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NASA NTRS2013

Additional Developments in Atmosphere Revitalization Modeling and Simulation

NASA's Advanced Exploration Systems (AES) program is developing prototype systems, demonstrating key capabilities, and validating operational concepts for future human missions beyond Earth orbit. These forays beyond the confines of earth's gravity will place unprecedented demands on launch systems. They must launch the supplies needed to sustain a crew over longer periods for exploration missions beyond earth's moon. Thus all spacecraft systems, including those for the separation of metabolic carbon dioxide and water from a crewed vehicle, must be minimized with respect to mass, power, and volume. Emphasis is also placed on system robustness both to minimize replacement parts and ensure crew safety when a quick return to earth is not possible. Current efforts are focused on improving the current state-of-the-art systems utilizing fixed beds of sorbent pellets by evaluating structured sorbents, seeking more robust pelletized sorbents, and examining alternate bed configurations to improve system efficiency and reliability. These development efforts combine testing of sub-scale systems and multi-physics computer simulations to evaluate candidate approaches, select the best performing options, and optimize the configuration of the selected approach. This paper describes the continuing development of atmosphere revitalization models and simulations in support of the Atmosphere Revitalization Recovery and Environmental Monitoring (ARREM)

Coker, Robert F.↗

NASA NTRS2013

Additional Developments in Atmosphere Revitalization Modeling and Simulation

Coker, Robert F.↗

NASA NTRS2013

Abort Options for Human Missions to Earth-Moon Halo Orbits

Abort trajectories are optimized for human halo orbit missions about the translunar libration point (L2), with an emphasis on the use of free return trajectories. Optimal transfers from outbound free returns to L2 halo orbits are numerically optimized in the four-body ephemeris model. Circumlunar free returns are used for direct transfers, and cislunar free returns are used in combination with lunar gravity assists to reduce propulsive requirements. Trends in orbit insertion cost and flight time are documented across the southern L2 halo family as a function of halo orbit position and free return flight time. It is determined that the maximum amplitude southern halo incurs the lowest orbit insertion cost for direct transfers but the maximum cost for lunar gravity assist transfers. The minimum amplitude halo is the most expensive destination for direct transfers but the least expensive for lunar gravity assist transfers. The on-orbit abort costs for three halos are computed as a function of abort time and return time. Finally, an architecture analysis is performed to determine launch and on-orbit vehicle requirements for halo orbit missions.

Jesick, Mark C.↗

NASA NTRS2010

Ares I Flight Control System Design

The Ares I launch vehicle represents a challenging flex-body structural environment for flight control system design. This paper presents a design methodology for employing numerical optimization to develop the Ares I flight control system. The design objectives include attitude tracking accuracy and robust stability with respect to rigid body dynamics, propellant slosh, and flex. Under the assumption that the Ares I time-varying dynamics and control system can be frozen over a short period of time, the flight controllers are designed to stabilize all selected frozen-time launch control systems in the presence of parametric uncertainty. Flex filters in the flight control system are designed to minimize the flex components in the error signals before they are sent to the attitude controller. To ensure adequate response to guidance command, step response specifications are introduced as constraints in the optimization problem. Imposing these constraints minimizes performance degradation caused by the addition of the flex filters. The first stage bending filter design achieves stability by adding lag to the first structural frequency to phase stabilize the first flex mode while gain stabilizing the higher modes. The upper stage bending filter design gain stabilizes all the flex bending modes. The flight control system designs provided here have been demonstrated to provide stable first and second stage control systems in both Draper Ares Stability Analysis Tool (ASAT) and the MSFC 6DOF nonlinear time domain simulation.

Jang, Jiann-Woei↗

NASA NTRS2010

Parametric Analysis of Life Support Systems for Future Space Exploration Missions

