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At least 667 records · Page 37

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x(t)) + the sum to m terms(i=1) u sub i (t)g sub i (x(t)) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications

Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulatns.

Armstrong, Jeffrey B.↗

First Stage of a Highly Reliable Reusable Launch System

Electromagnetic launch assist has the potential to provide a highly reliable reusable first stage to a space access system infrastructure at a lower overall cost. This paper explores the benefits of a smaller system that adds the advantages of a high specific impulse air-breathing stage and supersonic launch speeds. The method of virtual specific impulse is introduced as a tool to emphasize the gains afforded by launch assist. Analysis shows launch assist can provide a 278-s virtual specific impulse for a first-stage solid rocket. Additional trajectory analysis demonstrates that a system composed of a launch-assisted first-stage ramjet plus a bipropellant second stage can provide a 48-percent gross lift-off weight reduction versus an all-rocket system. The combination of high-speed linear induction motors and ramjets is identified, as the enabling technologies and benchtop prototypes are investigated. The high-speed response of a standard 60 Hz linear induction motor was tested with a pulse width modulated variable frequency drive to 150 Hz using a 10-lb load, achieving 150 mph. A 300-Hz stator-compensated linear induction motor was constructed and static-tested to 1900 lbf average. A matching ramjet design was developed for use on the 300-Hz linear induction motor.

Kloesel, Kurt J.↗

Ocular Reflex Phase During Off-Vertical Axis Rotation In Humans Is Modified By Head-On-Trunk Position

Constant velocity Off-Vertical Axis Rotation (OVAR) imposes a continuously varying orientation of the head and body relative to gravity. The ensuing ocular reflexes include modulation of both horizontal and torsional eye velocity as a function of the varying linear acceleration along the lateral plane. The purpose of this study was to examine whether the modulation of these ocular reflexes would be modified by different head-on-trunk positions. Ten human subjects were rotated in darkness about their longitudinal axis 20 deg off-vertical at constant rates of 45 and 180 deg/s, corresponding to 0.125 and 0.5 Hz. Binocular responses were obtained with video-oculography with the head and trunk aligned, and then with the head turned relative to the trunk 40 deg to the right or left of center. Sinusoidal curve fits were used to derive amplitude, phase and bias velocity of the eye movements across multiple cycles for each head-on-trunk position. Consistent with previous studies, the modulation of torsional eye movements was greater at 0.125 Hz while the modulation of horizontal eye movements was greater at 0.5 Hz. Neither amplitude nor bias velocities were significantly altered by head-on-trunk position. The phases of both torsional and horizontal ocular reflexes, on the other hand, shifted towards alignment with the head. These results are consistent with the modulation of torsional and horizontal ocular reflexes during OVAR being primarily mediated by the otoliths in response to the sinusoidally varying linear acceleration along the interaural head axis.

Wood, Scott↗

An analysis of aircraft lateral-directional handling qualities using pilot models.

An analytical study of the combined pilot-aircraft system to develop a procedure for computing pilot ratings for the lateral-directional response. In the analytical procedure the pilot is represented by a linear, second-order pilot model, and the aircraft by linear equations of motion. Two levels of pilot response were described by the pilot model. The first level contains a static gain and a second-order lag function with a time constant of 0.2 second. The second level added a 1-sec lead time constant. The second level is assumed to represent a greater effort on the part of the pilot. If the system response characteristics can be achieved with the first-level pilot model, it is concluded that the aircraft will be given a pilot rating of satisfactory. If the aircraft characteristics are such that the second-level pilot model is required to achieve the prescribed system response, it is concluded that the aircraft will be rated tolerable.

Adams, J. J.↗

Influence of dynamic inflow on the helicopter vertical response

A study was conducted to investigate the effects of dynamic inflow on rotor-blade flapping and vertical motion of the helicopter in hover. Linearized versions of two dynamic inflow models, one developed by Carpenter and Fridovich and the other by Pitt and Peters, were incorporated in simplified rotor-body models and were compared for variations in thrust coefficient and the blade Lock number. In addition, a comparison was made between the results of the linear analysis, and the transient and frequency responses measured in flight on the CH-47B variable-stability helicopter. Results indicate that the correlations are good, considering the simplified model used. The linear analysis also shows that dynamic inflow plays a key role in destabilizing the flapping mode. The destabilized flapping mode, along with the inflow mode that the dynamic inflow introduces, results in a large initial overshoot in the vertical acceleration response to an abrupt input in the collective pitch. This overshoot becomes more pronounced as either the thrust coefficient or the blade Lock number is reduced. Compared with Carpenter's inflow model, Pitt's model tends to produce more oscillatory responses because of the less stable flapping mode predicted by it.

