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NASA NTRS2006

Gain-Scheduled Fault Tolerance Control Under False Identification

An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

Shin, Jong-Yeob↗

NASA NTRS1973

Apollo experience report: Guidance and control systems. Engineering simulation program

The Apollo Program experience from early 1962 to July 1969 with respect to the engineering-simulation support and the problems encountered is summarized in this report. Engineering simulation in support of the Apollo guidance and control system is discussed in terms of design analysis and verification, certification of hardware in closed-loop operation, verification of hardware/software compatibility, and verification of both software and procedures for each mission. The magnitude, time, and cost of the engineering simulations are described with respect to hardware availability, NASA and contractor facilities (for verification of the command module, the lunar module, and the primary guidance, navigation, and control system), and scheduling and planning considerations. Recommendations are made regarding implementation of similar, large-scale simulations for future programs.

Gilbert, D. W.↗

NASA NTRS2016

A Network Scheduling Model for Distributed Control Simulation

Distributed engine control is a hardware technology that radically alters the architecture for aircraft engine control systems. Of its own accord, it does not change the function of control, rather it seeks to address the implementation issues for weight-constrained vehicles that can limit overall system performance and increase life-cycle cost. However, an inherent feature of this technology, digital communication networks, alters the flow of information between critical elements of the closed-loop control. Whereas control information has been available continuously in conventional centralized control architectures through virtue of analog signaling, moving forward, it will be transmitted digitally in serial fashion over the network(s) in distributed control architectures. An underlying effect is that all of the control information arrives asynchronously and may not be available every loop interval of the controller, therefore it must be scheduled. This paper proposes a methodology for modeling the nominal data flow over these networks and examines the resulting impact for an aero turbine engine system simulation.

distributed control↗

NASA NTRS1982

Software and system level tests of a test flight mercury ion thruster subsystem

A U.S. Air Force technology spacecraft flight is scheduled to carry an Ion Auxiliary Propulsion System (IAPS) as part of its experimental payload. This paper presents the results of the successful flight-software qualification and system-level tests which were performed on IAPS. The software tests were performed with an operating engineering model ion thruster and power processing unit, and failure/off-normal recovery modes, operation with and without temperature telemetry from the thruster vaporizers, and with closed-loop control or fixed setpoint operation of the thruster vaporizers. The system-level tests cover a wide range of thermal and operating conditions with the entire system exposed to a simulated space environment.

Robson, R. R.↗

NASA NTRS1989

A variable-gain output feedback control design methodology

A digital control system design technique is developed in which the control system gain matrix varies with the plant operating point parameters. The design technique is obtained by formulating the problem as an optimal stochastic output feedback control law with variable gains. This approach provides a control theory framework within which the operating range of a control law can be significantly extended. Furthermore, the approach avoids the major shortcomings of the conventional gain-scheduling techniques. The optimal variable gain output feedback control problem is solved by embedding the Multi-Configuration Control (MCC) problem, previously solved at ICS. An algorithm to compute the optimal variable gain output feedback control gain matrices is developed. The algorithm is a modified version of the MCC algorithm improved so as to handle the large dimensionality which arises particularly in variable-gain control problems. The design methodology developed is applied to a reconfigurable aircraft control problem. A variable-gain output feedback control problem was formulated to design a flight control law for an AFTI F-16 aircraft which can automatically reconfigure its control strategy to accommodate failures in the horizontal tail control surface. Simulations of the closed-loop reconfigurable system show that the approach produces a control design which can accommodate such failures with relative ease. The technique can be applied to many other problems including sensor failure accommodation, mode switching control laws and super agility.

Halyo, Nesim↗

NASA NTRS2009

Open-Loop Pitch Table Optimization for the Maximum Dynamic Pressure Orion Abort Flight Test

NASA has scheduled the retirement of the space shuttle orbiter fleet at the end of 2010. The Constellation program was created to develop the next generation of human spaceflight vehicles and launch vehicles, known as Orion and Ares respectively. The Orion vehicle is a return to the capsule configuration that was used in the Mercury, Gemini, and Apollo programs. This configuration allows for the inclusion of an abort system that safely removes the capsule from the booster in the event of a failure on launch. The Flight Test Office at NASA's Dryden Flight Research Center has been tasked with the flight testing of the abort system to ensure proper functionality and safety. The abort system will be tested in various scenarios to approximate the conditions encountered during an actual Orion launch. Every abort will have a closed-loop controller with an open-loop backup that will direct the vehicle during the abort. In order to provide the best fit for the desired total angle of attack profile with the open-loop pitch table, the table is tuned using simulated abort trajectories. A pitch table optimization program was created to tune the trajectories in an automated fashion. The program development was divided into three phases. Phase 1 used only the simulated nominal run to tune the open-loop pitch table. Phase 2 used the simulated nominal and three simulated off nominal runs to tune the open-loop pitch table. Phase 3 used the simulated nominal and sixteen simulated off nominal runs to tune the open-loop pitch table. The optimization program allowed for a quicker and more accurate fit to the desired profile as well as allowing for expanded resolution of the pitch table.

