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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Improved Sensitivity Relations in State Constrained Optimal Control

Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjoint state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because it is validated for a stronger set of necessary conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Phase-field modeling and experiments of dynamic fracture in single crystal quartz

Predicting the onset and characteristics of brittle fracture is important for a wide range of engineering and geological material applications. In this paper, we study important aspects of brittle fracture in α-quartz by phase-field modeling and experiments using a top-down approach. In the modeling framework, the work term in the Griffith energy balance is replaced with internal energy contributions that represent surface energy, thermal energy, and elastic strain energy stored in defects. This allows parametrization of individual energy contributions in terms of internal state variables and keeps track of energy partitioning after the onset of fracture. The path and history dependence of fracture is included in evolution laws for internal state variables, e.g., entropy evolution, while the energy remains a true potential. In the experimental part, dynamic compression experiments coupled with X-ray phase contrast imaging are performed on cube-like samples with a hole. In the top-down analysis, dynamic compression and three point bending experiments from the literature are simulated with the developed phase-field damage model. In conclusion, the fitted model highlights the strain rate, size, and stress state dependence of damage nucleation and evolution in single crystal α-quartz.

36 MATERIALS SCIENCE↗
NASA NTRS1983

Decoupling and observation theory applied to control of a long flexible beam in orbit

Techniques which use decoupling theory and state variable feedback to control the pitch attitude and the flexible mode amplitudes of a long, thin beam are discussed. An observer based on the steady state Kalman filter was incorporated into the control design procedure in order to estimate the values of the modal state variables required for the feedback control law.

Hamer, H. A.↗
DOE OSTI2025

Hypercomplex Automatic Differentiation in the Eulerian Hydrocode PAGOSA

Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

A 'type one' servo explicit model following adaptive scheme.

This paper describes 'type 1' servo techniques applied to explicit model following systems. The advantages of using these are: (1) steady-state decoupling is provided for the controlled state variables as determined by a reference input (the pilot command for example), (2) overall stability of the decoupled adaptive scheme is guaranteed, (3) a zero steady-state error for those state variables incorporating integral feedback, to a constant input reference, and (4) improved transient performance. Example calculations have been performed using a mathematical model for a typical fighter aircraft and a desired performance reference model based on satisfactory aircraft flying qualities. Numerical results are given.

Tiroshi, I.↗
DOE OSTI2019

Dynamic parameter estimation of generators

Various examples are provided for parameter estimation of generators. In one example, among others, a method includes collecting data corresponding to a generator using a phasor management unit (PMU) and estimating dynamic parameters of the generator using extended Kalman filtering (EKF) and the collected PMU data. In another example, a system includes at least one application executable in a processing device that obtains operational data corresponding to a generator and estimates a dynamic parameter of the generator using EKF and the operational data. In another example, an EKF estimator includes a dynamics estimator configured to estimate a state variable of a generator, a geometry estimator configured to estimate phasor values associated with the generator, and a Kalman filter gain configured to determine a correction to the state variable.

Miao, Zhixin↗
NASA NTRS1987

A new state space model for the NASA/JPL 70-meter antenna servo controls

A control axis referenced model of the NASA/JPL 70-m antenna structure is combined with the dynamic equations of servo components to produce a comprehansive state variable (matrix) model of the coupled system. An interactive Fortran program for generating the linear system model and computing its salient parameters is described. Results are produced in a state variable, block diagram, and in factored transfer function forms to facilitate design and analysis by classical as well as modern control methods.

Hill, R. E.↗
NASA NTRS2018

Plasticity and Damage Modeling of Stress Asymmetry and Dynamic Behavior of AFS Additive Manufactured Aluminum Alloy 2219

