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At least 55 records · Page 3

Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N = 2, additive Runge-Kutta ARK2 methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK2 methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z(exp [I]) goes to infinity, and retain high stability efficiency in the absence of stiffness, z(exp [I]) goes to zero. Extrapolation-type stage-value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK2 error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods while offering error control and stage-value predictors.

Kennedy, Christopher A.↗

Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one- dimensional convection-diffusion-reaction (CDR) equations. Accuracy, stability, conservation, and dense-output are first considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, (N = 2), additive Runge-Kutta (ARK(sub 2)) methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms of the partitioned method are of equal order to those of the elemental methods. Derived ARK(sub 2) methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z['] yields -infinity, and retain high stability efficiency in the absence of stiffness, z['] yield 0. Extrapolation-type stage- value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK(sub 2) error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK(sub 2) methods.

Kennedy, Christopher A.↗

Rotary balance data for a typical single-engine general aviation design for an angle-of-attack range of 20 to 90 deg. 3: Influence of control deflection on predicted model D spin modes

The influence of control deflections on the rotational flow aerodynamics and on predicted spin modes is discussed for a 1/6-scale general aviation airplane model. The model was tested for various control settings at both zero and ten degree sideslip angles. Data were measured, using a rotary balance, over an angle-of-attack range of 30 deg to 90 deg, and for clockwise and counter-clockwise rotations covering an omegab/2V range of 0 to 0.5.

Ralston, J. N.↗

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Managing Flap Vortices via Separation Control

A pilot study was conducted on a flapped semi-span model to investigate the concept and viability of near-wake vortex management by means of boundary layer separation control. Passive control was achieved using a simple fairing and active control was achieved via zero mass-flux blowing slots. Vortex sheet strength, estimated by integrating surface pressures, was used to predict vortex characteristics based on inviscid rollup relations and vortices trailing the flaps were mapped using a seven-hole probe. Separation control was found to have a marked effect on vortex location, strength, tangential velocity, axial velocity and size over a wide range of angles of attack and control conditions. In general, the vortex trends were well predicted by the inviscid rollup relations. Manipulation of the separated flow near the flap edges exerted significant control over either outboard or inboard edge vortices while producing small lift and moment excursions. Unsteady surface pressures indicated that dynamic separation and attachment control can be exploited to perturb vortices at wavelengths shorter than a typical wingspan. In summary, separation control has the potential for application to time-independent or time-dependent wake alleviation schemes, where the latter can be deployed to minimize adverse effects on ride-quality and dynamic structural loading.

Greenblatt, David↗

Management of Vortices Trailing Flapped Wings via Separation Control

A pilot study was conducted on a flapped semi-span model to investigate the concept and viability of near-wake vortex management via separation control. Passive control was achieved by means of a simple fairing and active control was achieved via zero mass-flux blowing slots. Vortex sheet strength, estimated by integrating surface pressure ports, was used to predict vortex characteristics by means of inviscid rollup relations. Furthermore, vortices trailing the flaps were mapped using a seven-hole probe. Separation control was found to have a marked effect on vortex location, strength, tangential velocity, axial velocity and size over a wide range of angles of attack and control conditions. In general, the vortex trends were well predicted by the inviscid rollup relations. Manipulation of the separated flow near the flap edges exerted significant control over both outboard and inboard edge vortices while producing negligible lift excursions. Dynamic separation and attachment control was found to be an effective means for dynamically perturbing the vortex from arbitrarily long wavelengths down to wavelengths less than a typical wingspan. In summary, separation control has the potential for application to time-independent or time-dependent wake alleviation schemes, where the latter can be deployed to minimize adverse effects on ride-quality and dynamic structural loading.

Greenblatt, David↗

Averaging analysis of adaptive control algorithms

The method of averaging is used to analyze discrete-time indirect adaptive control. The analysis focuses on various prediction-error-driven identification algorithms coupled with a general linear control law. The plant is not required to be in the model set of the identifier, which accounts for systems with unmodeled plant dynamics. Exogenous input signals including known command signals and unknown disturbances are also included. Both gradient and Newton-based algorithms are considered.

Phillips, Stephen M.↗

Navier-Stokes calculations and turbulence modeling in the trailing edge region of a circulation control airfoil

The accurate prediction of turbulent flows over curved surfaces in general and over the trailing edge region of circulation control airfoils in particular requires the coupled efforts of turbulence modelers, numerical analysts and experimentalists. The purpose of the research program in this area is described. Then, the influence on turbulence modeling of the flow characteristics over a typical circulation control wing is discussed. Next, the scope of this effort to study turbulence in the trailing edge region of a circulation control airfoil is presented. This is followed by a brief overview of the computation scheme, including the grid, governing equations, numerical method, boundary conditions and turbulence models applied to date. Then, examples of applications of two algebraic eddy viscosity models to the trailing edge region of a circulation control airfoil is presented. The results from the calculations is summarized, and conclusions drawn based on examples. Finally, the future directions of the program is outlined.

