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At least 1,369 records · Page 76

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NASA NTRS1991

The semi-infinite strip problem in the mechanics of composite materials

Many problems, ranging from interface-fiber fracture to determining the strength of fiber-matrix interfaces in composites, can be greatly assisted by a complete understanding of the boundary value problem of a semi-infinite strip. The specific boundary value problem of a semi-infinite strip with symmetric tractions on the transverse edges and normal loads on the end is investigated in the present study. The nature of the singular behavior in the slope of the end vertical displacement at the corner points is found. An asymptotic analysis of the solution shows that, depending on the nature of the applied stresses in the vicinity of the corner points, the singularity in the slope of the end vertical displacement may either be a power or logarithmic type, both, or not exist at all. Illustrative examples, for which exact or numerical results are known, are given. Numerical procedures are also given. The direct application of the results of the paper are illustrated for several problems in the mechanics of composite materials.

Kaw, Autar K.↗

NASA NTRS1991

Application of a directed search to global steering of single gimballed CMGs

A guided depth-first search that manages null motion about torque-producing trajectories calculated with a singularity-robust (SR) inverse is proposed as a practical feedforward steering law that can globally avoid (or minimize the impact of) singular states in minimally-redundant single gimballed CMG systems. Cost and heuristic functions are defined to guide the search procedure in improving CMG trajectories. On-orbit implementation of the steering law is proposed as an extension to momentum management algorithms. A set of simulation examples is presented, illustrating the search performance for a 4-CMG pyramid-mounted array. Sensitivities of feedforward gimbal trajectories are examined in the presence of unmodeled disturbances, and techniques are proposed for avoiding excessive divergence.

Paradiso, Joseph A.↗

NASA NTRS1991

Robustness analysis of multirate and periodically time varying systems

A new method for analyzing the stability and robustness of multirate and periodically time varying systems is presented. It is shown that a multirate or periodically time varying system can be transformed into an equivalent time invariant system. For a SISO system, traditional gain and phase margins can be found by direct application of the Nyquist criterion to this equivalent time invariant system. For a MIMO system, structured and unstructured singular values can be used to determine the system's robustness. The limitations and implications of utilizing this equivalent time invariant system for calculating gain and phase margins, and for estimating robustness via singular value analysis are discussed.

Berg, Martin C.↗

NASA NTRS1991

A kinematic analysis of the Space Station remote manipulator system (SSRMS)

An efficient reverse analysis of three 6-degree-of-freedom (dof) subchains of the 7-dof SSRMS is presented. The first subchain is formed by locking the seventh joint. The second subchain is formed by locking the second joint, while the third subchain is formed by locking the first joint (the grounded joint is counted as the first joint in the chain). There are a maximum of eight different arm configurations in each of the three subchains, and these were determined by employing a computer-efficient algorithm, which required the rooting of only at most quadratic polynomials. The algorithms were implemented, and the SSRMS was employed in an animated environment to perform and practice a number of useful tasks for Space Station servicing. The locking of the second joint has the advantage in that an operator can choose the orientation of the plane that contains the two longest links so as to avoid collisions with obstacles. However, it has the disadvantage that when the second joint angle equals 0 deg or 180 deg, the manipulator is in a singularity configuration. This plane can also be oriented by specifying the first joint angle, so that the plane can be oriented arbitrarily and, in this, the singularity is avoided.

Crane, Carl D., III↗

NASA NTRS1990

Input/output system identification - Learning from repeated experiments

The paper describes three approaches and possible variations for the determination of the Markov parameters for forced response data using general inputs. It is shown that, when the parameters in the solution procedure are bootstrapped, the results can be obtained very efficiently, but the errors propagate throughout all parameters. By arranging the data in a different form and using singular value decomposition, the resulting identified parameters are more accurate, in the least number of successive experiments, at the expense of a large matrix singular value decomposition. When a recursive procedure is employed, the calculations can be performed very efficiently, but the number of repetitions of the experiments is much greater for a given accuracy than for any of the previous approaches. An alternative formulation is proposed to combine the advantages of each of the approaches.

