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At least 145 records · Page 8

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NASA NTRS1985

Optimal landing of a helicopter in autorotation

Gliding descent in autorotation is a maneuver used by helicopter pilots in case of engine failure. The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. The OH-58A helicopter was used. Helicopter vertical and horizontal velocities, vertical and horizontal displacement, and the rotor angle speed were modeled. An empirical approximation for the induced veloctiy in the vortex-ring state were provided. The cost function of the optimal control problem is a weighted sum of the squared horizontal and vertical components of the helicopter velocity at touchdown. Optimal trajectories are calculated for entry conditions well within the horizontal-vertical restriction curve, with the helicopter initially in hover or forwared flight. The resultant two-point boundary value problem with path equality constraints was successfully solved using the Sequential Gradient Restoration Technique.

Lee, A. Y. N.↗

NASA NTRS1985

Single step optimization strategies for constrained retargeting maneuvers

The present consideration of recent advancements in the nonlinear guidance of spacecraft, using feedback linearization and decoupling to generate exact nominal commands, gives attention to the correction of saturation effects and oscillation prevention in saturated operating regimes. In the case of spacecraft maneuvered by momentum-transfer devices, real time command generation is possible by means of pointwise minimization of the sum of the squares of the norms of the 'next state error' for the equivalent system and the linear system input. It is also possible to track a nominal trajectory, such as a critically damped harmonic oscillator response, by minimizing the square of the norm of the error between the actual and the tracked states.

Dwyer, T. A. W., III↗

NASA NTRS1987

Optimal trajectories for aeroassisted, coplanar orbital transfer

Classical and minimax optimal control problems arising in the study of aeroassisted coplanar orbit transfer from a high planetary orbit to a low one are considered. Attention is given to (1) the minimization of the energy required for the maneuver; (2) minimization of the time integral of the heating rate; (3) minimization of the time of flight during the atmospheric portion of the trajectory; (4) maximization of the time of flight during the atmospheric portion of the trajectory; (5) minimization of the time integral of the path inclination; and (6) minimization of the sum of the squares of the entry and exit path inclinations.

Miele, A.↗

NASA NTRS1987

An analytical solution to obtain the optimum source location using multiple direction finders on a spherical surface

An analytical solution is presented for determining the optimum location of a radiating source on the surface of a sphere, given multiple bearings. The bearings are assumed to have small errors of the order of 0-10 deg. The optimum location is found by minimizing the sum of the squares of the perpendicular great-circle distances from the source to the bearing lines. This is achieved analytically through an eigenvalue approach, rather than the usual iterative, numerical approach. Bearings of different weight are taken into account by approximating the distance from each direction finder to the source. The result is general and may have wide application. Since it is simple and nearly as fast as the triangulation technique for source location, it is now used in the SUNY-Albany East Coast Lightning Detection Network to compute the optimum location for lightning in real time.

Orville, Richard E., Jr.↗

NASA NTRS1988

Redundant manipulators for momentum compensation in a micro-gravity environment

This paper is concerned with the implementation and assessment of joint motion management strategies for kinematically redundant robotic manipulators operating in the micro-gravity environment of Space Station. These robots must be capable of conducting experiments and manufacturing processes without disturbing the micro-gravity environment through base reactions/motions. The redundant degrees of freedom of the manipulator permit the inverse kinematic problem to be solved simultaneously with the minimization of a cost function. The cost function in this case is the weighted sum of the squares of the base forces and moments and is minimized over discrete time segments. The Generalized Inverse Method and Rayleigh Ritz technique are used to solve the combined optimization/inverse kinematics problem. Numerical examples include various robotic configurations and degrees of manipulator redundancy.

