A second-order feedback method for optimal control computations.
Second order feedback method for computing optimal control corrections from state perturbations, noting results for nonlinear examples based of van der Pol equation
Bullock, T. E.↗
SEARCH · Engineering Papers
Results for “Perturbative methods”
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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On the determination of near body orbits using mass concentration models
Mathematical model for near-body orbit calculation using mass concentration, perturbation theory, nonlinear equations, geopotentials, and least squares method
Childs, B.↗
A numerical study of electromagnetic scattering from ocean like surfaces
The integral equations describing electromagnetic scattering from one dimensional conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometric optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root mean square surface roughness is less than one-tenth of a wavelength.
Lentz, R. R.↗
Upper atmospheric planetary-wave and gravity-wave observations
Previously collected data on atmospheric pressure, density, temperature and winds between 25 and 200 km from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others were analyzed by a daily-difference method, and results on the magnitude of atmospheric perturbations interpreted as gravity waves and planetary waves are presented. Traveling planetary-wave contributions in the 25-85 km range were found to have significant height and latitudinal variation. It was found that observed gravity-wave density perturbations and wind are related to one another in the manner predicted by gravity-wave theory. It was determined that, on the average, gravity-wave energy deposition or reflection occurs at all altitudes except the 55-75 km region of the mesosphere.
Justus, C. G.↗
A numerical study of electromagnetic scattering from ocean-like surfaces
The integral equations describing electromagnetic scattering from cylindrical, perfectly conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometrical optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root-mean-square surface roughness is less than one tenth of a wavelength.
Lentz, R. R.↗
Numerical implications of stabilization by the use of integrals
Liapunov or energy restraint methods for dynamic stabilization in two body motion perturbation problems are considered. Results of computerized orbital stabilization estimates show that the application of energy restraint prevents the occurrence of consistent timing errors in the stepwise integration of equations of motion for a nearly circular orbit.
Beaudet, P. R.↗
A variational approach to the question of temporal stability of equilibrium models of solar prominences. I - The formal theory
A Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences is presented. Seven quantities are derived which, by analogy to the concepts of energy, momentum, and angular momentum, are conserved under conditions corresponding to ignorable coordinates of classical mechanics. It is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigenfrequencies for the perturbation equations when numerical techniques are used. The method is capable of handling complicated spatial dependences and has internal criteria for assessing the accuracy of any given numerical convergence scheme.
Lerche, I.↗
Dynamic stability of a rotor blade using finite element analysis
The aeroelastic stability of flap bending, lead-lag bending, and torsion of a helicopter rotor blade in hover is examined using a finite element formulation based on the principle of virtual work. Quasi-steady two-dimensional airfoil theory is used to obtain the aerodynamic loads. The rotor blade is discretized into beam elements, each with ten modal degrees of freedom. The resulting nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The flutter solution is calculated assuming blade motion to be a small perturbation about the steady solution. The normal mode method based on the coupled rotating natural modes about the steady deflections is used to reduce the number of equations in the flutter eigenanalysis. Results are presented for hingeless and articulated rotor blade configurations.
Sivaneri, N. T.↗
Density measurement in air with a saturable absorbing seed gas
A method for making density measurements in a compressible flow by using off resonance laser induced fluorescence is studied. The seed molecule chosen for study is the iodine molecule which is excited with the 514.5 nm line of the argon ion laser whose output is frequency tuned, by as much as 3 GHz, relative to a strong iodine transition using an intracavity etalon. The theory which was developed to analyze the effect will be used in conjunction with two experiments being conducted to further study the method an acoustic resonance tube in which controlled perturbations about a uniform state are produced, and a small supersonic jet in which the conditions of the flow vary widely from point to point.
Baganoff, D.↗
Direct structural parameter identification by modal test results
A direct identification procedure is proposed to obtain the mass and stiffness matrices based on the test measured eigenvalues and eigenvectors. The method is based on the theory of matrix perturbation in which the correct mass and stiffness matrices are expanded in terms of analytical values plus a modification matrix. The simplicity of the procedure enables real time operation during the structural testing.
Chen, J.-C.↗
Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field
An analytical method has been developed to estimate the unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.
Norman, T.↗
Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades
The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.
Subrahmanyam, K. B.↗
Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field
An analytical method has been developed to estimate tne unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.
Norman, T. R.↗
Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades
The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree goemetric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of Pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.
Subrahmanyam, K. B.↗
A methodology for formulating a minimal uncertainty model for robust control system design and analysis
In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.
Belcastro, Christine M.↗
A complex permittivity and permeability measurement system for elevated temperatures
The three goals of this research include: (1) to fully develop a method to measure the permittivity and permeability of special materials as a function of frequency in the range of 2.6 to 18 GHz, and of temperature in the range of 25 to 1100 C; (2) to assist LeRC in setting up an in-house system for the measurement of high-temperature permittivity and permeability; and (3) to measure the complex permittivity and permeability of special materials as a function of frequency and temperature to demonstrate the capability of the method. The method chosen for characterizing the materials relies on perturbation of a resonant cavity with a small volume of sample material. Different field configurations in the cavity can be used to separate electric and magnetic effects. The cavity consists of a section of rectangular waveguide terminated at each end of a vertical slot iris. In the center of one wall is a small hole through which the sample is introduced.
Friederich, Paul↗
A complex permittivity and permeability measurement system for elevated temperatures
The three goals of this research include: (1) to fully develop a method to measure the permittivity and permeability of special materials as a function of frequency in the range of 2.6 to 18 GHz, and of temperatures in the range of 25 to 1100 C; (2) to assist LeRC in setting up an in-house system for the measurement of high-temperature permittivity and permeability; and (3) to measure the complex permittivity and permeability of special materials as a function of frequency and temperature to demonstrate the capability of the method. The method chosen for characterizing the materials relies on perturbation of a resonant cavity with a small volume of sample material. Different field configurations in the cavity can be used to separate electric and magnetic effects. The cavity consists of a section of rectangular waveguide terminated at each end of a vertical slot iris. The center of one wall is a small hole through which the sample is introduced.
Friederich, Paul↗
Computations Of Breakup Of A Capillary Jet
Report describes computations of breakup of round jet of liquid in gas or vacuum. Breakup occurs both spontaneously and when stimulated by vibrations giving rise to surface waves, some of which grow until drops pinch off. Study focusses on formation of satellite drops, taking advantage of advanced computers and computational methods to carry theoretical analysis beyond small-perturbation, linear regime.
Mansour, Nagi N.↗