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At least 451 records · Page 25

A FORTRAN program for the analysis of linear continuous and sample-data systems

A FORTRAN digital computer program which performs the general analysis of linearized control systems is described. State variable techniques are used to analyze continuous, discrete, and sampled data systems. Analysis options include the calculation of system eigenvalues, transfer functions, root loci, root contours, frequency responses, power spectra, and transient responses for open- and closed-loop systems. A flexible data input format allows the user to define systems in a variety of representations. Data may be entered by inputing explicit data matrices or matrices constructed in user written subroutines, by specifying transfer function block diagrams, or by using a combination of these methods.

Edwards, J. W.↗

Dynamic regulation of heart rate during acute hypotension: new insight into baroreflex function

To examine the dynamic properties of baroreflex function, we measured beat-to-beat changes in arterial blood pressure (ABP) and heart rate (HR) during acute hypotension induced by thigh cuff deflation in 10 healthy subjects under supine resting conditions and during progressive lower body negative pressure (LBNP). The quantitative, temporal relationship between ABP and HR was fitted by a second-order autoregressive (AR) model. The frequency response was evaluated by transfer function analysis. Results: HR changes during acute hypotension appear to be controlled by an ABP error signal between baseline and induced hypotension. The quantitative relationship between changes in ABP and HR is characterized by a second-order AR model with a pure time delay of 0.75 s containing low-pass filter properties. During LBNP, the change in HR/change in ABP during induced hypotension significantly decreased, as did the numerator coefficients of the AR model and transfer function gain. Conclusions: 1) Beat-to-beat HR responses to dynamic changes in ABP may be controlled by an error signal rather than directional changes in pressure, suggesting a "set point" mechanism in short-term ABP control. 2) The quantitative relationship between dynamic changes in ABP and HR can be described by a second-order AR model with a pure time delay. 3) The ability of the baroreflex to evoke a HR response to transient changes in pressure was reduced during LBNP, which was due primarily to a reduction of the static gain of the baroreflex.

Clinical Trial↗

Determining the response of sea level to atmospheric pressure forcing using TOPEX/POSEIDON data

The static response of sea level to the forcing of atmospheric pressure, the so-called inverted barometer (IB) effect, is investigated using TOPEX/POSEIDON data. This response, characterized by the rise and fall of sea level to compensate for the change of atmospheric pressure at a rate of -1 cm/mbar, is not associated with any ocean currents and hence is normally treated as an error to be removed from sea level observation. Linear regression and spectral transfer function analyses are applied to sea level and pressure to examine the validity of the IB effect. In regions outside the tropics, the regression coefficient is found to be consistently close to the theoretical value except for the regions of western boundary currents, where the mesoscale variability interferes with the IB effect. The spectral transfer function shows near IB response at periods of 30 degrees is -0.84 +/- 0.29 cm/mbar (1 standard deviation). The deviation from = 1 cm /mbar is shown to be caused primarily by the effect of wind forcing on sea level, based on multivariate linear regression model involving both pressure and wind forcing. The regression coefficient for pressure resulting from the multivariate analysis is -0.96 +/- 0.32 cm/mbar. In the tropics the multivariate analysis fails because sea level in the tropics is primarily responding to remote wind forcing. However, after removing from the data the wind-forced sea level estimated by a dynamic model of the tropical Pacific, the pressure regression coefficient improves from -1.22 +/- 0.69 cm/mbar to -0.99 +/- 0.46 cm/mbar, clearly revealing an IB response. The result of the study suggests that with a proper removal of the effect of wind forcing the IB effect is valid in most of the open ocean at periods longer than 20 days and spatial scales larger than 500 km.

Fu, Lee-Lueng↗

Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.

