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NASA NTRS1993

Advanced Multi-Phase Flow CFD Model Development for Solid Rocket Motor Flowfield Analysis

It is known that the simulations of solid rocket motor internal flow field with AL-based propellants require complex multi-phase turbulent flow model. The objective of this study is to develop an advanced particulate multi-phase flow model which includes the effects of particle dynamics, chemical reaction and hot gas flow turbulence. The inclusion of particle agglomeration, particle/gas reaction and mass transfer, particle collision, coalescence and breakup mechanisms in modeling the particle dynamics will allow the proposed model to realistically simulate the flowfield inside a solid rocket motor. The Finite Difference Navier-Stokes numerical code FDNS is used to simulate the steady-state multi-phase particulate flow field for a 3-zone 2-D axisymmetric ASRM model and a 6-zone 3-D ASRM model at launch conditions. The 2-D model includes aft-end cavity and submerged nozzle. The 3-D model represents the whole ASRM geometry, including additional grain port area in the gas cavity and two inhibitors. FDNS is a pressure based finite difference Navier-Stokes flow solver with time-accurate adaptive second-order upwind schemes, standard and extended k-epsilon models with compressibility corrections, multi zone body-fitted formulations, and turbulence particle interaction model. Eulerian/Lagrangian multi-phase solution method is applied for multi-zone mesh. To simulate the chemical reaction, penalty function corrected efficient finite-rate chemistry integration method is used in FDNS. For the AL particle combustion rate, the Hermsen correlation is employed. To simulate the turbulent dispersion of particles, the Gaussian probability distribution with standard deviation equal to (2k/3)(exp 1/2) is used for the random turbulent velocity components. The computational results reveal that the flow field near the juncture of aft-end cavity and the submerged nozzle is very complex. The effects of the turbulent particles affect the flow field significantly and provide better prediction of the ASRM performance. The multi-phase flow analysis using the FDNS code in the present research can be used as a design tool for solid rocket motor applications.

Liaw, Paul↗

NASA NTRS2003

Calculation of Supersonic Combustion Using Implicit Schemes

One of the technology goals of NASA for advanced space transportation is to develop highly efficient propulsion systems to reduce the cost of payload for space missions. Developments of rockets for the second generation Reusable Launch Vehicle (RLV) in the past several years have been focused on low-cost versions of conventional engines. However, recent changes in the Integrated Space Transportation Program to build a crew transportation vehicle to extend the life of the Space Shuttle fleet might suggest that air-breathing rockets could reemerge as a possible propulsion system for the third generation RLV to replace the Space Shuttle after 2015. The weight of the oxygen tank exceeds thirty percent of the total weight of the Space Shuttle at launch while the payload is only one percent of the total weight. The air-breathing rocket propulsion systems, which consume oxygen in the air, offer clear advantages by making vehicles lighter and more efficient. Experience in the National Aerospace Plane Program in the late 1980s indicates that scramjet engines can achieve high specific impulse for low hypersonic vehicle speeds. Whether taking a form of Rocket Based Combined Cycle (RBCC) or Turbine Based Combined Cycle (TBCC), the scramjet is an essential mode of operation for air-breathing rockets. It is well known that fuel-air mixing and rapid combustion are of crucial importance for the success of scramjet engines since the spreading rate of the supersonic mixing layer decreases as the Mach number increases. A factored form of the Gauss-Seidel relaxation method has been widely used in hypersonic flow research since its first application to non-equilibrium flows. However, difficulties in stability and convergence have been encountered when there is strong interaction between fluid motion and chemical reaction, such as multiple fuel injection problems. The present paper reports the results from investigation of the effect of modifications to the original algorithm on the performance for multiple injectors.

