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Frequency domain stability criteria for dynamical systems with random parameters, considering open loop stability, stochastic gain element rms value and linear element effective bandwidth
Gradient search procedures application for nonlinear system unknown parameters identification from system dynamic response observations
The UCSD solar X-ray experiment on the OSO-7 observes X-rays in the 2 to 15 keV range with a proportional counter and in the 10.6 to 300 keV range with a scintillation counter. The dynamic range and instrument parameters are chosen to separate X-ray emission due to a hot thermal plasma from that due to nonthermal electron populations for a large number of X-ray events associated with small flares. Many different morphological classes have been observed in the 200 or so principal events observed between October 1971 and June 1972. For events which have both a thermal and nonthermal component, we can perform an analysis which shows that in not all events is it possible for the nonthermal electrons to energize the thermal plasma. We observe many events which have no nonthermal component, at least one event which was purely power law on initiation, and several events which had a long, slow decay of the hard X-rays.
Consideration of the problem of characterizing optimal controls for a class of distributed parameter systems. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables. Boundary conditions on the state are in the form of a finite number of algebraic relations between the state and boundary control variables. A few directions are outlined in which the results obtained may be extended further.
Analysis of the Skylab S194 L-band radiometer experiment data provided significant results pertaining to the actual realized performance during flight. Analysis of preflight test data provided a baseline from which to compare the experiment flight performance, although many radiometric data performance capabilities could only be demonstrated in the flight environment. The final results establish the overall hardware performance of the S194 system from which prospective users of the flight data can refer for various scientific applications. Instrument performance is presented in the areas of housekeeping and internal calibration parameters, antenna system integrity, dynamic range, linearity, precision, resolution, and absolute accuracy. Supplementary evaluations were included for an error analysis of system calibration stability. Results of the evaluation show that the instrument performance was generally as expected. Conclusions are drawn from the final evaluation results, and recommendations for improving the effectiveness of a future program are offered.
Washington, D.C., microbarograph records for Mar. 18, 1969 reveal gravity-wave-associated pressure oscillations which appear to be directly related to upper tropospheric wave structure observed at the same time with a Wallops Island 10-cm wavelength radar. The consistency between the two sets of data provides observational support for the hypothesis that shear instability in the upper tropospheric flow is the mechanism responsible for the generation of such waves. The comparison presented suggests that microbarograph arrays might be useful adjuncts to future radar studies of upper tropospheric wave dynamics, supplying such wave parameters as phase velocity and wavelength in favorable cases. The radar data pertinent to this event show an apparent vertical wave phase variation, permitting a very approximate and somewhat uncertain estimate of the wave-associated vertical flux of horizontal momentum, which is found to be about 4 dyn per sq cm. Wave generation by shear instability in the upper tropospheric air flow and the resulting vertical momentum transport may be an important element of the global atmospheric momentum budget.
Preliminary designs and the supporting analysis for both the Aeromaneuvering Orbit-to-Orbit Shuttle (AMOOS) and the Aeromaneuvering Recovery System (AMRS) are presented. The AMOOS design is shown to yield from twice to almost three times the high energy, round-trip payloads as a purely propulsive vehicle of the same weight. Typically AMOOS can perform a crew rotation mission to equatorial geosynchronous orbit in one space shuttle launch. The flight test program analysis modeled parameters such as maximum dynamic pressure, heating rates, guidance, stability and recovery. Two model flight schedules were developed, one consisting of four flights and the other of two flights. The former is considered a very low risk, high information return program whereas the latter is a minimal cost program consistent with reasonable data returns and chance of success. The AMOOS and AMRS guidance scheme developed using linear regulator theory proved a precise and accurate guidance scheme. Both it and a classical linear system's based scheme were evaluated using 65 simulated trajectories in which the position in the entry corridor and the atmospheric density were varied randomly.
