The stabilization of a nonlinear system using a linear system estimator
Nonlinear systems stabilization with linear system estimator output state to provide feedback for asymptotic stability of overall system
SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Nonlinear systems stabilization with linear system estimator output state to provide feedback for asymptotic stability of overall system
An equation of state is presented for liquid and gaseous nitrogen for temperatures from 115 R to 3500 R and pressures to 150,000 psia. All of the pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been identified and applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation in representing the data. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data and, simultaneously, to constant volume data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and saturated vapor. The methods of weighting the various data for simultaneous fitting are presented and discussed. The equation of state is estimated to be accurate to within 0.5 percent in the liquid region, to within 0.1 percent for supercritical isotherms up to 15,000 psia, and to within 0.3 percent from 15,000 to 150,000 psia.
A simple resonance theory of three-body ion-atom association reactions is presented. The reaction is considered as proceeding through the formation of a long lived orbiting resonance complex between the atom and the ion. The population of these quasi-bound states is estimated assuming thermal equilibrium. A stable molecular ion may then be formed upon deactivation of the complex by collision with a third body. Various simplifying approximations to the potential curves and surfaces are employed. Furthermore, the deactivation cross sections for the relevant complexes are estimated from the corresponding atomic 'sizes.' A simple analytical formula for the three-body rate constant is thus derived. Reasonable agreement with experiment is obtained for He(+) in He and fair agreement for other light systems.
The fixed-point smoothing problem of sequentially correlated processes is considered. The filtering technique of such processes is extended to smoothing problems by simultaneously estimating the state and the accumulated contribution of process noise. Suboptimal filtering and smoothing are also discussed when data noise is regarded white in designing filters although it is actually sequentially correlated.-
An autopilot logic is designed here for controlling a helicopter with a hanging load. A 16th order model for the system is decoupled into four subsystems: (1) a second order system for yawing motion, (2) a second order system for vertical motion, (3) a sixth order system for longitudinal motion, and (4) a sixth order system for lateral motion. A measuring scheme, which could be used in remote areas, is developed and filters are designed to estimate the state variables from these measurements. The autopilot can be used to move the load over short distances without retracting the cables. This is done by automatically shifting the autopilot modes from position-hold (hover) to acceleration-hold to velocity-hold (cruise) to deceleration-hold to velocity-hold (near hover) to position-hold (hover). Use of such an autopilot might save considerable turnaround time. The Sikorsky S-61 helicopter is chosen as an example vehicle. The performance of the controlled system is studied in the presence of longitudinal and lateral winds.
A method proposed by Potter of applying the Kalman-Bucy filter to the problem of estimating the state of a dynamic system is described, in which the square root of the state error covariance matrix is used to process the observations. A new technique which propagates the covariance square root matrix in lower triangular form is given for the discrete observation case. The technique is faster than previously proposed algorithms and is well-adapted for use with the Carlson square root measurement algorithm.
The paper reports on differential and integral cross sections for scattering of 4.5 eV electrons by ground state (x 3 Sigma g minus) and metastable (a 1 Delta g) oxygen molecules in the -2.0 eV to plus 2.0 eV energy loss range. The cross section for the (a 1 Delta g to b 1 Sigma g plus) transition was found to be more than an order of magnitude larger than that of the excitation of the b state from the ground state. It was found that the principle of detailed balance can be applied to the rotationally unresolved inelastic and superelastic electronic transitions between the (x 3 Sigma g minus) and (a 1 Delta g) states, which indicates that for this transition one may neglect the very different rotational level structure of the two states in estimating superelastic cross section from inelastic data to an accuracy of about 15 per cent.
A straightforward self-consistent method was developed to estimate solid state electrostatic potentials, fields and field gradients in ionic solids. The method is a direct practical application of basic electrostatics to solid state and also helps in the understanding of the principles of crystal structure. The necessary mathematical equations, derived from first principles, were presented and the systematic computational procedure developed to arrive at the solid state electrostatic field gradients values was given.
A method is presented for extracting hadron-neutron scattering amplitudes from hadron-proton and hadron-deuteron measurements within the framework of the Glauber approximation. This method, which involves the solution of a linear integral equation, is applied to pn collisions between 15 and 275 GeV/c. Effects arising from inelastic intermediate states are estimated.
