Engineering Papers⌕ Search

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.

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

At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1999

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Kurdila, Andrew J.↗
NASA NTRS2000

X-33 Ascent Flight Controller Design by Trajectory Linearization: A Singular Perturbational Approach

The flight control of X-33 poses a challenge to conventional gain-scheduled flight controllers due to its large attitude maneuvers from liftoff to orbit and reentry. In addition, a wide range of uncertainties in vehicle handling qualities and disturbances must be accommodated by the attitude control system. Nonlinear tracking and decoupling control by trajectory linearization can be viewed as the ideal gain-scheduling controller designed at every point on the flight trajectory. Therefore it provides robust stability and performance at all stages of flight without interpolation of controller gains and eliminates costly controller redesigns due to minor airframe alteration or mission reconfiguration. In this paper, a prototype trajectory linearization design for an X-33 ascent flight controller is presented along with 3-DOF and 6-DOF simulation results. It is noted that the 6-DOF results were obtained from the 3-DOF design with only a few hours of tuning, which demonstrates the inherent robustness of the design technique. It is this "plug-and-play" feature that is much needed by NASA for the development, test and routine operations of the RLV'S. Plans for further research are also presented, and refined 6-DOF simulation results will be presented in the final version of the paper.

Zhu, J. Jim↗
NASA NTRS2000

Reconfigurable Flight Control Using Nonlinear Dynamic Inversion with a Special Accelerometer Implementation

This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.

Bacon, Barton J.↗
NASA NTRS1997

Feedback Implementation of Zermelo's Optimal Control by Sugeno Approximation

This paper proposes an approach to implement optimal control laws of nonlinear systems in real time. Our methodology does not require solving two-point boundary value problems online and may not require it off-line either. The optimal control law is learned using the original Sugeno controller (OSC) from a family of optimal trajectories. We compare the trajectories generated by the OSC and the trajectories yielded by the optimal feedback control law when applied to Zermelo's ship steering problem.

Clifton, C.↗
NASA NTRS2001

Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.

Pelaez, Juan↗
NASA NTRS2001

Reduced-Order Modeling: New Approaches for Computational Physics

In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. Emphasis is given to methods ba'sed on Volterra series representations and the proper orthogonal decomposition. Results are reported for different nonlinear systems to provide clear examples of the construction and use of reduced-order models, particularly in the multi-disciplinary field of computational aeroelasticity. Unsteady aerodynamic and aeroelastic behaviors of two- dimensional and three-dimensional geometries are described. Large increases in computational efficiency are obtained through the use of reduced-order models, thereby justifying the initial computational expense of constructing these models and inotivatim,- their use for multi-disciplinary design analysis.

Beran, Philip S.↗
NASA NTRS2001

Reduced-Order Modeling: Cooperative Research and Development at the NASA Langley Research Center

Cooperative research and development activities at the NASA Langley Research Center (LaRC) involving reduced-order modeling (ROM) techniques are presented. Emphasis is given to reduced-order methods and analyses based on Volterra series representations, although some recent results using Proper Orthogonal Deco in position (POD) are discussed as well. Results are reported for a variety of computational and experimental nonlinear systems to provide clear examples of the use of reduced-order models, particularly within the field of computational aeroelasticity. The need for and the relative performance (speed, accuracy, and robustness) of reduced-order modeling strategies is documented. The development of unsteady aerodynamic state-space models directly from computational fluid dynamics analyses is presented in addition to analytical and experimental identifications of Volterra kernels. Finally, future directions for this research activity are summarized.