Yoon, Seokkwan↗

NASA NTRS2009

Constructing LDPC Codes from Loop-Free Encoding Modules

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Divsalar, Dariush↗

NASA NTRS2009

In-flight Assessment of Lower Body Negative Pressure as a Countermeasure for Post-flight Orthostatic Intolerance

Introduction. We investigated the efficacy of combining fluid loading with sustained lower body negative pressure (LBNP) to reverse orthostatic intolerance associated with weightlessness during and immediately after Space Shuttle missions. Methods. Shuttle astronauts (n=13) underwent 4 hours of LBNP at -30 mm(Hg) and ingested water and salt ( soak treatment) during flight in two complementary studies. In the first study (n=8), pre-flight heart rate (HR) and blood pressure (BP) responses to an LBNP ramp (5-min stages of -10 mm(Hg) steps to -50 mm(Hg) were compared to responses in-flight one and two days after LBNP soak treatment. In the second study (n=5), the soak was performed 24 hr before landing, and post-flight stand test results of soak subjects were compared with those of an untreated cohort (n=7). In both studies, the soak was scheduled late in the mission and was preceded by LBNP ramp tests at approximately 3-day intervals to document the in-flight loss of orthostatic tolerance. Results. Increased HR and decreased BP responses to LBNP were evident early in-flight. In-flight, one day after LBNP soak, HR and BP responses to LBNP were not different from pre-flight, but the effect was absent the second day after treatment. Post-flight there were no between-group differences in HR and BP responses to standing, but all 5 treatment subjects completed the 5-minute stand test whereas 2 of 7 untreated cohort subjects did not. Discussion. Exaggerated HR and BP responses to LBNP were evident within the first few days of space flight, extending results from Skylab. The combined LBNP and fluid ingestion countermeasure restored in-flight LBNP HR and BP responses to pre-flight levels and provided protection of post-landing orthostatic function. Unfortunately, any benefits of the combined countermeasure were offset by the complexity of its implementation, making it inappropriate for routine application during Shuttle flights.

Charles, J. B.↗

NASA NTRS2014

Additive Manufacturing Thermal Performance Testing of Single Channel GRCop-84 SLM Components

The surface finish found on components manufactured by sinter laser manufacturing (SLM) is rougher (0.013 - 0.0006 inches) than parts made using traditional fabrication methods. Internal features and passages built into SLM components do not readily allow for roughness reduction processes. Alternatively, engineering literature suggests that the roughness of a surface can enhance thermal performance within a pressure drop regime. To further investigate the thermal performance of SLM fabricated pieces, several GRCop-84 SLM single channel components were tested using a thermal conduction rig at MSFC. A 20 kW power source running at 25% duty cycle and 25% power level applied heat to each component while varying water flow rates between 2.1 - 6.2 gallons/min (GPM) at a supply pressure of 550 to 700 psi. Each test was allowed to reach quasi-steady state conditions where pressure, temperature, and thermal imaging data were recorded. Presented in this work are the heat transfer responses compared to a traditional machined OHFC Copper test section. An analytical thermal model was constructed to anchor theoretical models with the empirical data.

Garcia, Chance P.↗

NASA NTRS2015

Thermal Performance Testing of Single Channel GRCop-84 SLM Components

The surface finish found on components manufactured by sinter laser manufacturing (SLM) is rougher (0.013 - 0.0006 inches) than parts made using traditional fabrication methods. Internal features and passages built into SLM components do not readily allow for roughness reduction processes. Alternatively, engineering literature suggests that the roughness of a surface can enhance thermal performance within a pressure drop regime. To further investigate the thermal performance of SLM fabricated pieces, several GRCop‐84 SLM single channel components were tested using a thermal conduction rig at MSFC. A 20 kW power source running at 25% duty cycle and 25% power level applied heat to each component while varying water flow rates between 2.1 - 6.2 gallons/min (GPM) at a supply pressure of 500 to 750 psi. Each test was allowed to reach quasi‐steady state conditions where pressure, temperature, and thermal imaging data were recorded. Presented in this work are the heat transfer responses compared to a traditional machined OHFC Copper test section. An analytical thermal model was constructed to anchor theoretical models with the empirical data.