Having adopted a flexible path approach to space exploration, the National Aeronautics and Space Administration is in a process of evaluating future targets for space exploration. In order to maintain the welfare of a crew during future missions, a suite of life support technology is responsible for oxygen and water generation, carbon dioxide control, the removal of trace concentrations of organic contaminants, processing and recovery of water, and the storage and reclamation of solid waste. For each particular life support subsystem, a variety competing technologies either exist or are under aggressive development efforts. Each individual technology has strengths and weaknesses with regard to launch mass, power and cooling requirements, volume of hardware and consumables, and crew time requirements for operation. However, from a system level perspective, the favorability of each life support architecture is better assessed when the sub-system technologies are analyzed in aggregate. In order to evaluate each specific life support system architecture, the measure of equivalent system mass (ESM) was employed to benchmark system favorability. Moreover, the results discussed herein will be from the context of loop-closure with respect to the air, water, and waste sub-systems. Specifically, closure relates to the amount of consumables mass that crosses the boundary of the vehicle over the lifetime of a mission. As will be demonstrated in this manuscript, the optimal level of loop closure is heavily dependent upon mission requirements such as duration and the level of extra- vehicular activity (EVA) performed. Sub-system level trades were also considered as a function of mission duration to assess when increased loop closure is practical. Although many additional factors will likely merit consideration in designing life support systems for future missions, the ESM results described herein provide a context for future architecture design decisions toward a flexible path program.

Swickrath, Michael J.↗

NASA NTRS2011

Parametric Analysis of Life Support Systems for Future Space Exploration Missions

The National Aeronautics and Space Administration is in a process of evaluating future targets for space exploration. In order to maintain the welfare of a crew during future missions, a suite of life support technology is responsible for oxygen and water generation, carbon dioxide control, the removal of trace concentrations of organic contaminants, processing and recovery of water, and the storage and reclamation of solid waste. For each particular life support subsystem, a variety competing technologies either exist or are under aggressive development efforts. Each individual technology has strengths and weaknesses with regard to launch mass, power and cooling requirements, volume of hardware and consumables, and crew time requirements for operation. However, from a system level perspective, the favorability of each life support architecture is better assessed when the sub-system technologies are analyzed in aggregate. In order to evaluate each specific life support system architecture, the measure of equivalent system mass (ESM) was employed to benchmark system favorability. Moreover, the results discussed herein will be from the context of loop-closure with respect to the air, water, and waste sub-systems. Specifically, closure relates to the amount of consumables mass that crosses the boundary of the vehicle over the lifetime of a mission. As will be demonstrated in this manuscript, the optimal level of loop closure is heavily dependent upon mission requirements such as duration and the level of extra-vehicular activity (EVA) performed. Sub-system level trades were also considered as a function of mission duration to assess when increased loop closure is practical. Although many additional factors will likely merit consideration in designing life support systems for future missions, the ESM results described herein provide a context for future architecture design decisions toward a flexible path program.

Swickrath, Michael J.↗

NASA NTRSDate not supplied

Dragonfly Rotor Optimization using Machine Learning Applied to an OVERFLOW Generated Airfoil Database

NASA’s 4th New Frontiers Mission is the Titan Dragonfly relocatable lander. This coaxial quadrotor vehicle will be launched on a rocket to Titan in 2028. Following a gravity assisted Earth flyby and an approximate 6-year transit, Dragonfly will enter the Titan atmosphere around 2034 with the goal of exploring Titan’s pre-biotic chemistry and habitability. The multirotor design for this unique application has continually evolved since 2016 with constraints such as Titan’s cryogenic atmosphere at 95 Kelvin (-288 F), gravity 14% that of Earth’s, atmospheric density 440% of standard sea-level air, and the inability to test the entire system together under all these conditions until the first flight on Titan. This paper focuses on rotor design aspects of the Dragonfly lander and introduces a novel framework for multirotor design optimization considering multiple flight conditions. The methodology leverages machine learning methods and is demonstrated in the context of Dragonfly. A new OVERFLOW Machine Learning Airfoil Performance (PALMO) database is first presented. PALMO is then wrapped inside a Bayesian optimization framework and applied to a 4-rotor system (one side of the Dragonfly lander). Training data is generated on each iteration of the optimization using the CAMRAD-II comprehensive analysis software to evaluate successive rotor designs in multiple relevant flight conditions. An optimal design for the 4-rotor system was found with approximately 900 rotor designs analyzed in CAMRAD-II, which required 9 million queries of the PALMO surrogate models. This demonstration case evaluated 10,000,000 potential candidate rotor designs in 5.5 hours on 114 CPU cores using uniform inflow, and in 27.8 hours using the prescribed wake model. This work thus enables mid-fidelity rotor design optimization without requiring access to high-performance computing.