Silva, Walter A.↗
NASA NTRS1999

X-33 Ascent Flight Controller Design by Trajectory Linearization: A Singular Perturbational Approach

The flight control of X-33 poses a challenge to conventional gain-scheduled flight controllers due to its large attitude maneuvers from liftoff to orbit and reentry. In addition, a wide range of uncertainties in vehicle handling qualities and disturbances must be accommodated by the attitude control system. Nonlinear tracking and decoupling control by trajectory linearization can be viewed as the ideal gain-scheduling controller designed at every point on the flight trajectory. Therefore it provides robust stability and performance at all stages of flight without interpolation of controller gains, and eliminates costly controller redesigns due to minor airframe alteration or mission reconfiguration. A prototype trajectory linearization design for X-33 ascent flight controller was designed and tested with 3-DOF and 6-DOF simulations during the 10 weeks SFFP. It is noted that the 6-DOF results were obtained from the 3-DOF design with only a few hours of tuning, which demonstrates the inherent robustness of the design technique. It is this "plug-and-play" feature that is much needed by NASA for the development, test and routine operations of the RLVs. Plans for further research are also presented.

Zhu, J. Jim↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2002

Wavelet Approximation in Data Assimilation

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew↗
NASA NTRS2003

Stochastic Optimal Control via Bellman's Principle

This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.

Crespo, Luis G.↗
NASA NTRS2004

Sliding Mode Control of a Thermal Mixing Process

In this paper we consider the robust control of a thermal mixer using multivariable Sliding Mode Control (SMC). The mixer consists of a mixing chamber, hot and cold fluid valves, and an exit valve. The commanded positions of the three valves are the available control inputs, while the controlled variables are total mass flow rate, chamber pressure and the density of the mixture inside the chamber. Unsteady thermodynamics and linear valve models are used in deriving a 5th order nonlinear system with three inputs and three outputs, An SMC controller is designed to achieve robust output tracking in the presence of unknown energy losses between the chamber and the environment. The usefulness of the technique is illustrated with a simulation.

Richter, Hanz↗
NASA NTRS2004

Monitoring the Performance of a Neuro-Adaptive Controller

Traditional control has proven to be ineffective to deal with catastrophic changes or slow degradation of complex, highly nonlinear systems like aircraft or spacecraft, robotics, or flexible manufacturing systems. Control systems which can adapt toward changes in the plant have been proposed as they offer many advantages (e.g., better performance, controllability of aircraft despite of a damaged wing). In the last few years, use of neural networks in adaptive controllers (neuro-adaptive control) has been studied actively. Neural networks of various architectures have been used successfully for online learning adaptive controllers. In such a typical control architecture, the neural network receives as an input the current deviation between desired and actual plant behavior and, by on-line training, tries to minimize this discrepancy (e.g.; by producing a control augmentation signal). Even though neuro-adaptive controllers offer many advantages, they have not been used in mission- or safety-critical applications, because performance and safety guarantees cannot b e provided at development time-a major prerequisite for safety certification (e.g., by the FAA or NASA). Verification and Validation (V&V) of an adaptive controller requires the development of new analysis techniques which can demonstrate that the control system behaves safely under all operating conditions. Because of the requirement to adapt toward unforeseen changes during operation, i.e., in real time, design-time V&V is not sufficient.

Schumann, Johann↗
NASA NTRS1999

Control of the NASA Langley 16-Foot Transonic Tunnel with the Self-Organizing Map

A predictive, multiple model control strategy is developed based on an ensemble of local linear models of the nonlinear system dynamics for a transonic wind tunnel. The local linear models are estimated directly from the weights of a self-organizing map (SOM). Multiple self-organizing maps collectively model the global response of the wind tunnel to a finite set of representative prototype controls. These prototype controls partition the control space and incorporate experiential knowledge gained from decades of operation. Each SOM models the combination of the tunnel with one of the representative controls, over the entire range of operation. The SOM based linear models are used to predict the tunnel response to a larger family of control sequences which are clustered on the representative prototypes. The control sequence which corresponds to the prediction that best satisfies the requirements on the system output is applied as the external driving signal.

Mark A. Motter↗
NASA NTRS2004

A New Approach to Aircraft Robust Performance Analysis

A recently developed algorithm for nonlinear system performance analysis has been applied to an F16 aircraft to begin evaluating the suitability of the method for aerospace problems. The algorithm has a potential to be much more efficient than the current methods in performance analysis for aircraft. This paper is the initial step in evaluating this potential.

Gregory, Irene M.↗