Garcia, Chance P.↗

NASA NTRS2019

Astrophysics and Technical Study of a Solar Neutrino Spacecraft: NIAC (NASA Innovative Advanced Concepts) Grant - NASA 2018-Phase-1

We report on our study of the design of a neutrino detector, shielding and veto array needed to operate a neutrino detector in space close to the Sun. This study also took into account the expected rates of Galactic gamma and cosmic rays in addition to the particles from the Sun.These preliminary studies show that we can devise a detector such that a small signal of neutrino interactions can be extracted from a large random number of events from the background sources using a double timing method from the conversion electron produced in the neutrino interaction and a secondary delayed signal from the nuclear excited state produced from the initial neutrino interaction; in our case the conversion of Ga 69 or 71 into Ge 69 or 71, but this method could apply to other nuclei with large neutrino cross sections such as Ir 115. Although these types of events need to be above 0.405 megaelectronvolt (MeV) neutrino energy and are only 66 percent of all conversion neutrino interactions on Gallium, this is a small price to pay for an increase of 10,000 by going close to the Sun to enhance the neutrino rate over the background combatorical fake-signal events. The conclusion of this Phase-1 study is very positive in that we can get the backgrounds less than 20 percent fake signals, and in addition to this we have devised another shielding method that makes the Galactic gamma-ray rate a hundred fold less which will make further improvements over these initial estimates. Although these studies are very encouraging it suggests that the next step is a NIAC Phase-II to actually build a test device,measuring basic principles such as light attention within the scintillator with high dopants and to take data in the lab with a cosmic-ray test stand and triggered X-ray source for comparison with simulated expected performance of the detector. This would be the perfect lead into a future proposal beyond a NIAC (NASA Innovative Advanced Concepts) Phase-II for a test flight of a small one-pint detector in orbit of the detector concept beyond Earth outside of the radiation belts.

Astrophysics↗

NASA NTRS2019

Microbial Monitoring of Astromaterials Curation Labs Reveals Inter-Lab Diversity

The Astromaterials Curation Division at NASA’s Johnson Space Center houses seven sample collections stored in separate clean rooms to avoid cross-contamination. Prior to receiving new sample collections from carbon rich asteroids, we instituted a monitoring program to characterize the microbial ecology of these labs and to understand how organisms could interact with and potentially contaminate current and future collections. Methods: Beginning in Oct. 2017 we sampled the Meteorite (ISO 7 equivalent) and Pristine Lunar (ISO 5 equivalent) labs on a monthly basis. Surface samples were collected using dry swabs. Air samples were collected using an impactor style air sampler. Cultivable organisms were identified and characterized. Aliquots of each sample were also preserved for DNA sequencing. For each sampling event recovery rate was calculated as the percentage of samples showing microbial growth1. Fungal colonies were selected for amino acid extraction and analysis via Ultra- Performance Liquid Chromatography with Fluorescence Detection and Mass Spectrometry.

Regberg, A. B.↗

NASA NTRS2020

Impact Testing of Inconel 718 for Material Impact Model Development

One of the difficulties with developing and verifying accurate impact models is that parameters such as high strain-rate material properties, failure modes, static properties, and impact test measurements are often obtained from a variety of different sources using different materials, with little control over consistency among the different sources. In addition, there is often a lack of quantitative measurements in impact tests to which the models can be compared. To alleviate some of these problems, a project is underway to develop a consistent set of material property, impact test data, and failure analysis for a variety of aircraft materials that can be used to develop improved impact failure and deformation models. This project is jointly funded by the NASA Glenn Research Center and the Federal Aviation Administration (FAA) William J. Hughes Technical Center. Unique features of this set of data are that all material property and impact test data are obtained using traceable material, the test methods and procedures are extensively documented, and all of the raw data is available. Four parallel efforts are currently underway. The Ohio State University conducts both measurement of material deformation and failure response over a wide range of strain rates and temperatures and failure analysis of material property specimens and impact test articles. The George Mason University conducts the development of improved numerical modeling techniques for deformation and failure. Glenn conducts the impact testing of flat panels and substructures. This report describes impact testing performed on Inconel 718 sheet and plate samples of different thicknesses with different types of projectiles, one a regular cylinder and one with a more complex geometry incorporating features representative of a jet engine fan blade. Data from this testing will be used in validating material models developed under this program. The material tests and the material models developed in this program will be published in separate reports.

