Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic derivatives”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Analytical derivation and verification of zero-gyro control for the IUE satellite

The International Ultraviolet Explorer (IUE) satellite was launched January 26, 1978 into a geosynchronous orbit over South America. From its stationary position, the telescope maintains continuous communication with the control centers at NASA's Goddard Space Flight Center in Greenbelt, Maryland, and at the European Space Agency's (ESA's) Villagranca del Castillo Satellite Tracking Station in Spain. Since its launch in 1978, the satellite has gradually lost four of the original six gyroscopes in the Inertial Reference Assembly (IRA). In August 1985, the fourth of the original six gyros failed and a two-gyro system developed by NASA-GSFC was uplinked to the satellite and is currently in use. A one-gyro system also developed by NASA-GSFC is ready for use in case of another gyro failure. In the event that the sixth gyro should also fail, a zero-gyro system is being developed. The goal of this system is to provide interial target pointing without the use of gyroscopes. The satellite has sun sensors to provide attitude information about two of the three axes. It relies upon the exchange of reaction wheel momenta to determine angular position and rate of the third axis.

Bowles, Tiffany↗
NASA NTRS2002

Comparison of ISS Power System Telemetry with Analytically Derived Data for Shadowed Cases

Accurate International Space Station (ISS) power prediction requires the quantification of solar array shadowing. Prior papers have discussed the NASA Glenn Research Center (GRC) ISS power system tool SPACE (System Power Analysis for Capability Evaluation) and its integrated shadowing algorithms. On-orbit telemetry has become available that permits the correlation of theoretical shadowing predictions with actual data. This paper documents the comparison of a shadowing metric (total solar array current) as derived from SPACE predictions and on-orbit flight telemetry data for representative significant shadowing cases. Images from flight video recordings and the SPACE computer program graphical output are used to illustrate the comparison. The accuracy of the SPACE shadowing capability is demonstrated for the cases examined.

Fincannon, H. James↗
NASA NTRS2003

International Space Station Power System Telemetry Compared With Analytically Derived Data for Shadowed Cases

This article highlights fiscal year 2002 work performed by NASA Glenn Research Center personnel to validate algorithms and data developed in-house to predict shadowing effects on the International Space Station (ISS) solar arrays power generation. The validation effort utilized video footage and on-orbit telemetry for cases spanning a 1-yr period. Validation was required because of the uncertainty of various aspects involved in shadowing analysis. Results show that a good comparison exists between actual and predicted shadowed power system performance for solar array front and backside shadowing.

Fincannon, H. James↗
NASA NTRS2006

Analytical Derivation of the Vegetation Optical Depth from the Microwave Polarization Difference Index

A numerical solution for the canopy optical depth in an existing microwave-based land surface parameter retrieval model is presented. The optical depth is derived from the microwave polarization difference index and the dielectric constant of the soil. The original procedure used an approximation in the form of a logarithmic decay function to define this relationship, and was derived through a series of lengthy polynomials. These polynomials had to be recalculated when the scattering albedo or antenna incidence angle changes. The new procedure is computationally more efficient and accurate.

Meesters, Antoon G. C. A.↗
NASA NTRS2014

Partial Derivatives of the Lambert Problem

A procedure for deriving analytic partial derivatives of the Lambert problem is presented. Using the universal, cosine based Lambert formulation; first order partial derivatives of the velocities with respect to the positions and times are developed. Taking advantage of inherent symmetries and intermediate variables, the derivatives are expressed in a computationally efficient form. The added cost of computing these partials is found to be approximately 10% to approximately 60% of the Lambert compute cost. The availability of analytic partial derivatives increases optimization speed, efficiency and allows for trajectory optimization formulations that implicitly enforce continuity constraints via embedded Lambert problems.

trajectory computation↗
NASA NTRS1972

Analytic partial derivatives for estimating low-thrust parameters.

Analytic partial derivatives for estimating orbital low-thrust parameters via differential correction are developed and compared with two different numerical methods. The formulation is independent of the particular thrust model used and is applicable to all physically possible elliptic orbits. The starting point for the development is the set of variational equations of the elliptic orbital elements in the form due to Lagrange. The first time derivatives of the elements are transformed to derivatives with respect to the space variable, true anomaly, and integrated to first order in closed form in a straightforward general perturbations approach, with one exception: particular attention is given to the mean anomaly as influenced by thrust perturbations in the semimajor axis so that the complete first-order effect is included. The partials of the elements are then taken with respect to any given thrust parameter. Two comparisons are made with numerical methods for computing these thrust partials: numerical quotients and numerical integration of the variational equations for thrust.