Guo, Tong-Yi↗

Parametric Robust Control and System Identification: Unified Approach

During the period of this support, a new control system design and analysis method has been studied. This approach deals with control systems containing uncertainties that are represented in terms of its transfer function parameters. Such a representation of the control system is common and many physical parameter variations fall into this type of uncertainty. Techniques developed here are capable of providing nonconservative analysis of such control systems with parameter variations. We have also developed techniques to deal with control systems when their state space representations are given rather than transfer functions. In this case, the plant parameters will appear as entries of state space matrices. Finally, a system modeling technique to construct such systems from the raw input - output frequency domain data has been developed.

Keel, L. H.↗

Analysis of ground reflection of jet noise obtained with various microphone arrays over an asphalt surface

Ground reflection effects on the propagation of jet noise over an asphalt surface are discussed for data obtained using a 33.02-cm diameter nozzle with microphones at several heights and distances from the nozzle axis. Ground reflection effects are analyzed using the concept of a reflected signal transfer function which represents the influence of both the reflecting surface and the atmosphere on the propagation of the reflected signal in a mathematical model. The mathematical model used as a basis for the computer program was successful in significantly reducing the ground reflection effects. The range of values of the single complex number used to define the reflected signal transfer function was larger than expected when determined only by the asphalt surface. This may indicate that the atmosphere is affecting the propagation of the reflected signal more than the asphalt surface. The selective placement of the reinforcements and cancellations in the design of an experiment to minimize ground reflection effects is also discussed.

Miles, J. H.↗

Shake test of rotor test apparatus with balance dampers in the 40 by 80 foot wind tunnel

A shake test was conducted to determine the dynamic characteristics of a rotor test apparatus on two strut systems with balance dampers in the Ames 40- by 80-ft wind tunnel. The rotor-off hub transfer function (acceleration per unit force as a function of frequency) was measured in the longitudinal and lateral directions, using a combination of broadband and discrete frequency excitation techniques. The dynamic data are summarized for the configurations tested, giving the following properties for each mode identified: the natural frequency, the hub response at resonance, the fixed system damping, the damping ratio, and the modal mass. The complete transfer functions are presented, and the detailed test results are included as an appendix.

Johnson, W.↗

Analysis of ground reflection of jet noise obtained with various microphone arrays over an asphalt surface

Ground reflection effects on the propagation of jet noise over an asphalt surface are discussed for data obtained using a 33.02 cm (13-in.) diameter nozzle with microphones at several heights and distances from the nozzle axis. Analysis of ground reflection effects is accomplished using the concept of a reflected signal transfer function which represents the influence of both the reflecting surface and the atmosphere on the propagation of the reflected signal in a mathematical model. The mathematical model used as a basis for the computer program was successful in significantly reducing the ground reflection effects. The range of values of the single complex number used to define the reflected signal transfer function was larger than expected when determined only by the asphalt surface. This may indicate that the atmosphere is affecting the propagation of the reflected signal more than the asphalt surface. Also discussed is the selective placement of the reinforcements and cancellations in the design of an experiment to minimize ground reflection effects.

Miles, J. H.↗

Optimizing an Actuator Array for the Control of Multi-Frequency Noise in Aircraft Interiors

Techniques developed for selecting an optimized actuator array for interior noise reduction at a single frequency are extended to the multi-frequency case. Transfer functions for 64 actuators were obtained at 5 frequencies from ground testing the rear section of a fully trimmed DC-9 fuselage. A single loudspeaker facing the left side of the aircraft was the primary source. A combinatorial search procedure (tabu search) was employed to find optimum actuator subsets of from 2 to 16 actuators. Noise reduction predictions derived from the transfer functions were used as a basis for evaluating actuator subsets during optimization. Results indicate that it is necessary to constrain actuator forces during optimization. Unconstrained optimizations selected actuators which require unrealistically large forces. Two methods of constraint are evaluated. It is shown that a fast, but approximate, method yields results equivalent to an accurate, but computationally expensive, method.

