Combined optimum control and estimation theory
Combined optimum control and estimation theory to determine noisy measurement optimal controls on randomly disturbed plant
RANDOM NOISE↗
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Some applications of stochastic differential equations to optimal nonlinear filtering.
Stochastic differential equations specifying dynamical structure of filters generating posterior probability distribution when inputs are time functions
PROBABILITY DISTRIBUTION↗
Stability properties of shaping filters.
Stable linear system /shaping filter/ synthesis transforming stationary white noise into random process having given covariance function
Brandenburg, L. H.↗
Nonlinear filtering for random signals in statistically unknown noise.
Natural and effective formulation of the filtering problem involved in satellite orbit determination, aircraft navigation, and missile tracking. The problem arises because the environment of the sensor keeps changing from time to time, and it is quite impractical and sometimes impossible to collect the statistical data of the noise incurred in the observation. Computable filtering equations are deduced. The idea of invariant imbedding along with stochastic differential calculus is used to derive differential equations for the optimal estimate.
Loo, J. T.↗
Control system design using frequency domain models and parameter optimization, with application to supersonic inlet controls
A technique is described for designing feedback control systems using frequency domain models, a quadratic cost function, and a parameter optimization computer program. FORTRAN listings for the computer program are included. The approach is applied to the design of shock position controllers for a supersonic inlet. Deterministic or random system disturbances, and the presence of random measurement noise are considered. The cost function minimization is formulated in the time domain, but the problem solution is obtained using a frequency domain system description. A scaled and constrained conjugate gradient algorithm is used for the minimization. The approach to a supersonic inlet included the calculations of the optimal proportional-plus integral (PI) and proportional-plus-integral-plus-derivative controllers. A single-loop PI controller was the most desirable of the designs considered.
Seidel, R. C.↗
A design method for minimizing sensitivity to plant parameter variations
A method is described for minimizing the sensitivity of multivariable systems to parameter variations. The variable parameters are considered as random variables and their effect is included in a quadratic performance index. The performance index is a weighted sum of the state and control covariances that stem from both the random system disturbances and the parameter uncertainties. The numerical solution of the problem is described and application of the method to several initially sensitive tracking systems is discussed. The sensitivity factor of reduction was typically 2 or 3 over a system based on random system noise only, and yet resulted in state RMS increases of only about a factor of two.
Hadass, Z.↗
Remote sounding of stratospheric temperatures using high resolution radiance measurements from the IRIS-D
Remote sounding of stratospheric temperatures up to 3.2 millibars is attempted using high resolution (unapodized) radiance measurements in the 15 micron CO2 band from the Infrared Interferometer Spectrometer on Nimbus 4. Inversions are performed using the Chahine relaxation technique. Radiance data and simultaneous in situ temperature profiles are obtained from the Rocket/Nimbus Sounder Comparison. Numerical tests with synthetic radiance data show that the uncertainty in the retrieved temperatures due to random instrument noise is about 1.1 K when averaged over layers about 10 km thick. However, comparison of the measured radiances with the radiances calculated from the in situ profiles show the calculated radiances to be systematically higher than the measured radiances. The evidence indicates that systematic errors exist in both the radiance and the in situ measurements.
Gallery, W. O.↗
A Statistical Approach to Establishing Subsystem Environmental Test Specifications
Results are presented of a research task to evaluate structural responses at various subsystem mounting locations during spacecraft level test exposures to the environments of mechanical shock, acoustic noise, and random vibration. This statistical evaluation is presented in the form of recommended subsystem test specifications for these three environments as normalized to a reference set of spacecraft test levels and are thus suitable for extrapolation to a set of different spacecraft test levels. The recommendations are dependent upon a subsystem's mounting location in a spacecraft, and information is presented on how to determine this mounting zone for a given subsystem.
Keegan, W. B.↗
Design of optimal partial state feedback controllers for linear systems in stochastic environments
The problem of obtaining an optimal control law, which is constrained to be a feedback of the available measurements, is considered for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite duration cases. The feedback gain matrices are constrained to be constant for the infinite duration cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. Computational aspects are discussed via application to two continuous time processes, including a helicopter/slung load system subjected to measurement noise and random wind gust input.
Joshi, S. M.↗
Radar error statistics for the space shuttle
Radar error statistics of C-band and S-band that are recommended for use with the groundtracking programs to process space shuttle tracking data are presented. The statistics are divided into two parts: bias error statistics, using the subscript B, and high frequency error statistics, using the subscript q. Bias errors may be slowly varying to constant. High frequency random errors (noise) are rapidly varying and may or may not be correlated from sample to sample. Bias errors were mainly due to hardware defects and to errors in correction for atmospheric refraction effects. High frequency noise was mainly due to hardware and due to atmospheric scintillation. Three types of atmospheric scintillation were identified: horizontal, vertical, and line of sight. This was the first time that horizontal and line of sight scintillations were identified.
Lear, W. M.↗
An upper limit on ultraviolet shot noise from Cygnus X-1
Rapid photometry of Cygnus X-1 through an ultraviolet filter centered on 0.35 micron has been obtained at 100-ms sampling intervals. The autocorrelation function of these data has been examined for shot noise analogous to the behavior of the X-ray light curve. The ultraviolet data are entirely consistent with white noise. Considering randomly occurring ultraviolet shots with the same duration (0.5 s) and average rate (1 per sec) as the X-ray shots, a 3-sigma upper limit on the ratio of optical to X-ray energies per shot is estimated to be 0.13, before the ultraviolet light is attenuated by interstellar dust. This limit is then generalized for shots of arbitrary duration and rate.
