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At least 379 records · Page 21

Fracture behavior of large-scale thin-sheet aluminum alloy

A series of fracture tests on large-scale, pre-cracked, aluminum alloy panels is being carried out to examine and to characterize the process by which cracks propagate and link up in this material. Extended grips and test fixtures were specially designed to enable the panel specimens to be loaded in tension, in a 1780-kN-capacity universal testing machine. Twelve panel specimens, each consisting of a single sheet of bare 2024-T3 aluminum alloy, 3988 mm high, 2286 mm wide, and 1.016 mm thick are being fabricated with simulated through-cracks oriented horizontally at mid-height. Using existing information, a test matrix has been set up that explores regions of failure that are controlled by fracture mechanics, with additional tests near the boundary between plastic collapse and fracture. In addition, a variety of multiple site damage (MSD) configurations have been included to distinguish between various proposed linkage mechanisms. All tests but one use anti-buckling guides. At this writing seven specimens have been tested. Three were fabricated with a single central crack, three others had multiple cracks on each side of the central crack, and one had a single crack but no anti-buckling guides. Each fracture event was recorded on film, video, computer, magnetic tape, and occasionally optical microscopy. The visual showed the crack tip with a load meter in the field of view, using motion picture film for one tip and SVHS video tape for the other. The computer recorded the output of the testing machine load cell, the stroke, and twelve strain gages at 1.5 second intervals. A wideband FM magnetic tape recorder was used to record data from the same sources. The data were analyzed by two different procedures: (1) the plastic zone model based on the residual strength diagram; and (2) the R-curve. The first three tests were used to determine the basic material properties, and these results were then used in the analysis of the two subsequent tests with MSD cracks. There is good agreement between measured values and results obtained from the model.

Dewit, Roland↗

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗

Assessing Organic Preservation and the Implications for Potential Biosignatures in the Bastide Member of the Séítah Formation, Jezero Crater

