Search NASA⌕ Search

SEARCH · Search NASA

Results for “nonlinear dynamical 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.

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

At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Centralized, decentralized, and independent control of a flexible manipulator on a flexible base

The dynamics and control of a flexible manipulator arm with payload mass on a flexible base in space are considered. The controllers are provided by one torquer at the center of the base and one torquer at the connection joint of the robot and the base. The nonlinear dynamics of the system is modeled by applying the finite element method and Lagrangian formula. Three control strategies are considered and compared, i.e., centralized control, decentralized control, and independent control. All these control designs are based on the linear quadratic regulator theory. A mathematical decomposition is used in the decentralization process so that the coupling between the subsystems is weak, while a physical decomposition is used in the independent control design process. For both the decentralized and the independent controls, the stability of the overall linear system is checked before a numerical simulations is initiated. Two numerical examples show that the response of the independent control system are close to those of the centralized control system, while the responses of the decentralized control system are not.

Li, Feiyue↗
NASA NTRS1991

A second order iteration procedure for correlation of analysis frequencies with test data

A second derivative frequency modification procedure is developed to iteratively change analysis modeling parameters for the more rapid convergence of analytically determined frequencies to those obtained by structural dynamic testing. A nonlinear system of algebraic equations in the modeling parameters is derived and a rapidly converging iterative method for their solution is presented. Numerical results obtained show that the higher order formulation and nonlinear predictor-corrector solution procedure yields results which are more rapidly convergent than those obtained using only the usual linear first-order parameter modification procedure. The proposed higher order theory also connverges in some cases when the ordinary linear theory does not.

Ojalvo, I. U.↗
NASA NTRS1983

Nonlinear dynamics and control of a vibrating rectangular plate

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Shebalin, J. V.↗
NASA NTRS1989

Application of finite-element methods to dynamic analysis of flexible spatial and co-planar linkage systems, part 2

An approach is described to modeling the flexibility effects in spatial mechanisms and manipulator systems. The method is based on finite element representations of the individual links in the system. However, it should be noted that conventional finite element methods and software packages will not handle the highly nonlinear dynamic behavior of these systems which results form their changing geometry. In order to design high-performance lightweight systems and their control systems, good models of their dynamic behavior which include the effects of flexibility are required.

Dubowsky, Steven↗
NASA NTRS1981

Parametric Analytical Studies for the Nonlinear Dynamic Response of the Tile/Pad Space Shuttle Thermal Protection System

The studies examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. Studies are performed using the computer code DYNOTA which takes into account the highly nonlinear stiffening hysteresis and viscous behavior of the pad joining the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude.

Edighoffer, H.↗
NASA NTRS1990

Application of dynamical systems theory to the high angle of attack dynamics of the F-14

Dynamical systems theory has been used to study the nonlinear dynamics of the F-14. An eight degree of freedom model that does not include the control system present in operational F-14s has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearities as functions of the angles of attack and sideslip, the rotation rate, and the elevator deflection. A continuation method has been used to calculate the steady states of the F-14 as continuous functions of the control surface deflections. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena which cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations.

Jahnke, Craig C.↗
NASA NTRS1985

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

The bearingless rotorcraft offers reduced weight, less complexity and superior flying qualities. Almost all the current industrial structural dynamic programs of conventional rotors which consist of single load path rotor blades employ the transfer matrix method to determine natural vibration characteristics because this method is ideally suited for one dimensional chain like structures. This method is extended to multiple load path rotor blades without resorting to an equivalent single load path approximation. Unlike the conventional blades, it isk necessary to introduce the axial-degree-of-freedom into the solution process to account for the differential axial displacements in the different load paths. With the present extension, the current rotor dynamic programs can be modified with relative ease to account for the multiple load paths without resorting to the equivalent single load path modeling. The results obtained by the transfer matrix method are validated by comparing with the finite element solutions. A differential stiffness matrix due to blade rotation is derived to facilitate the finite element solutions.

