. The formulation of the optimization problem is presented along with SNR measurements of actual quantized data. Postprocessing applications are considered in which the seven spectral bands are clustered into 256 clusters using a k-means algorithm and analyzed using the Los Alamos multispectral data analysis program, SPECTRUM, both before and after being compressed using the WVQ program.

Bradley, Jonathan N.↗

The initial-value problem for viscous channel flows

Plane viscous channel flows are perturbed and the ensuing initial-value problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this works offers a means whereby completely arbitrary initial input can be specified without having to resort to eigenfunction expansions. The full temporal behavior, including both early time transients and the long time asymptotics, can be determined for any initial disturbance. Effects of three-dimensionality can be assessed. The bases for the analysis are: (a) linearization of the governing equations; (b) Fourier decomposition in the spanwise and streamwise directions of the flow; and (c) direct numerical integration of the resulting partial differential equations. All of the stability data that are known for such flows can be reproduced. Also, the optimal initial condition can be determined in a straight forward manner and such optimal conditions clearly reflect transient growth data that is easily determined by a rational choice of a basis for the initial conditions. Although there can be significant transient growth for subcritical values of the Reynolds number using this approach it does not appear possible that arbitrary initial conditions will lead to the exceptionally large transient amplitudes that have been determined by optimization of normal modes. The approach is general and can be applied to other classes of problems where only a finite discrete spectrum exists, such as the boundary layer for example.

Criminale, W. O.↗

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Interplanetary Mission Design Using Chemical Propulsion

The customer (scientist or project manager) most often does not want just one point solution to the mission design problem Instead, an exploration of a multi-objective trade space is required. For a typical main-belt asteroid mission the customer might wish to see the trade-space of: Launch date vs. Flight time vs. Deliverable mass, while varying the destination asteroid, planetary flybys, launch year, etcetera. To address this question we use a multi-objective discrete outer-loop which defines many single objective real-valued inner-loop problems.

Design↗