SEARCH · Engineering Papers

Results for “nonlinear systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,045 records · Page 58

All sources NASA NTRS DOE OSTI

NASA NTRS1993

Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback

This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.

Gettman, Chang-Ching LO↗

DOE OSTI2022

Signal-Compensation-Based Adaptive PID Control for Fused Magnesia Smelting Processes

For fused magnesia smelting processes, the proportional-integral-derivative (PID) controller is difficult to regulate the smelting currents within desired ranges due to unexpected variations of the dynamics caused by material feeding operations. To solve this problem, we first proposed its dynamic model composed of a linear model and an uncertain nonlinear dynamic system that describes the unknown time-varying dynamics of nonlinearity and strong couplings among controlled variables. Then, using the accurately calculated value of the uncertain part at the previous sampling time instant and the tracking error that reflects the influence of its change rate, we developed a feedforward and a one-step optimal control to obtain two signal compensators to eliminate the impact of frequent variations of the uncertainties. For the compensators, we proposed a weight selection method to minimize the sum of the squared tracking error with ensured closed-loop stability. Based on the abovementioned modeling and control structure, we finally developed a novel adaptive PID controller augmented with signal compensators to control the whole process. Industrial applications have shown that the proposed method can always keep the tracking error and the control input within their targeted ranges, leading to a significantly reduced energy consumption per ton and increased fused magnesia production.

Wang, Weizhou↗

NASA NTRS2004

Nonlinear Acoustical Assessment of Precipitate Nucleation

The purpose of the present work is to show that measurements of the acoustic nonlinearity parameter in heat treatable alloys as a function of heat treatment time can provide quantitative information about the kinetics of precipitate nucleation and growth in such alloys. Generally, information on the kinetics of phase transformations is obtained from time-sequenced electron microscopical examination and differential scanning microcalorimetry. The present nonlinear acoustical assessment of precipitation kinetics is based on the development of a multiparameter analytical model of the effects on the nonlinearity parameter of precipitate nucleation and growth in the alloy system. A nonlinear curve fit of the model equation to the experimental data is then used to extract the kinetic parameters related to the nucleation and growth of the targeted precipitate. The analytical model and curve fit is applied to the assessment of S' precipitation in aluminum alloy 2024 during artificial aging from the T4 to the T6 temper.

Cantrell, John H.↗

NASA NTRS2003

Extension of Liouville Formalism to Postinstability Dynamics

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Zak, Michail↗

NASA NTRS1972

A note on exponential absolute stability.

A new sufficient condition is formulated for the Lur'e type nonlinear continuous system to be exponentially absolutely stable. The condition relaxes the assumptions on the nonlinear characteristic by modifying the requirements on the linear part of the system.

Siljak, D. D.↗

NASA NTRS1984

The solution of non-linear hyperbolic equation systems by the finite element method

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Loehner, R.↗

NASA NTRS2019

Modal Analysis of a Two-Parachute System

The Orion capsule is designed to land under a nominal configuration of three main parachutes; however, the system is required to be fault tolerant and land successfully if one of the main parachutes fails to open. The Capsule Parachute Assembly System (CPAS) Team performed a series of drop tests in order to characterize the performance of the system with two main parachutes. During the series of drop tests, several distinct dynamical modes were observed. The most consequential of these is the pendulum mode. Three other modes are benign: flyout (scissors), maypole, and breathing. The actual multi-body system is nonlinear, flexible, and possesses significant cross-coupling. Rather than perform analysis of this highly complex system directly, we conduct analysis of each dynamical mode observed during flight, based on first principles. This approach is analogous to traditional aircraft flight dynamics analysis in which the full nonlinear behavior of the airframe is decomposed into longitudinal dynamics (phugoid and short-period modes) and lateral dynamics (spiral, roll-subsidence, and dutch-roll modes). This analysis is intended to supplement multi-body nonlinear simulations in order to provide further insight into the system.