Introduction: Olivine has the highest CO2 trapping potential of ultramafic minerals, due to its rapid rate of dissolution and high percentage of divalent cations/unpolymerized silicate tetrahedra [1]. It generates divalent carbonates from CO2 and sequesters CO2 into the mineral matrix of the target lithology. The co-occurrence of olivine and carbonate within abraded targets from the Bastide Member of the Séítah Formation (Fm) of the Jezero crater floor [2] suggests the carbonation of olivine occurred within the mineral matrix hosted in a subsurface system. Hydrothermal origins for the subsurface system are hypothesized from orbital data [3]. This is supported by the detection of hydration features within the rock as well as the carbonate features are solely detected within the abrasion patch but not the rock’s surface. Organic preservation potential of abrasion patches: We incorporated the SHERLOC/WATSON results acquired from the Dourbes, Garde, and Quartier abrasion patches in the Séítah Fm to investigate the organomineral associations, and determine the biosignature preservation potential of these rocks. Dourbes is dominated by olivine and has minor amounts of carbonate, hydrated Ca-sulfate, and amorphous or microcrystalline silicate. Fluorescence features (330-340 nm) are detected in discrete locales and could be consistent with double ring aromatic organic molecules; yet, these features do not appear to be associated with an identified mineral phase. Dark subhedral to euhedral olivine grains within the Garde abrasion patch often co-occur with carbonate-consistent spectral signatures in all analyzed scans. The availability of Fe2+ is a known influence on olivine dissolution rates [1] and SuperCam estimates of the olivine composition (Forsterite-60 average for Sols 202-234) may thereby provide a constraint on the carbonation extent. Carbonated olivine phenocrysts within the matrix may be due to aqueous alteration, as the carbonation of nodules is consistent with observations in other hydrothermal systems and within Martian meteorites (ALH84001) [4]. In comparison, the Quartier abrasion patch represents an extensively altered endmember within the Bastide Member of the Séítah Fm. It contains a fluorescence doublet at 305/325 nm that coexists with multiple species of Na-sulfate and Mg-sulfate, Mg-carbonates, olivine [5]. Aqueous alteration and implications for habitability: The identification of primary and secondary mineral phases observed in the Bastide Member suggests the release of cations from primary ultramafic minerals through aqueous alteration. Within Garde, the carbonate detected appears to be Mg-rich and likely formed from the in situ alteration of Mg-rich olivine within the region as carbonate has only been detected within the rock via in situ analysis. Carbonates derived from abiotic and biotic reactions preserve biosignatures (i.e. indices of habitability) on Earth. The detected carbonate phase found in association with fluorescent features within the rock matrix may also indicate potential organic compounds preserved in a putative hydrothermal system. Fluorescent features (~330 nm) are unique to Garde and Dourbes, though they are co-located to carbonate signatures solely within Garde, and between the light toned minerals. Identification of these fluorescent features may be consistent with 1-2 ring aromatic compounds. The limit of detection for Raman is multiple orders of magnitude greater than the limit of detection required for fluorescence [6]. Implications for provenance: Hydrothermal systems represent disequilibrium chemical conditions that are hypothesized to have supported the emergence of life and also preserve ancient carbon within precipitated carbonates [7]. Hydrothermal system associated carbonates are capable of preserving biosignatures up to an estimated ~3.77 – 4.28 Gya [8]. Thus, carbonated olivine found within the Séítah Fm may represent a high-potential biosignature preserving environment on Mars. The formation of carbonates by an aqueous alteration process, such as carbonation of olivine is also consistent with hypotheses for carbonate within the greater regional-olivine bearing unit [2,3], which contains Garde, Dourbes, and Quartier. Acknowledgments: This work was carried out at the Jet Propulsion Laboratory, The California Institute of Technology under a contract from NASA. References: [1] Wood et al., (2019) ES&T, 6, 10. [2] Stack, K. et al., (2020) Space Sci Rev, 216, 127. [3] Tarnas, J. et al., (2021) JGR: Planets, 126, 11. [4] Steele et al., (2007) Meteorit. Planet. Sci., 42, 9. [5] Murphy, A.E. et al., (2022) LPSC [6] Bhartia et al., (2021) Space Sci Rev, 217, 58. [7] Luther (2021) GRL, 48, e2021GL094869. [8] Dodd et al., (2017) Nature, 543, 60-64

E L Cardarelli↗

Solar system applications of Mie theory and of radiative transfer of polarized light

A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.

Whitehill, L. P.↗

Full resolution hologram-like autostereoscopic display

Under this program, Dimension Technologies Inc. (DTI) developed a prototype display that uses a proprietary illumination technique to create autostereoscopic hologram-like full resolution images on an LCD operating at 180 fps. The resulting 3D image possesses a resolution equal to that of the LCD along with properties normally associated with holograms, including change of perspective with observer position and lack of viewing position restrictions. Furthermore, this autostereoscopic technique eliminates the need to wear special glasses to achieve the parallax effect. Under the program a prototype display was developed which demonstrates the hologram-like full resolution concept. To implement such a system, DTI explored various concept designs and enabling technologies required to support those designs. Specifically required were: a parallax illumination system with sufficient brightness and control; an LCD with rapid address and pixel response; and an interface to an image generation system for creation of computer graphics. Of the possible parallax illumination system designs, we chose a design which utilizes an array of fluorescent lamps. This system creates six sets of illumination areas to be imaged behind an LCD. This controlled illumination array is interfaced to a lenticular lens assembly which images the light segments into thin vertical light lines to achieve the parallax effect. This light line formation is the foundation of DTI's autostereoscopic technique. The David Sarnoff Research Center (Sarnoff) was subcontracted to develop an LCD that would operate with a fast scan rate and pixel response. Sarnoff chose a surface mode cell technique and produced the world's first large area pi-cell active matrix TFT LCD. The device provided adequate performance to evaluate five different perspective stereo viewing zones. A Silicon Graphics' Iris Indigo system was used for image generation which allowed for static and dynamic multiple perspective image rendering. During the development of the prototype display, we identified many critical issues associated with implementing such a technology. Testing and evaluation enabled us to prove that this illumination technique provides autostereoscopic 3D multi perspective images with a wide range of view, smooth transition, and flickerless operation given suitable enabling technologies.

