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New method of computation for optimal stochastic nonlinear and adaptive control undergoing development. Solves systematically stochastic dynamic programming equations forward in time, using nested-stochastic-approximation technique. Main advantage, simplicity of programming and reduced complexity with clear performance/computation trade-offs.
An adaptive method in which cruise and nonlinear orbit determination problems can be solved using a single program is presented. It involves singular value decomposition augmented with an extended partial step algorithm. The extended partial step algorithm constrains the size of the correction to the spacecraft state and other solve-for parameters. The correction is controlled by an a priori covariance and a user-supplied bounds parameter. The extended partial step method is an extension of the update portion of the singular value decomposition algorithm. It thus preserves the numerical stability of the singular value decomposition method, while extending the region over which it converges. In linear cases, this method reduces to the singular value decomposition algorithm with the full rank solution. Two examples are presented to illustrate the method's utility.
The primary objective of this research program is the study of the magnetohydrodynamic (MHD) shocks and nonlinear simple waves produced as a result of the interaction of ejected lower coronal plasma with the ambient corona. The types of shocks and nonlinear simple waves produced for representative coronal conditions and disturbance velocities were determined. The wave system and the interactions between the ejecta and ambient corona were studied using both analytic theory and numerical solutions of the time-dependent, nonlinear MHD equations. Observations from the SMM coronagraph/polarimeter provided both guidance and motivation and are used extensively in evaluating the results. As a natural consequence of the comparisons with the data, the simulations assisted in better understanding the physical interactions in coronal mass ejections (CME's).
In this paper we present a preliminary optimal orbit analysis for the Laser Interferometer Space Antenna (LISA). LISA is a NASA/ESA mission to study gravitational waves and test predictions of general relativity. The nominal formation consists of three spacecraft in heliocentric orbits at 1 AU and trailing the Earth by twenty degrees. This configuration was chosen as a trade off to reduce the noise sources that will affect the instrument and to reduce the fuel to achieve the final orbit. We present equations for the nominal orbit design and discuss several different measures of performance for the LISA formation. All of the measures directly relate the formation dynamics to science performance. Also, constraints on the formation dynamics due to spacecraft and instrument limitations are discussed. Using the nominal solution as an initial guess, the formation is optimized using Sequential Quadratic Programming to maximize the performance while satisfying a set of nonlinear constraints. Results are presented for each of the performance measures.
We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-based, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system) and a factor of 5 in a non-diffusive system.
We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-brused, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system, and a factor of 5 in a non-diffusive system.
In this research three artificial intelligent (AI)-based techniques are proposed to regulate the voltage and frequency of a grid-connected inverter. The increase in the penetration of renewable energy sources (RESs) into the power grid has led to the increase in the penetration of fast-responding inertia-less power converters. The increase in the penetration of these power electronics converters changes the nature of the conventional grid, in which the existing kinetic inertia in the rotating parts of the enormous generators plays a vital role. The concept of virtual inertia control scheme is proposed to make the behavior of grid connected inverters more similar to the synchronous generators, by mimicking the mechanical behavior of a synchronous generator. Conventional control techniques lack to perform optimally in nonlinear, uncertain, inaccurate power grids. Besides, the decoupled control assumption in conventional VSGs makes them nonoptimal in resistive grids. The neural network predictive controller, the heuristic dynamic programming, and the dual heuristic dynamic programming techniques are presented in this research to overcome the draw backs of conventional VSGs. The nonlinear characteristics of neural networks, and the online training enable the proposed methods to perform as robust and optimal controllers. The simulation and the experimental laboratory prototype results are provided to demonstrate the effectiveness of the proposed techniques.
In order to improve the atom spin gyroscope's operational accuracy and compensate the random error caused by the nonlinear and weak-stability characteristic of the random atomic spin gyroscope (ASG) drift, the hybrid random drift error model based on autoregressive (AR) and genetic programming (GP) + genetic algorithm (GA) technique is established. The time series of random ASG drift is taken as the study object. The time series of random ASG drift is acquired by analyzing and preprocessing the measured data of ASG. The linear section model is established based on AR technique. After that, the nonlinear section model is built based on GP technique and GA is used to optimize the coefficients of the mathematic expression acquired by GP in order to obtain a more accurate model. The simulation result indicates that this hybrid model can effectively reflect the characteristics of the ASG's random drift. The square error of the ASG's random drift is reduced by 92.40%. Comparing with the AR technique and the GP + GA technique, the random drift is reduced by 9.34% and 5.06%, respectively. The hybrid modeling method can effectively compensate the ASG's random drift and improve the stability of the system.
