Effective construction of linear state-variable models from input/output functions.
Algorithm for minimal realization of linear finite-dimensional dynamical system displayed by Markov parameters
DYNAMIC MODEL↗
SEARCH · Search NASA
Results for “linear chain model”
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.
Modeling of Interfacial Modification Effects on Thermal Conductivity of Carbon Nanotube Composites
The effect of functionalization of carbon nanotubes on the thermal conductivity of nanocomposites has been studied using a multi-scale modeling approach. These results predict that grafting linear hydrocarbon chains to the surface of a single wall carbon nanotube with covalent chemical bonds should result in a significant increase in the thermal conductivity of these nanocomposites. This is due to the decrease in the interfacial thermal (Kapitza) resistance between the single wall carbon nanotube and the surrounding polymer matrix upon chemical functionalization. The nanocomposites studied here consist of single wall carbon nanotubes in a bulk poly(ethylene vinyl acetate) matrix. The nanotubes are functionalized by end-grafting linear hydrocarbon chains of varying length to the surface of the nanotube. The effect which this functionalization has on the interfacial thermal resistance is studied by molecular dynamics simulation. Interfacial thermal resistance values are calculated for a range of chemical grafting densities and with several chain lengths. These results are subsequently used in an analytical model to predict the resulting effect on the bulk thermal conductivity of the nanocomposite.
Clancy, Thomas C.↗
Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems
The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.
Murthy, V. R.↗
Uncertainty Estimates of Psychoacoustic Thresholds Obtained from Group Tests
Adaptive psychoacoustic test methods, in which the next signal level depends on the response to the previous signal, are the most efficient for determining psychoacoustic thresholds of individual subjects. In many tests conducted in the NASA psychoacoustic labs, the goal is to determine thresholds representative of the general population. To do this economically, non-adaptive testing methods are used in which three or four subjects are tested at the same time with predetermined signal levels. This approach requires us to identify techniques for assessing the uncertainty in resulting group-average psychoacoustic thresholds. In this presentation we examine the Delta Method of frequentist statistics, the Generalized Linear Model (GLM), the Nonparametric Bootstrap, a frequentist method, and Markov Chain Monte Carlo Posterior Estimation and a Bayesian approach. Each technique is exercised on a manufactured, theoretical dataset and then on datasets from two psychoacoustics facilities at NASA. The Delta Method is the simplest to implement and accurate for the cases studied. The GLM is found to be the least robust, and the Bootstrap takes the longest to calculate. The Bayesian Posterior Estimate is the most versatile technique examined because it allows the inclusion of prior information.
Rathsam, Jonathan↗
Numerical methods in Markov chain modeling
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Philippe, Bernard↗
Spinning Rocket Simulator Turntable Design
Contained herein is the research and data acquired from the Turntable Design portion of the Spinning Rocket Simulator (SRS) project. The SRS Project studies and eliminates the effect of coning on thrust-propelled spacecraft. This design and construction of the turntable adds a structural support for the SRS model and two degrees of freedom. The two degrees of freedom, radial and circumferential, will help develop a simulated thrust force perpendicular to the plane of the spacecraft model while undergoing an unstable coning motion. The Turntable consists of a ten-foot linear track mounted to a sprocket and press-fit to a thrust bearing. A two-inch high column grounded by a Triangular Baseplate supports this bearing and houses the slip rings and pressurized, air-line swivel. The thrust bearing allows the entire system to rotate under the moment applied through the chain-driven sprocket producing a circumferential degree of freedom. The radial degree of freedom is given to the model through the helically threaded linear track. This track allows the Model Support and Counter Balance to simultaneously reposition according to the coning motion of the Model. Two design factors that hinder the linear track are bending and twist due to torsion. A Standard Aluminum "C" channel significantly reduces these two deflections. Safety considerations dictate the design of all the components involved in this project.
Miles, Robert W.↗
Multiscale Modeling of Thermal Conductivity of Polymer/Carbon Nanocomposites
Molecular dynamics simulation was used to estimate the interfacial thermal (Kapitza) resistance between nanoparticles and amorphous and crystalline polymer matrices. Bulk thermal conductivities of the nanocomposites were then estimated using an established effective medium approach. To study functionalization, oligomeric ethylene-vinyl alcohol copolymers were chemically bonded to a single wall carbon nanotube. The results, in a poly(ethylene-vinyl acetate) matrix, are similar to those obtained previously for grafted linear hydrocarbon chains. To study the effect of noncovalent functionalization, two types of polyethylene matrices. -- aligned (extended-chain crystalline) vs. amorphous (random coils) were modeled. Both matrices produced the same interfacial thermal resistance values. Finally, functionalization of edges and faces of plate-like graphite nanoparticles was found to be only modestly effective in reducing the interfacial thermal resistance and improving the composite thermal conductivity
Clancy, Thomas C.↗
Stress stiffening and approximate equations in flexible multibody dynamics
A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.
Padilla, Carlos E.↗
Dynamic workspace analysis of two cooperating robot arms
The main objective of dynamic workspace analysis is to determine the maximum force/moment that the robots can generate jointly at each point within their common workspace. The authors develop a conceptually simple procedure to solve this problem. This procedure models the two cooperating robot arms as a closed-chain system and is based on the theory of linear transformations and the properties of mechanics.
Tarn, T. J.↗
An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations
An approach to the control of constrained dynamic systems such as multiple arm systems, multifingered grippers, and walking vehicles is described. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus input to control the constraint or interaction forces and moments in the closed chain. A dynamic control model for the closed chain is derived that is suitable for designing a controller in which the trajectory and the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. These ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method.
Yun, Xiaoping↗
New nonlinear control algorithms for multiple robot arms
Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.