Eichenlaub, Jesse B.↗

Uncertainty Modeling for Structural Control Analysis and Synthesis

The development of an accurate model of uncertainties for the control of structures that undergo a change in operational environment, based solely on modeling and experimentation in the original environment is studied. The application used throughout this work is the development of an on-orbit uncertainty model based on ground modeling and experimentation. A ground based uncertainty model consisting of mean errors and bounds on critical structural parameters is developed. The uncertainty model is created using multiple data sets to observe all relevant uncertainties in the system. The Discrete Extended Kalman Filter is used as an identification/parameter estimation method for each data set, in addition to providing a covariance matrix which aids in the development of the uncertainty model. Once ground based modal uncertainties have been developed, they are localized to specific degrees of freedom in the form of mass and stiffness uncertainties. Two techniques are presented: a matrix method which develops the mass and stiffness uncertainties in a mathematical manner; and a sensitivity method which assumes a form for the mass and stiffness uncertainties in macroelements and scaling factors. This form allows the derivation of mass and stiffness uncertainties in a more physical manner. The mass and stiffness uncertainties of the ground based system are then mapped onto the on-orbit system, and projected to create an analogous on-orbit uncertainty model in the form of mean errors and bounds on critical parameters. The Middeck Active Control Experiment is introduced as experimental verification for the localization and projection methods developed. In addition, closed loop results from on-orbit operations of the experiment verify the use of the uncertainty model for control analysis and synthesis in space.

Campbell, Mark E.↗

Adaptive Inverse Control for Rotorcraft Vibration Reduction

This thesis extends the Least Mean Square (LMS) algorithm to solve the mult!ple-input, multiple-output problem of alleviating N/Rev (revolutions per minute by number of blades) helicopter fuselage vibration by means of adaptive inverse control. A frequency domain locally linear model is used to represent the transfer matrix relating the higher harmonic pitch control inputs to the harmonic vibration outputs to be controlled. By using the inverse matrix as the controller gain matrix, an adaptive inverse regulator is formed to alleviate the N/Rev vibration. The stability and rate of convergence properties of the extended LMS algorithm are discussed. It is shown that the stability ranges for the elements of the stability gain matrix are directly related to the eigenvalues of the vibration signal information matrix for the learning phase, but not for the control phase. The overall conclusion is that the LMS adaptive inverse control method can form a robust vibration control system, but will require some tuning of the input sensor gains, the stability gain matrix, and the amount of control relaxation to be used. The learning curve of the controller during the learning phase is shown to be quantitatively close to that predicted by averaging the learning curves of the normal modes. For higher order transfer matrices, a rough estimate of the inverse is needed to start the algorithm efficiently. The simulation results indicate that the factor which most influences LMS adaptive inverse control is the product of the control relaxation and the the stability gain matrix. A small stability gain matrix makes the controller less sensitive to relaxation selection, and permits faster and more stable vibration reduction, than by choosing the stability gain matrix large and the control relaxation term small. It is shown that the best selections of the stability gain matrix elements and the amount of control relaxation is basically a compromise between slow, stable convergence and fast convergence with increased possibility of unstable identification. In the simulation studies, the LMS adaptive inverse control algorithm is shown to be capable of adapting the inverse (controller) matrix to track changes in the flight conditions. The algorithm converges quickly for moderate disturbances, while taking longer for larger disturbances. Perfect knowledge of the inverse matrix is not required for good control of the N/Rev vibration. However it is shown that measurement noise will prevent the LMS adaptive inverse control technique from controlling the vibration, unless the signal averaging method presented is incorporated into the algorithm.

Jacklin, Stephen A.↗

Multiple-mode nonlinear free and forced vibrations of beams using finite element method

Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.