Dragonfly↗

NASA NTRS2019

Electrochemical Solutions for Advanced Life Support

The Oxygen Generating Assembly (OGA) on-board the International Space Station (ISS) employs a polymer electrolyte membrane (PEM) water electrolysis cell stack to electrochemically dissociate water into its two components – oxygen and hydrogen. Oxygen is provided to the cabin atmosphere for crew respiration while the hydrogen is delivered to a carbon dioxide reduction system to recover oxygen as water. The design of the OGA evolved over a number of years to arrive at the system solution that is currently operational on ISS. Future manned missions to space will require advanced technologies that eliminate the need for resupply from earth and feature in-situ resource utilization to sustain crew life and to provide useful materials to the crew. The architects planning such missions should consider all potential solutions at their disposal to arrive at an optimal vehicle solution that minimizes crew maintenance time, launch weight, installed volume and energy consumption demands. Skyre is developing new technologies through funding from NASA, the Department of Energy, and internal investment based on PEM technology that could become an integral part of these new vehicle solutions. At varying stages of Technology Readiness Level (TRL) are: an oxygen concentrator and compressor that can separate oxygen from an air stream and provide an enriched oxygen resource for crew medical use and space suit recharge without any moving parts in the pure oxygen stream; a regenerative carbon dioxide removal system featuring a PEM-based sorbent regenerator; a carbon dioxide reduction system that electrochemically produces organic compounds that could serve as fuels or as a useful intermediary to more beneficial compounds; and an electrochemical hydrogen separator and compressor for hydrogen recycle. The technical maturity of these projects is presented along with pertinent performance test data that could be beneficial in future study efforts.

Roy, Robert J.↗

NASA NTRS2020

InSight Entry, Descent and Landing Pre-Flight Performance Predictions

On November 26, 2018, the Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) lander successfully touched down on the surface of Mars. Over its seven-plus year development, NASA Langley Research Center’s (LaRC) Program to Optimize Simulated Trajectories II (POST2) was used to assess the mission’s Entry, Descent and Landing (EDL) vehicle system performance against related requirements across the full range of possible environmental and spacecraft conditions. Much of the simulation code was derived from the Phoenix mission, for which this vehicle is very similar. The InSight six degree-of-freedom simulation included models for Mars atmosphere, gravity and digital elevation maps of the landing location. Additionally, vehicle specific aerodynamic, parachute, engine, navigation sensor, flight software and landing radar models were also included. A set of dispersions for each model, as well as for additional simulation input parameters, were also included in order to provide a statistical, Monte Carlo prediction of the EDL system performance. An overview of the pre-flight performance assessments completed, including the various simulation campaigns used, will be provided. Ultimately, this work was critical in the assessment of readiness for InSight launch. A brief description of the use of this simulation in support of flight operations is also discussed.

Robert W Maddock↗

NASA NTRSDate not supplied

Mars Sample Return Mars Ascent Vehicle Separation Analysis Utilizing the CLVTOPS Toolchain

A key element of the joint NASA and European Space Agency (ESA) Mars Sample Return (MSR) Campaign is the Mars Ascent Vehicle (MAV), which is being developed primarily by NASA Marshall Space Flight Center (MSFC), in association with NASA’s Jet Propulsion Laboratory (JPL) and Langley Research Center (LaRC). The MAV is a Mars-launched rocket that is responsible for transporting soil samples collected by the Perseverance rover from the Martian surface into orbit, where they will be captured by ESA's Earth Return Orbiter (ERO) for the return journey to Earth. The MAV design concept developed during the MAV Systems Requirement Cycle (SRC) and Preliminary Design Cycle (PDC) consisted of a two-solid-stage configuration, where the second stage is completely unguided in order to reduce vehicle and overall mission mass. The unguided second stage design presents technical challenges for the stage separation event, as the second stage trajectory and the payload’s ability to rendezvous with the ERO is extremely sensitive to disturbances during vehicle staging. The MSFC-developed CLVTOPS multibody dynamics toolchain was utilized to quickly assess multiple stage separation hardware options and to optimize the separation Concept of Operations (ConOps) in order to ensure successful near-field stage separation performance and maximize the orbital accuracy of the payload. This paper will describe how the CLVTOPS toolchain was used to assess the MAV stage separation event and help inform and optimize the MAV design and ConOps.