Quinn, R. D.↗

NASA NTRS1989

The effects of control order, feedback, practice, and input device on tracking performance and perceived workload

The present experiment examined the influence of several task-related factors on tracking performance and concomitant workload. The manipulated factors included tracking order, the presence or absence of knowledge of performance, and the control device. Summed root mean square error (rmse) and perceived workload were measured at the termination of each trial. Perceived workload was measured using the NASA Task Load Index (TLX) and the Subjective Workload Assessment Technique (SWAT). Results indicated a large and expected effect for track order on both performance and the perception of load. In general, trackball input was more accurate and judged for lower load than input using a mouse. The presence or absence of knowledge of performance had little effect on either performance or workload. There were a number of interactions between factors shown in performance that were mirrored by perceived workload scores. Results from each workload scale were equivalent in terms of sensitivity to task manipulations. The pattern of results affirm the utility of these workload measures in assessing the imposed load of multiple task-related variables.

Hancock, P. A.↗

NASA NTRS1991

The effect of bandwidth on telerobot system performance

The purpose of the experiment was to determine the effect that various slave-joint bandwidths have on telerobot system performance. The telerobot system consisted of a slave arm controlled by a master. The slave incorporated an impedance loop to provide local compliance in addition to the compliance provided by the operator via force feedback. Three joint bandwidths, 0.5, 1.0, and 2.0 Hz, were used. The performance measures were the task completion time and the sums of the squared forces and moments exerted on the environment. The task consisted of peg-in-hole insertion and removal. The results of the experiment indicate a significant performance decrease at 0.5-Hz bandwidth relative to the 1- and 2-Hz bandwidths. There was no significant change in performance between the 1- and 2-Hz bandwidths.

Uebel, Mark↗

NASA NTRS1994

Gain weighted eigenspace assignment

This report presents the development of the gain weighted eigenspace assignment methodology. This provides a designer with a systematic methodology for trading off eigenvector placement versus gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. This is accomplished by forming a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. For this development the scalar measure of gain magnitude is chosen to be a weighted sum of the squares of all the individual elements of the feedback gain matrix. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors close to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.

Davidson, John B.↗

NASA NTRS1994

Active minimization of energy density in three-dimensional enclosures

The objective of this research project is to further investigate and develop a novel approach for actively controlling the sound field in enclosures. Typically the acoustic field in an enclosure has been controlled by minimizing the sum of the squared pressures from several microphones distributed throughout the enclosure. The approach being investigated in this project involves minimizing the acoustic energy density at the sensor locations, rather than the squared pressure. Previous research in a simple one-dimensional enclosure showed that improved global attenuation of the acoustic field is often obtained by minimizing the energy density, rather than the pressure. The current project builds on the previous research by extending the method of controlling the acoustic energy density to three-dimensional enclosures. The results will establish if improved control can still be expected in a more general enclosure. Pending successful results, the method could be applied to control problems such as attenuating the acoustic noise in an aircraft fuselage, an automobile cabin, or other general enclosures. The research project was set up as a two-year project designed to achieve both numerical and experimental results. The primary focus of the first year of research (now being completed) was on the analytical/numerical modeling of the method of controlling the acoustic energy density. During the second year, the research focuses on experimental verification of the approach and extending our understanding of the method.

Sommerfeldt, Scott D.↗

NASA NTRS1993

New dynamic variables for rotating spacecraft

This paper introduces two new seven-parameter representations for spacecraft attitude dynamics modeling. The seven parameters are the three components of the total system angular momentum in the spacecraft body frame; the three components of the angular momentum in the inertial reference frame; and an angle variable. These obey a single constraint as do parameterizations that include a quaternion; in this case the constraint is the equality of the sum of the squares of the angular momentum components in the two frames. The two representations are nonsingular if the system angular momentum is non-zero and obeys certain orientation constraints. The new parameterizations of the attitude matrix, the equations of motion, and the relation of the solution of these equations to Euler angles for torque-free motion are developed and analyzed. The superiority of the new parameterizations for numerical integration is shown in a specific example.

