Iterative solution of nonlinear optimal control problems.
Mathematical programming methods for solving nonlinear state-constrained discrete optimal control problems
DYNAMIC PROGRAMMING↗
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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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Occupant Responses in a Full-Scale Crash Test of the Sikorsky ACAP Helicopter
A full-scale crash test of the Sikorsky Advanced Composite Airframe Program (ACAP) helicopter was performed in 1999 to generate experimental data for correlation with a crash simulation developed using an explicit nonlinear, transient dynamic finite element code. The airframe was the residual flight test hardware from the ACAP program. For the test, the aircraft was outfitted with two crew and two troop seats, and four anthropomorphic test dummies. While the results of the impact test and crash simulation have been documented fairly extensively in the literature, the focus of this paper is to present the detailed occupant response data obtained from the crash test and to correlate the results with injury prediction models. These injury models include the Dynamic Response Index (DRI), the Head Injury Criteria (HIC), the spinal load requirement defined in FAR Part 27.562(c), and a comparison of the duration and magnitude of the occupant vertical acceleration responses with the Eiband whole-body acceleration tolerance curve.
Jackson, Karen E.↗
Occupant Responses in a Full-Scale Crash Test of the Sikorsky ACAP Helicopter
A full-scale crash test of the Sikorsky Advanced Composite Airframe Program (ACAP) helicopter was performed in 1999 to generate experimental data for correlation with a crash simulation developed using an explicit nonlinear, transient dynamic finite element code. The airframe was the residual flight test hardware from the ACAP program. For the test, the aircraft was outfitted with two crew and two troop seats, and four anthropomorphic test dummies. While the results of the impact test and crash simulation have been documented fairly extensively in the literature, the focus of this paper is to present the detailed occupant response data obtained from the crash test and to correlate the results with injury prediction models. These injury models include the Dynamic Response Index (DRI), the Head Injury Criteria (HIC), the spinal load requirement defined in FAR Part 27.562(c), and a comparison of the duration and magnitude of the occupant vertical acceleration responses with the Eiband whole-body acceleration tolerance curve.
Jackson, Karen E.↗
Analyses of Multishaft Rotor-Bearing Response
Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).
Nelson, H. D.↗
Hybrid Differential Dynamic Programming with Stochastic Search
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Aziz, Jonathan↗
Predicting the Dynamic Behavior of High-Speed Roller Bearings
Computer program developed for solving nonlinear differential equations of motion of high-speed, lightly loaded, cylindrical roller bearing. Program organized into three major parts: Main program, controls input and output; differential equation solver; and subroutines, used to evaluate vector function. Program has capability of performing either twodimensional or three-dimensional simulation.
Conry, T. F.↗
Hybrid Differential Dynamic Programming with Stochastic Search
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Aziz, Jonathan↗
Influence of thermal distortion on the anomalous behavior of a gravity gradient satellite
Consideration of the problem of determining the influence of solar heating on the low-frequency dynamic stability of a gravity-gradient satellite. The scope of the effort includes the development of a computer program that uses a quasi-static approach for describing a satellite's unsteady orbital motion. The essential feature of the quasi-static approach is that the satellite's long, slender booms reach their thermal equilibrium position solely as a result of thermal bending without consideration of the dynamic effects of boom vibration. A nonlinear analytical model and a corresponding computer program have been developed to study the effect of absorptivity, sun angle, and hinge stiffness on the stability of a satellite's motion.
Goldman, R. L.↗
Advanced control techniques for modern inertia based inverters
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.
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Program Solves Euler Equations Of Supersonic Flow
EMTAC (Euler Marching Technique For Accurate Computation) computer program employs Euler marching algorithm for computing supersonic flows. Enables accurate nonlinear analysis of nonlinear dynamics of supersonic flow over wide range of supersonic mach numbers and angles of attack. Based on exact equations of dynamics of inviscid gas and valid for computations of flows at low and high supersonic mach numbers exhibiting strong shocks and rotational effects. Program also used for inviscid three-dimensional flows fully subsonic or transonic (subsonic with supersonic pockets). Written in FORTRAN V.
Szema, Kuo-Yen↗
Hubble space telescope: Pointing error effects on nonlinear ball joints
The Hubble Space Telescope pointing error produced by optical benches mounted on free ball joints is examined. Spacecraft cable connections are assumed to produce translational and rotational damping and restoring forces which act through the optical bench center of mass. The nonlinear dynamics are modeled and then implemented using an existing computer program for simulating the vehicle dynamics and pointing control system algorithm. Results are presented for the test case which indicate acceptable performance.