J Michael Pereira↗

NASA NTRSDate not supplied

Solid-state Architecture Batteries for Enhanced Rechargeability and Safety (SABERS) for Extended Deep Space Applications

Extended duration deep space missions as well as permanent space habitats face numerous technical challenges, key among them is energy generation and energy storage. There are considerable monetary and technical barriers to the generation of power in space. Therefore, it is important to store and be able to access power in an efficient and safe manner over a large number of cycles. Energy storage and in particular, batteries, are vital to the operation of next-generation extraterrestrial shuttles, rovers, habitats and extravehicular activity (EVA) space suits. The performance metrics for extended duration space missions are at least 2 times greater than those set for terrestrial applications such as electric automobiles. Furthermore, safety is essential for operation of space missions particularly involving astronauts such as shuttles, habitats and EVA space suits. Preliminary systems level analysis has indicated that there are five key properties which must be optimized for successful implementation of battery systems. Those five key criteria are: safety, energy density, power, packaging design and scalability. Current state-of-the-art (SOA) lithium-ion batteries can meet or exceed the requirements for certain space applications in the areas of power and scalability, yet are insufficient in the key performance criteria of energy, safety and packaging design. The SABERS concept proposes a battery that meets all five key performance criteria through development of a solid-state architecture battery utilizing high capacity sulfur-selenium cathode and lithium metal anode. The combination of sulfur and selenium offers a balanced energy-to-power density ratio, which can be tailored to the specific application by altering the stoichiometric ratios of sulfur to selenium. This hybrid cathode will be developed by implementing NASA patented holey graphene technology as a highly conductive, ultra-lightweight electrode scaffold. A solid-state electrolyte will be used as a safe, non-flammable replacement to the highly flammable liquid organic electrolytes currently used in SOA lithium-ion batteries. This solid-state lithium-sulfur/selenium cell will be designed into a serial stacking configuration to enable dense packaging of the battery cells. The serial stacking configuration is termed a bipolar stack, which has the advantages of reducing overall cell weight, simplifying the interfaced connections for the cell, and minimizing the cooling requirements for the cell. Lastly, optimization of battery components will occur through a robust and rigorous combination of various computational modeling techniques covering multiple length scales. The expected result will be a fully solid-state battery with operational temperatures up to 150 °C which provides the required energy density, discharge rates, and inherent safety to meet the strict space mission performance criteria. In particular, the wide operational temperature window is required for the large temperature ranges which are experienced across a broad range of potential space missions. This presentation will show initial results that demonstrate the SABERS team has developed a composite carbon-sulfur cathode which exceeds 1100 Wh/kg at a discharge rate of 0.4C, and 804 Wh/kg at a discharge rate of 1C. Additionally, this presentation will show the SABERS team multiscale computational modeling approach and has produced a novel particle dynamics method called Solid Electrolyte Sphere Approximation Model (SESAM). SESAM is on the 1-10 µm scale and provides electromechanical and grain interactions for predictive design guidelines for the experimental team to follow.

Urban Air Mobility (UAM) Vehicles↗

NASA NTRSDate not supplied

Evaluation of Particle Degradation of a Ytterbium Disilicate Gas Turbine Coating in a Combustion Environment

Ytterbium disilicate (Yb2Si2O7) is a state-of-the-art topcoat material used in environmental barrier coatings (EBCs) to protect SiC-SiC composites from water vapor corrosion in gas turbine engines. However, it’s degradation by thermochemical and thermomechanical particle interactions may limit its use in next generation engine systems. Several static furnace tests have been performed on Yb2Si2O7 to elucidate methods of degradation, although dynamic testing in an engine-relevant environment has not been carried out. Ultimately, testing and evaluation of materials that incorporates all environmental damage modes will allow for an accurate assessment of long-term durability and operating lifetime. This work details the investigation of particle-induced erosion and corrosion of Yb2Si2O7 in NASA Glenn’s Erosion Burner Rig Facility. Coating durability was investigated as a function of test temperature, particle size, and deposition rate. Thermal cycling was also incorporated into testing to determine the interplay of heating/cooling cycles with particle degradation. Overall, these analyses will be used to determine coating robustness in an engine relevant environment.