Chen, Robert T. N.↗

Noise levels of operational helicopters of the OH-6 type designed to meet the LOH mission

Formulas relating overall sound pressure level (OASPL) to parameters such as horsepower required, tip speed, and thrust for main and tail rotors are presented for standard and quieted helicopters. Formulas relating OASPL to engine parameters such as horsepower output and percent power turbine rpm are presented for unmuffled and muffled engines. The linear scale was used in preference to any of the weighted scales because it resulted in more consistent agreement with the test data when the SPL is expressed in the usual parameters of tip speed, thrust generated and power required. It is recognized that the linear scale does not adequately reflect hearing response, and hence is not a good absolute measure for detection by humans. However, linear OASPL is believed to be useful as a relative means of comparing noise level variations of individual components in similar helicopters with reasonably modest design changes.

Wagner, R. A.↗

Analysis of the dynamic response of a supersonic inlet to flow-field perturbations upstream of the normal shock

A linearized mathematical analysis is presented for determining the response of normal shock position and subsonic duct pressures to flow-field perturbations upstream of the normal shock in mixed-compression supersonic inlets. The inlet duct cross-sectional area variation is approximated by constant-area sections; this approximation results in one-dimensional wave equations. A movable normal shock separates the supersonic and subsonic flow regions, and a choked exit is assumed for the inlet exit condition. The analysis leads to a closed-form matrix solution for the shock position and pressure transfer functions. Analytical frequency response results are compared with experimental data and a method of characteristics solution.

Cole, G. L.↗

Influence of dynamic inflow on the helicopter vertical response

A study has been conducted to investigate the effects of dynamic inflow on rotor-blade flapping and vertical motion of the helicopter in hover. Linearized versions of two dynamic inflow models, one developed by Carpenter and Fridovich and the other by Pitt and Peters, were incorporated in simplified rotor-body models and were compared for variations in thrust coefficient and the blade Lock number. In addition, a comparison was made between the results of the linear analysis, and the transient and frequency responses measured in flight on the CH-47B variable-stability helicopter. Results indicate that the correlations are good, considering the simplified model used. The linear analysis also shows that dynamic inflow plays a key role in destabilizing the flapping mode. The destabilized flapping mode, along with the inflow mode that the dynamic inflow introduces, results in a large initial overshoot in the vertical acceleration response to an abrupt input in the collective pitch. This overshoot becomes more pronounced as either the thrust coefficient or the blade Lock number is reduced. Compared with Carpenter's inflow model, Pitt's model tends to produce more oscillatory responses because of the less stable flapping mode predicted by it.

Chen, Robert T. N.↗

Calibration of high-temperature, fiber-optic, microbend, pressure transducers

The microbend pressure transducer was evaluated on the basis of a series of specified tests to determine the pressure, temperature, overpressure, and vibration response. The response was found to be approximately linear with a pressure in the range of -690 to + 690 kPa. The transducer exhibited high sensitivity to diaphragm deflection and rapid response to pressure changes and was insensitive to vibration for frequencies of 50 to 2500 Hz. The microbend transducer test data showed acceptable sensitivity and stability as a function of temperature and pressure to be used as the basis for a compensatable transducer.

Berthold, J. W.↗

Experimental Dynamic Characterization of a Reconfigurable Adaptive Precision Truss

The dynamic behavior of a reconfigurable adaptive truss structure with non-linear joints is investigated. The objective is to experimentally examine the effects of the local non-linearities on the global dynamics of the structure. Amplitude changes in the frequency response functions are measured at micron levels of motion. The amplitude and frequency variations of a number of modes indicate a non-linear Coulomb friction response. Hysteretic bifurcation behavior is also measured at an amplitude approximately equal to the specified free-play in the joint. Under the 1 g pre-load, however, the non-linearity was dominantly characteristic of Coulomb friction with little evidence of free-play stiffening.

Hinkle, J. D.↗

Surface acoustic-wave piezoelectric crystal aerosol mass microbalance

The development of a particulate mass-sensing instrument based on a quartz-crystal microbalance and enhanced with the new surface acoustic-wave (SAW) technology is reported. Mass sensitivity comparisons of a 158-MHz SAW piezoelectric microbalance and a conventional 10-MHz quartz-crystal microbalance show that the SAW crystal is 266 times more sensitive, in good agreement with the theoretical value of 250. The frequency stability of a single SAW resonator is 6 parts in 10 to the 8th over 1 min. The response to temperature changes is found to be very linear over the range +30 to -30 C. A strong response to 15 ppm SO2 has been demonstrated on a chemically coated SAW crystal.