Juang, Jer-Nan↗

NASA NTRS1991

A wall interference assessment/correction system

The Hackett method (a Wall Pressure Signature Method) was selected to be adapted for the 12 ft Wind Tunnel WIAC system. This method uses limited measurements of the static pressure at the wall, in conjunction with the solid wall boundary condition, to determine the strength and distribution of singularities representing the test article. The singularities are used in term for estimating wall interference at the model location. Hackett's method will have to be formulated for application to the unique geometry of the 12 ft tunnel. The WIAC code will be validated by conducting numerically simulated experiments rather than actual wind tunnel experiments. The simulations will be used to generate both free air and confined wind tunnel flow fields for each of the test articles over a range of test configurations. Specifically the pressure signature at the test section wall will be computed for the confined case to provide the simulated 'measured' data. These data will serve as the input for the WIAC method. The performance of the WIAC method then may be evaluated by comparing the corrected parameters with those for the free air simulation.

Lo, C. F.↗

NASA NTRS1991

Black holes in magnetic monopoles

We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs field vacuum expectation value v is less than or equal to a critical value v sub cr, which is of the order of the Planck mass. In the limiting case, the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For v less than v sub cr, we find additional solutions which are singular at f = 0, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of v and of the total mass M and their relation to the Reissner-Nordstrom solutions is discussed.

Lee, Kimyeong↗

NASA NTRS1992

Robust adaptive kinematic control of redundant robots

The paper presents a general method for the resolution of redundancy that combines the Jacobian pseudoinverse and augmentation approaches. A direct adaptive control scheme is developed to generate joint angle trajectories for achieving desired end-effector motion as well as additional user defined tasks. The scheme ensures arbitrarily small errors between the desired and the actual motion of the manipulator. Explicit bounds on the errors are established that are directly related to the mismatch between actual and estimated pseudoinverse Jacobian matrix, motion velocity and the controller gain. It is shown that the scheme is tolerant of the mismatch and consequently only infrequent pseudoinverse computations are needed during a typical robot motion. As a result, the scheme is computationally fast, and can be implemented for real-time control of redundant robots. A method is incorporated to cope with the robot singularities allowing the manipulator to get very close or even pass through a singularity while maintaining a good tracking performance and acceptable joint velocities. Computer simulations and experimental results are provided in support of the theoretical developments.

Tarokh, M.↗

NASA NTRS1992

Confining potential in momentum space

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.

Norbury, John W.↗

NASA NTRS1991

A geometric approach to regulator and tracker design for an aerospace plane

The paper presents a nonlinear design approach drawing from singular perturbations, feedback linearization, and variable structure control, that leads to regulators with automatic gain scheduling which exhibit similar dynamic behavior over the entire flight envelope of the aerospace plane. Additionally, design approach provides for a systematic way to counter disturbance effects as well as modeling uncertainties. The unifying feature of the three nonlinear feedback control methodologies is that they all have a geometric interpretation. First, the translational dynamics are decomposed into reduced-order slow and fast dynamics by way of a formal singular perturbation analysis. After feedback linearization the fast dynamics are robustly stabilized via a variable structure control approach. The slow dynamics are stabilized using conventional proportional-integral compensation based on the nominal slow dynamics. A number of sample command and disturbance responses at opposite ends of the flight envelope are presented for a nonlinear aerospace plane model.

Van Buren, Mark A.↗

NASA NTRS1992

Effect of contact stresses in four-point bend testing of graphite/epoxy and graphite/PMR-15 composite beams

The results of in-plane four-point bend experiments on unidirectionally reinforced composite beams are presented for graphite/epoxy (T300/934) and graphite/polyimide (G30-500/PMR-15) composites. The maximum load and the location of cracks formed during failure were measured for testpieces with fibers oriented at various angles to the beam axis. Since most of the beams failed near one or more of the load points, the strength of the beams was evaluated in terms of a proposed model for the local stress distribution. In this model, an exact solution to the problem of a localized contact force acting on a unidirectionally reinforced half plane is used to describe the local stress field. The stress singularity at the load points is treated in a manner similar to the stress singularity at a crack tip in fracture mechanisms problems. Using this approach, the effect of fiber angle and elastic material properties on the strength of the beam is described in terms of a load intensity factor. For fiber angles less than 45 deg from the beam axis, a single crack is initiated near one of the load points at a critical value of the load intensity factor. The critical load intensity factor decreases with increasing fiber angle. For larger fiber angles, multiple cracks occur at locations both near and away from the load points, and the load intensity factor at failure increases sharply with increasing fiber angle.

