Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear models”

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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Flight flutter testing technology at Grumman

Analysis techniques used in the automated telemetry station (ATS) for on line data reduction are encompassed in a broad range of software programs. Concepts that form the basis for the algorithms used are mathematically described. The control the user has in interfacing with various on line programs is discussed. The various programs are applied to an analysis of flight data which includes unimodal and bimodal response signals excited via a swept frequency shaker and/or random aerodynamic forces. A nonlinear response error modeling analysis approach is described. Preliminary results in the analysis of a hard spring nonlinear resonant system are also included.

Perangelo, H. J.↗
NASA NTRS1982

A variable structure approach to robust control of VTOL aircraft

This paper examines the application of variable structure control theory to the design of a flight control system for the AV-8A Harrier in a hover mode. The objective in variable structure design is to confine the motion to a subspace of the total state space. The motion in this subspace is insensitive to system parameter variations and external disturbances that lie in the range space of the control. A switching type of control law results from the design procedure. The control system was designed to track a vector velocity command defined in the body frame. For comparison purposes, a proportional controller was designed using optimal linear regulator theory. Both control designs were first evaluated for transient response performance using a linearized model, then a nonlinear simulation study of a hovering approach to landing was conducted. Wind turbulence was modeled using a 1052 destroyer class air wake model.

Calise, A. J.↗
NASA NTRS1991

Bilinear modeling and state estimation of slew-induced deformations of a flexible multibody system

A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformations are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.

Dwyer, Thomas A. W., III↗
NASA NTRS2012

A Cross-Validation Approach to Approximate Basis Function Selection of the Stall Flutter Response of a Rectangular Wing in a Wind Tunnel

The stall flutter response of a rectangular wing in a low speed wind tunnel is modelled using a nonlinear difference equation description. Static and dynamic tests are used to select a suitable model structure and basis function. Bifurcation criteria such as the Hopf condition and vibration amplitude variation with airspeed were used to ensure the model was representative of experimentally measured stall flutter phenomena. Dynamic test data were used to estimate model parameters and estimate an approximate basis function.

Kukreja, Sunil L.↗
NASA NTRSDate not supplied

A Comparison of Model Predictive Control Architectures for Application to Electrified Aircraft Propulsion Systems

As electrified aircraft propulsion (EAP) systems continue to mature, more sophisticated hardware and software are being developed to balance operations among electric machines and gas-turbine engines. In hybrid-electric propulsion systems, the increased complexity resulting from integrating turbine-engine shafts with electric machines necessitates control methodologies to account for various physical domains. Ideal controllers for hybrid-electric engines manage systems, subsystems, and their interactions in a coordinated fashion, able to account for safety and performance goals while being computationally efficient. In a previous work, linear model predictive control (MPC) schemes were implemented in centralized and distributed frameworks on a nonlinear turbofan engine model as a proof of concept. However, these schemes were not evaluated for computational complexity, prompting further study. The research presented here develops hierarchical MPC schemes to reduce the computational burden of the previous MPC schemes. A two-tier framework is implemented, where a slower sampling MPC controls electric machines and determines fan-speed tracking goals for a faster sampling controller, which is either a MPC or a proportional-integral (PI) controller. The proposed designs are compared to the centralized MPC investigated previously, and performance is measured via fan speed tracking error, energy storage state-of-charge, and computation time. Results reveal that the hierarchical MPC scheme employing a lower-level PI controller improves computation time while maintaining comparable tracking and state-of-charge regulation to the centralized scheme.

model predictive control↗
NASA NTRSDate not supplied

A Comparison of Model Predictive Control Architectures for Application to Electrified Aircraft Propulsion Systems