Markley, F. Landis↗

NASA NTRS1996

Active minimization of energy density in three-dimensional enclosures

The objective of this study was to further investigate and develop a novel approach for actively controlling the sound field in enclosures that is based on the acoustic energy density. Typically the acoustic field in an enclosure has been controlled by minimizing the sum of the squared pressures from several microphones distributed throughout the enclosure. The approach investigated in this study involved minimizing the acoustic energy density at the sensor locations, rather than the squared pressure. Research previous to this study in a simple one-dimensional enclosure showed that improved global attenuation of the acoustic field is often obtained by minimizing the energy density, rather than the pressure. The current study built on the previous research by extending the method of controlling the acoustic energy density to three-dimensional enclosures. The study was intended to help establish if improved control can still be expected in a more general enclosure. The study was designed to be both analytical/numerical and experimental in nature.

Sommerfeldt, Scott D.↗

NASA NTRS1996

Dual Brushless Resolver Rate Sensor

This invention relates to dual analog angular rate sensors which are implemented without the use of mechanical brushes. A resolver rate sensor which includes two brushless resolvers which are mechanically coupled to the same output shaft is provided with inputs which are provided to each resolver by providing the first resolver with a DC input and the second resolver with an AC sinusoidal input. A trigonometric identity in which the sum of the squares of the sin and cosine components equal one is used to advantage in providing a sensor of increased accuracy. The first resolver may have a fixed or variable DC input to permit dynamic adjustment of resolver sensitivity thus permitting a wide range of coverage. Novelty and advantages of the invention reside in the excitation of a resolver with a DC signal and in the utilization of two resolvers and the trigonometric identity of cos(exp 2)(theta) + sin(exp 2)(theta) = 1 to provide an accurate rate sensor which is sensitive to direction and accurate through zero rate.

Howard, David E.↗

NASA NTRS1997

Dual Brushless Resolver Rate Sensor

A resolver rate sensor is disclosed in which dual brushless resolvers are mechanically coupled to the same output shaft. Diverse inputs are provided to each resolver by providing the first resolver with a DC input and the second resolver with an AC sinusoidal input. A trigonometric identity in which the sum of the squares of the sin and cosine components equal one is used to advantage in providing a sensor of increased accuracy. The first resolver may have a fixed or variable DC input to permit dynamic adjustment of resolver sensitivity thus permitting a wide range of coverage. In one embodiment of the invention the outputs of the first resolver are directly inputted into two separate multipliers and the outputs of the second resolver are inputted into the two separate multipliers, after being demodulated in a pair of demodulator circuits. The multiplied signals are then added in an adder circuit to provide a directional sensitive output. In another embodiment the outputs from the first resolver is modulated in separate modulator circuits and the output from the modulator circuits are used to excite the second resolver. The outputs from the second resolver are demodulated in separate demodulator circuit and added in an adder circuit to provide a direction sensitive rate output.

Howard, David E.↗

NASA NTRS1996

Adjustment of Sensor Locations During Thermal Property Parameter Estimation

The temperature dependent thermal properties of a material may be evaluated from transient temperature histories using nonlinear parameter estimation techniques. The usual approach is to minimize the sum of the squared errors between measured and calculated temperatures at specific locations in the body. Temperature measurements are usually made with thermocouples and it is customary to take thermocouple locations as known and fixed during parameter estimation computations. In fact, thermocouple locations are never known exactly. Location errors on the order of the thermocouple wire diameter are intrinsic to most common instrumentation procedures (e.g., inserting a thermocouple into a drilled hole) and additional errors can be expected for delicate materials, difficult installations, large thermocouple beads, etc.. Thermocouple location errors are especially significant when estimating thermal properties of low diffusively materials which can sustain large temperature gradients during testing. In the present work, a parameter estimation formulation is presented which allows for the direct inclusion of thermocouple positions into the primary parameter estimation procedure. It is straightforward to set bounds on thermocouple locations which exclude non-physical locations and are consistent with installation tolerances. Furthermore, bounds may be tightened to an extent consistent with any independent verification of thermocouple location, such as x-raying, and so the procedure is entirely consonant with experimental information. A mathematical outline of the procedure is given and its implementation is illustrated through numerical examples characteristic of light-weight, high-temperature ceramic insulation during transient heating. The efficacy and the errors associated with the procedure are discussed.