Murthy, V. R.↗
NASA NTRS2001

Applications of the Hilbert-Huang Transform

A new method, the Hilbert-Huang Transform, has been developed for analyzing nonlinear and nonstationary data. The key part of the method is the Empirical Mode Decomposition with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An M is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies'as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. With this technique we can examine the detailed dynamics characteristics of a nonlinear system through the instantaneous frequency rather than harmonics. Thus it constitutes a new view of the nonlinear dynamics. Examples of classic nonlinear equations and other nonlinear and nonstationary data sets will be used as examples to illustrate the advantage of the application of this new data analysis method.

Huang, Norden E.↗
NASA NTRS1981

Wind energy system time-domain (WEST) analyzers

A portable analyzer which simulates in real time the complex nonlinear dynamics of horizontal axis wind energy systems was constructed. Math models for an aeroelastic rotor featuring nonlinear aerodynamic and inertial terms were implemented with high speed digital controllers and analog calculation. This model was combined with other math models of elastic supports, control systems, a power train and gimballed rotor kinematics. A stroboscopic display system graphically depicting distributed blade loads, motion, and other aerodynamic functions on a cathode ray tube is included. Limited correlation efforts showed good comparison between the results of this analyzer and other sophisticated digital simulations. The digital simulation results were successfully correlated with test data.

Dreier, M. E.↗
NASA NTRSDate not supplied

Modal Correlation of Complex Aerospace Joints Using Automated Variable Substitution

A critical task involved with being able to predict flight loads accurately in aerospace finite element models (FEMs) is the prior verification of the FEMs by conducting modal survey testing (MST). Experience comparing dynamic response of initial FEMs to MST data tends to demonstrate that FEMs can have unacceptable accuracy even when best modeling practices are followed. One inherent source of inaccuracy in linear dynamic FEMs is the modeling of nonlinear joints with mechanisms such as spherical bearings. These joints are usually designed to freely translate or rotate under the high levels of loading experienced in flight. Engineers who create linear FEMs conventionally model these joints without any stiffness in the mechanism degrees of freedom to meet this design intent. However, inaccuracy is observed during test validation of these FEMs, which usually relies on low-level force excitation orders of magnitude below flight load levels. This low-level modal test rarely overcomes the joint friction that is present, and thus the mechanism joints are able to react loads. This divide between the test results and the FEM creates a significant challenge to the engineer who is performing the correlation, in that the engineer has no basis for what stiffness value should be used to make the FEM match the test results. A compounding challenge is that complicated built-up aerospace structures commonly have multiple joints through a load path where each joint will “stick” and “slip” at different levels of force input. Explicitly matching the dynamics of a system containing these nonlinear mechanisms would require a nonlinear FEM, which is prohibitively costly for dynamic simulations of most aerospace systems. The objective of this paper is to present a workflow that can efficiently cycle through many iterations of a FEM, allowing a Monte Carlo style examination of the design space to identify candidate stiffness values for nonlinear mechanism joints. The outlined approach is specific to MSC Nastran and utilizes MSC Nastran’s symbolic substitution capabilities, coupled with the IMAT™ and Attune™ software packages developed by ATA Engineering, Inc. (ATA). The workflow is demonstrated with a case study from the correlation effort for The Boeing Company’s Crew Space Transportation (CST)-100 Starliner FEM. Keywords: Correlation, MSC Nastran, IMAT™, Attune™, Finite Element Model, Modal Testing

Correlation↗
NASA NTRS2015

A Versatile Nonlinear Method for Predictive Modeling

As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.

nonlinear modeling↗
DOE OSTI2025

Grey-Box System Identification of Grid-Forming Inverters

This paper demonstrates the use of grey-box system identification methods for simplifying and understanding the nonlinear power dynamics of grid-forming inverters (GFMs). The power and frequency outputs of complex high-order GFM models are fed into system identification software in order to fit them to a predetermined LTI system and learn system parameters such as (synthetic) inertia and droop constants. The same process is then run for a high-order synchronous generator model, and the outputs are fit to the same set of LTI equations. Simulation of a network of GFM inverters with diverse control architecture is also performed for the same process. The intent is threefold: first, to demonstrate the appropriateness of unified LTI models for describing the power and frequency dynamics of individual resources and connected networks, in order to facilitate analysis of larger heterogeneous networked systems; second, to discover the relationship between internal control parameters of GFMs and their externally observed values; and third, to validate that grey-box data-driven system identification techniques can be a valuable tool to discover the values of important parameters in the absence of explicit vendor models.