Duthie, J. G.↗
Integrated optics for fiber gyro's
Expected advantages of incorporating integrated optical waveguide components into fiber gyroscopes are summarized. The structural-simplicity benefits which can be achieved through the use of solid-state lasers, and integrated and fiber optics are examined; angular rate noise and random walk drift for the current technology in the 0.84-micron wavelength region are reported as 0.00001 deg/sec and 0.0002 deg/hr to the 1/2, respectively. The state-of-the-art in the pertinent materials research is reviewed; lithium niobate, suggested to be used as a waveguide substrate material, is noted to have a complex chemistry that is not yet fully understood. However, most of the optical and electrooptical components of a fiber gyro are conceptually understood and have been demonstrated.
Goss, W.↗
The design of a turboshaft speed governor using modern control techniques
The objectives of this program were: to verify the model of off schedule compressor variable geometry in the T700 turboshaft engine nonlinear model; to evaluate the use of the pseudo-random binary noise (PRBN) technique for obtaining engine frequency response data; and to design a high performance power turbine speed governor using modern control methods. Reduction of T700 engine test data generated at NASA-Lewis indicated that the off schedule variable geometry effects were accurate as modeled. Analysis also showed that the PRBN technique combined with the maximum likelihood model identification method produced a Bode frequency response that was as accurate as the response obtained from standard sinewave testing methods. The frequency response verified the accuracy of linear models consisting of engine partial derivatives and used for design. A power turbine governor was designed using the Linear Quadratic Regulator (LQR) method of full state feedback control. A Kalman filter observer was used to estimate helicopter main rotor blade velocity. Compared to the baseline T700 power turbine speed governor, the LQR governor reduced droop up to 25 percent for a 490 shaft horsepower transient in 0.1 sec simulating a wind gust, and up to 85 percent for a 700 shaft horsepower transient in 0.5 sec simulating a large collective pitch angle transient.
Delosreyes, G.↗
The Feasibility of the Disturbance Accommodating Controller for Precision Antenna Pointing
The objective of this study is to investigate the feasibility of a pointing (position loop) controller for the NASA-JPL Deep Space Network (DSN) antennas using the Disturbance Accommodating Control (DAC) theory. A model that includes state dependent disturbances was developed, and an example demonstrating the noise estimator is presented as an initial phase in the controller design. The goal is to improve pointing accuracy by the removal of the systematic errors caused by the antenna misalignment as well as sensor noise and random wind and thermal disturbances. Preliminary simulation results show that the DAC technique is successful in both cancelling the imposed errors and maintaining an optimal control policy.
Gresham, L. L.↗
Integrated tools for control-system analysis
The basic functions embedded within a user friendly software package (MATRIXx) are used to provide a high level systems approach to the analysis of linear control systems. Various control system analysis configurations are assembled automatically to minimize the amount of work by the user. Interactive decision making is incorporated via menu options and at selected points, such as in the plotting section, by inputting data. There are five evaluations such as the singular value robustness test, singular value loop transfer frequency response, Bode frequency response, steady-state covariance analysis, and closed-loop eigenvalues. Another section describes time response simulations. A time response for random white noise disturbance is available. The configurations and key equations used for each type of analysis, the restrictions that apply, the type of data required, and an example problem are described. One approach for integrating the design and analysis tools is also presented.
Ostroff, Aaron J.↗
Vela X-1 pulse timing. II - Variations in pulse frequency
The pulsed X-ray emission of Vela X-1 during May 1978 and December-January 1978-1979 is investigated analytically on the basis of published satellite observations. The data are compiled in tables and graphs and discussed in detail, with reference to data for the entire 1975-1982 period. Variations in pulse frequency are identified on time scales from 2 to 2600 days; the lower nine octaves are characterized as white noise (or random walk in pulse frequency), while the longer-period variations are attributed to changes in neutron-star rotation rates.
Deeter, J. E.↗
Comparison of three controllers applied to helicopter vibration
A comparison was made of the applicability and suitability of the deterministic controller, the cautious controller, and the dual controller for the reduction of helicopter vibration by using higher harmonic blade pitch control. A randomly generated linear plant model was assumed and the performance index was defined to be a quadratic output metric of this linear plant. A computer code, designed to check out and evaluate these controllers, was implemented and used to accomplish this comparison. The effects of random measurement noise, the initial estimate of the plant matrix, and the plant matrix propagation rate were determined for each of the controllers. With few exceptions, the deterministic controller yielded the greatest vibration reduction (as characterized by the quadratic output metric) and operated with the greatest reliability. Theoretical limitations of these controllers were defined and appropriate candidate alternative methods, including one method particularly suitable to the cockpit, were identified.
Leyland, Jane A.↗
The topology of large-scale structure. V - Two-dimensional topology of sky maps
A 2D algorithm is applied to observed sky maps and numerical simulations. It is found that when topology is studied on smoothing scales larger than the correlation length, the topology is approximately in agreement with the random phase formula for the 2D genus-threshold density relation, G2(nu) varies as nu(e) exp-nu-squared/2. Some samples show small 'meatball shifts' similar to those seen in corresponding 3D observational samples and similar to those produced by biasing in cold dark matter simulations. The observational results are thus consistent with the standard model in which the structure in the universe today has grown from small fluctuations caused by random quantum noise in the early universe.
Gott, J. R., III↗