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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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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Some optimal considerations in attitude control systems

The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.

Boland, J. S., III↗
NASA NTRS1985

A unique set of micromechanics equations for high temperature metal matrix composites

A unique set of micromechanic equations is presented for high temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Hopkins, D. A.↗
NASA NTRS1989

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Danabasoglu, G.↗
NASA NTRS1980

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Chakravarthy, S. R.↗
NASA NTRS1990

A Chebyshev matrix method for the spatial modes of the Orr-Sommerfeld equation

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blasius boundary layer. The problems is linearized by the companion matrix technique for semiinfinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Danabasoglu, Gokhan↗
NASA NTRS1989

Computational complexities and storage requirements of some Riccati equation solvers

The linear optimal control problem of an nth-order time-invariant dynamic system with a quadratic performance functional is usually solved by the Hamilton-Jacobi approach. This leads to the solution of the differential matrix Riccati equation with a terminal condition. The bulk of the computation for the optimal control problem is related to the solution of this equation. There are various algorithms in the literature for solving the matrix Riccati equation. However, computational complexities and storage requirements as a function of numbers of state variables, control variables, and sensors are not available for all these algorithms. In this work, the computational complexities and storage requirements for some of these algorithms are given. These expressions show the immensity of the computational requirements of the algorithms in solving the Riccati equation for large-order systems such as the control of highly flexible space structures. The expressions are also needed to compute the speedup and efficiency of any implementation of these algorithms on concurrent machines.

Utku, Senol↗
NASA NTRS1988

A unique set of micromechanics equations for high-temperature metal matrix composites

A unique set of micromechanic equations is presented for high-temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Hopkins, Dale A.↗
NASA NTRS1986

Time scale analysis of a closed-loop discrete optimal control system

A two-time scale discrete control system is considered. The closed-loop optimal linear quadratic (LQ) regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystems. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the closed-loop optimal control of digital flight systems.

Naidu, D. S.↗
NASA NTRS1979

On reliable control system designs with and without feedback reconfigurations

This paper contains an overview of a theoretical framework for the design of reliable multivariable control systems, with special emphasis on actuator failures and necessary actuator redundancy levels. Using a linear model of the system, with Markovian failure probabilities and quadratic performance index, an optimal stochastic control problem is posed and solved. The solution requires the iteration of a set of highly coupled Riccati-like matrix difference equations; if these converge one has a reliable design; if they diverge, the design is unreliable, and the system design cannot be stabilized. In addition, it is shown that the existence of a stabilizing constant feedback gain and the reliability of its implementation is equivalent to the convergence properties of a set of coupled Riccati-like matrix difference equations. In summary, these results can be used for offline 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.↗
NASA NTRS1972

An efficient algorithm using matrix methods to solve wind tunnel force-balance equations

An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.

Smith, D. L.↗
NASA NTRS1986

Optimal control of quaternion propagation errors in spacecraft navigation

Optimal control techniques are used to drive the numerical error (truncation, roundoff, commutation) in computing the quaternion vector to zero. The normalization of the quaternion is carried out by appropriate choice of a performance index, which can be optimized. The error equations are derived from Friedland's (1978) theoretical development, and a matrix Riccati equation results for the computation of the gain matrix. Simulation results show that a high precision of the order of 10 to the -12th can be obtained using this technique in meeting the q(T)q=1 constraint. The performance of the estimator in the presence of the feedback control that maintains the normalization, is studied.

Vathsal, S.↗
NASA NTRS1966

Matrix quadratic solutions.

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients

OPTIMAL CONTROL↗
NASA NTRS1983

Structural design for dynamic response reduction

A computer program for redesigning structural modes to reduce response has been initiated. The linear regulator approach in modal coordinates has been implemented. It is noted that the transformation of solution to physical structure is a major problem. It is concluded that the solution of stiffness equations and damping equations can be done separately as NXN set of (matrix Riccati) equations.

Hanks, B. R.↗
NASA NTRS1983

Numerical studies of major and minor stratospheric warmings caused by orographic forcing

A primitive equation spectral model using spherical harmonics is formulated to study dynamic interactions between the troposphere and stratosphere in association with sudden stratospheric warmings. Using sigma coordinates for five tropospheric layers and log-pressure coordinates for 26 stratospheric and mesospheric layers, separate model equations for each system are combined to form single matrix governing equations. The gradual introduction of large scale topography to balanced initial states representative of observed mean winter conditions in the Northern Hemisphere is used for the generation of planetary waves during 40-day time integrations. Results of these integrations indicate that stratospheric warmings can be simulated by this orographic forcing and that mean momentum flux divergence due to zonal mean motion appears to be an essential mechanism of these simulated sudden warmings. It was found that the strength of the polar night jet can be a determining factor whether a warming becomes 'major' or 'minor'.

Koermer, J. P.↗