The laser velocimeter (LV) technique has so far been successfully applied to many flow situations to obtain mean velocity and turbulence level measurements. The paper deals with a unique LV system employing a digital frequency counter for measurements of turbulence spectra within the objectives of achieving higher accuracies and a wider range of velocities than were possible by previous analog systems. Systematic analysis of the effects of LV system errors in the accuracy of the turbulence power spectral measurements is performed and shown to agree reasonably with the experimental LV spectra results. Sufficient understanding of the accuracy and limitations of the digital frequency counter LV spectral measurement system is obtained. Among the major system errors encountered in a typical digital frequency counter LV processor, the truncation error is regarded as the most serious source of error. The quantizing step size defined as the ratio of Doppler frequency to processor clock frequency is an important parameter in determining the dynamic range of a turbulence power spectrum.
The theories of differential games and generalized dynamic systems are used to deduce stabilizing controllers for quasi-linear systems. Attention is given to a class of dynamic systems subject to parameter and input uncertainty whose values range in a given compact set. Using a worst case design philosophy, a feedback control is derived that assures uniform asymptotic (Liapunov) stability of the origin under all admissible uncertainties.
This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.
An approximate indicial lift function associated with circulation was developed for tapered, swept wings in incompressible flow. The function is derived by representing the wings with a simple vortex system. The results from the derived equations compare well with the limited available results from more rigorous and complex methods. The equations, as derived, are not very convenient for calculating the dynamic response of aircraft, parameter extraction, or for determining frequency-response curves for wings. Therefore, an expression is developed to convert the indicial response function to an exponential form which is more convenient for these purposes.
This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.
Aircraft noise prediction theoretical methods are given. The prediction of data which affect noise generation and propagation is addressed. These data include the aircraft flight dynamics, the source noise parameters, and the propagation effects.
A general approach for distributed parameter modeling of complex dynamical systems is described. The method consists of dividing the system in parts which can be modeled by simple partial differential equations and coupling the equations thus obtained by applying Hamilton's variational formalism to the entire system. The modeling of a large, offset-fed, wrap-rib antenna is presented to illustrate the approach. Although such models are perhaps not as precise as finite element models, they can be useful for initial physical insight and parametric design.
Large space structures, or any mechanically flexible structures, are inherently distributed parameter systems (DPS) whose dynamics are modeled by partial, rather than ordinary, differential equations. Such DPS are described by operator equations on an infinite-dimensional Hilbert (or Banach) space. However, any feedback controller for such a DPS must be a finite-dimensional (and discrete-time) system in order to be implemented with on-line digital computers and a finite (small) number of actuators and sensors. There are many ways to synthesize such controllers; the Galerkin or finite-element approach is emphasized.
The relationship between crop growth and spectra reflectance parameters was studied. The dynamic behavior of canopy reflectance versus time and the relationship of trajectories to canopy dynamics, ontogeny and morphology was investigated. The determination of which transformations of spectral data best suited for observing key canopy characteristics, such as leaf area index and vegetation identification are understood. A physical basis to understand how various spectral transform trajectories depend on vegetation type and models that describe the time delayed interaction of reflectance in the chlorophyll and water absorption bands to monitor stress were formulated. The general process of physical understanding of canopy reflectance is evaluated and existing canopy models are improved.
The attainment of high computing speed as measured by the computational throughput is seen as one of the most challenging requirements. It is noted that high speed is cardinal in several distinct classes of applications. These classes are then discussed; they comprise (1) the real-time simulation of dynamic systems , (2) distributed parameter systems, and (3) mixed lumped and distributed systems. From the 1950s on, the quest for high speed in digital simulators concentrated on overcoming the limitations imposed by the so-called von Neumann bottleneck. Two major architectural approaches have made ig possible to circumvent this bottleneck and attain high speeds. These are pipelining and parallelism. Supercomputers, peripheral array processors, and microcomputer networks are then discussed.
Important features of the Eigensystem Realization Algorithm (ERA) are summarized as follows: (1) from the computational standpoint, the algorithm is attractive, since only simple numerical operations are needed; (2) the computational procedure is numerically stable; (3) the structural dynamics requirements for modal parameter identification and the control design requirements for a reduced-state space model are satisfied; (4) data from more than one test can be used simultaneously to efficiently identify the closely spaced eigenvalues; and (5) no restrictions on number of measurements are imposed.