Mei, Chuh↗

Efficient dynamic simulation for multiple chain robotic mechanisms

An efficient O(mN) algorithm for dynamic simulation of simple closed-chain robotic mechanisms is presented, where m is the number of chains, and N is the number of degrees of freedom for each chain. It is based on computation of the operational space inertia matrix (6 x 6) for each chain as seen by the body, load, or object. Also, computation of the chain dynamics, when opened at one end, is required, and the most efficient algorithm is used for this purpose. Parallel implementation of the dynamics for each chain results in an O(N) + O(log sub 2 m+1) algorithm.

Lilly, Kathryn W.↗

Performance Evaluation of Fiber Bragg Gratings at Elevated Temperatures

The development of integrated fiber optic sensors for smart propulsion systems demands that the sensors be able to perform in extreme environments. In order to use fiber optic sensors effectively in an extreme environment one must have a thorough understanding of the sensor s limits and how it responds under various environmental conditions. The sensor evaluation currently involves examining the performance of fiber Bragg gratings at elevated temperatures. Fiber Bragg gratings (FBG) are periodic variations of the refractive index of an optical fiber. These periodic variations allow the FBG to act as an embedded optical filter passing the majority of light propagating through a fiber while reflecting back a narrow band of the incident light. The peak reflected wavelength of the FBG is known as the Bragg wavelength. Since the period and width of the refractive index variation in the fiber determines the wavelengths that are transmitted and reflected by the grating, any force acting on the fiber that alters the physical structure of the grating will change what wavelengths are transmitted and what wavelengths are reflected by the grating. Both thermal and mechanical forces acting on the grating will alter its physical characteristics allowing the FBG sensor to detect both temperature variations and physical stresses, strain, placed upon it. This ability to sense multiple physical forces makes the FBG a versatile sensor. This paper reports on test results of the performance of FBGs at elevated temperatures. The gratings looked at thus far have been either embedded in polymer matrix materials or freestanding with the primary focus of this paper being on the freestanding FBGs. Throughout the evaluation process, various parameters of the FBGs performance were monitored and recorded. These parameters include the peak Bragg wavelength, the power of the Bragg wavelength, and total power returned by the FBG. Several test samples were subjected to identical test conditions to allow for statistical analysis of the data. Test procedures, calibrations, and referencing techniques are presented in the paper along with directions for future research.

Juergens, Jeffrey↗

NASA Tech Briefs, August 2003

Topics covered include: Stable, Thermally Conductive Fillers for Bolted Joints; Connecting to Thermocouples with Fewer Lead Wires; Zipper Connectors for Flexible Electronic Circuits; Safety Interlock for Angularly Misdirected Power Tool; Modular, Parallel Pulse-Shaping Filter Architectures; High-Fidelity Piezoelectric Audio Device; Photovoltaic Power Station with Ultracapacitors for Storage; Time Analyzer for Time Synchronization and Monitor of the Deep Space Network; Program for Computing Albedo; Integrated Software for Analyzing Designs of Launch Vehicles; Abstract-Reasoning Software for Coordinating Multiple Agents; Software Searches for Better Spacecraft-Navigation Models; Software for Partly Automated Recognition of Targets; Antistatic Polycarbonate/Copper Oxide Composite; Better VPS Fabrication of Crucibles and Furnace Cartridges; Burn-Resistant, Strong Metal-Matrix Composites; Self-Deployable Spring-Strip Booms; Explosion Welding for Hermetic Containerization; Improved Process for Fabricating Carbon Nanotube Probes; Automated Serial Sectioning for 3D Reconstruction; and Parallel Subconvolution Filtering Architectures.

