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At least 289 records · Page 16

Modeling and control of flexible structures

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Gibson, J. S.↗

The effect of additional design parameters on the LQR based design of a control/structural system

A multiobjective cost function that includes a form of the standard LQR regulator cost and its partial variation with respect to the additional design parameters is presented in connection with the design of an orbiting control/structural system. Simple models of uniform solid and tubular beams are demonstrated with two typical additional payload masses, i.e., symmetrically distributed and asymmetrically distributed, with respect to the center of the beam. By regarding the transient response of pitch angle and free-free beam deformations in the orbital plane, the optimal outer diameter of the beam and all feedback control can be determined by numerical analysis with this multicriterial approach. It is concluded that the multicriteria design approach should give better results from both the structural designer's and the control designer's standpoints.

Bainum, Peter M.↗

Fuel optimal propulsive reboost of flexible spacecraft

This paper presents for the first time an exact solution to the fuel optimal propulsive reboost problem for flexible spacecraft. The spacecraft undergoes rigid-body motion and flexible-body motion and reboost is achieved propulsively through the use of reaction control jets. The exact fuel optimal solution to the associated minimization problem is found numerically based on an adaptive grid bisection search. The reboost of the floating harmonic oscillator reveals properties of the fuel optimal solution. Nondimensional plots of minimum fuel versus maneuver time expose the nature of the solution classes depending on the maneuver time. Some very interesting properties are observed, among them, the shifting of impulses to the smaller oscillator mass, and comparisons are made with near fuel optimal solutions obtained by other investigators.

Silverberg, Larry↗

Design of a model following, state variable feedback controller for the X-14 VTOL aircraft

A model-following, state variable feedback controller is designed for the roll axis of the X-14. The approach is to define a criterion on roll axis performance and to find the gradient of this criterion in the space of parameters (the feedback gains) of the controller. The gradient is then used in a conjungate gradient descent sequence to numerically optimize the parameters.

Hasdorff, L.↗

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.

Liu, K.↗

Robust eigenstructure assignment by a projection method - Applications using multiple optimization criteria

A methodology for robust eigenstructure assignment for multivariable feedback systems is presented. The algorithm is based upon a pole placement technique using projections onto subspaces of admissible eigenvectors. New ideas are introduced to generate target (desired) sets of unitary eigenvectors and determine optimal feasible eigenvectors in a least-square sense. Useful connections are established between the pole-placement by independent modal space control and the method introduced in this paper. A multicriterion optimization algorithm is also presented, which takes efficient advantage of the present eigenstructure assignment method. These developments show significant improvement over an earlier version of this algorithm in both computational cost and accuracy. This optimization process appears to be numerically robust and suitable for high-dimensional multicriterion optimizations; it is especially attractive for computer-aided design of control systems.

Rew, D. W.↗

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗

Randomized Sketching Algorithms for Low-Memory Dynamic Optimization

This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control; the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.

97 MATHEMATICS AND COMPUTING↗

Hamiltonian switching control of noisy bipartite qubit systems

Abstract We develop a Hamiltonian switching ansatz for bipartite control that is inspired by the quantum approximate optimization algorithm, to mitigate environmental noise on qubits. We demonstrate the control for a central spin coupled to bath spins via isotropic Heisenberg interactions, and then make physical applications to the protection of quantum gates performed on superconducting transmon qubits coupling to environmental two-level-systems (TLSs) through dipole-dipole interactions, as well as on such qubits coupled to both TLSs and a Lindblad bath. The control field is classical and acts only on the system qubits. We use reinforcement learning with policy gradient to optimize the Hamiltonian switching control protocols, using a fidelity objective for specific target quantum gates. We use this approach to demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) in the majority of our test cases and showing improvement beyond this to values of 0.999 999 999 (nine nines) upon a subsequent optimization by GRadient Ascent Pulse Engineering (GRAPE). We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite control of quantum gates.

Physics↗

Finite difference numerical methods for boundary control problems governed by hyperbolic partial differential equations

This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.

Chen, G.↗

Singular-Arc Time-Optimal Trajectory of Aircraft in Two-Dimensional Wind Field

This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a two-dimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control variable. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are computed using a shooting method with known starting values on the singular arc The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. The analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.

Nguyen, Nhan↗

Energy management of three-dimensional minimum-time intercept

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.