Palumbo, D. L.↗

Shake Test of a Propeller Test Rig in the 40- by 80-Foot Wind Tunnel

A shake test was conducted to determine the dynamic characteristics of a propeller test rig in the Ames 40- by 80-Foot Wind Tunnel. The rotor off hub transfer function (acceleration per unit force as a function of frequency) was measured in the longitudinal, lateral, and vertical directions for shaft angles of 0 and 90 deg corresponding to propeller and helicopter operation, respectively. The dynamic data are summarized for the configurations tested, giving the following properties for each mode identified: the natural frequency, the hub response at resonance, the damping coefficient, the damping ratio, and the modal mass. The complete transfer functions are presented, and the detailed test results are included.

Johnson, W.↗

Test-Anchored Vibration Response Predictions for an Acoustically Energized Curved Orthogrid Panel with Mounted Components

rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for component-loaded curved orthogrid panels typical of launch vehicle skin structures. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was applied to correlate the measured input sound pressures across the energized panel. This application quantifies the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software developed for the RPTF method allows easy replacement of the diffuse acoustic field with other pressure fields such as a turbulent boundary layer (TBL) model suitable for vehicle ascent. Structural responses using a TBL model were demonstrated, and wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this environment. Finally, design load factors were developed from the measured and predicted responses and compared with those derived from traditional techniques such as historical Mass Acceleration Curves and Barrett scaling methods for acreage and component-loaded panels.

Frady, Gregory P.↗

Test-Anchored Vibration Response Predictions for an Acoustically Energized Curved Orthogrid Panel with Mounted Components

A rich body of vibroacoustic test data was recently generated at Marshall Space Flight Center for a curved orthogrid panel typical of launch vehicle skin structures. Several test article configurations were produced by adding component equipment of differing weights to the flight-like vehicle panel. The test data were used to anchor computational predictions of a variety of spatially distributed responses including acceleration, strain and component interface force. Transfer functions relating the responses to the input pressure field were generated from finite element based modal solutions and test-derived damping estimates. A diffuse acoustic field model was employed to describe the assumed correlation of phased input sound pressures across the energized panel. This application demonstrates the ability to quickly and accurately predict a variety of responses to acoustically energized skin panels with mounted components. Favorable comparisons between the measured and predicted responses were established. The validated models were used to examine vibration response sensitivities to relevant modeling parameters such as pressure patch density, mesh density, weight of the mounted component and model form. Convergence metrics include spectral densities and cumulative root-mean squared (RMS) functions for acceleration, velocity, displacement, strain and interface force. Minimum frequencies for response convergence were established as well as recommendations for modeling techniques, particularly in the early stages of a component design when accurate structural vibration requirements are needed relatively quickly. The results were compared with long-established guidelines for modeling accuracy of component-loaded panels. A theoretical basis for the Response/Pressure Transfer Function (RPTF) approach provides insight into trends observed in the response predictions and confirmed in the test data. The software modules developed for the RPTF method can be easily adapted for quick replacement of the diffuse acoustic field with other pressure field models; for example a turbulent boundary layer (TBL) model suitable for vehicle ascent. Wind tunnel tests have been proposed to anchor the predictions and provide new insight into modeling approaches for this type of environment. Finally, component vibration environments for design were developed from the measured and predicted responses and compared with those derived from traditional techniques such as Barrett scaling methods for unloaded and component-loaded panels.

Frady, Gregory P.↗

Binaural Simulation Experiments in the NASA Langley Structural Acoustics Loads and Transmission Facility

A location and positioning system was developed and implemented in the anechoic chamber of the Structural Acoustics Loads and Transmission (SALT) facility to accurately determine the coordinates of points in three-dimensional space. Transfer functions were measured between a shaker source at two different panel locations and the vibrational response distributed over the panel surface using a scanning laser vibrometer. The binaural simulation test matrix included test runs for several locations of the measuring microphones, various attitudes of the mannequin, two locations of the shaker excitation and three different shaker inputs including pulse, broadband random, and pseudo-random. Transfer functions, auto spectra, and coherence functions were acquired for the pseudo-random excitation. Time histories were acquired for the pulse and broadband random input to the shaker. The tests were repeated with a reflective surface installed. Binary data files were converted to universal format and archived on compact disk.