Source record↗

Progressive Damage Analysis of Bonded Composite Joints

The present work is related to the development and application of progressive damage modeling techniques to bonded joint technology. The joint designs studied in this work include a conventional composite splice joint and a NASA-patented durable redundant joint. Both designs involve honeycomb sandwich structures with carbon/epoxy facesheets joined using adhesively bonded doublers.Progressive damage modeling allows for the prediction of the initiation and evolution of damage within a structure. For structures that include multiple material systems, such as the joint designs under consideration, the number of potential failure mechanisms that must be accounted for drastically increases the complexity of the analyses. Potential failure mechanisms include fiber fracture, intraply matrix cracking, delamination, core crushing, adhesive failure, and their interactions. The bonded joints were modeled using highly parametric, explicitly solved finite element models, with damage modeling implemented via custom user-written subroutines. Each ply was discretely meshed using three-dimensional solid elements. Layers of cohesive elements were included between each ply to account for the possibility of delaminations and were used to model the adhesive layers forming the joint. Good correlation with experimental results was achieved both in terms of load-displacement history and the predicted failure mechanism(s).

Leone, Frank A., Jr.↗

The updated statistical inversion technique to the evaluation of Umkehr observations

In the present study the standard retrieval Umkehr method to estimate the vertical distribution of ozone was updated using a statistical approach to the mathematical inversion scheme. The vertical ozone profile covariance matrix was used as a priori information for the inverse problem. A new method of the ozonesonde data organization according to air mass types helped to improve the covariance matrix quality. A retrieval method was developed using eigenvector technique. An optimal vertical ozone profile resolution was determined from the mathematical inversion scheme analysis based on the same technique. The sun radiation transfer was accounted for multiple scattering and atmospheric sphericity in this calculation. The retrievals using actual Umkehr Dobson spectrophotometer observations were also performed to provide the comparison of the standard and updated methods with concurrent ozone sound data at Boulder U.S. The comparison has revealed that the present method has some advantages in both resolution and accuracy, as compared to the standard one, especially for the atmospheric layers below ozone maximum.

Frolov, Alexander D.↗

Ring-Resonator/Sol-Gel Interferometric Immunosensor

A proposed biosensing system would be based on a combination of (1) a sensing volume containing antibodies immobilized in a sol-gel matrix and (2) an optical interferometer having a ring resonator configuration. The antibodies would be specific to an antigen species that one seeks to detect. In the ring resonator of the proposed system, light would make multiple passes through the sensing volume, affording greater interaction length and, hence, greater antibody- detection sensitivity.

Bearman, Gregory↗

Recombinant Collagenlike Proteins

A group of collagenlike recombinant proteins containing high densities of biologically active sites has been invented. The method used to express these proteins is similar to a method of expressing recombinant procollagens and collagens described in U. S. Patent 5,593,859, "Synthesis of human procollagens and collagens in recombinant DNA systems." Customized collagenous proteins are needed for biomedical applications. In particular, fibrillar collagens are attractive for production of matrices needed for tissue engineering and drug delivery. Prior to this invention, there was no way of producing customized collagenous proteins for these and other applications. Heretofore, collagenous proteins have been produced by use of such biological systems as yeasts, bacteria, and transgenic animals and plants. These products are normal collagens that can also be extracted from such sources as tendons, bones, and hides. These products cannot be made to consist only of biologically active, specific amino acid sequences that may be needed for specific applications. Prior to this invention, it had been established that fibrillar collagens consist of domains that are responsible for such processes as interaction with cells, binding of growth factors, and interaction with a number of structural proteins present in the extracellular matrix. A normal collagen consists of a sequence of domains that can be represented by a corresponding sequence of labels, e.g., D1D2D3D4. A collagenlike protein of the present invention contains regions of collagen II that contain multiples of a single domain (e.g., D1D1D1D1 or D4D4D4D4) chosen for its specific biological activity. By virtue of the multiplicity of the chosen domain, the density of sites having that specific biological activity is greater than it is in a normal collagen. A collagenlike protein according to this invention can thus be made to have properties that are necessary for tissue engineering.