MSR↗

NASA NTRS1998

X33 Reusable Launch Vehicle Control on Sliding Modes: Concepts for a Control System Development

Control of the X33 reusable launch vehicle is considered. The launch control problem consists of automatic tracking of the launch trajectory which is assumed to be optimally precalculated. It requires development of a reliable, robust control algorithm that can automatically adjust to some changes in mission specifications (mass of payload, target orbit) and the operating environment (atmospheric perturbations, interconnection perturbations from the other subsystems of the vehicle, thrust deficiencies, failure scenarios). One of the effective control strategies successfully applied in nonlinear systems is the Sliding Mode Control. The main advantage of the Sliding Mode Control is that the system's state response in the sliding surface remains insensitive to certain parameter variations, nonlinearities and disturbances. Employing the time scaling concept, a new two (three)-loop structure of the control system for the X33 launch vehicle was developed. Smoothed sliding mode controllers were designed to robustly enforce the given closed-loop dynamics. Simulations of the 3-DOF model of the X33 launch vehicle with the table-look-up models for Euler angle reference profiles and disturbance torque profiles showed a very accurate, robust tracking performance.

Shtessel, Yuri B.↗

NASA NTRS1972

Thermal characterization of reusable external insulation for the space shuttle.

Thermal protection systems utilizing reusable ceramic external insulations are under study for application to the orbiter vehicle of NASA's space shuttle system which is to be launched by an expendable booster, remain in orbit for a week or two, reenter the earth's atmosphere, and land like a conventional aircraft. The required reuse capability is for 100 missions. The thermal characterization of the reusable external insulation (REI) is described. Thermal conductivity measurements are described for a series of mullite-based REIs with densities ranging from 100 to 300 kg/cu m, including opacified variations of the mullite material designed for reduction of the radiant component of heat transport. The results of thermal conductivity measurements performed on guarded-hot-plate equipment from 150 to above 1200 K in different vacuum and gaseous environments are described. Measurements were also made with exceptionally large temperature differences to detect transparency effects in the unopacified REIs. These measurements were made to provide design data for the flight conditions, and to aid in theoretical computations aimed at separating and optimizing the heat transport components.

Brazel, J. P.↗

NASA NTRS2008

Sensor Selection and Data Validation for Reliable Integrated System Health Management

For new access to space systems with challenging mission requirements, effective implementation of integrated system health management (ISHM) must be available early in the program to support the design of systems that are safe, reliable, highly autonomous. Early ISHM availability is also needed to promote design for affordable operations; increased knowledge of functional health provided by ISHM supports construction of more efficient operations infrastructure. Lack of early ISHM inclusion in the system design process could result in retrofitting health management systems to augment and expand operational and safety requirements; thereby increasing program cost and risk due to increased instrumentation and computational complexity. Having the right sensors generating the required data to perform condition assessment, such as fault detection and isolation, with a high degree of confidence is critical to reliable operation of ISHM. Also, the data being generated by the sensors needs to be qualified to ensure that the assessments made by the ISHM is not based on faulty data. NASA Glenn Research Center has been developing technologies for sensor selection and data validation as part of the FDDR (Fault Detection, Diagnosis, and Response) element of the Upper Stage project of the Ares 1 launch vehicle development. This presentation will provide an overview of the GRC approach to sensor selection and data quality validation and will present recent results from applications that are representative of the complexity of propulsion systems for access to space vehicles. A brief overview of the sensor selection and data quality validation approaches is provided below. The NASA GRC developed Systematic Sensor Selection Strategy (S4) is a model-based procedure for systematically and quantitatively selecting an optimal sensor suite to provide overall health assessment of a host system. S4 can be logically partitioned into three major subdivisions: the knowledge base, the down-select iteration, and the final selection analysis. The knowledge base required for productive use of S4 consists of system design information and heritage experience together with a focus on components with health implications. The sensor suite down-selection is an iterative process for identifying a group of sensors that provide good fault detection and isolation for targeted fault scenarios. In the final selection analysis, a statistical evaluation algorithm provides the final robustness test for each down-selected sensor suite. NASA GRC has developed an approach to sensor data qualification that applies empirical relationships, threshold detection techniques, and Bayesian belief theory to a network of sensors related by physics (i.e., analytical redundancy) in order to identify the failure of a given sensor within the network. This data quality validation approach extends the state-of-the-art, from red-lines and reasonableness checks that flag a sensor after it fails, to include analytical redundancy-based methods that can identify a sensor in the process of failing. The focus of this effort is on understanding the proper application of analytical redundancy-based data qualification methods for onboard use in monitoring Upper Stage sensors.