Pei, Jing↗

DOE OSTI2022

Data-driven chaos indicator for nonlinear dynamics and applications on storage ring lattice design

A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a metric for the predictability of nonlinear motions in a given system. When using the indicator to implement a tune-scan for a quadratic Hénon map, the main resonances and their asymmetric stop-band widths can be identified. When applied to particle transportation in a storage ring, as particle motion becomes more chaotic, its surrogate model prediction accuracy decreases correspondingly. So, the prediction accuracy, acting as a chaos indicator, can be used directly as the objective for nonlinear beam dynamics optimization. This method provides a different perspective on nonlinear beam dynamics and an efficient method for nonlinear lattice optimization. Applications in dynamic aperture optimization are demonstrated as real world examples.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Data-driven Chaos Indicator for Nonlinear Dynamics and Applications on Storage Ring Lattice Design

A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a metric for the predictability of nonlinear motions in a given system. When using the indicator to implement a tune-scan for a quadratic Hénon map, the main resonances and their asymmetric stop-band widths can be identified. When applied to particle transportation in a storage ring, as particle motion becomes more chaotic, its surrogate model prediction accuracy decreases correspondingly. Therefore, the prediction accuracy, acting as a chaos indicator, can be used directly as the objective for nonlinear beam dynamics optimization. This method provides a different perspective on nonlinear beam dynamics and an efficient method for nonlinear lattice optimization. Applications in dynamic aperture optimization are demonstrated as real world examples.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Learning Constrained Parametric Differentiable Predictive Control Policies With Guarantees

We present differentiable predictive control (DPC), a method for offline learning of constrained neural control policies for nonlinear dynamical systems with performance guarantees. We show that the sensitivities of the parametric optimal control problem can be used to obtain direct policy gradients. Specifically, we employ automatic differentiation (AD) to efficiently compute the sensitivities of the model predictive control (MPC) objective function and constraints penalties. To guarantee safety upon deployment, we derive probabilistic guarantees on closed-loop stability and constraint satisfaction based on indicator functions and Hoeffding’s inequality. We empirically demonstrate that the proposed method can learn neural control policies for various parametric optimal control tasks. In particular, we show that the proposed DPC method can stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input constraints. Our DPC method has practical time savings compared to alternative approaches for fast and memory-efficient controller design. Specifically, DPC does not depend on a supervisory controller as opposed to approximate MPC based on imitation learning. We demonstrate that, without losing performance, DPC is scalable with greatly reduced demands on memory and computation compared to implicit and explicit MPC while being more sample efficient than model-free reinforcement learning (RL) algorithms.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Using adaptive grid in modeling rocket nozzle flow

The mechanical behavior of a rocket motor internal flow field results in a system of nonlinear partial differential equations which cannot be solved analytically. However, this system of equations called the Navier-Stokes equations can be solved numerically. The accuracy and the convergence of the solution of the system of equations will depend largely on how precisely the sharp gradients in the domain of interest can be resolved. With the advances in computer technology, more sophisticated algorithms are available to improve the accuracy and convergence of the solutions. An adaptive grid generation is one of the schemes which can be incorporated into the algorithm to enhance the capability of numerical modeling. It is equivalent to putting intelligence into the algorithm to optimize the use of computer memory. With this scheme, the finite difference domain of the flow field called the grid does neither have to be very fine nor strategically placed at the location of sharp gradients. The grid is self adapting as the solution evolves. This scheme significantly improves the methodology of solving flow problems in rocket nozzles by taking the refinement part of grid generation out of the hands of computational fluid dynamics (CFD) specialists and place it into the computer algorithm itself.