Tarn, T. J.↗
On reliable control system designs
A mathematical model for use in the design of reliable multivariable control systems is discussed with special emphasis on actuator failures and necessary actuator redundancy levels. The model consists of a linear time invariant discrete time dynamical system. Configuration changes in the system dynamics are governed by a Markov chain that includes transition probabilities from one configuration state to another. The performance index is a standard quadratic cost functional, over an infinite time interval. The actual system configuration can be deduced with a one step delay. The calculation of the optimal control law requires the solution of a set of highly coupled Riccati-like matrix difference equations. Results can be used for off-line studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.
Birdwell, J. D.↗
Nonlinear feedback control of multiple robot arms
Multiple coordinated robot arms are modeled by considering the arms: (1) as closed kinematic chains, and (2) as a force constrained mechanical system working on the same object simultaneously. In both formulations a new dynamic control method is discussed. It is based on a feedback linearization and simultaneous output decoupling technique. Applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, by choosing a general output equation, researchers can superimpose the position and velocity error feedback with the force-torque error feedback in the task space simultaneously.
Tarn, T. J.↗
Manipulation strategies for massive space payloads
Control for the bracing strategy is being examined. It was concluded earlier that trajectory planning must be improved to best achieve the bracing motion. Very interesting results were achieved which enable the inverse dynamics of flexible arms to be calculated for linearized motion in a more efficient manner than previously published. The desired motion of the end point beginning at t=0 and ending at t=t sub f is used to calculate the required torque at the joint. The solution is separated into a causal function that is zero for t is less than 0 and an accusal function which is zero for t is greater than t sub f. A number of alternative end point trajectories were explored in terms of the peak torque required, the amount of anticipatory action, and other issues. The single link case is the immediate subject and an experimental verification of that case is being performed. Modeling with experimental verification of closed chain dynamics continues. Modeling effort has pointed out inaccuracies that result from the choice of numerical techniques used to incorporate the closed chain constraints when modeling our experimental prototype RALF (Robotic Arm Large and Flexible). Results were compared to TREETOPS, a multi body code. The experimental verification work is suggesting new ways to make comparisons with systems having structural linearity and joint and geometric nonlinearity. The generation of inertial forces was studied with a small arm that will damp the large arm's vibration.
Book, Wayne J.↗
Nonlinear strain-displacement relations and flexible multibody dynamics
Dynamics of chains of flexible bodies undergoing large rigid body motions, but small elastic deflections are considered. The role of nonlinear strain-displacement relations in the development of the motion equations correct to first order in elastic deflections is investigated. The general form of these equations linearized only in the small elastic deflections is presented, and the relative significance of various nonlinear terms is studied both analytically and through the use of the numerical simulations. Numerical simulations are performed for a two link chain constrained to move in the plane, subject to hinge torques. Each link is modeled as a thin beam. Slew maneuver simulation results are compared for models with and without properly modeled kinematics of deformation. The goal of this case study is to quantify the importance of the terms in the equations of motion which arise from the inclusion of nonlinear strain-displacement relations. It is concluded that unless the consistently linearized equations in elastic deflections and speeds are available and necessary, the inconsistently (prematurely) linearized equations should be replaced in all cases by ruthlessly linearized equations: equations in which all nonlinear terms involving the elastic deflections and speeds are ignored.
Padilla, Carlos E.↗
Modelling and control of two coordinated robot arms
Two coordinated robot arms are modeled by considering the two arms as working on the same object simultaneously and as a closed kinematic chain. In both formulations, a novel dynamic control method is used which is based on feedback linearization and simultaneous output decoupling.
Tarn, T. J.↗
Momentum-Based Dynamics for Spacecraft with Chained Revolute Appendages
An efficient formulation is presented for a sub-class of multi-body dynamics problems that involve a six degree-of-freedom base body and a chain of N rigid linkages connected in series by single degree-of-freedom revolute joints. This general method is particularly well suited for simulations of spacecraft dynamics and control that include the modeling of an orbiting platform with or without internal degrees of freedom such as reaction wheels, dampers, and/or booms. In the present work, particular emphasis is placed on dynamic simulation of multi-linkage robotic manipulators. The differential equations of motion are explicitly given in terms of linear and angular momentum states, which can be evaluated recursively along a serial chain of linkages for an efficient real-time solution on par with the best of the O(N3) methods.
Queen, Steven↗
Summary of Research/Publications
Summary of research/publications include:(1) Comment on broadening of water microwave lines by collisions with helium atoms; (2) Calculations of ion-molecule deuterium fractionation reactions involving HD; (3) Ab initio predictions on the rotational spectra of carbon-chain carbene molecules; (4) Theoretical IR spectra of ionized naphthalene; (5) Improved collisional excitation rates for interstellar water; (6) Calculations on the competition between association and reaction for C3H+ + H2; (7) Theoretical infrared spectra of some model polycyclic aromatic hydrocarbons: effect of ionization; (8) Calculations concerning interstellar isomeric abundance ratios for C3H and C3H2; (9) New calculations on the ion-molecule processes C2H2+ + H2 C2H3+ + H and C2H2+ + H2 C2H4+; (10) Anisotropic rigid rotor potential energy function for H2O-H2; (11) A correlated ab initio study of linear carbon-chain radicals CnH (n=2-7); (12) Ab initio characterization of MgCCH, MgCCH+, and MgC2 and pathways to their formation in the interstellar medium; (13) Why HOC+ is detectable in interstellar clouds: The rate of the reaction between HOC+ and H2; (14) A correlated ab initio study of the X 2A 1 and A 2E states of MgCH3; (15) On the stability of interstellar carbon clusters: The rate of the reaction between C3 and O; and (16) The rate of the reaction between CN and C2H2 at interstellar temperatures.
Source record↗