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NASA NTRS1991

Centralized, decentralized, and independent control of a flexible manipulator on a flexible base

The dynamics and control of a flexible manipulator arm with payload mass on a flexible base in space are considered. The controllers are provided by one torquer at the center of the base and one torquer at the connection joint of the robot and the base. The nonlinear dynamics of the system is modeled by applying the finite element method and Lagrangian formula. Three control strategies are considered and compared, i.e., centralized control, decentralized control, and independent control. All these control designs are based on the linear quadratic regulator theory. A mathematical decomposition is used in the decentralization process so that the coupling between the subsystems is weak, while a physical decomposition is used in the independent control design process. For both the decentralized and the independent controls, the stability of the overall linear system is checked before a numerical simulations is initiated. Two numerical examples show that the response of the independent control system are close to those of the centralized control system, while the responses of the decentralized control system are not.

Li, Feiyue↗

NASA NTRS2002

Small-Scale Tropopause Dynamics and TOMS Total Ozone

This project used Earth Probe Total Ozone Mapping Spectrometer (EP TOMS) along-track ozone retrievals, in conjunction with ancillary meteorological fields and modeling studies, for high resolution investigations of upper troposphere and lower stratosphere dynamics. Specifically, high resolution along-track (Level 2) EP TOMS data were used to investigate the beautiful fine-scale structure in constituent and meteorological fields prominent in the evolution of highly non-linear baroclinic storm systems. Comparison was made with high resolution meteorological models. The analyses provide internal consistency checks and validation of the EP TOMS data which are vital for monitoring ozone depletion in both polar and midlatitude regions.

Stanford, John L.↗

NASA NTRS2003

Quantum Dynamics Scattering Study of AB+CDE Reactions: A Seven Dimensional Treatment for the H2+C2H Reaction

A time-dependent wave-packet approach is presented for the quantum dynamics study of the AB+CDE reaction system for zero total angular momentum. A seven-degree-of-freedom calculation is employed to study the chemical reaction of H2+C2H yields H + C2H2 by treating C2H as a linear molecule. Initial state selected reaction probabilities are presented for various initial ro-vibrational states. This study shows that vibrational excitation of H2 enhances the reaction probability, whereas the excitation of C2H has only a small effect on the reactivity. An integral cross section is also reported for the initial ground states of H2 and C2H. The theoretical and experimental results agree with each other very well when the calculated seven dimensional results are adjusted to account for the lower transition state barrier heights found in recent ab initio calculations.

Wang, Dunyou↗

NASA NTRS1992

Spatial orientation of the vestibular system

1. A simplified three-dimensional state space model of visual vestibular interaction was formulated. Matrix and dynamical system operators representing coupling from the semicircular canals and the visual system to the velocity storage integrator were incorporated into the model. 2. It was postulated that the system matrix for a tilted position was a composition of two linear transformations of the system matrix for the upright position. One transformation modifies the eigenvalues of the system matrix while another rotates the pitch and roll eigenvectors with the head, while maintaining the yaw axis eigenvector approximately spatially invariant. Using this representation, the response characteristics of the pitch, roll, and yaw eye velocity were obtained in terms of the eigenvalues and associated eigenvectors. 3. Using OKAN data obtained from monkeys and comparing to the model predictions, the eigenvalues and eigenvectors of the system matrix were identified as a function of tilt to the side or of tilt to the prone positions, using a modification of the Marquardt algorithm. The yaw eigenvector for right-side-down tilt and for downward pitch cross-coupling was approximately 30 degrees from the spatial vertical. For the prone position, the eigenvector was computed to be approximately 20 degrees relative to the spatial vertical. For both side-down and prone positions, oblique OKN induced along eigenvector directions generated OKAN which decayed to zero along a straight line with approximately a single time constant. This was verified by a spectral analysis of the residual sequence about the straight line fit to the decaying data. The residual sequence was associated with a narrow autocorrelation function and a wide power spectrum. 4. Parameters found using the Marquardt algorithm were incorporated into the model. Diagonal matrices in a head coordinate frame were introduced to represent the direct pathway and the coupling of the visual system to the integrator. Model simulations predicted the behavior of yaw and pitch OKN and OKAN when the animal was upright, as well as the cross-coupling in the tilted position. The trajectories in velocity space were also accurately simulated. 5. There were similarities between the monkey eigenvectors and human perception of the spatial vertical. For side-down tilts and downward eye velocity cross-coupling, there was only an Aubert (A) effect. For upward eye velocity cross-coupling there were both Muller (E) and Aubert (A) effects. The mean of the eigenvectors for upward and downward eye velocities overlay human 1 x g perceptual data.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Neuroscience↗