As electrified aircraft propulsion (EAP) systems continue to mature, more sophisticated hardware and software are being developed to balance operations among electric machines and gas-turbine engines. In hybrid-electric propulsion systems, the increased complexity resulting from integrating turbine-engine shafts with electric machines necessitates control methodologies to account for various physical domains. Ideal controllers for hybrid-electric engines manage systems, subsystems, and their interactions in a coordinated fashion, able to account for safety and performance goals while being computationally efficient. In a previous work, linear model predictive control (MPC) schemes were implemented in centralized and distributed frameworks on a nonlinear turbofan engine model as a proof of concept. However, these schemes were not evaluated for computational complexity, prompting further study. The research presented here develops hierarchical MPC schemes to reduce the computational burden of the previous MPC schemes. A two-tier framework is implemented, where a slower sampling MPC controls electric machines and determines fan-speed tracking goals for a faster sampling controller, which is either a MPC or a proportional-integral (PI) controller. The proposed designs are compared to the centralized MPC investigated previously, and performance is measured via fan speed tracking error, energy storage state-of-charge, and computation time. Results reveal that the hierarchical MPC scheme employing a lower-level PI controller improves computation time while maintaining comparable tracking and state-of-charge regulation to the centralized scheme.

model predictive control↗
NASA NTRS1989

On discrete control of nonlinear systems with applications to robotics

Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.

Eslami, Mansour↗
NASA NTRS1990

Nonlinear feedback control for high alpha flight

Analytical aerodynamic models are derived from a high alpha 6 DOF wind tunnel model. One detail model requires some interpolation between nonlinear functions of alpha. One analytical model requires no interpolation and as such is a completely continuous model. Flight path optimization is conducted on the basic maneuvers: half-loop, 90 degree pitch-up, and level turn. The optimal control analysis uses the derived analytical model in the equations of motion and is based on both moment and force equations. The maximum principle solution for the half-loop is poststall trajectory performing the half-loop in 13.6 seconds. The agility induced by thrust vectoring capability provided a minimum effect on reducing the maneuver time. By means of thrust vectoring control the 90 degrees pitch-up maneuver can be executed in a small place over a short time interval. The agility capability of thrust vectoring is quite beneficial for pitch-up maneuvers. The level turn results are based currently on only outer layer solutions of singular perturbation. Poststall solutions provide high turn rates but generate higher losses of energy than that of classical sustained solutions.

Stalford, Harold↗
NASA NTRS1987

Experimental and analytic studies of the triggered lightning environment of the F106B

The triggered lightning environment of the F106B aircraft is investigated. Scale modeling of the F106B with a metallized model was done to measure electric field enhancement factors on the aircraft and on canonically shaped conducting objects. These are then compared to numerically determined quantities. Detailed numerical modeling is done of the development of the triggered lightning channel. This is done using nonlinear air chemistry models to model a variety of physical phenomena which occur in a triggered lightning event. The effect of a triggered lightning strike on internal wires in the F106B is investigated using finite difference models and transmission line models to calculate the electromagnetic coupling of lightning currents through seams and joints of the aircraft to internal cables. Time domain waveforms are computed and compared to measured waveforms. The effect of thunderstorm particles on the initial triggering of a lightning strike is investigated. The electric field levels needed to cause air breakdown in the presence and absence of thunderstorm particles are calculated. This is done as a function of the size, shape, and density of the particles.

Rudolph, Terence↗
NASA NTRS1988

Large-scale structure from cosmic-string loops in a baryon-dominated universe

The results are presented of a numerical simulation of the formation of large-scale structure in a universe with Omega(0) = 0.2 and h = 0.5 dominated by baryons in which cosmic strings provide the initial density perturbations. The numerical model yields a power spectrum. Nonlinear evolution confirms that the model can account for 700 km/s bulk flows and a strong cluster-cluster correlation, but does rather poorly on smaller scales. There is no visual 'filamentary' structure, and the two-point correlation has too steep a logarithmic slope. The value of G mu = 4 x 10 to the -6th is significantly lower than previous estimates for the value of G mu in baryon-dominated cosmic string models.