The Solid State Additive Manufacturing (AM) process referred as MELD that fabricated the samples in this study, provides a new path for repairing, coating, joining and additive manufacturing metals and metal matrix composites. This research will be the first application of a physics-based microstructure dependent internal state variable (ISV) plasticity and damage material model to capture the mechanical response of an AM Aluminum Alloy (AA) 2219 via the MELD process. In this research, a microstructure-based internal state variable (ISV) plasticity-damage model was used to capture the mechanical behavior of AFS 2219 aluminum alloy. Aeroprobe Corporation, creator and patent holder for the MELD process, fabricated the material by pushing a solid filler rod of AA2219-T861 material through a hollow rotating tool onto an AA2219 T851 plate substrate. As feedstock, solid or powder precursor metals are pushed through a nonconsumable rotating cylindrical tool. Herein, added layers are deposited and metallurgically bonded to substrate material or previously deposited layers by the heat generated from the rotating tool through plastic deformation of the filler material. Once a layer has been added, the tool height increases, and starts the deposition of the next layer. This process results in beneficial properties such as grain refinement, homogenization and reduced porosity (fully dense). This process will experience temperatures similar to those in the weld nugget zone (WNZ) in friction stir welding (FSW), ranging from 0.6-0.9 Tm, with Tm being the melting point of the material. MELD is highly scalable with AA deposition rates reaching over 1000 cm3/hr, which allows for MELD being used for repairs, coatings, and building components. A motivating factor driving the research for physics-based history dependent material modeling of MELD components is the ability to accurately capture the stress-state and strain rate dependence in the material caused by variations in material microstructure from the MELD processing of new or repaired components. The ISV model incorporates microstructural content and is consistent with continuum level kinematics, kinetics, and thermodynamics. These features allow the ISV model to capture large deformations at the structural scale using the kinematic and isotropic hardening, while microscale damage is obtained from the microstructural features. The benefits of the ISV model arise from the inclusion of structure-property relationships identified from microstructural characterization and experimentation. The Bauschinger effect (BE) is an important concept, vital in the accurate prediction of cyclic stress-strain response of ductile materials such as metals. The ISV model has been successfully used to capture the behavior and damage, and the BE of different aluminum alloys and steels. The ISV model uses kinematic and isotropic hardening to help capture deformations of the material at the macro scale. To understand this hardening relationship, calculating the kinematic and isotropic hardening relationship in the material is warranted for a high-fidelity model. Electron Backscattered Diffraction (EBSD) was used to characterize the as-fabricated microstructure, where a fully-dense equiaxed grain morphology with average grain size of 2.5 μm was observed. Microhardness mapping of the as-built structures, monotonic tension and compression experiments at both quasi-static (0.001/s) strain rates, tension-followed-by-compression and compression-followed-by-tension experiments were performed to obtain the set of plasticity and damage constants necessary to capture strain rate and stress state behavior of this additive material. To calibrate the plasticity-damage model, a single set of constants were determined to capture the different stress states the MELD AA2219. One set of the constants was determined from experimental true stress-strain curves for the tension and compression data. Additionally, microstructural information and data from the open literature were used as the other model constants. This research is a first of its kind for AFS AA2219, includes correlating the ISV model to the monotonic experimental results that capture the isotropic and kinematic plasticity mechanical response.

Rivera, O. G.↗
NASA NTRS1992

A study of the control problem of the shoot side environment delivery system of a closed crop growth research chamber

The details of our initial study of the control problem of the crop shoot environment of a hypothetical closed crop growth research chamber (CGRC) are presented in this report. The configuration of the CGRC is hypothetical because neither a physical subject nor a design existed at the time the study began, a circumstance which is typical of large scale systems control studies. The basis of the control study is a mathematical model which was judged to adequately mimic the relevant dynamics of the system components considered necessary to provide acceptable realism in the representation. Control of pressure, temperature, and flow rate of the crop shoot environment, along with its oxygen, carbon dioxide, and water concentration is addressed. To account for mass exchange, the group of plants is represented in the model by a source of oxygen, a source of water vapor, and a sink for carbon dioxide. In terms of the thermal energy exchange, the group of plants is represented by a surface with an appropriate temperature. Most of the primitive equations about an experimental operating condition and a state variable representation which was extracted from the linearized equations are presented. Next, we present the results of a real Jordan decomposition and the repositioning of an undesirable eigenvalue via full state feedback. The state variable representation of the modeling system is of the nineteenth order and reflects the eleven control variables and eight system disturbances. Five real eigenvalues are very near zero, with one at zero, three having small magnitude positive values, and one having a small magnitude negative value. A Singular Value Decomposition analysis indicates that these non-zero eigenvalues are not results of numerical error.

Blackwell, C. C.↗
DOE OSTI2018

Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, we derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Grid State Estimation Tool

This software code is designed to track generator state variables in real time using the Ensemble Kalman Filter method with the aid of PMU measurements. This code can also be used to calibrate dynamic model parameters by augmenting parameters in the state variable vector.