Viegas, John R.↗

Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.

97 MATHEMATICS AND COMPUTING↗

Transport and confinement physics: Chapter 2 of the special issue: on the path to tokamak burning plasma operation

Progress in physics understanding and theoretical model development of plasma transport and confinement (TC) in the ITPA TC Topical Group since the publication of the ITER Physics Basis (IPB) document (Doyle et al 2007 Nucl. Fusion 47 S18) was summarized focusing on the contributions to ITER and burning plasma prediction and control. This paper provides a general and streamlined overview on the advances that were mainly led by the ITPA TC joint experiments and joint activities for the last 15 years (see JEX/JA table in appendix). This paper starts with the scientific strategy and scope of the ITPA TC Topical group and overall picture of the major progress, followed by the progress of each research field: particle transport, impurity transport, ion and electron thermal turbulent transport, momentum transport, impact of 3D magnetic fields on transport, confinement mode transitions, global confinement, and reduced transport modeling. Cross references with other Topical Groups are given in order to highlight overlapped topics, such as the 3D effect on the plasma transport in the edge and L-H transition physics. The increasing overlap between the topical groups is a reflection of the progress on integrating the known physics into comprehensive models that are better and better able to reproduce the plasma transport. In recent years, such integration has become increasingly prevalent when considering transport from the SOL, through the edge pedestal, and into the plasma core. In the near future, increased collaboration also with the magneto-hydrodynamic and energetic particles community will be important as we approach burning plasma conditions in next-step fusion devices. A summary of remaining challenges and next steps for each research field is given in the Summary section.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Interpolation of a surface from sets of discrete height data of different statistical characteristics

This paper presents and analyzes a method for the interpolation of a unique surface from two sets of independent digital height data of differing statistical characteristics. This method is based on linear prediction and thus relies on the concepts of auto- and cross-covariance functions. The linear prediction algorithm for two sets of digital height measurements is first derived and then evaluated using the method of moving averages and bilinear interpolation for comparison. It is found that the overall root mean square interpolation errors of linear prediction are similar to those from moving averages and bilinear interpolation. This accuracy performance, together with the well known potential for controlled filtering of measuring errors and good-behavior in areas of poor control, makes linear prediction a versatile and general method for interpolating a unique surface from two sets of digital height data, with applications in photogrammetric mapping, remote sensing, and other fields.

Leberl, F.↗

General Aviation Technology Conference, Hampton, VA, July 10-12, 1984, Technical Papers

The present conference on general aviation aircraft design considers the performance tradeoffs involved in two- and three-control surface aerodynamic configurations, wing design criteria for increased resistance to spins, the performance levels obtained by flight and wind tunnel tests of an 'electroimpulse' deicing system, and the chracteristics of lightning strikes experienced by the NASA F-106B research aircraft. Also considered are the application of speech recognition and synthesis systems to general aviation cockpits, control and display requirements for single-pilot Instrument Flight Rules, pilot interfacing with advanced avionics and automated cockpit systems, the feasibility of sidestick controllers for general aviation aircraft, the acoustic prediction methods incorporated by the NASA Generalized Advanced Propeller Analysis System, and the adhesively bonded structure of the Citation II business jet aircraft.

Source record↗

Recent observations of high voltage spacecraft-environment interaction at LEO altitudes using sounding rockets

The paper addresses the subject of the interaction of positively and negatively charged bodies with the terrestrial ionosphere at low earth orbit altitudes. Data from two recent sounding rocket flights are used to establish that the current collected by exposed conductors biassed positively at up to 45kV relative to the ionospheric plasma generally follow predictions which account for strong control of electron flow by the geomagnetic field. If the biased structure is in the vicinity of disturbing influences such as an emitted charged particle beam, or locally enhanced gas pressure, then large deviations from the space-charge-limited return currents occur.

Raitt, W. J.↗

An Investigation of the Low-speed Stability and Control Characteristics of Swept-forward and Swept-back Wing in the Ames 40- by 80-foot Wind Tunnel

An investigation has been made at large scale of the characteristics of highly swept wings. Data were obtained at several angles of sideslip on wings having angles of sweep of plus or minus 45 degrees, plus or minus 30 degrees, and 0 degrees. The airfoil sections of the wings varied from approximately NACA 0015 at the root to NACA 23009 at the tip. Each wing was investigated with flaps under flection, partial-span split flaps deflected 60 degrees, full-span split flaps defected 60 degrees and split-flap-type ailerons deflected plus or minus 15 degrees. Values of maximum lift were obtained at Reynolds numbers raging from 5.7 to 9.2 times 10 to the 6th power. In this report the summarized results are compared with the predictions made by use of the simplified theory for the effect of sweep and with existing small-scale data. The basic wind-tunnel results from which these summary data were taken are included in an appendix. The primary problems accompanying the use of weep as revealed by this investigation are the loss in maximum lift, the high effective dihedral, and the sharp reduction in lateral-control effectiveness. In general, simple theory enables good predictions to be made of the gross effects of sweep but further refinements are necessary to obtain the accuracy required for design purposes. In cases where comparisons can be made, the indications are that, as sweep increases, scale effects diminish and large-scale results approach small-scale results.