Jamesa L Stokes↗

NASA NTRSDate not supplied

Evaluation of Particle Degradation of a Ytterbium Disilicate Gas Turbine Coating in a Combustion Environment

Jamesa L Stokes↗

NASA NTRS2013

Tuning and Robustness Analysis for the Orion Absolute Navigation System

The Orion Multi-Purpose Crew Vehicle (MPCV) is currently under development as NASA's next-generation spacecraft for exploration missions beyond Low Earth Orbit. The MPCV is set to perform an orbital test flight, termed Exploration Flight Test 1 (EFT-1), some time in late 2014. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to show the efforts made to-date in tuning the filter for the EFT-1 mission and instilling appropriate robustness into the system to meet the requirements of manned space ight. Filter performance is affected by many factors: data rates, sensor measurement errors, tuning, and others. This paper focuses mainly on the error characterization and tuning portion. Traditional efforts at tuning a navigation filter have centered around the observation/measurement noise and Gaussian process noise of the Extended Kalman Filter. While the Orion MODE team must certainly address those factors, the team is also looking at residual edit thresholds and measurement underweighting as tuning tools. Tuning analysis is presented with open loop Monte-Carlo simulation results showing statistical errors bounded by the 3-sigma filter uncertainty covariance. The Orion filter design uses 24 Exponentially Correlated Random Variable (ECRV) parameters to estimate the accel/gyro misalignment and nonorthogonality. By design, the time constant and noise terms of these ECRV parameters were set to manufacturer specifications and not used as tuning parameters. They are included in the filter as a more analytically correct method of modeling uncertainties than ad-hoc tuning of the process noise. Tuning is explored for the powered-flight ascent phase, where measurements are scarce and unmodelled vehicle accelerations dominate. On orbit, there are important trade-off cases between process and measurement noise. On entry, there are considerations about trading performance accuracy for robustness. Process Noise is divided into powered flight and coasting ight and can be adjusted for each phase and mode of the Orion EFT-1 mission. Measurement noise is used for the integrated velocity measurements during pad alignment. It is also used for Global Positioning System (GPS) pseudorange and delta- range measurements during the rest of the flight. The robustness effort has been focused on maintaining filter convergence and performance in the presence of unmodeled error sources. These include unmodeled forces on the vehicle and uncorrected errors on the sensor measurements. Orion uses a single-frequency, non-keyed GPS receiver, so the effects due to signal distortion in Earth's ionosphere and troposphere are present in the raw measurements. Results are presented showing the efforts to compensate for these errors as well as characterize the residual effect for measurement noise tuning. Another robustness tool in use is tuning the residual edit thresholds. The trade-off between noise tuning and edit thresholds is explored in the context of robustness to errors in dynamics models and sensor measurements. Measurement underweighting is also presented as a method of additional robustness when processing highly accurate measurements in the presence of large filter uncertainties.

Holt, Greg N.↗

NASA NTRS1984

Development and Certification of a New Stall Warning and Avoidance System

Several methods may be employed to improve natural stall characteristics. The method employed on all learjets to obtain improved stall characteristics is a stall warning and avoidance system that employs angle of attack vanes, an electronic computer, a control column shaker motor, and a torquer which drives the control column in a pusher mode to avoid unwanted further buildup of angle of attack. The new system was developed with changes that improve system response with no performance penalty or increase in turbulence sensitivity. The following changes were made included modified system time constants and (alpha) time rate of change of vane angle dead zone and the addition of an alpha signal limiter and an alpha cut out below a specified angle of attack.