Milos, Frank S.↗

NASA NTRS1999

Method of Conjugate Radii for Solving Linear and Nonlinear Systems

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

Nachtsheim, Philip R.↗

NASA NTRS2006

Equivalent Plate Analysis of Aircraft Wing with Discrete Source Damage

An equivalent plate procedure is developed to provide a computationally efficient means of matching the stiffness and frequencies of flight vehicle wing structures for prescribed loading conditions. First, the equivalent plate is used to match the stiffness of a stiffened panel without damage and the stiffness of a stiffened panel with damage. For both stiffened panels, the equivalent plate models reproduce the deformation of a corresponding detailed model exactly for the given loading conditions. Once the stiffness was matched, the equivalent plate models were then used to predict the frequencies of the panels. Two analytical procedures using the lumped-mass matrix were used to match the first five frequencies of the corresponding detailed model. In both the procedures, the lumped-mass matrix for the equivalent plate is constructed by multiplying the diagonal terms of the consistent-mass matrix by a proportionality constant. In the first procedure, the proportionality constant is selected such that the total mass of the equivalent plate is equal to that of the detailed model. In the second method, the proportionality constant is selected to minimize the sum of the squares of the errors in a set of pre-selected frequencies between the equivalent plate model and the detailed model. The equivalent plate models reproduced the fundamental first frequency accurately in both the methods. It is observed that changing only the mass distribution in the equivalent plate model did not provide enough flexibility to match all of the frequencies.

Krishnamurthy, T.↗

NASA NTRS2005

High Frequency QRS ECG Accurately Detects Cardiomyopathy

High frequency (HF, 150-250 Hz) analysis over the entire QRS interval of the ECG is more sensitive than conventional ECG for detecting myocardial ischemia. However, the accuracy of HF QRS ECG for detecting cardiomyopathy is unknown. We obtained simultaneous resting conventional and HF QRS 12-lead ECGs in 66 patients with cardiomyopathy (EF = 23.2 plus or minus 6.l%, mean plus or minus SD) and in 66 age- and gender-matched healthy controls using PC-based ECG software recently developed at NASA. The single most accurate ECG parameter for detecting cardiomyopathy was an HF QRS morphological score that takes into consideration the total number and severity of reduced amplitude zones (RAZs) present plus the clustering of RAZs together in contiguous leads. This RAZ score had an area under the receiver operator curve (ROC) of 0.91, and was 88% sensitive, 82% specific and 85% accurate for identifying cardiomyopathy at optimum score cut-off of 140 points. Although conventional ECG parameters such as the QRS and QTc intervals were also significantly longer in patients than controls (P less than 0.001, BBBs excluded), these conventional parameters were less accurate (area under the ROC = 0.77 and 0.77, respectively) than HF QRS morphological parameters for identifying underlying cardiomyopathy. The total amplitude of the HF QRS complexes, as measured by summed root mean square voltages (RMSVs), also differed between patients and controls (33.8 plus or minus 11.5 vs. 41.5 plus or minus 13.6 mV, respectively, P less than 0.003), but this parameter was even less accurate in distinguishing the two groups (area under ROC = 0.67) than the HF QRS morphologic and conventional ECG parameters. Diagnostic accuracy was optimal (86%) when the RAZ score from the HF QRS ECG and the QTc interval from the conventional ECG were used simultaneously with cut-offs of greater than or equal to 40 points and greater than or equal to 445 ms, respectively. In conclusion 12-lead HF QRS ECG employing RAZ scoring is a simple, accurate and inexpensive screening technique for cardiomyopathy. Although HF QRS ECG is highly sensitive for cardiomyopathy, its specificity may be compromised in patients with cardiac pathologies other than cardiomyopathy, such as uncomplicated coronary artery disease or multiple coronary disease risk factors. Further studies are required to determine whether HF QRS might be useful for monitoring cardiomyopathy severity or the efficacy of therapy in a longitudinal fashion.

Schlegel, Todd T.↗

NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