Chow, Alan S.↗

NASA NTRS2001

Mechanisms for the Crystallization of Zblan

The heavy metal fluoride glasses represent a class of reasonably good glass forming compositions with very unique infrared optical properties that have been of interest to researchers for 20 years. The most extensively studied glass with the most potential for practical applications is ZBLAN which contains the fluorides of zirconium, barium, lanthanum, aluminum, and sodium. It has a broad transmission range (0.3-6 um), low index of refraction (about 1.43), low dispersion, low Raleigh scattering, ultra-low thermal 2 dispersion, and potential ultra-low signal attenuation. Potential applications include fiber amplifiers, fiber optic gyroscopes, delivery systems for laser cutting, drilling and surgery, radiation resistant data links, nonlinear optical systems, and ultra-low-loss repeater-less transcontinental and transoceanic optical fiber. Potential markets for these materials are in the tens of billions of dollars per year. Optical fiber from this system possess excellent transmission characteristics in the IR, but the glass is somewhat susceptible to nucleation and crystallization. The theoretical intrinsic loss coefficient for ZBLAN at 2 microns is 0.00 1 dB/Km. Extrinsic losses, however, cause significant attenuation. The lowest loss coefficient measured is 0.7 dB/Km. This compares with the loss coefficient for fiber optic grade fused silica glass of 0.2 dB/Km. The extrinsic losses in ZBLAN have been attributed to 1) impurities which might be lowered by containerless processing and 2) to scattering from micro-crystallites that form during glass preform production or during fiber drawing.

Ethridge, Edwin C.↗

NASA NTRS1991

Maneuver simulations of flexible spacecraft by solving TPBVP

The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.

Bainum, Peter M.↗

DOE OSTI2021

Data-driven Distributed Learning of Multi-agent Systems: A Koopman Operator Approach

Koopman operator theory provides a model-free technique for studying nonlinear dynamical systems purely from data. Since the Koopman operator is infinite-dimensional, researchers have developed several methods that provide a finite-dimensional approximation of the Koopman operator so that it can be applied for practical use cases. One common thing with most of the methods is that their solutions are obtained by solving a centralized minimization problem. In this work, we treat the dynamical system to be a multi-agent system and propose an algorithm to compute the finite-dimensional approximation of the Koopman operator in a distributed manner using the knowledge of the topology of the underlying multi-agent system. The proposed distributed approach is shown to be equivalent to the centralized learning problem and results in a sparse Koopman whose block structure mimics the Laplacian of the multi-agent system. Extensive simulation studies illustrate the proposed framework on the network of oscillators and the IEEE 68 bus system.

Nandanoori, Sai Pushpak↗

NASA NTRS1985

Development and validation of a general purpose linearization program for rigid aircraft models

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

Duke, E. L.↗

NASA NTRS1985

Development and validation of a general purpose linearization program for rigid aircraft models

This paper discusses a FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high-performance aircraft.

Duke, E. L.↗

NASA NTRS1990

Neural networks for self-learning control systems

It is shown how a neural network can learn of its own accord to control a nonlinear dynamic system. An emulator, a multilayered neural network, learns to identify the system's dynamic characteristics. The controller, another multilayered neural network, next learns to control the emulator. The self-trained controller is then used to control the actual dynamic system. The learning process continues as the emulator and controller improve and track the physical process. An example is given to illustrate these ideas. The 'truck backer-upper,' a neural network controller that steers a trailer truck while the truck is backing up to a loading dock, is demonstrated. The controller is able to guide the truck to the dock from almost any initial position. The technique explored should be applicable to a wide variety of nonlinear control problems.

Nguyen, Derrick H.↗

NASA NTRS1972

Nonlinear programming in design of control systems with specified handling qualities.

A method is described for using nonlinear programing in the computer-aided design of aircraft control systems. It is assumed that the quality of such systems depends on many criteria. These criteria are included in the constraints vector, and the design proceeds through a sequence of nonlinear programing solutions in which the designer varies the specification of sets of requirements levels. The method is applied to design of a lateral stability augmentation system (SAS) for a fighter aircraft, in which the requirements vector is chosen from the official handling-qualities specifications. Results are shown for several simple SAS configurations designed to obtain desirable handling qualities over all design flight conditions with minimum feedback gains.

Schy, A. A.↗