NASA NTRS2009

The Influence of the 2006 Indonesian Biomass Burning Aerosols on Tropical Dynamics Studied with the GEOS-5 AGCM

The direct and semi-direct effects of aerosols produced by Indonesian biomass burning (BB) during August November 2006 on tropical dynamics have been examined using NASA's Goddard Earth Observing System, Version 5 (GEOS-5) atmospheric general circulation model (AGCM). The AGCM includes CO, which is transported by resolved and sub-grid processes and subject to a linearized chemical loss rate. Simulations were driven by two sets of aerosol forcing fields calculated offline, one that included Indonesian BB aerosol emissions and one that did not. In order to separate the influence of the aerosols from internal model variability, the means of two ten-member ensembles were compared. Diabatic heating from BB aerosols increased temperatures over Indonesia between 150 and 400 hPa. The higher temperatures resulted in strong increases in upward grid-scale vertical motion, which increased water vapor and CO over Indonesia. In October, the largest increases in water vapor were found in the mid-troposphere (~25%) while the largest increases in CO occurred just below the tropopause (80 ppbv or ~50%). Diabatic heating from the Indonesian BB aerosols caused CO to increase by 9% throughout the tropical tropopause layer in November and 5% in the lower stratosphere in December. The results demonstrate that aerosol heating plays an important role in the transport of BB pollution and troposphere-to-stratosphere transport. Changes in vertical motion and cloudiness induced by aerosol heating can also alter the transport and phase of water vapor in the upper troposphere/lower stratosphere.

Ott, Lesley↗

NASA NTRS2010

Free-Free Transitions in the Presence of Laser Fields at Very Low Incident Electron Energy

We study the free-free transition in electron-hydrogenic systems in ground state in presence of an external laser field at very loud incident energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The laser field is chosen to be monochromatic, linearly polarized and homogeneous. The incident electron is considered to be dressed by the laser in a nonperturbative manner by choosing a Volkov wave function for it. The scattering weave function for the electron is solved numerically by taking into account the effect of the electron exchange, short-range as well as of the long-range interactions to get the S and P wave phase shifts while for the higher angular momentum phase shifts the exchange approximation has only been considered. We calculate the laser assisted differential cross sections (LADCS) for the aforesaid free-free transition process for single photon absorption/emission. The laser intensity is chosen to be much less than the atomic field intensity. A strong suppression is noted in the LADCS as compared to the field free (FF) cross sections. Unlike the FF ones, the LADCS exhibit some oscillations having a distinct maximum at a low value of the scattering angle depending on the laser parameters as well as on the incident energies.

Bhatia, A. K.↗

NASA NTRS2009

Free-Free Transitions in the Presence of Laser Fields at Very Low Incident Electron Energy

We study the free-free transition in electron-hydrogenic systems in ground state in presence of an external laser field at very low incident energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The laser field is chosen to be monochromatic, linearly polarized and homogeneous. The incident electron is considered to be dressed by the laser in a nonperturbative manner by choosing a Volkov wave function for it The scattering wave function for the electron is solved numerically by taking into account the effect of the electron exchange, short-range as well as of the long-range interactions to get the S and P wave phase shifts while for the higher angular momentum phase shifts, the exchange approximation has only been considered. We calculate the laser-assisted differential cross sections (LADCS) for the aforesaid free-free transition process for single photon absorption/emission. The laser intensity is chosen to be much less than the atomic field intensity. A strong suppression is noted in the LADCS as compared to the field free (FF) cross sections. Unlike the FF ones, the LADCS exhibit some oscillations having a distinct maximum at a low value of the scattering angle depending on the laser parameters as well as on the incident energies.

