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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Computer aided design of digital controller for radial active magnetic bearings

A five degree of freedom Active Magnetic Bearing (AMB) system is developed which is controlled by digital controllers. The model of the radial AMB system is linearized and the state equation is derived. Based on the state variables feedback theory, digital controllers are designed. The performance of the controllers are evaluated according to experimental results. The Computer Aided Design (CAD) method is used to design controllers for magnetic bearings. The controllers are implemented with a digital signal processing (DSP) system. The control algorithms are realized with real-time programs. It is very easy to change the controller by changing or modifying the programs. In order to identify the dynamic parameters of the controlled magnetic system, a special experiment was carried out. Also, the online Recursive Least Squares (RLS) parameter identification method is studied. It can be realized with the digital controllers. Online parameter identification is essential for the realization of an adaptive controller.

Cai, Zhong↗
DOE OSTI2023

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Attitude stability of a spinning spacecraft during appendage deployment/retraction

The work presented is motivated by the need for a national satellite rescue policy, not the ad hoc policy now in place. In studying different approaches for a national policy, the issue of capture and stabilization of a tumbling spacecraft must be addressed. For a rescue mission involving a tumbling spacecraft, it may be advantageous to have a rescue vehicle which is compact and 'rigid' during the rendezvous/capture phase. After capture, passive stabilization techniques could be utilized as an efficient means of detumbling the resulting system (i.e., both the rescue vehicle and captures spacecraft). Since the rescue vehicle is initially compact and 'rigid,' significant passive stabilization through energy dissipation can only be achieved through the deployment of flexible appendages. Once stabilization is accomplished, retraction of the appendages before maneuvering the system to its final destination may also prove advantageous. It is therefore of paramount interest that we study the effect of appendage deployment/retraction on the attitude stability of a spacecraft. Particular interest should be paid to appendage retraction, since if this process is destabilizing, passive stabilization as proposed may not be useful. Over the past three decades, it has been an 'on-again-off-again affair' with the problem of spacecraft appendage deployment. In most instances, these studies have been numerical simulations of specific spacecraft configurations for which there were specific concerns. The primary focus of these studies was the behavior of the appendage during deployment; the effects of appendage retraction was considered only in one of these studies. What is missing in the literature is a thorough study of the effects of appendage deployment/retraction on the attitude stability of a spacecraft. This paper presents a rigorous analysis of the stability of a spinning spacecraft during the deployment or the retraction of an appendage. The analysis is simplified such that meaningful insights into the problem can be inferred; it is not overly simplified such that critical dynamical behavior is neglected. The system is analyzed assuming that the spacecraft hub is rigid. The appendage deployment mechanism is modeled as a point mass on a massless rod whose length undergoes prescribed changes. Simplified flexibility effects of the appendage are included. The system is examined for stability by linearizing the equations in terms of small deviations from steady, noninterfering coning motion. Routh's procedure for analyzing small deviations from steady motion in dynamical systems is utilized in the analysis. The system of equations are nondimensionalized to facilitate parametric studies. The results are presented in terms of a reduced number of nondimensional parameters so that some general conclusions may be drawn. Verification of the linear analysis is presented through numerical simulations of the complete nonlinear, nonautonomous, coupled equations.

Fitz-Coy, Norman↗
NASA NTRS1975

Error magnitude estimation in model-reference adaptive systems

A second order approximation is derived from a linearized error characteristic equation for Lyapunov designed model-reference adaptive systems and is used to estimate the maximum error between the model and plant states, and the time to reach this peak following a plant perturbation. The results are applicable in the analysis of plants containing magnitude-dependent nonlinearities.

Colburn, B. K.↗
NASA NTRS1990

Algorithm for "Bang-Bang" Control Laws

Switching times updated to minimize errors in final positions. Algorithm computes "bang-bang" control laws for single- or multiple-input systems, both those describable by linear dynamical equations and those describable by nonlinear dynamical equations that are linear in control vectors. Algorithm needed because analytical solutions of "bang-bang" control problems intractable for all but simplest systems.

Wen, John Ting-Yung↗
NASA NTRS1974

Discretized partial differential equations - Examples of control systems defined on modules

The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.

Brockett, R. W.↗
NASA NTRS1990

Stabilization and control of distributed systems with time-dependent spatial domains

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.

Wang, P. K. C.↗
DOE OSTI2023

Modeling diffusion and types I-V sorption of water vapor in heterogeneous systems

Here, a sorption and diffusion model is developed using a mobile-immobile decomposition of the vapor concentration. Henry’s mode represents the mobile species which diffuses through the solid, while Langmuir and pooling modes represent possible immobilization processes that cause nonlinearities in sorption capacity. The model can simulate the five classical sorption types and can incorporate additional dynamics compared to models based on thermodynamic equilibrium. Additionally, the framework allows for discontinuities in material properties encountered in multi-material systems. The resulting non-linear coupled equations are solved by employing a finite element method to discretize in space, and a backward Euler method to discretize in time. The discretized system of equations is solved via a Newton-type iteration scheme at each time-step. Four different materials are parameterized for the model, which are then used in examples to demonstrate the model’s ability to capture complex sorption processes in multi-material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Planetary-scale circulations in the presence of climatological and wave-induced heating