analytical models↗
NASA NTRS2004

A "Kane's Dynamics" Model for the Active Rack Isolation System Part Two: Nonlinear Model Development, Verification, and Simplification

Many microgravity space-science experiments require vibratory acceleration levels that are unachievable without active isolation. The Boeing Corporation's active rack isolation system (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station. Effective model-based vibration isolation requires: (1) An isolation device, (2) an adequate dynamic; i.e., mathematical, model of that isolator, and (3) a suitable, corresponding controller. This Technical Memorandum documents the validation of that high-fidelity dynamic model of ARIS. The verification of this dynamics model was achieved by utilizing two commercial off-the-shelf (COTS) software tools: Deneb's ENVISION(registered trademark), and Online Dynamics Autolev(trademark). ENVISION is a robotics software package developed for the automotive industry that employs three-dimensional computer-aided design models to facilitate both forward and inverse kinematics analyses. Autolev is a DOS-based interpreter designed, in general, to solve vector-based mathematical problems and specifically to solve dynamics problems using Kane's method. The simplification of this model was achieved using the small-angle theorem for the joint angle of the ARIS actuators. This simplification has a profound effect on the overall complexity of the closed-form solution while yielding a closed-form solution easily employed using COTS control hardware.

Beech, G. S.↗
NASA NTRS2005

Diagnosing Hybrid Systems: a Bayesian Model Selection Approach

In this paper we examine the problem of monitoring and diagnosing noisy complex dynamical systems that are modeled as hybrid systems-models of continuous behavior, interleaved by discrete transitions. In particular, we examine continuous systems with embedded supervisory controllers that experience abrupt, partial or full failure of component devices. Building on our previous work in this area (MBCG99;MBCG00), our specific focus in this paper ins on the mathematical formulation of the hybrid monitoring and diagnosis task as a Bayesian model tracking algorithm. The nonlinear dynamics of many hybrid systems present challenges to probabilistic tracking. Further, probabilistic tracking of a system for the purposes of diagnosis is problematic because the models of the system corresponding to failure modes are numerous and generally very unlikely. To focus tracking on these unlikely models and to reduce the number of potential models under consideration, we exploit logic-based techniques for qualitative model-based diagnosis to conjecture a limited initial set of consistent candidate models. In this paper we discuss alternative tracking techniques that are relevant to different classes of hybrid systems, focusing specifically on a method for tracking multiple models of nonlinear behavior simultaneously using factored sampling and conditional density propagation. To illustrate and motivate the approach described in this paper we examine the problem of monitoring and diganosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.

McIlraith, Sheila A.↗
NASA NTRS2011

Nonlinear Oscillators in Space Physics

We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.

Lester,Daniel↗
DOE OSTI2025

Light induced ion migration studies in perovskite solar cell using nonlinear impedance spectroscopy

Complex interactions between mobile ions and charge carriers in perovskite solar cells (PSCs) make it challenging to fully understand their dynamic interplay. Exposure to light further complicates these interactions, altering the system’s dynamics and inducing nonlinear effects that lead to changes in the J−V curve. Understanding these effects is crucial for improving the operational stability of PSCs. Impedance spectroscopy (IS) is a powerful technique for evaluating relaxation processes in the frequency domain; however, it is limited in capturing nonlinear contributions. Here, in this work, nonlinear impedance spectroscopy (NLIS) is employed to analyze the higher harmonic response to AC perturbation, both in the dark and after short-term light exposure. A shift in the low-frequency (LF) higher harmonic peak is observed after open-circuit light exposure, attributed to an altered electric field suggesting ion re-distribution, whereas closed-circuit exposure shows no LF shift, indicating minimal ion movement. Additionally, light exposure reduces higher-order admittance, more notably in open-circuit conditions, suggesting decreased recombination. Temperature-dependent analysis was conducted to characterize the activation energy of migrating species, identifying iodide as the dominant migrating ion.

14 SOLAR ENERGY↗
DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