A technique for objectively evaluating different displays by sensitivity analysis is described. First, the mathematical model used to analyze static displays is developed. The technique is based on formulating functional relationships between the state variables and the variables observable in the display. The matrix of the partial derivatives of the display variables with respect to the state variables, together with the observer's acuity function, is used to calculate expected errors in the state vector estimation. The technique is expanded by the use of Kalman filtering to process a time series of observation vectors. This provides a tool for analyzing displays of dynamic processes by means of a dynamic display evaluation computer program. Results are reported using this program to simulate an Instrument Landing System approach.
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
HEAO 1 observations of soft X-ray emission from a point source in the vicinity of Alpha Cen are reported. The source, designated H1437-61, is tentatively identified with Alpha Cen, and an X-ray luminosity comparable to that of the sun in an active state is estimated. A temperature of about 500,000 K and an emission integral of 5 x 10 to the 50th per cu cm are obtained. Coronal emission is suggested as the X-ray-producing mechanism.
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete-time Kalman filter is derived. The resultant compensated Kalman filter has the property that steady-state bias estimation errors, resulting from modelling errors, are eliminated. The implementation of the compensated Kalman filter involves the use of accumulators in the residual channels in addition to the nominal dynamic model of the stochastic system.
The observation of intense blue-green spontaneous emission attributed to IF from electron-beam-excited Ar/CF3I/NF3 gas mixtures is reported. Intense emission from a structured band centered at a wavelength of 484 nm was observed when mixtures of 2000-4000 Torr AR (or He or Ne), 3 Torr CF3I and 1 Torr NF3 (or F2) were irradiated with a 3-nsec FWHM electron beam. Analysis of ICl and IBr spectra, which the present spectrum closely resembles, indicates that the 484-nm emission originates from the E to A 3 pi 1 transition of IF. Examination of the time dependence of metastable IF and I2 emission reveals that the IF (E) level is formed primarily by excitation transfer from metastable I(4P) states. The fluorescence efficiency of the E-A transition and the radiative lifetime of the metastable IF (E) state are estimated to be approximately 6% and 15 nsec, respectively, and it is suggested that metastable IF is an attractive candidate for a blue-green laser.
Parameters for a photolytically pumped alkyl iodide lasant gas by the nuclear-induced XeBr excimer fluorescence are calculated according to a detailed kinetic model. High gain on the atomic iodine 2P1/2 state is estimated and 100-mJ pulses with an average power output on the order of 1 kW appear possible.
The potential size of the onfarm-pumped irrigation market for solar thermal parabolic dish systems in seven high-insolation states is estimated. The study is restricted to the displacement of three specific fuels: gasoline, diesel and natural gas. The model was developed to estimate the optimal number of parabolic dish modules per farm based on the minimum cost mix of conventional and solar thermal energy required to meet irrigation needs. The study concludes that the potential market size for onfarm-pumped irrigation applications ranges from 101,000 modules when a 14 percent real discount rate is assumed to 220,000 modules when the real discount rate drops to 8 percent. Arizona, Kansas, Nebraska, New Mexico and Texas account for 98 percent of the total demand for this application, with the natural gas replacement market accounting for the largest segment (71 percent) of the total market.
Metallic vapor lasers of Na2 and Li2 are examined as solar energy converters. The absorbed photons cause transitions to vibrational-rotational levels in an upper electronic state. With broad band absorption the resultant levels can have quantum numbers considerably higher than the upper lasing level. The excited molecule then relaxes to the upper lasing level which is one of the lower vibrational levels in the upper electronic state. The relaxation occurs from collisions, provided the molecule is not quenched into the ground level electronic state. Lasing occurs with a transition to a vibrational level in the lower electronic state. Rough estimates of solar power efficiencies are 1 percent for Na2 and probably a similar figure for Li2. The nondissociative lasers from a family distinct from materials which dissociate to yield an excited atom.
An overview of the current status of the ROSAT X-Ray satellite project is given. Areas discussed include an overview of problem areas, systems and mechanical subsystems, the electrical subsystem, power supply, data processing and transmission, the wide field camera, ground support equipment and the production scheduling. It is shown that the project is proceeding according to schedule, including the hardware production and costs. However, it is stated that estimated additional costs will exceed the plan. The previous schedule for production of the flight model will no longer be met. A modified milestone plan has been worked out with Dornier Systems. The current working schedule calls for a launch data of December 21, 1987; however, this does not take into account a 4-week buffer prior to transporting the flight model to the launch site. As of the date of this report, milestone M5 has been met. Previous problems with the gold vapor deposition on the flight model mirror due to contamination have been eliminated.