Interaction between the large-scale circulation and the convective pattern is investigated in a coupled system governed by the linearized primitive equations. Convection is represented in terms of two components of heating: A 'climatological component' is prescribed stochastically to represent convection that is maintained by fixed distributions of land and sea and sea surface temperature (SST). An 'induced component' is defined in terms of the column-integrated moisture flux convergence to represent convection that is produced through feedback with the circulation. Each component describes the envelope organizing mesoscale convective activity. As SST on the equator is increased, induced heating amplifies in the gravest zonal wavenumbers at eastward frequencies, where positive feedback offsets dissipation. Under barotropic stratification, a critical SST of 29.5 C results in positive feedback exactly cancelling dissipation in wavenumber 1 for an eastward phase speed of 6 m/s. Sympathetic interaction between the circulation and the induced heating is the basis for 'frictional wave-Conditional Instability of the Second Kind (CISK)', which is distinguished from classical wave-CISK by rendering the gravest zonal dimensions most unstable. Under baroclinic stratification, the coupled system exhibits similar behavior. The critical SST is only 26.5 C for conditions representative of equinox, but in excess of 30 C for conditions representative of solstice. Having the form of an unsteady Walker circulation, the disturbance produced by frictional wave-CISK compares favorably with the observed life cycle of the Madden-Julian oscillation (MJO). SST above the critical value produces an amplifying disturbance in which enhanced convection coincides with upper-tropospheric westerlies and is positively correlated with temperature and surface convergence. Conversely, SST below the critical value produces a decaying disturbance in which enhanced convection coincides with upper-tropospheric easterlies and is nearly in quadrature with temperature and surface convergence. While sharing essential features with the MJO in the Eastern Hemisphere, frictional wave-CISK does not explain observed behavior in the Western Hemisphere, where the convective signal is largely absent. Comprised of Kelvin structure with the same frequency, observed behavior in the Western Hemisphere can be understood as a propagating response that is excited in and radiates away from the fluctuation of convection in the Eastern Hemisphere.

Salby, Murry L↗
NASA NTRS1988

Studies of the dynamics of the twin-lift system

A full set of equations of motion for the twin lift system, linearized about a hover trim condition were derived and presented. It is shown that this full set of equations of motion decouples into simpler sets of equations of motion if the aerodynamic coupling derivatives of the helicopters are neglected. One of these decoupled sets of equations of motion (referred to as the planar set) was studied at length. The other decoupled set (referred to as the nonplanar set) is examined here. It is shown that when the geometric configuration of the twin-lift is symmetric that a further decoupling is possible into antisymmetric and symmetric sets of equations. One set of these reduced equations of motion referred to as the antisymmetric set is directly equivalent to the longitudinal motion of a single helicopeter with a sling load. The second set, referred to as the symmetric set corresponds to the rotation of the entire system without load motion. As in the case of the planar symmetric motion, the location of the tether attachment point influences the stability of the nonplanar symmetric mode. The trend is opposite however in the nonplanar case in that an attachment point below the helicopter center of gravity gives a favorable effect on the stability. The effect is not as strong however as the unfavorable effect on the planar symmetric mode.

Curtiss, H. C., Jr.↗
NASA NTRS1983

Finite-dimensional discrete-time control of linear distributed parameter systems

Systems described by partial differential equations have an infinite-dimensional state space. Feedback control of such distributed parameter systems must be accomplished by finite-dimensional controllers to be implemented by on-line digital computers. A further practical constraint is that the controller must operate in discrete (rather than continuous) time. This paper investigates the stability of such distributed parameter feedback controllers in closed-loop with the actual system.

Balas, M. J.↗
DOE OSTI2020

Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form

We propose a one-parameter family of low-dissipation centred numerical schemes for solving hyperbolic equations in conservative or non-conservative form, using finite volume or discontinuous Galerkin finite element methods. The new schemes spring out from the multi-dimensional FORCE method and are determined by a single parameter α ≥ 1. Given an increasing sequence of real numbers 1 ≤ α 1 < α 2 < . . . < α K , there corresponds a sequence of numerical schemes with stability restriction associated to a decreasing sequence of Courant numbers 1 > c 1 > c 2 > . . . > c K > 0 and a decreasing sequence of corresponding numerical viscosity functions d 1 > d 2 > . . . > d K . For a given Courant number c k ≤ 1 there is a real number α k > 0 and a corresponding stable scheme with minimal numerical viscosity d k . The proposed schemes suit very well the family of high-order discontinuous Galerkin finite element methods and the recently proposed class of ADER-TR schemes, whose orders of accuracy define decreasing sequences of Courant numbers, as the order of accuracy increases. The centred methods of this paper are stable in 2D and 3D in the frame of simultaneous updating formulae, unlike other centred methods, such as 1D FORCE, which are not. Furthermore, the schemes are highly accurate for slowly-moving waves, which is precisely the kind of waves that traditional centred methods smear disastrously. Additional features of the proposed schemes include ease of implementation and applicability to any hyperbolic system either in conservative or non-conservative form. Here, the proposed schemes are analysed and computationally assessed through a suite of test problems for a linear model system, for the Euler equations in one and two space dimensions, and for the Baer-Nunziato equations for compressible two-phase flow.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Computer experiments on periodic systems identification using rotor blade transient flapping-torsion responses at high advance ratio

Computer experiments are described which used transient responses in flap-bending and torsion of a rotor blade at high advance ratio. It was found that a simple system identification method applying a linear sequential estimator also called equation of motion estimator, is suitable for this periodic system and can be used directly, if only the acceleration data are noise-polluted. In the case where noise is also present in the state-variable data, the direct application of the estimator gave poor results. However after prefiltering the data with a digital Graham filter having a cutoff frequency above the natural blade torsion frequency, the linear sequential estimator successfully recovered the parameters of the periodic coefficient analytical model.

Hohenemser, K. H.↗
DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