Optimal stabilization of nonlinear dynamical systems
Optimization of nonlinear closed-loop dynamic control systems - integral performance function for partial ordering of closed loop controls
DYNAMIC STABILITY↗
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Results for “nonlinear function”
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.
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Stability of systems with delay
Generalized Liapunov functions for motion stability of linear and nonlinear systems with time lag
Shimanov, S. N.↗
Minimum time control of a nonlinear system.
Time optimal control for nonlinear systems, expressing optimal control law as function of state variables
Fluegge-Lotz, I.↗
Optimum adaptive reception for binary sequences
Optimum adaptive reception for binary sequences, using posteriori probability density function computing device synthesized from correlator, instantaneous nonlinearity and multiplier
Wintz, P. A.↗
Thermal regime and temperature stresses in bodies during thermoradiational heating
An approach is developed to the application of the perturbation method for the solution of problems with essential external nonlinearities, based on identification in the boundary condition of a small nonlinear complex which is considered a perturbing function. The solutions obtained in the first approximation with error of 1 to 2% in calculating the unsteady temperature fields are then used to determine the temperature stresses and deformations in solid bodies of classical form.
Chistopyanova, N. V.↗
Discrete optimal control approach to a four-dimensional guidance problem near terminal areas
Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.
Nagarajan, N.↗
Microwave remote sensing of a two-layer random medium
A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.
Tsang, L.↗
Controllability of delay systems with restrained controls
Using a geometric growth condition, both the function space and Euclidean controllability of a nonlinear delay system which has a compact and convex control set are characterized. This extends analogous results for ordinary differential systems, and it yields conditions under which perturbed nonlinear delay controllable systems are controllable.
Chukwu, E. N.↗
An analysis of a nonlinear instability in the implementation of a VTOL control system
The contributions to nonlinear behavior and unstable response of the model following yaw control system of a VTOL aircraft during hover were determined. The system was designed as a state rate feedback implicit model follower that provided yaw rate command/heading hold capability and used combined full authority parallel and limited authority series servo actuators to generate an input to the yaw reaction control system of the aircraft. Both linear and nonlinear system models, as well as describing function linearization techniques were used to determine the influence on the control system instability of input magnitude and bandwidth, series servo authority, and system bandwidth. Results of the analysis describe stability boundaries as a function of these system design characteristics.
Weber, J. M.↗
Postbuckling of long orthotropic plates in combined shear and compression
The nonlinear large-deflection partial differential equations of von karman for orthotropic plates loaded in combined shear and compression are converted into a set of first-order nonlinear ordinary differential equations by assuming trigonometric functions in one direction. These equations are solved numerically using a two point boundary problem solver which makes use of Newton's method. Results are obtained which determine the postbuckling behavior of rectangular plates with loading up to about three times the buckling load. Both isotropic and orthotropic composite plates are considered. Results show that orthotropic plates may behave quite differently than isotropic plates and that in-plane boundary conditions are important for plates loaded in shear.
Stein, M.↗
Magnetic and thermodynamic structure of the solar corona during sunspot minimum
A model of the solar corona during sunspot minimum was constructed. It was suggested that pole-equator asymmetry is caused by interaction of global azimuthal electric currents in the corona and potential magnetic fields originating below the corona. The problem was reduced to a nonlinear ordinary differential equation for a structural function. Taking the difference in electron density between the equatorial plane and the polar direction from observations, the basic equation was solved and the global electric current distribution around the Sun along with the magnetic and thermodynamic structures of the solar corona was derived. The asymmetry between the two hemispheres, which can be due to the magnetic quadrupole, is considered in detail. It is shown that an additional quadrupole term in the magnetic field representation affects the position of polar coronal hole boundaries differently in the two hemispheres. As a result, the outflow from the two polar regions is found to be different.
Osherovich, V. A.↗
Numerical solution of Euler's equation by perturbed functionals
A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.
Dey, S. K.↗
Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends
Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.
Robertson, D. K.↗
Optimal placement of critical speeds in rotor-bearing systems
The design of a rotor-bearing system is an iterative process in which the parameters that influence the design are modified until the desired design objectives are achieved. Primary among the design objectives is the minimization of the response amplitude within the operating range of the rotor system. An automated design procedure for the optimal placement of the critical speeds of a rotor is presented. The desired design objective is cast as a nonlinear programming problem that minimizes an objective function subject to constraints. The optimization program interacts with an analysis program to search for the feasible optimal design.
Rajan, M.↗
A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment
A method is proposed for treating steady-state, thermally driven convection using the full direct interaction approximation to treat the nonlinear energy transfer and a prescribed instability function to model the eenrgy input. The instability function used is the growth rate of the mechanism generating the turbulence. This methodology can be easily generalized and applied to other driving mechanisms. The 1/3 power law form of the N vs. R relation for water is duplicated here and the coefficient is computed, using a two-point closure, to be less than about 0.08.
Hartke, Gregory J.↗
On 3D inelastic analysis methods for hot section components
Accomplishments are described for the 2-year program, to develop advanced 3-D inelastic structural stress analysis methods and solution strategies for more accurate and cost effective analysis of combustors, turbine blades and vanes. The approach was to develop a matrix of formulation elements and constitutive models. Three constitutive models were developed in conjunction with optimized iterating techniques, accelerators, and convergence criteria within a framework of dynamic time incrementing. Three formulations models were developed; an eight-noded mid-surface shell element, a nine-noded mid-surface shell element and a twenty-noded isoparametric solid element. A separate computer program was developed for each combination of constitutive model-formulation model. Each program provides a functional stand alone capability for performing cyclic nonlinear structural analysis. In addition, the analysis capabilities incorporated into each program can be abstracted in subroutine form for incorporation into other codes or to form new combinations.
Mcknight, R. L.↗
Robust computer-aided synthesis and optimization of linear multivariable control systems with varying plant dynamics via AUTOCON
AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.
Lefkowitz, C. P.↗
Development of a funding, cost, and spending model for satellite projects
The need for a predictive budget/funging model is obvious. The current models used by the Resource Analysis Office (RAO) are used to predict the total costs of satellite projects. An effort to extend the modeling capabilities from total budget analysis to total budget and budget outlays over time analysis was conducted. A statistical based and data driven methodology was used to derive and develop the model. Th budget data for the last 18 GSFC-sponsored satellite projects were analyzed and used to build a funding model which would describe the historical spending patterns. This raw data consisted of dollars spent in that specific year and their 1989 dollar equivalent. This data was converted to the standard format used by the RAO group and placed in a database. A simple statistical analysis was performed to calculate the gross statistics associated with project length and project cost ant the conditional statistics on project length and project cost. The modeling approach used is derived form the theory of embedded statistics which states that properly analyzed data will produce the underlying generating function. The process of funding large scale projects over extended periods of time is described by Life Cycle Cost Models (LCCM). The data was analyzed to find a model in the generic form of a LCCM. The model developed is based on a Weibull function whose parameters are found by both nonlinear optimization and nonlinear regression. In order to use this model it is necessary to transform the problem from a dollar/time space to a percentage of total budget/time space. This transformation is equivalent to moving to a probability space. By using the basic rules of probability, the validity of both the optimization and the regression steps are insured. This statistically significant model is then integrated and inverted. The resulting output represents a project schedule which relates the amount of money spent to the percentage of project completion.
Johnson, Jesse P.↗