Grosveld, Ferdinand W.↗

A scaling theory for linear systems

A theory of scaling for rational (transfer) functions in terms of transformation groups is developed. Two different four-parameter scaling groups which play natural roles in studying linear systems are identified and the effect of scaling on Fisher information and related statistical measures in system identification are studied. The scalings considered include change of time scale, feedback, exponential scaling, magnitude scaling, etc. The scaling action of the groups studied is tied to the geometry of transfer functions in a rather strong way as becomes apparent in the examination of the invariants of scaling. As a result, the scaling process also provides new insight into the parameterization question for rational functions.

Brockett, R. W.↗

Module theoretic zero structures for system matrices

The coordinate-free module-theoretic treatment of transmission zeros for MIMO transfer functions developed by Wyman and Sain (1981) is generalized to include noncontrollable and nonobservable linear dynamical systems. Rational, finitely-generated-modular, and torsion-divisible interpretations of the Rosenbrock system matrix are presented; Gamma-zero and Omega-zero modules are defined and shown to contain the output-decoupling and input-decoupling zero modules, respectively, as submodules; and the cases of left and right invertible transfer functions are considered.

Wyman, Bostwick F.↗

Research on output feedback control

In designing fixed order compensators, an output feedback formulation has been adopted by suitably augmenting the system description to include the compensator states. However, the minimization of the performance index over the range of possible compensator descriptions was impeded due to the nonuniqueness of the compensator transfer function. A controller canonical form of the compensator was chosen to reduce the number of free parameters to its minimal number in the optimization. In the MIMO case, the controller form requires a prespecified set of ascending controllability indices. This constraint on the compensator structure is rather innocuous in relation to the increase in convergence rate of the optimization. Moreover, the controller form is easily relatable to a unique controller transfer function description. This structure of the compensator does not require penalizing the compensator states for a nonzero or coupled solution, a problem that occurs when following a standard output feedback synthesis formulation.

Calise, A. J.↗

Some easily analyzable convolutional codes

Convolutional codes have played and will play a key role in the downlink telemetry systems on many NASA deep-space probes, including Voyager, Magellan, and Galileo. One of the chief difficulties associated with the use of convolutional codes, however, is the notorious difficulty of analyzing them. Given a convolutional code as specified, say, by its generator polynomials, it is no easy matter to say how well that code will perform on a given noisy channel. The usual first step in such an analysis is to computer the code's free distance; this can be done with an algorithm whose complexity is exponential in the code's constraint length. The second step is often to calculate the transfer function in one, two, or three variables, or at least a few terms in its power series expansion. This step is quite hard, and for many codes of relatively short constraint lengths, it can be intractable. However, a large class of convolutional codes were discovered for which the free distance can be computed by inspection, and for which there is a closed-form expression for the three-variable transfer function. Although for large constraint lengths, these codes have relatively low rates, they are nevertheless interesting and potentially useful. Furthermore, the ideas developed here to analyze these specialized codes may well extend to a much larger class.

Mceliece, R.↗

Robust Stabilizing Compensators for Flexible Structures with Collocated Controls

For flexible structures with collocated rate and attitude sensors/actuators, we characterize compensator transfer functions which guarantee modal stability even when stiffness/inertia parameters are uncertain. While the compensators are finite-dimensional, the structure models are allowed to be infinite-dimensional (continuum models), with attendant complexity of the notion of stability; thus exponential stability is not possible and the best we can obtain is strong stability. Robustness is interpreted essentially as maintaining stability in the worst case. The conditions require that the compensator transfer functions be positive real and use is made of the Kalman-Yakubovic lemma to characterize them further. The concept of positive realness is shown to be equivalent to dissipativity in infinite dimensions. In particular we show that for a subclass of compensators it is possible to make the system strongly stable as well as dissipative in an appropriate energy norm.

Balakrishman, A. V.↗