Melott, Adrian L.↗
NASA NTRS1992

Modeling and control study of the NASA 0.3-meter transonic cryogenic tunnel for use with sulfur hexafluoride medium

The NASA Langley 0.3-m Transonic Cryogenic Tunnel is to be modified to operate with sulfur hexafluoride gas while retaining its present capability to operate with nitrogen. The modified tunnel will provide high Reynolds number flow on aerodynamic models with two different test gases. The document details a study of the SF6 tunnel performance boundaries, thermodynamic modeling of the tunnel process, nonlinear dynamical simulation of math model to yield tunnel responses, the closed loop control requirements, control laws, and mechanization of the control laws on the microprocessor based controller.

Balakrishna, S.↗
NASA NTRS2006

Hybrid Kalman Filter: A New Approach for Aircraft Engine In-Flight Diagnostics

In this paper, a uniquely structured Kalman filter is developed for its application to in-flight diagnostics of aircraft gas turbine engines. The Kalman filter is a hybrid of a nonlinear on-board engine model (OBEM) and piecewise linear models. The utilization of the nonlinear OBEM allows the reference health baseline of the in-flight diagnostic system to be updated to the degraded health condition of the engines through a relatively simple process. Through this health baseline update, the effectiveness of the in-flight diagnostic algorithm can be maintained as the health of the engine degrades over time. Another significant aspect of the hybrid Kalman filter methodology is its capability to take advantage of conventional linear and nonlinear Kalman filter approaches. Based on the hybrid Kalman filter, an in-flight fault detection system is developed, and its diagnostic capability is evaluated in a simulation environment. Through the evaluation, the suitability of the hybrid Kalman filter technique for aircraft engine in-flight diagnostics is demonstrated.

Kobayashi, Takahisa↗
NASA NTRS1981

Chaotic /strange/ and periodic behavior in instability saturation by the oscillating two-stream instability

The nonlinear Schroedinger equation with linear growth and damping is truncated to three waves. The resulting system of nonlinear ordinary differential equations describes the excitation of linearly damped waves by the oscillating two-stream instability driven by a linearly unstable pump wave. This system represents a simple model for the nonlinear saturation of a linearly unstable wave. The model is examined analytically and numerically as a function of the dimensionless parameters of the system. It is found that the model can exhibit a wealth of characteristic dynamical behavior including stationary equilibria, Hopf bifurcations to periodic orbits, period doubling bifurcations, chaotic solutions characteristic of a strange attractor, tangent bifurcations from chaotic to periodic solutions, transient chaos, and hysteresis. Many of these features are shown to be explainable on the basis of one-dimensional maps. In the case of chaotic solutions, evidence for the presence of a strange attractor is provided by demonstrating Cantor set-like structure (i.e., scale invariance) in the surface of section.

Russell, D. A.↗
NASA NTRS1984

A finite element method for nonlinear forced vibrations of beams

Techniques for defining a finite element model (FEM) for analysis of nonlinear vibrations in beam structures subjected to harmonic excitation are presented. The resulting model covers longitudinal deformation and inertial effects. The nonlinear oscillations of a beam element under forced excitation are modeled by a harmonic force matrix based on first order approximations of the Jacobian elliptic forcing function. Harmonic force and nonlinear stiffness matrices are derived and the nonlinear forced responses of beams are calculated under various boundary conditions. The results of FEM computations for simply-supported and clamped beams show that midplane stretching caused by large deflections increases the nonlinearity. Axially-restrained beams experience only hardening nonlinearity, while axially-free beams have reduced nonlinearity in deformation and inertia and an increase in linearity due to large deflection.

Mei, C.↗
NASA NTRS1994

A rapid-pressure correlation representation consistent with the Taylor-Proudman theorem materially-frame-indifferent in the 2D limit

A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.

Ristorcelli, J. R.↗
NASA NTRS2000

High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering

When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.

Fibich, Gadi↗
NASA NTRS2013

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology. Appendix C -- Finite Element Models Solution Database File, Appendix D -- Benchmark Finite Element Models Solution Database File

No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

Allen, Phillip A.↗