Huang, Zhenyu↗
NASA NTRS1988

A constitutive model with damage for high temperature superalloys

A unified constitutive model is searched for that is applicable for high temperature superalloys used in modern gas turbines. Two unified inelastic state variable constitutive models were evaluated for use with the damage parameter proposed by Kachanov. The first is a model (Bodner, Partom) in which hardening is modeled through the use of a single state variable that is similar to drag stress. The other (Ramaswamy) employs both a drag stress and back stress. The extension was successful for predicting the tensile, creep, fatigue, torsional and nonproportional response of Rene' 80 at several temperatures. In both formulations, a cumulative damage parameter is introduced to model the changes in material properties due to the formation of microcracks and microvoids that ultimately produce a macroscopic crack. A back stress/drag stress/damage model was evaluated for Rene' 95 at 1200 F and is shown to predict the tensile, creep, and cyclic loading responses reasonably well.

Sherwood, J. A.↗
NASA NTRS2003

Flux-Based Deadbeat Control of Induction-Motor Torque

An improved method and prior methods of deadbeat direct torque control involve the use of pulse-width modulation (PWM) of applied voltages. The prior methods are based on the use of stator flux and stator current as state variables, leading to mathematical solutions of control equations in forms that do not lend themselves to clear visualization of solution spaces. In contrast, the use of rotor and stator fluxes as the state variables in the present improved method lends itself to graphical representations that aid in understanding possible solutions under various operating conditions. In addition, the present improved method incorporates the superposition of high-frequency carrier signals for use in a motor-self-sensing technique for estimating the rotor shaft angle at any speed (including low or even zero speed) without need for additional shaft-angle-measuring sensors.

Kenny, Barbara H.↗
DOE OSTI2017

Feature selection based on PCA and the transient identification in nuclear power plants - 289

For the sake of enhancing safety and achieving more economic benefits, it is very important to timely and correctly identify the transients during the operation of nuclear power plants. There are thousands of monitoring signals in a nuclear power plant. It is difficult to complete the calculations timely if all the related signals are chosen for an algorithm of transient identification. Moreover, the irrelevant state variables may also do harm to the correctness of the identification process. Thus, one of the key tasks for transient identification is to figure out effective methods to extract the features from state variables. In this paper, we will address an efficient method for feature selection and transient identification based on principal component analysis (PCA). The effectiveness of the method are illustrated by the tests based on the data from the simulator designed for the High Temperature gas-cooled Reactor Pebble-bed Module (HTR-PM), which is under construction in China and the construction will be completed around 2017. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Delay compensation in integrated communication and control systems. I - Conceptual development and analysis

A procedure for compensating for the effects of distributed network-induced delays in integrated communication and control systems (ICCS) is proposed. The problem of analyzing systems with time-varying and possibly stochastic delays could be circumvented by use of a deterministic observer which is designed to perform under certain restrictive but realistic assumptions. The proposed delay-compensation algorithm is based on a deterministic state estimator and a linear state-variable-feedback control law. The deterministic observer can be replaced by a stochastic observer without any structural modifications of the delay compensation algorithm. However, if a feedforward-feedback control law is chosen instead of the state-variable feedback control law, the observer must be modified as a conventional nondelayed system would be. Under these circumstances, the delay compensation algorithm would be accordingly changed. The separation principle of the classical Luenberger observer holds true for the proposed delay compensator. The algorithm is suitable for ICCS in advanced aircraft, spacecraft, manufacturing automation, and chemical process applications.

Luck, Rogelio↗
NASA NTRS1972

Design of non-interacting multivariable discrete time systems

The theory of decoupling a multivariable system with the help of state variable feedback is applied to discrete time systems. The system differential equations in the continuous time domain are converted to a discrete time representation. A discrete time controller is designed to control the overall input to the system such that a specified desired decoupled output response is obtained. The decoupled system behaves as a set of single-input, single-output systems and state variable techniques can be easily applied to control each output individually. Control is achieved by periodically sampling the inputs and all the states and feeding them back through a controller. For linear time invariant systems the control is time invariant. The basic theory of decoupling involves feeding back all the states twice, first to decouple the system and then to achieve a desired response. The states of the system are computed with the help of a state estimator which calculates all the present states of the system so that on-line control can be applied to real time systems. The theory is applied to a model of a nuclear rocket engine.

Agrawal, B. L.↗
NASA NTRS1988

Anisotropic constitutive modeling for nickel base single crystal superalloys using a crystallographic approach

A micromechanical model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the effect of back stress in single crystals. The results showed that (1) the back stress is orientation dependent; and (2) the back stress state variable in the inelastic flow equation is necessary for predicting anelastic behavior of the material. The model also demonstrated improved fatigue predictive capability. Model predictions and experimental data are presented for single crystal superalloy Rene N4 at 982 C.

Stouffer, D. C.↗