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At least 1,279 records · Page 71

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NASA NTRS1988

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.↗

NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on an MIMD (multiple instruction/multiple data stream) parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed, one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the iPSC/860.

Venkatakrishnan, V.↗

NASA NTRS1995

An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Fukumori, Ichiro↗

NASA NTRS1997

LQR Control of Shell Vibrations Via Piezoceramic Actuators

A model-based Linear Quadratic Regulator (LQR) method for controlling vibrations in cylindrical shells is presented. Surface-mounted piezo-ceramic patches are employed as actuators which leads to unbounded control input operators. Modified Donnell-Mushtari shell equations incorporating strong or Kelvin-Voigt damping are used to model the system. The model is then abstractly formulated in terms of sesquilinear forms. This provides a framework amenable for proving model well-posedness and convergence of LQR gains using analytic semigroup results combined with LQR theory for unbounded input operators. Finally, numerical examples demonstrating the effectiveness of the method are presented.

delRosario, R. C. H.↗

NASA NTRS1999

Recent Development in the Analytical Investigation of Shipboard Rotorcraft Engage and Disengage Operations

This paper presents an overview of recent developments in an effort to predict transient aeroelastic rotor response during shipboard engage and disengage sequences. The blade is modeled as an elastic beam undergoing in flap, lag, extension and torsion. The blade equations of motion are formulated using Hamilton's principle and they are spatially discretized using the finite element method. The discretized blade equations of motion are integrated for a specified rotor speed run-up or run-down profile. Blade element theory is used to calculate quasi-steady or unsteady aerodynamic loads in linear and nonlinear regimes. The analysis is capable of simulating both articulated, hingeless, and gimballed rotor systems. Validation of the rotor code is discussed, including correlation with droop stop impact tests and wind tunnel experiments. Predictions of safe engagement and disengagement envelopes, limited by excessive blade tip deflections or hub moments, are presented. Future directions of study are also discussed.

Smith, Edward C.↗

NASA NTRS1994

An Approximate Kalman Filter for Ocean Data Assimilation; An Example with an Idealized Gulf Stream Model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady-state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudo measurements is examined, including velocity, density, and volume transport at localized arrays, and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform a previous study that used an empirical nudging scheme. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

['Kalman↗

NASA NTRS1994

Nonlinear evolution of tidally distorted accretion disks: Two-dimensional simulations

According to a previously published linear analysis, the tidal distortion of accretion disks in binary star systems produces a local hydrodynamic instability to m = 1 internal waves, which may have arbitrarily small wavelengths in the absence of viscosity. The instability is three-dimensional and approximately incrompressible. To explore the nonlinear outcome of this instability, we develop a shearing-sheet approximation on scales comparable to the disk thickness. The large-scale azimuthal variation of the disk is represented by varying the local metric with time (local orbital phase). The hydrodynamic equations can then be posed two-dimensionally on local meridional planes. We solve these equations with a second-order gasdynamical code based on the Total-Variation-Diminishing scheme. Our simulations confirm the predicted linear growth rate. The modes saturate chaotically at velocities scaling as the product of the linear growth rate and the wavelength. If the wavelength is small compared with the disk thickness, the modes remain nearly incompressible even when nonlinear. The two-dimensional power spectrum of velocities after saturation is roughly isotropic and extends over a broad range of scales in an approximately power-law fashion. We measure the heating rate associated with the nonlinear dissipation of the modes. The dissipation implies a secular torque on the disk and a return of angular momentum to the secondary star via the tidal potential. The estimated torque is somewhat larger than the tidal torque produced by maximal disk viscosity (alpha approximately 1). At least in these two-dimensional simulations, however, there is no significant angular momentum flux within the disk.

Ryu, Dongsu↗

NASA NTRS1980

Cost decomposition of linear systems with application to model reduction

A means is provided to assess the value or 'cst' of each component of a large scale system, when the total cost is a quadratic function. Such a 'cost decomposition' of the system has several important uses. When the components represent physical subsystems which can fail, the 'component cost' is useful in failure mode analysis. When the components represent mathematical equations which may be truncated, the 'component cost' becomes a criterion for model truncation. In this latter event component costs provide a mechanism by which the specific control objectives dictate which components should be retained in the model reduction process. This information can be valuable in model reduction and decentralized control problems.