Fertala, Andzej↗

Combining Multiple Gyroscope Outputs for Increased Accuracy

A proposed method of processing the outputs of multiple gyroscopes to increase the accuracy of rate (that is, angular-velocity) readings has been developed theoretically and demonstrated by computer simulation. Although the method is applicable, in principle, to any gyroscopes, it is intended especially for application to gyroscopes that are parts of microelectromechanical systems (MEMS). The method is based on the concept that the collective performance of multiple, relatively inexpensive, nominally identical devices can be better than that of one of the devices considered by itself. The method would make it possible to synthesize the readings of a single, more accurate gyroscope (a virtual gyroscope) from the outputs of a large number of microscopic gyroscopes fabricated together on a single MEMS chip. The big advantage would be that the combination of the MEMS gyroscope array and the processing circuitry needed to implement the method would be smaller, lighter in weight, and less power-hungry, relative to a conventional gyroscope of equal accuracy. The method (see figure) is one of combining and filtering the digitized outputs of multiple gyroscopes to obtain minimum-variance estimates of rate. In the combining-and-filtering operations, measurement data from the gyroscopes would be weighted and smoothed with respect to each other according to the gain matrix of a minimum- variance filter. According to Kalman-filter theory, the gain matrix of the minimum-variance filter is uniquely specified by the filter covariance, which propagates according to a matrix Riccati equation. The present method incorporates an exact analytical solution of this equation.

Bayard, David S.↗

Sintering Behaviors of ZrC, NbC, and TaC Mono-and Binary Carbides

Nuclear Thermal Propulsion (NTP) has undergone development as an alternate in-space propulsion system to traditional chemical propulsion methods since the 1950s. In an NTP system, the energy released from fission in the core is utilized as the heat source to directly heat a propellant for propulsion, rather than chemical combustion in a traditional rocket. NTP has many desirable capabilities including flexible mission launch dates and reduced transit times due to it’s capability for high specific impulse. One of the main challenges with NTP systems is the structural integrity of the fuel. The fuel form required in the reactor core must withstand temperatures above 2700 Kelvin. Ceramic-metallic matrix fuel, ceramic-ceramic matrix fuel, and solid solution carbide fuels are the three strongest candidates for the extreme environments. Solid solution carbides have the potential to exhibit promising behavior as a fuel form in an NTP system. Of the multiple refractory metal carbides of interest, here we focus on zirconium carbide (ZrC), niobium carbide (NbC), and tantalum carbide (TaC). ZrC, NbC, and TaC powders were consolidated in monocarbide (ZrC, NbC, and TaC) and bi-carbide (ZrC-NbC, ZrC-TaC, NbC-TaC) forms using spark plasma sintering (SPS). In addition to the pure endpoint carbides, the examined compositions of the various bi-carbides ranged from 25-75 mol%. The sintering temperatures, pressures, and hold times were varied to determine the ideal sintering conditions. Grain size analysis, Archimedes’ density, scanning electron microscopy (SEM), X-ray diffraction (XRD), and energy dispersion spectroscopy (EDS) were used to determine and characterize the grain size, ideal density, porosity, phase stability, and chemical composition of each sample. The data from each sample was then used to generate a Master Sintering Curve (MSC) unique to each monocarbide or bi-carbide.

nuclear thermal propulsion↗

Failure detection and correction for turbofan engines

In this paper, a failure detection and correction strategy for turbofan engines is discussed. This strategy allows continuing control of the engines in the event of a sensor failure. An extended Kalman filter is used to provide the best estimate of the state of the engine based on currently available sensor outputs. Should a sensor failure occur the control is based on the best estimate rather than the sensor output. The extended Kalman filter consists of essentially two parts, a nonlinear model of the engine and up-date logic which causes the model to track the actual engine. Details on the model and up-date logic are presented. To allow implementation, approximations are made to the feedback gain matrix which result in a single feedback matrix which is suitable for use over the entire flight envelope. The effect of these approximations on stability and response is discussed. Results from a detailed nonlinear simulation indicate that good control can be maintained even under multiple failures.

Corley, R. C.↗