Bhatia, Anand K.↗

NASA NTRS2015

Proportional and Integral Thermal Control System for Large Scale Heating Tests

The National Aeronautics and Space Administration Armstrong Flight Research Center (Edwards, California) Flight Loads Laboratory is a unique national laboratory that supports thermal, mechanical, thermal/mechanical, and structural dynamics research and testing. A Proportional Integral thermal control system was designed and implemented to support thermal tests. A thermal control algorithm supporting a quartz lamp heater was developed based on the Proportional Integral control concept and a linearized heating process. The thermal control equations were derived and expressed in terms of power levels, integral gain, proportional gain, and differences between thermal setpoints and skin temperatures. Besides the derived equations, user's predefined thermal test information generated in the form of thermal maps was used to implement the thermal control system capabilities. Graphite heater closed-loop thermal control and graphite heater open-loop power level were added later to fulfill the demand for higher temperature tests. Verification and validation tests were performed to ensure that the thermal control system requirements were achieved. This thermal control system has successfully supported many milestone thermal and thermal/mechanical tests for almost a decade with temperatures ranging from 50 F to 3000 F and temperature rise rates from -10 F/s to 70 F/s for a variety of test articles having unique thermal profiles and test setups.

Thermal Control System↗

NASA NTRS2016

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

Zubair, Mohammad↗

NASA NTRS1999

Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Ravindran, S. S.↗

NASA NTRS1975

Decentralized regulation of dynamic systems

A special class of decentralized control problem is discussed in which the objectives of the control agents are to steer the state of the system to desired levels. Each agent is concerned about certain aspects of the state of the entire system. The state and control equations are given for linear time-invariant systems. Stability and coordination, and the optimization of decentralized control are analyzed, and the information structure design is presented.

Chu, K. C.↗

NASA NTRS1985

Periodic orbits of the general three-body problem for the sun-Jupiter-Saturn system

Two families of symmetric periodic orbits of the planar, general, three-body problem are presented. The masses of the three bodies include ratios equal to the sun-Jupiter-Saturn system and the periods of the orbits of Jupiter and Saturn are in a 2:5 resonance. The (linear) stability of the orbits are studied in relation to eccentricity and mass variations. The generation of the two families of periodic orbits follows a systematic approach and employs (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to the elliptic restricted problem and from the circular and elliptic problems to the general problem through bifurcation phenomena relating the three dynamical systems. The approach also provides insight into the evolutionary process of periodic orbits continued from the restricted problems to the general problem.

Kwok, J. H.↗

NASA NTRS1995

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Goodrich, John W.↗

NASA NTRS2001

Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs

Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.

Starin, Scott R.↗

NASA NTRS1998

A Magnetic Suspension and Excitation System for Spin Vibration Testing of Turbomachinery Blades

The Dynamic Spin Rig (DSR) is used to perform vibration tests of turbomachinery blades and components under spinning conditions in a vacuum. A heteropolar radial active magnetic bearing was integrated into the DSR to provide non-contact magnetic suspension and mechanical excitation of the rotor to induce turbomachinery blade vibrations. The magnetic bearing replaces one of the two existing conventional radial ball bearings. Prior operation of the DSR used two voice-coil type linear electromagnetic shakers which provided axial excitation of the rotor. The new magnetic suspension and excitation system has provided enhanced testing capabilities. Tests were performed at high rotational speeds for longer duration and higher vibration amplitudes. Some characteristics of the system include magnetic bearing stiffness values up to 60,000 lb./in., closed loop control bandwidth around 500 Hz, and multi-directional radial excitation of the rotor. This paper reports on the implementation and operation of this system and presents some test results using this system.

Johnson, Dexter↗

NASA NTRS1971

The synthesis of optimal controls for linear, time-optimal problems with retarded controls.

Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.

Banks, H. T.↗

NASA NTRS1978

On the optimization of discrete structures with aeroelastic constraints

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Mcintosh, S. C., Jr.↗

NASA NTRS1989

Application of stochastic robustness to aircraft control systems

Stochastic robustness, a simple numerical procedure for estimating the stability robustness of linear, time-invariant systems, is applied to a forward-swept-wing aircraft control system. Based on Monte Carlo evaluation of the system's closed-loop eignevalues, this analysis approach introduces the probability of instability as a scalar stability robustness measure. The related stochastic root locus provides insight into robustness characteristics of the closed-loop system. Three Linear Quadratic controllers of decreasing robustness are chosen to demonstrate the use of stochastic robustness to analyze and compare control designs. Examples are presented illustrating the use of stochastic robustness analysis to address the effects of actuator dynamics and unmodeled dynamics on the stability robustness of the forward-swept-wing aircraft.

Stengel, Robert F.↗