Bowers, W. D.↗

How cereal grass shoots perceive and respond to gravity

The leaf-sheath pulvinus of grasses presents a unique system for studying gravitropism, primarily because of its differences from other organs. The mature pulvinus is a discrete organ specialized for gravitropism: it is nongrowing in the absence of gravistimulation and capable of displaying a graviresponse independent of the rest of the plant. In this paper we present a model for gravitropism in pulvini based on recent findings from studies on the mechanisms of graviperception and graviresponse. According to this model, amyloplasts play an essential role in perceiving a change in the orientation of the pulvinus. The perception of this reorientation leads to the enhanced synthesis and release from conjugate of the auxin IAA, and the increased conjugation of gibberellin, on a localized basis. Because there is a graded growth promotion across the gravistimulated pulvinus, it is suggested that the observed hormonal asymmetry is actually an indication of a linear gradient of hormone concentration, as well as hormone response, across the pulvinus. It is further suggested that the linear gradient of hormone concentration may be predominantly the result of local changes in hormone level, rather than a product of hormonal movement into or across the pulvinus.

NASA Discipline Number 40-99↗

Structural Response of Compression-Loaded, Tow-Placed, Variable Stiffness Panels

Results of an analytical and experimental study to characterize the structural response of two compression-loaded variable stiffness composite panels are presented and discussed. These variable stiffness panels are advanced composite structures, in which tows are laid down along precise curvilinear paths within each ply and the fiber orientation angle varies continuously throughout each ply. The panels are manufactured from AS4/977-3 graphite-epoxy pre-preg material using an advanced tow placement system. Both variable stiffness panels have the same layup, but one panel has overlapping tow bands and the other panel has a constant-thickness laminate. A baseline cross-ply panel is also analyzed and tested for comparative purposes. Tests performed on the variable stiffness panels show a linear prebuckling load-deflection response, followed by a nonlinear response to failure at loads between 4 and 53 percent greater than the baseline panel failure load. The structural response of the variable stiffness panels is also evaluated using finite element analyses. Nonlinear analyses of the variable stiffness panels are performed which include mechanical and thermal prestresses. Results from analyses that include thermal prestress conditions correlate well with measured variable stiffness panel results. The predicted response of the baseline panel also correlates well with measured results.

Wu, K. Chauncey↗

Dose--response of initial G2-chromatid breaks induced in normal human fibroblasts by heavy ions

PURPOSE: To investigate initial chromatid breaks in prematurely condensed G2 chromosomes following exposure to heavy ions of different LET. MATERIAL AND METHODS: Exponentially growing human fibroblast cells AG1522 were irradiated with gamma-rays, energetic carbon (13 keV/ microm, 80 keV/microm), silicon (55 keV/microm) and iron (140 keV/microm, 185keV/microm, 440keV/microm) ions. Chromosomes were prematurely condensed using calyculin-A. Initial chromatid-type and isochromatid breaks in G2 cells were scored. RESULTS: The dose response curves for total chromatid breaks were linear regardless of radiation type. The relative biological effectiveness (RBE) showed a LET-dependent increase, peaking around 2.7 at 55-80keV/microm and decreasing at higher LET. The dose response curves for isochromatid-type breaks were linear for high-LET radiations, but linear-quadratic for gamma-rays and 13 keV/microm carbon ions. The RBE for the induction of isochromatid breaks obtained from linear components increased rapidly between 13keV/microm (about 7) and 80keV/microm carbon (about 71), and decreased gradually until 440 keV/microm iron ions (about 66). CONCLUSIONS: High-LET radiations are more effective at inducing isochromatid breaks, while low-LET radiations are more effective at inducing chromatid-type breaks. The densely ionizing track structures of heavy ions and the proximity of sister chromatids in G2 cells result in an increase in isochromatid breaks.

Non-NASA Center↗

Vestibular adaptation to space in monkeys

Otolith-induced eye movements of rhesus monkeys were studied before and after the 1989 COSMOS 2044 and the 1992 to 1993 COSMOS 2229 flights. Two animals flew in each mission for approximately 2 weeks. After flight, spatial orientation of the angular vestibulo-ocular reflex was altered. In one animal the time constant of postrotatory nystagmus, which had been shortened by head tilts with regard to gravity before flight, was unaffected by the same head tilts after flight. In another animal, eye velocity, which tended to align with a gravitational axis before flight, moved toward a body axis after flight. This shift of orientation disappeared by 7 days after landing. After flight, the magnitude of compensatory ocular counter-rolling was reduced by about 70% in both dynamic and static tilts. Modulation in vergence in response to naso-occipital linear acceleration during off-vertical axis rotation was reduced by more than 50%. These changes persisted for 11 days after recovery. An up and down asymmetry of vertical nystagmus was diminished for 7 days. Gains of the semicircular canal-induced horizontal and vertical angular vestibulo-ocular reflexes were unaffected in both flights, but the gain of the roll angular vestibulo-ocular reflex was decreased. These data indicate that there are short- and long-term changes in otolith-induced eye movements after adaptation to microgravity. These experiments also demonstrate the unique value of the monkey as a model for studying effects of vestibular adaptation in space. Eye movements can be measured in three dimensions in response to controlled vestibular and visual stimulation, and the results are directly applicable to human beings. Studies in monkeys to determine how otolith afferent input and central processing is altered by adaptation to microgravity should be an essential component of future space-related research.

Cosmos 2229 Project↗