Farmer, J. E.↗
Enhanced rotor modeling tailored for rub dynamic stability analysis and simulation
New methods are presented that allow straightforward application of complex nonlinearities to finite element based rotor dynamic analyses. The key features are: (1) the methods can be implemented with existing finite element or dynamic simulation programs, (2) formulation is general for simple application to a wide range of problems, and (3) implementation is simplified because nonlinear aspects are separated from the linear part of the model. The new techniques are illustrated with examples of inertial nonlinearity and torquewhirl which can be important in rubbing turbomachinery. The sample analyses provide new understanding of these nonlinearities which are discussed.
Davis, R. R.↗
New second-order and first-order algorithms for determining optimal control - A differential dynamic programming approach.
Differential dynamic programming algorithms of second and first order for optimal control, considering nonlinear unconstrained and constrained problems
Jacobson, D. H.↗
Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations
This paper discusses numerical aspects of computing maximum likelihood estimates for linear dynamical systems in state-vector form. Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined. The problems due to singular Hessian or singular information matrix that are common in practice are discussed in detail and methods for their solution are proposed. New results on the calculation of state sensitivity functions via reduced order models are given. Several methods for speeding convergence and reducing computation time are also discussed.
Gupta, N. K.↗
Formulation and validation of high-order linearized models of helicopter flight mechanics
A high-order linearized model of helicopter flight dynamics is extracted from a nonlinear time domain simulation. The model has 29 states that describe the fuselage rigid body degrees of freedom, the flap and lag dynamics in a nonrotating coordinate system, the inflow dynamics, the delayed entry of the horizontal tail into the main rotor wake, and, approximately, the blade torsion dynamics. The nonlinear simulation is obtained by extensively modifying the GENHEL computer program. The results indicate that the agreement between the linearized and the nonlinear model is good for small perturbations, and deteriorates for large amplitude maneuvers.
Kim, Frederick D.↗
Optimal active control for Burgers equations
A method for active fluid flow control based on control theory is discussed. Dynamic programming and fixed point successive approximations are used to accommodate the nonlinear control problem. The long-term goal of this project is to establish an effective method applicable to complex flows such as turbulence and jets. However, in this report, the method is applied to stochastic Burgers equation as an intermediate step towards this goal. Numerical results are compared with those obtained by gradient search methods.
Ikeda, Yutaka↗
NASA LeRC/Akron University Graduate Cooperative Fellowship Program and Graduate Student Researchers Program
The requisite methodology to solve linear and nonlinear problems associated with the static and dynamic analysis of rotating machinery, their static and dynamic behavior, and the interaction between the rotating and nonrotating parts of an engine is developed. Linear and nonlinear structural engine problems are investigated by developing solution strategies and interactive computational methods whereby the man and computer can communicate directly in making analysis decisions. Representative examples include modifying structural models, changing material, parameters, selecting analysis options and coupling with interactive graphical display for pre- and postprocessing capability.
Fertis, D. G.↗
Dynamic Finite Element Predictions for Mars Sample Return Cellular Impact Test #4
The nonlinear finite element program MSC.Dytran was used to predict the impact pulse for (he drop test of an energy absorbing cellular structure. This pre-test simulation was performed to aid in the design of an energy absorbing concept for a highly reliable passive Earth Entry Vehicle (EEV) that will directly impact the Earth without a parachute. In addition, a goal of the simulation was to bound the acceleration pulse produced and delivered to the simulated space cargo container. EEV's are designed to return materials from asteroids, comets, or planets for laboratory analysis on Earth. The EEV concept uses an energy absorbing cellular structure designed to contain and limit the acceleration of space exploration samples during Earth impact. The spherical shaped cellular structure is composed of solid hexagonal and pentagonal foam-filled cells with hybrid graphite-epoxy/Kevlar cell walls. Space samples fit inside a smaller sphere at the enter of the EEV's cellular structure. The material models and failure criteria were varied to determine their effect on the resulting acceleration pulse. Pre-test analytical predictions using MSC.Dytran were compared with the test results obtained from impact test #4 using bungee accelerator located at the NASA Langley Research Center Impact Dynamics Research Facility. The material model used to represent the foam and the proper failure criteria for the cell walls were critical in predicting the impact loads of the cellular structure. It was determined that a FOAMI model for the foam and a 20% failure strain criteria for the cell walls gave an accurate prediction of the acceleration pulse for drop test #4.
Fasanella, Edwin L.↗