Garg, Sanjay↗

NASA NTRSDate not supplied

Advanced Supersonic Parachute Inflation Research Experiment 2 (ASPIRE2) Flight Mechanics and Parachute Performance

The Advanced Supersonic Parachute Inflation Re-search Experiment-2 (ASPIRE2) program consists of a sounding rocket flight test to be launched at Wallops Flight Facility (WFF) in 2025. This effort seeks to qualify the supersonic parachute for the Sample Retrieval Lander (SRL) under the Mars Sample Return (MSR) program, building off the successes of its predecessor program, ASPIRE, which launched in both 2017 and 2018. The conops for the ASPIRE2 mission are shown in Figure 1 relative to its predecessor. While the ASPIRE pro-gram qualified a 21.5 m diameter disk-gap band parachute deployed at Mach 1.7, the SRL parachute will be increased to 24 m in diameter and target a Mach 2.1 parachute deployment condition, the largest diameter supersonic parachute deployed at the highest Mach number to date. These requirements are driven by the increased landing mass of the sample retrieval lander, which is roughly a 50% increase over that of the Mars2020 entry vehicle. These changes necessitate ASPIRE2 to certify the parachute performance under similar deployment conditions. This work will cover the 6-DoF para-chute model implementation and flight mechanics performance for the ASPIRE2 campaign and discuss how these results will impact the design of the test article. The ASPIRE2 trajectory is simulated using a multi-body flight dynamics tool, Program to Optimize Simulated Trajectories II (POST2). This work will summarize both the flight mechanics and parachute modeling (from payload separation until splashdown) and performance for this mission. Various design trades will be assessed such as para-chute tuning parameters as well as vehicle center of gravity location.

Evan Roelke↗

NASA NTRS2016

Flat H Frangible Joint Evolution

Space vehicle staging and separation events require pyrotechnic devices. They are single-use mechanisms that cannot be tested, nor can failure-tolerant performance be demonstrated in actual flight articles prior to flight use. This necessitates the implementation of a robust design and test approach coupled with a fully redundant, failure-tolerant explosive mechanism to ensure that the system functions even in the event of a single failure. Historically, NASA has followed the single failure-tolerant (SFT) design philosophy for all human-rated spacecraft, including the Space Shuttle Program. Following the end of this program, aerospace companies proposed building the next generation human-rated vehicles with off-the-shelf, non-redundant, zero-failure-tolerant (ZFT) separation systems. Currently, spacecraft and launch vehicle providers for both the Orion and Commercial Crew Programs (CCPs) plan to deviate from the heritage safety approach and NASA's SFT human rating requirements. Both programs' partners have base-lined ZFT frangible joints for vehicle staging and fairing separation. These joints are commercially available from pyrotechnic vendors. Non-human-rated missions have flown them numerous times. The joints are relatively easy to integrate structurally within the spacecraft. In addition, the separation event is debris free, and the resultant pyro shock is lower than that of other design solutions. It is, however, a serious deficiency to lack failure tolerance. When used for critical applications on human-rated vehicles, a single failure could potentially lead to loss of crew (LOC) or loss of mission (LOM)). The Engineering and Safety & Mission Assurance directorates within the NASA Johnson Space Center took action to address this safety issue by initiating a project to develop a fully redundant, SFT frangible joint design, known as the Flat H. Critical to the ability to retrofit on launch vehicles being developed, the SFT mechanisms must fit within the same three-dimensional envelope as current designs as well as meet structural loads requirements. There is increased mass associated with the redundant design, and the goal is to minimize the weight impact as much as possible. These requirements presented significant challenges, both technically and financially; these challenges will be explored in this paper. Perhaps greater than the technical issues confronted during this design process, were the financial considerations. These were a significant part of the story of this design and development plan. Insufficient financial and labor resources were formidable barriers to completing this project. Nevertheless, JSC personnel successfully conducted several test series at JSC with very useful results. The many lessons learned drove design improvements, performance efficiency, and increased functional reliability. This paper examines the significant technical and financial challenges that these requirements posed to the project team. It discusses the evolution of the SFT frangible joint design, including optimization, testing, and successful partnering of the Johnson Space Center (JSC) engineering and JSC safety organizations, to enhance the flight safety margin for America's next generation of human-rated space vehicles.