Cunningham, G. W.↗
NASA NTRS1993

Control system design for flexible structures using data models

The dynamics and control of flexible aerospace structures exercises many of the engineering disciplines. In recent years there has been considerable research in the developing and tailoring of control system design techniques for these structures. This problem involves designing a control system for a multi-input, multi-output (MIMO) system that satisfies various performance criteria, such as vibration suppression, disturbance and noise rejection, attitude control and slewing control. Considerable progress has been made and demonstrated in control system design techniques for these structures. The key to designing control systems for these structures that meet stringent performance requirements is an accurate model. It has become apparent that theoretically and finite-element generated models do not provide the needed accuracy; almost all successful demonstrations of control system design techniques have involved using test results for fine-tuning a model or for extracting a model using system ID techniques. This paper describes past and ongoing efforts at Ohio University and NASA MSFC to design controllers using 'data models.' The basic philosophy of this approach is to start with a stabilizing controller and frequency response data that describes the plant; then, iteratively vary the free parameters of the controller so that performance measures become closer to satisfying design specifications. The frequency response data can be either experimentally derived or analytically derived. One 'design-with-data' algorithm presented in this paper is called the Compensator Improvement Program (CIP). The current CIP designs controllers for MIMO systems so that classical gain, phase, and attenuation margins are achieved. The center-piece of the CIP algorithm is the constraint improvement technique which is used to calculate a parameter change vector that guarantees an improvement in all unsatisfied, feasible performance metrics from iteration to iteration. The paper also presents a recently demonstrated CIP-type algorithm, called the Model and Data Oriented Computer-Aided Design System (MADCADS), developed for achieving H(sub infinity) type design specifications using data models. Control system design for the NASA/MSFC Single Structure Control Facility are demonstrated for both CIP and MADCADS. Advantages of design-with-data algorithms over techniques that require analytical plant models are also presented.

Irwin, R. Dennis↗
NASA NTRS1989

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.

Fenyes, Peter A.↗
NASA NTRSDate not supplied

Analytical Partial Derivatives of the Q-Law Guidance Algorithm

One method of producing low-thrust trajectories is the closed-loop Q-Law guidance algorithm. This work wraps Q-Law inside a nonlinear programming problem to search for locally optimal gain combinations and enforce nonlinear constraints on the initial state. Gradient-based trajectory optimization has been shown to benefit greatly when analytical partial derivatives are supplied to the optimizer. This paper presents the Q-Law optimization problem setup and derives the Q-Law thrust vector partial derivatives for the State Transition Matrix required by standard nonlinear optimization software.

Jackson L Shannon↗
NASA NTRS2011

Linearized T-Matrix and Mie Scattering Computations

We present a new linearization of T-Matrix and Mie computations for light scattering by non-spherical and spherical particles, respectively. In addition to the usual extinction and scattering cross-sections and the scattering matrix outputs, the linearized models will generate analytical derivatives of these optical properties with respect to the real and imaginary parts of the particle refractive index, and (for non-spherical scatterers) with respect to the ''shape'' parameter (the spheroid aspect ratio, cylinder diameter/height ratio, Chebyshev particle deformation factor). These derivatives are based on the essential linearity of Maxwell's theory. Analytical derivatives are also available for polydisperse particle size distribution parameters such as the mode radius. The T-matrix formulation is based on the NASA Goddard Institute for Space Studies FORTRAN 77 code developed in the 1990s. The linearized scattering codes presented here are in FORTRAN 90 and will be made publicly available.

Analytic linearization↗
NASA NTRS1999

Experimental and Numerical Optimization of a High-Lift System to Improve Low-Speed Performance, Stability, and Control of an Arrow-Wing Supersonic Transport

An investigation was performed to evaluate leading-and trailing-edge flap deflections for optimal aerodynamic performance of a High-Speed Civil Transport concept during takeoff and approach-to-landing conditions. The configuration used for this study was designed by the Douglas Aircraft Company during the 1970's. A 0.1-scale model of this configuration was tested in the Langley 30- by 60-Foot Tunnel with both the original leading-edge flap system and a new leading-edge flap system, which was designed with modem computational flow analysis and optimization tools. Leading-and trailing-edge flap deflections were generated for the original and modified leading-edge flap systems with the computational flow analysis and optimization tools. Although wind tunnel data indicated improvements in aerodynamic performance for the analytically derived flap deflections for both leading-edge flap systems, perturbations of the analytically derived leading-edge flap deflections yielded significant additional improvements in aerodynamic performance. In addition to the aerodynamic performance optimization testing, stability and control data were also obtained. An evaluation of the crosswind landing capability of the aircraft configuration revealed that insufficient lateral control existed as a result of high levels of lateral stability. Deflection of the leading-and trailing-edge flaps improved the crosswind landing capability of the vehicle considerably; however, additional improvements are required.