Binienda, W. K.↗

NASA NTRS1992

Gravitational lensing, time delay, and gamma-ray bursts

The probability distributions of time delay in gravitational lensing by point masses and isolated galaxies (modeled as singular isothermal spheres) are studied. For point lenses (all with the same mass) the probability distribution is broad, and with a peak at delta(t) of about 50 S; for singular isothermal spheres, the probability distribution is a rapidly decreasing function with increasing time delay, with a median delta(t) equals about 1/h month, and its behavior depends sensitively on the luminosity function of galaxies. The present simplified calculation is particularly relevant to the gamma-ray bursts if they are of cosmological origin. The frequency of 'recurrent' bursts due to gravitational lensing by galaxies is probably between 0.05 and 0.4 percent. Gravitational lensing can be used as a test of the cosmological origin of gamma-ray bursts.

Mao, Shude↗

NASA NTRS1992

Controllability and observability of flexible structures with proof-mass actuators

Relationships between Hankel singular values of a structure with a proof-mass actuator to those of a structure with an ideal actuator are analyzed. They indicate that the proof-mass actuator has little influence on Hankel singular values of a structure if the natural frequency of the actuator is much lower than the structural frequencies. This fact significantly simplifies controllability/observability analysis and model reduction of flexible structures. Results from numerical simulations verify the conclusions.

Gawronski, W.↗

NASA NTRS1992

Wave diffraction in weak cosmic-ray-modified shocks

Weakly multidirectional, long-wavelength cosmic-ray-modified shocks are studied via multiple scale perturbation techniques. The effects of diffraction are discussed in terms of Green's function solutions of the linearized 1 + 3D Burgers and 1 + 3D KdVB equations, and also in terms of solutions with singular Dirac delta initial distributions. The solutions show a monotonic decrease of the wave-front curvature with increasing time owing to the effects of wave diffraction. The shape of the wave surface is discussed in terms of solutions S to the wave eikonal equation corresponding to singular initial conditions. For the fast magnetosonic wave propagating in the positive x-direction, the wave phase surface S = 0 has elliptic cross sections with the planes x = constant and has a convex paraboloidal shape. Plane-wave solutions of the 1 + 3D KdVB equation are discussed.

Webb, G. M.↗

NASA NTRS1992

An analytic formula for H-infinity norm sensitivity with applications to control system design

An analytic formula for the sensitivity of singular value peak variation with respect to parameter variation is derived. As a corollary, the derivative of the H-infinity norm of a stable transfer function with respect to a parameter is presented. It depends on some of the first two derivatives of the transfer function with respect to frequency and the parameter. For cases when the transfer function has a linear system realization whose matrices depend on the parameter, analytic formulas for these first two derivatives are derived, and an efficient algorithm for calculating them is discussed. Examples are given which provide numerical verification of the H-infinity norm sensitivity formula and which demonstrate its utility in designing control systems satisfying H-infinity norm constraints. In the appendix, derivative formulas for singular values are paraphrased.

Giesy, Daniel P.↗

NASA NTRS1992

Simultaneous H2/H-infinity optimal control - The state feedback case

A simultaneous H2/H-infinity control problem is considered. This problem seeks to minimize the H2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H-infinity norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H2/H-infinity problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H2 norm performance measure. This class of problems subsumes the class of regular problems.

Saberi, Ali↗

NASA NTRS1992

Controller design for microgravity vibration isolation systems

Control aspects of the vibration isolation problem of manned orbiters are investigated, and a viable robust control is proposed. The application of modern control theory to this problem, incorporating frequency-weighting and disturbance accommodation techniques, is investigated. The resulting controller achieves excellent performance for plants within a reasonable range of variations from the nominal. Robust stability and performance guarantees are measured by singular value and structured singular value checks, yielding guarantees on allowable real plant parameter uncertainties and on acceptable controller and sensor phase and gain variations. The problem of unmodeled HG modes is eliminated by using frequency weighting to reduce controller bandwidth. The method is applied successfully to the single-degree-of-freedom isolation problem.

Hampton, R. D.↗

NASA NTRS1993

Extended-Task-Space Control For Robotic Manipulators

Extended-task-space concept provides unified approach for control of both redundant and nonredundant manipulators: theoretical framework for complete description of set of mechanism commands in terms of task-space commands, and singularity-avoidance scheme providing robustness at and near singular points of workspace while not degrading performance in nonsingular regions.

Backes, Paul G.↗