Skelton, R. E.↗

NASA NTRS2010

Linear Stability of Binary Alloy Solidification for Unsteady Growth Rates

An extension of the Mullins and Sekerka (MS) linear stability analysis to the unsteady growth rate case is considered for dilute binary alloys. In particular, the stability of the planar interface during the initial solidification transient is studied in detail numerically. The rapid solidification case, when the system is traversing through the unstable region defined by the MS criterion, has also been treated. It has been observed that the onset of instability is quite accurately defined by the "quasi-stationary MS criterion", when the growth rate and other process parameters are taken as constants at a particular time of the growth process. A singular behavior of the governing equations for the perturbed quantities at the constitutional supercooling demarcation line has been observed. However, when the solidification process, during its transient, crosses this demarcation line, a planar interface is stable according to the linear analysis performed.

Mazuruk, K.↗

NASA NTRS1962

Use of an Inertia Sphere to Damp the Angular Motions of Spinning Space Vehicles

A theoretical study was made of a device which might be used to damp the angular motions of spin-stabilized space vehicles with constant moments of inertia. the device was assumed to consist of a rate gyro, a servo control, and a rotor mounted in a single gimbal. The investigation was conducted by considering the general equations of motion of the vehicle-damper system and noting that simplification would result if the damper had a spherical inertia distribution. Such a distribution was assumed thereafter, and a control command was defined so that the gimbal angle would be proportional to the angular velocity of the vehicle about the gimbal axis. The resulting equations were linearized, and the Routh-Hurwitz criterion was applied to determine the conditions for stability. The study included two numerical examples showing possible application of inertia-sphere rate dampers. The general conditions for stability were found to be feasible for practical applications. A simplified stability criterion covers a large class of practical problems.

SPHERE↗

NASA NTRS1975

Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations with applications to flutter

A general formulation is presented for the analysis of steady and unsteady, subsonic and supersonic aerodynamics for complex aircraft configurations. The theoretical formulation, the numerical procedure, the description of the program SOUSSA (steady, oscillatory and unsteady, subsonic and supersonic aerodynamics) and numerical results are included. In particular, generalized forces for fully unsteady (complex frequency) aerodynamics for a wing-body configuration, AGARD wing-tail interference in both subsonic and supersonic flows as well as flutter analysis results are included. The theoretical formulation is based upon an integral equation, which includes completely arbitrary motion. Steady and oscillatory aerodynamic flows are considered. Here small-amplitude, fully transient response in the time domain is considered. This yields the aerodynamic transfer function (Laplace transform of the fully unsteady operator) for frequency domain analysis. This is particularly convenient for the linear systems analysis of the whole aircraft.

Tseng, K.↗

NASA NTRS1979

A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators

The paper describes a laboratory design facility for digital microprocessor implementation of Linear-Quadratic-Gaussian feedback compensators. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems are conditioned for implementation on a laboratory microcomputer system. The software consists of two parts: (1) an off-line high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains, and (2) a cross compiler/macro assembler which generates object code for the target microprocessor system. Application to the control of a two dimensional inverted pendulum and expanding the design/prototyping system to other target machine architectures are discussed.

Houpt, P. K.↗

NASA NTRS1983

Legendre-Tau approximations for functional differential equations

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

Ito, K.↗

NASA NTRS1984

Finite elements and the method of conjugate gradients on a concurrent processor

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.

Lyzenga, G. A.↗

NASA NTRS1985

Finite elements and the method of conjugate gradients on a concurrent processor

Lyzenga, G. A.↗

NASA NTRS1986

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Banks, H. T.↗

NASA NTRS1991

A hierarchy for modeling high speed propulsion systems

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Hartley, Tom T.↗

NASA NTRS1997

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

Cockburn, Bernardo↗