Mccormack, Gerald M↗

Automatic releveling of calibration stands for wind tunnel force and moment measurement instrumentation

Wind tunnel force and moment measuring instrumentation at NASA LaRC are calibrated by applying NIST certified dead loads, to generate forces and moments in three orthogonal axes, in twenty five percent increments, up to full-load and down to no-load in a nine point continuous procedure, using specially built calibration stands. The measuring instruments deflect upon the application of loads. These deflections must be cancelled to minimize loading interactions. The older calibration stands, integrated with AC induction motors, or DC motors, have provisions for manually releveling the loading point after each load. A newer stand, with integrated DC stepper motors, relevels automatically under software control. It was proposed to extend automation to the old stands. An algorithm to control the unwieldy induction motors to relevel a calibration stand, to within two arcseconds of horizontal direction automatically, was developed. The system developed uses coasting prediction and load adaptation in a general type robust stability control configuration with noncoincidental feedback. Automatic releveling cuts the releveling time to approximately half of the time required to do it manually. The principal constraint for shorter times is the time constant of the angular position feedback transducer.

Perazza, Manuel Rodriguez↗

Artificial neural network implementation of a near-ideal error prediction controller

A theory has been developed at the University of Virginia which explains the effects of including an ideal predictor in the forward loop of a linear error-sampled system. It has been shown that the presence of this ideal predictor tends to stabilize the class of systems considered. A prediction controller is merely a system which anticipates a signal or part of a signal before it actually occurs. It is understood that an exact prediction controller is physically unrealizable. However, in systems where the input tends to be repetitive or limited, (i.e., not random) near ideal prediction is possible. In order for the controller to act as a stability compensator, the predictor must be designed in a way that allows it to learn the expected error response of the system. In this way, an unstable system will become stable by including the predicted error in the system transfer function. Previous and current prediction controller include pattern recognition developments and fast-time simulation which are applicable to the analysis of linear sampled data type systems. The use of pattern recognition techniques, along with a template matching scheme, has been proposed as one realizable type of near-ideal prediction. Since many, if not most, systems are repeatedly subjected to similar inputs, it was proposed that an adaptive mechanism be used to 'learn' the correct predicted error response. Once the system has learned the response of all the expected inputs, it is necessary only to recognize the type of input with a template matching mechanism and then to use the correct predicted error to drive the system. Suggested here is an alternate approach to the realization of a near-ideal error prediction controller, one designed using Neural Networks. Neural Networks are good at recognizing patterns such as system responses, and the back-propagation architecture makes use of a template matching scheme. In using this type of error prediction, it is assumed that the system error responses be known for a particular input and modeled plant. These responses are used in the error prediction controller. An analysis was done on the general dynamic behavior that results from including a digital error predictor in a control loop and these were compared to those including the near-ideal Neural Network error predictor. This analysis was done for a second and third order system.

Mcvey, Eugene S.↗

Formations of Tethered Spacecraft as Stable Platforms for Far IR and Sub-mm Astronomy

In this paper we describe current research in tethered formations for interferometry, and a roadmap to demonstrating the required key technologies via on-ground and in-orbit testing. We propose an integrated kilometer-size tethered spacecraft formation flying concept which enables Far IR and Sub-mm astronomy observations from space. A rather general model is used to predict the dynamics, control, and estimation performance of formations of spacecraft connected by tethers in LEO and deep space. These models include the orbital and tethered formation dynamics, environmental models, and models of the formation estimator/controller/commander. Both centralized and decentralized control/sensing/estimation schemes are possible, and dynamic ranges of interest for sensing/control are described. Key component/subsystem technologies are described which need both ground-based and in-orbit demonstration prior to their utilization in precision space interferometry missions using tethered formations. Defining an orbiting formation as an ensemble of orbiting spacecraft performing a cooperative task, recent work has demonstrated the validity of the tethering the spacecraft to provide both the required formation rigidity and satisfy the formation reconfiguration needs such as interferometer baseline control. In our concept, several vehicles are connected and move along the tether, so that to reposition them the connecting tether links must vary in length. This feature enables variable and precise baseline control while the system spins around the boresight. The control architecture features an interferometer configuration composed of one central combiner spacecraft and two aligned collector spacecraft. The combiner spacecraft acts as the formation leader and is also where the centralized sensing and estimation functions reside. Some of the issues analyzed with the model are: dynamic modes of deformation of the distributed structure, architecture of the formation sensor, and sources of dynamical perturbation that need to be mitigated for precision operation in space. Examples from numerical simulation of an envisioned scenario in heliocentric orbit demonstrate the potential of the concept for space interferometry.

Quadrelli, Marco B.↗