An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.
A number of computer codes are available for performing thermal analysis of solid rocket motor nozzles. Aerotherm Chemical Equilibrium (ACE) computer program can be used to perform one-dimensional gas expansion to determine the state of the gas at each location of a nozzle. The ACE outputs can be used as input to a computer program called Momentum/Energy Integral Technique (MEIT) for predicting boundary layer development development, shear, and heating on the surface of the nozzle. The output from MEIT can be used as input to another computer program called Aerotherm Charring Material Thermal Response and Ablation Program (CMA). This program is used to calculate oblation or decomposition response of the nozzle material. A code called Failure Analysis Nonlinear Thermal and Structural Integrated Code (FANTASTIC) is also likely to be used for performing thermal analysis of solid rocket motor nozzles after the program is duly verified. A part of the verification work on FANTASTIC was done by using one and two dimension heat transfer examples with known answers. An attempt was made to prepare input for performing thermal analysis of the CCT nozzle using the FANTASTIC computer code. The CCT nozzle problem will first be solved by using ACE, MEIT, and CMA. The same problem will then be solved using FANTASTIC. These results will then be compared for verification of FANTASTIC.
Versions B and C of the unified subsonic and supersonic aerodynamic analysis program, USSAERO, are described. Version B incorporates a new symmetrical singularity method to provide improved surface pressure distributions on wings in subsonic flow. Version C extends the range of application of the program to include the analysis of multiple engine nacelles or finned external stores. In addition, nonlinear compressibility effects in high subsonic and supersonic flows are approximated using a correction based on the local Mach number at panel control points. Several examples are presented comparing the results of these programs with other panel methods and experimental data.
The purpose of the crash safety program is to support development of the technology to define and demonstrate new structural concepts for improved crash safety and occupant survivability in general aviation aircraft. The program involves three basic areas of research: full-scale crash simulation testing, nonlinear structural analyses necessary to predict failure modes and collapse mechanisms of the vehicle, and evaluation of energy absorption concepts for specific component design. Both analytical and experimental methods are being used to develop expertise in these areas. Analyses include both simplified procedures for estimating energy absorption capabilities and more complex computer programs for analysis of general airframe response. Full-scale tests of typical structures as well as tests on structural components are being used to verify the analyses and to demonstrate improved design concepts.
A computer program has been developed that computes the locus of intersection of a quadric cone and a sphere. The outputs of the program are a list of the longitude and latitude coordinates of the locus of intersection and a plot of the locus. It was written primarily to define the area of the earth covered by a narrow beam antenna carried on a synchronous satellite in circular, near equatorial orbits. The program was written for use with a CalComp 570/563 off-line plotting system and uses the standard CalComp subroutines supplied with the system. The plot is drawn using linear longitude and latitude scales and nonlinear scales such as Mercator scales cannot be used. It should be noted that this program assumes the earth to be spherical rather than oblate is it actually is. However, by assuming a spherical earth, maximum error distances of about 11.5 nautical miles are introduced. For many purposes, this error can be ignored.
In recent years much attention has been given to the development of methods and programs for the calculation of the aerodynamic characteristics of multiblade, saber-shaped air propellers. Most existing methods are based on the theory of lifting lines. Elsewhere, the theory of a lifting surface is used to calculate screw and lifting propellers. In this work, methods of discrete eddies are described for the calculation of the aerodynamic characteristics of propellers using the linear and nonlinear theories of lifting surfaces.
This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Realtime Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory.
Simulated characteristics mimic those of advanced turbofan engines. Computer program developed to offer those interested in engine dynamics and controls research efficient, realistic, and easily-used engine simulation. Simulation developed from linearized operating-point models but still retains essential nonlinear engine effects. Representative of hypothetical, low-bypass-ratio, twin-spool, axialflow turbofan engine. Program written in FORTRAN IV.
This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Real-Time Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory. The control methodology essentially employs loop shaping to implement linear control laws. while utilizing nonlinear elements as means of ameliorating the effects of actuator saturation in its coarse, main, and vernier stages. The linear controllers were implemented as high-order digital filters and were designed using Bode integral techniques to determine the loop shape. The nonlinear techniques encompass the areas of exact linearization, anti-windup control, nonlinear rate limiting and modal control. Details of the design procedure are given as well as data from the actual mechanism.
The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.