Gertsen, W. M.↗

NASA NTRS1987

Performance of an electromagnetic bearing for the vibration control of a supercritical shaft

The flexural vibrations of a rotating shaft, running through one or more critical speeds, can be reduced to an acceptably low level by applying suitable control forces at an intermediate span position. If electromagnets are used to produce the control forces then it is possible to implement a wide variety of control strategies. A test rig is described which includes a microprocessor-based controller, in which such strategies can be realised in terms of software-based algorithms. The electromagnet configuration and the method of stabilising the electromagnet force-gap characteristic are discussed. The bounds on the performance of the system are defined. A simple control algorithm is outlined, where the control forces are proportional to the measured displacement and velocity at a single point on the shaft span; in this case the electromagnet behaves in a similar manner to that of a parallel combination of a linear spring and damper. Experimental and predicted performance of the system are compared, for this type of control, where various programmable rates of damping are applied.

Bradfield, C. D.↗

NASA NTRS1988

Computational simulation methods for composite fracture mechanics

Structural integrity, durability, and damage tolerance of advanced composites are assessed by studying damage initiation at various scales (micro, macro, and global) and accumulation and growth leading to global failure, quantitatively and qualitatively. In addition, various fracture toughness parameters associated with a typical damage and its growth must be determined. Computational structural analysis codes to aid the composite design engineer in performing these tasks were developed. CODSTRAN (COmposite Durability STRuctural ANalysis) is used to qualitatively and quantitatively assess the progressive damage occurring in composite structures due to mechanical and environmental loads. Next, methods are covered that are currently being developed and used at Lewis to predict interlaminar fracture toughness and related parameters of fiber composites given a prescribed damage. The general purpose finite element code MSC/NASTRAN was used to simulate the interlaminar fracture and the associated individual as well as mixed-mode strain energy release rates in fiber composites.

Murthy, Pappu L. N.↗

NASA NTRS1998

1-D Transient Thermal Modeling of an Ablative Material (MCC-1) Exposed to a Simulated Convective Titan 4 Launch Environment

The purpose of the work is to demonstrate that the flat test panel substrate temperatures are consistent with analysis predictions for MCC-1 applied to a aluminum substrate. The testing was performed in an aerothermal facility on samples of three different thicknesses of MCC-1 on an aluminum substrate. The results of the test were compared with a Transient Thermal model. The key assumptions of the Transient Thermal model were: (1) a one-dimensional heat transfer; (2) a constant ablation recession rate (determined from pre and post-test measurements); (3) ablation temperature of 540 degrees F; (4) Char left behind the ablation front; and (5) temperature jump correction for incident heat transfer coefficient. Two methods were used to model the heating of bare MCC-1: (1) Directly input surface temperature as a function of time; and (2) Aerothermal heating using calibration plate data and subtracting the radiation losses to tunnel walls. The results are presented as graphs. This article is presented in Viewgraph format.

Reinarts, Thomas R.↗

NASA NTRS2000

Sliding Mode Control of the X-33 with an Engine Failure

Ascent flight control of the X-3 is performed using two XRS-2200 linear aerospike engines. in addition to aerosurfaces. The baseline control algorithms are PID with gain scheduling. Flight control using an innovative method. Sliding Mode Control. is presented for nominal and engine failed modes of flight. An easy to implement, robust controller. requiring no reconfiguration or gain scheduling is demonstrated through high fidelity flight simulations. The proposed sliding mode controller utilizes a two-loop structure and provides robust. de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of engine failure, bounded external disturbances (wind gusts) and uncertain matrix of inertia. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues. Conditions that restrict engine failures to robustness domain of the sliding mode controller are derived. Overall stability of a two-loop flight control system is assessed. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in the presence of external disturbances and vehicle inertia uncertainties, as well as the single engine failed case. The designed robust controller will significantly reduce the time and cost associated with flying new trajectory profiles or orbits, with new payloads, and with modified vehicles

Shtessel, Yuri B.↗