Hahne, David E.↗
NASA NTRS1972

A multiple-impulse function for orbital transfer and its derivatives

A multiple-impulse function is represented as a sequence of single-impulse functions. The single-impulse transfer which yields the velocity change required to transfer from a specified initial orbit to a partially specified final orbit is developed. Analytic derivatives of the function are obtained for use in optimization techniques. A four-impulse transfer is outlined. The analytic derivatives may allow more efficient optimization than numerical derivatives do.

Kibler, J. F.↗
NASA NTRS1978

Efficiency of unconstrained minimization techniques in nonlinear analysis

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Kamat, M. P.↗
NASA NTRS1977

The design of hydraulic pressure regulators that are stable without the use of sensing line restrictors or frictional dampers

Parameters controlled in design determine the stability of hydraulic pressure regulators in service. The non-linear sensing line restrictor can provide stability, but degrades the transient response. Linear damping is not always physically realizable and is sensitive to clearance and viscosity. Design relationships are analytically derived through which regulators can be made to be stable without the use of either of these damping means. The analytical distinctions between the parameters derived and those in prior literature are discussed. An analytically derived circuit component that stabilizes an otherwise unstable regulator and its experimental verification is described.

Gold, H.↗
NASA NTRS2003

Rate Constant for the Reaction CH3 + CH3 Yields C2H6 at T = 155 K and Model Calculation of the CH3 Abundance in the Atmospheres of Saturn and Neptune

The column abundances of CH3 observed by the Infrared Space Observatory (ISO) satellite on Saturn and Neptune were lower than predicted by atmospheric photochemical models, especially for Saturn. It has been suggested that the models underestimated the loss of CH3 due to poor knowledge of the rate constant k of the CH3 + CH3 self-reaction at the low temperatures and pressures of these atmospheres. Motivated by this suggestion, we undertook a combined experimental and photochemical modeling study of the CH3 + CH3 reaction and its role in determining planetary CH3 abundances. In a discharge flow-mass spectrometer system, k was measured at T = 155 K and three pressures of He. The results in units of cu cm/molecule/s are k(0.6 Torr) = 6.82 x 10(exp -11), k(1.0 Torr) = 6.98 x 10(exp -11), and k(1.5 Torr) = 6.91 x 10(exp -11). Analytical expressions for k were derived that (1) are consistent with the present laboratory data at T = 155 K, our previous data at T = 202 K and 298 K, and those of other studies in He at T = 296-298 K and (2) have some theoretical basis to provide justification for extrapolation. The derived analytical expressions were then used in atmospheric photochemical models for both Saturn and Neptune. These model results reduced the disparity with observations of Saturn, but not with observations of Neptune. However, the disparity for Neptune is much smaller. The solution to the remaining excess CH3 prediction in the models relative to the ISO observations lies, to a large extent, elsewhere in the CH3 photochemistry or transport, not in the CH3 + CH3 rate.

Cody, Regina J.↗
NASA NTRS1990

An alternative formulation of the global sensitivity equations

To optimize the performance of any system, the sensitivity derivatives of the system's output variables with respect to its input variables must be readily available. It is also desirable that these derivatives be inexpensive to calculate as the optimization process requires many evaluations of the output variables and their derivatives. Optimization methods that have been developed for use in automated structural design programs may not be extended for use in integrated multidisciplinary design programs until adequate means of calculating accurate sensitivity derivatives of complex, internally coupled systems have been developed. Until the development of the Global Sensitivity Equations (GSE), the only method of determining the sensitivity derivatives of coupled systems has been by using finite differences. Analytical or semi-analytical derivatives do not exist as there is no analytical solution to the coupled problem. Also, difficulties arise because the finite difference method is expensive as the system has to iterate to a converged solution for each incremental input variable. The method may not be accurate, and the choice of the input variable increment may cause the difference in the output variable to be insignificant compared to computer numerical error if the choice is too small, or the process may not predict the true value of the output variable if the increment is too large. The GSE allow the system's sensitivity derivatives to be calculated as functions of the component subsystem's (local) sensitivity derivatives. These local sensitivity derivatives are calculated from specifically decoupled subsystems, whereas the GSE account for total system coupling. Since the subsystems are decoupled, it may be possible for the local derivatives to be calculated by analytical or semi-analytical methods, which generally reduce cost and improve accuracy. Several academic problems have been solved using GSE and have demonstrated encouraging results.

James, Benjamin B.↗