Kelley, H. J.↗

Multivariate Bayesian Optimization of CoO Nanoparticles for CO 2 Hydrogenation Catalysis

The hydrogenation of CO 2 holds promise for transforming the production of renewable fuels and chemicals. However, the challenge lies in developing robust and selective catalysts for this process. Transition metal oxide catalysts, particularly cobalt oxide, have shown potential for CO 2 hydrogenation, with performance heavily reliant on crystal phase and morphology. Achieving precise control over these catalyst attributes through colloidal nanoparticle synthesis could pave the way for catalyst and process advancement. Yet, navigating the complexities of colloidal nanoparticle syntheses, governed by numerous input variables, poses a significant challenge in systematically controlling resultant catalyst features. We present a multivariate Bayesian optimization, coupled with a data-driven classifier, to map the synthetic design space for colloidal CoO nanoparticles and simultaneously optimize them for multiple catalytically relevant features within a target crystalline phase. The optimized experimental conditions yielded small, phase-pure rock salt CoO nanoparticles of uniform size and shape. These optimized nanoparticles were then supported on SiO 2 and assessed for thermocatalytic CO 2 hydrogenation against larger, polydisperse CoO nanoparticles on SiO 2 and a conventionally prepared catalyst. The optimized CoO/SiO 2 catalyst consistently exhibited higher activity and CH 4 selectivity (ca. 98%) across various pretreatment reduction temperatures as compared to the other catalysts. This remarkable performance was attributed to particle stability and consistent H* surface coverage, even after undergoing the highest temperature reduction, achieving a more stable catalytic species that resists sintering and carbon occlusion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Numerical Modeling & Optimization of the iProTech Pitching Inertial Pump (PIP) Wave Energy Converter (WEC) (CRADA Final Report)

This project represents a continuation of the collaboration between iProTech and NLR to simulate, optimize and design the iProTech Pitching Inertial Pump (PIP) device. The objectives of this TEAMER project are twofold: 1. Refining the physical characteristics of the existing iProTech PIP WEC-Sim model to enhance the model’s fidelity and include controllable components. Key model enhancements target the inclusion of Coulomb friction, the introduction of a controllable bypass valve, and the replacement of traditional check valves with advanced motorized ones. 2. Exploring traditional and advanced control algorithms. From traditional methods like latching control to cutting-edge reinforcement learning (RL) algorithms, the goal is to ensure the PIP device's adaptability and optimal performance across a range of ocean conditions. NLR is tasked with augmenting the WEC-Sim model and implementing the control algorithms, culminating in performance comparison analyses. iProTech will update their existing 3D models, advise on model improvements, and determine crucial system metrics. WEC-Sim, developed in MATLAB/SIMULINK with Simscape Multibody, is the main piece of software that will be used in this project. Coupled with the MATLAB RL Toolbox, it offers a robust platform for in-depth simulation and optimization of the iProTech PIP device. Building on previous work to explore the PIP design space and optimize its geometry, mass distribution, center of gravity and other key parameters, this project aims to refine iProTech’s existing numerical models and develop effective control algorithms that can seamlessly integrate into their future hardware testing campaigns.

16 TIDAL AND WAVE POWER↗

Southwest Wind Power R&D Test Site Development at the National Wind Technology Center (CRADA CRD-12-00472 Final Report)

Southwest Windpower, Inc. (SWWP) has been designing and distributing small wind turbines for more than 22 years and is the recognized global leader in the design, manufacturing and distribution of small wind systems (400-3000 watts). The company has been a pioneer in the development of wind technology and has built and shipped more than 170,000 wind turbines to over 120 countries worldwide. Headquartered in Flagstaff AZ, SWWP has sales representatives in over 88 countries. Applications for SWWP systems include residential homes, commercial properties, micro grids, remote cabins, telecom transmitters, offshore platforms, water pumping and sailboats. In addition, U.S. Department of Defense uses SWWP’s products in Forward Operating Bases (FOB’s), USGS uses them for remote monitoring of glacier movements and the CIA uses them to provide power seismic monitoring. Today, SWWP plans development of new technologies to address distributed energy market needs and become even more aggressive in international markets. This strategy includes extensive Research, Development, Demonstration & Deployment (RDD&D) activities to improve existing production line into more simple, reliable, and cost-effective wind turbine systems. Important part of such activities is the field testing of the new systems, which should provide: (i) validation of the reliable operation of hardware and software; (ii) validation of numerical models of the system and its components; (iii) field comparison of various control and optimization strategies; (iv) customized reliability testing; (v) customized monitoring and analysis testing; and (vi) IEC certification testing (vii) filed demonstration of system performance and reliability. Such field testing facility should encompass multiple towers and appropriate data acquisition systems. SWWP is exploring to move part of the engineering department to Colorado, and execute its RDD&D strategies in this new location. Partnership with NREL will provide great insights into SWWP’s RDD&D processes and more efficient commercialization by utilizing NWTC as the field testing site, and working close with NREL personnel. NWTC is ideally suited to strain the design. NREL is very experienced with customized and IEC testing. During this project, Southwest Windpower aims to improve the value proposition of distributed renewable energy, and make it a competitive choice in the energy markets. As of today, more then 170,000 small wind turbines, manufactured in the U.S., are installed in more then 180 countries. With the improved value proposition, Southwest Windpower wants to create and address new market needs, substantially increase its sales domestically and internationally, which should have positive impact on the creation of American jobs, competitiveness of U.S. economy, export or U.S. products, and the use of renewable energy.

17 WIND ENERGY↗

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.↗

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.↗