Diegelman, Thomas E.↗

NASA NTRS1991

Progress in GaAs/CuInSe2 tandem junction solar cells

Much more power is required for spacecraft of the future than current vehicles. To meet this increased demand for power while simultaneously meeting other requirements for launch, deployment, and maneuverability, the development of higher-efficiency, lighter-weight, and more radiation resistant photovoltaic cells is essential. Mechanically stacked tandem junction solar cells based on (AlGaAs)GaAs thin film CLEFT (Cleavage of Lateral Epitaxial Film for Transfer) top cells and CuInSe2(CIS) thin film bottom cells are being developed to meet these power needs. The mechanically stacked tandem configuration is chosen due to its interconnect flexibility allowing more efficient array level performance. It also eliminates cell fabrication processing constraints associated with monolithically integrated multi-junction approaches, thus producing higher cell fabrication yields. The GaAs cell is used as the top cell due to its demonstrated high efficiency, and good radiation resistance. Furthermore, it offers a future potential for bandgap tuning using AlGaAs as the absorber to maximize cell performance. The CuInSe2 cell is used as the bottom cell due to superb radiation resistance, stability, and optimal bandgap value in combination with an AlGaAs top cell. Since both cells are incorporated as thin films, this approach provides a potential for very high specific power. This high specific power (W/kg), combined with high power density (W/sq m) resulting from the high efficiency of this approach, makes these cells ideally suited for various space applications.

Kim, N. P.↗

NASA NTRS1996

Application of Optimization Techniques to Design of Unconventional Rocket Nozzle Configurations

Several current rocket engine concepts such as the bell-annular tri-propellant engine, and the linear aerospike being proposed for the X-33 require unconventional three dimensional rocket nozzles which must conform to rectangular or sector shaped envelopes to meet integration constraints. These types of nozzles exist outside the current experience database, therefore, the application of efficient design methods for these propulsion concepts is critical to the success of launch vehicle programs. The objective of this work is to optimize several different nozzle configurations, including two- and three-dimensional geometries. Methodology includes coupling computational fluid dynamic (CFD) analysis to genetic algorithms and Taguchi methods as well as implementation of a streamline tracing technique. Results of applications are shown for several geometeries including: three dimensional thruster nozzles with round or super elliptic throats and rectangualar exits, two- and three-dimensional thrusters installed within a bell nozzle, and three dimensional thrusters with round throats and sector shaped exits. Due to the novel designs considered for this study, there is little experience which can be used to guide the effort and limit the design space. With a nearly infinite parameter space to explore, simple parametric design studies cannot possibly search the entire design space within the time frame required to impact the design cycle. For this reason, robust and efficient optimization methods are required to explore and exploit the design space to achieve high performance engine designs. Five case studies which examine the application of various techniques in the engineering environment are presented in this paper.

Follett, W.↗

NASA NTRS2002

Direct Fault Tolerant RLV Altitude Control: A Singular Perturbation Approach

In this paper, we present a direct fault tolerant control (DFTC) technique, where by "direct" we mean that no explicit fault identification is used. The technique will be presented for the attitude controller (autopilot) for a reusable launch vehicle (RLV), although in principle it can be applied to many other applications. Any partial or complete failure of control actuators and effectors will be inferred from saturation of one or more commanded control signals generated by the controller. The saturation causes a reduction in the effective gain, or bandwidth of the feedback loop, which can be modeled as an increase in singular perturbation in the loop. In order to maintain stability, the bandwidth of the nominal (reduced-order) system will be reduced proportionally according to the singular perturbation theory. The presented DFTC technique automatically handles momentary saturations and integrator windup caused by excessive disturbances, guidance command or dispersions under normal vehicle conditions. For multi-input, multi-output (MIMO) systems with redundant control effectors, such as the RLV attitude control system, an algorithm is presented for determining the direction of bandwidth cutback using the method of minimum-time optimal control with constrained control in order to maintain the best performance that is possible with the reduced control authority. Other bandwidth cutback logic, such as one that preserves the commanded direction of the bandwidth or favors a preferred direction when the commanded direction cannot be achieved, is also discussed. In this extended abstract, a simplistic example is proved to demonstrate the idea. In the final paper, test results on the high fidelity 6-DOF X-33 model with severe dispersions will be presented.

Zhu, J. J.↗