Stillwater, Ryan A.↗

NASA NTRS2005

Evaluation of an Active Clearance Control System Concept

Reducing blade tip clearances through active tip clearance control in the high pressure turbine can lead to significant reductions in emissions and specific fuel consumption as well as dramatic improvements in operating efficiency and increased service life. Current engines employ scheduled cooling of the outer case flanges to reduce high pressure turbine tip clearances during cruise conditions. These systems have relatively slow response and do not use clearance measurement, thereby forcing cold build clearances to set the minimum clearances at extreme operating conditions (e.g., takeoff, reburst) and not allowing cruise clearances to be minimized due to the possibility of throttle transients (e.g., step change in altitude). In an effort to improve upon current thermal methods, a first generation mechanically-actuated active clearance control (ACC) system has been designed and fabricated. The system utilizes independent actuators, a segmented shroud structure, and clearance measurement feedback to provide fast and precise active clearance control throughout engine operation. Ambient temperature performance tests of this first generation ACC system assessed individual seal component leakage rates and both static and dynamic overall system leakage rates. The ability of the nine electric stepper motors to control the position of the seal carriers in both open- and closed-loop control modes for single and multiple cycles was investigated. The ability of the system to follow simulated engine clearance transients in closed-loop mode showed the system was able to track clearances to within a tight tolerance (0.001 in. error).

Steinetz, Bruce M.↗

NASA NTRS2005

Evaluation of an Active Clearance Control System Concept

Steinetz, Bruce M.↗

NASA NTRS2014

Asteroid Redirect Crewed Mission Space Suit and EVA System Architecture Trade Study

The Asteroid Redirect Crewed Mission (ARCM) requires a Launch/Entry/Abort (LEA) suit capability and short duration Extra Vehicular Activity (EVA) capability for Orion. The EVAs will involve a two-person crew for approximately four hours. Currently, two EVAs are planned with one contingency EVA in reserve. Providing this EVA capability is very challenging due to system level constraints and a new and unknown environment. The goal of the EVA architecture for ARCM is one that builds upon previously developed technologies and lessons learned, and that accomplishes the ARCM mission while providing a stepping stone to future missions and destinations. The primary system level constraints are to 1) minimize system mass and volume and 2) minimize the interfacing impacts to the baseline Orion design. In order to minimize the interfacing impacts and to not perturb the baseline Orion schedule, the concept of adding "kits" to the baseline system is proposed. These kits consist of: an EVA kit (converts LEA suit to EVA suit), EVA Servicing and Recharge Kit (provides suit consumables), the EVA Tools, Translation Aids & Sample Container Kit (the tools and mobility aids to complete the tasks), the EVA Communications Kit (interface between the EVA radio and the MPCV), and the Cabin Repress Kit (represses the MPCV between EVAs). This paper will focus on the trade space, analysis, and testing regarding the space suit (pressure garment and life support system). Historical approaches and lessons learned from all past EVA operations were researched. Previous and current, successfully operated EVA hardware and high technology readiness level (TRL) hardware were evaluated, and a trade study was conducted for all possible pressure garment and life support options. Testing and analysis was conducted and a recommended EVA system architecture was proposed. Pressure garment options that were considered for this mission include the currently in-use ISS EVA Mobility Unit (EMU), all variations of the Advanced Crew Escape Suit (ACES), and the Exploration Z-suit. For this mission, the pressure garment that was selected is the Modified ACES (MACES) with EVA enhancements. Life support options that were considered included short closed-loop umbilicals, long open-loop umbilicals, the currently in-use ISS EMU Portable Life Support System (PLSS), and the currently in development Exploration PLSS. For this mission, the life support option that was selected is the Exploration PLSS. The greatest risk in the proposed architecture is viewed to be the comfort and mobility of the baseline MACES and the delicate balance between adding more mobility features while not compromising landing safety. Feasibility testing was accomplished in low fidelity analogs and in the JSC Neutral Buoyancy Laboratory (NBL) to validate the concept before a final recommendation on the architecture was made. The proposed architecture was found to meet the mission constraints, but much more work is required to determine the details of the required suit upgrades, the integration with the PLSS, and the rest of the tools and equipment required to accomplish the mission. This work and further definition of the remaining kits will be conducted in government fiscal year 14.

Blanco, Raul A.↗

NASA NTRS2011

Magnetospheric Multiscale (MMS) Mission Attitude Ground System Design

This paper describes the attitude ground system (AGS) design to be used for support of the Magnetospheric MultiScale (MMS) mission. The AGS exists as one component of the mission operations control center. It has responsibility for validating the onboard attitude and accelerometer bias estimates, calibrating the attitude sensors and the spacecraft inertia tensor, and generating a definitive attitude history for use by the science teams. NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland is responsible for developing the MMS spacecraft, for the overall management of the MMS mission, and for mission operations. MMS is scheduled for launch in 2014 for a planned two-year mission. The MMS mission consists of four identical spacecraft flying in a tetrahedral formation in an eccentric Earth orbit. The relatively tight formation, ranging from 10 to 400 km, will provide coordinated observations giving insight into small-scale magnetic field reconnection processes. By varying the size of the tetrahedron and the orbital semi-major axis and eccentricity, and making use of the changing solar phase, this geometry allows for the study of both bow shock and magnetotail plasma physics, including acceleration, reconnection, and turbulence. The mission divides into two phases for science; these phases will have orbit dimensions of l.2xl2 Earth radii in the first phase and l.2x25 Earth radii in the second in order to study the dayside magnetopause and the nightside magnetotail, respectively. The orbital periods are roughly one day and three days for the two mission phases. Each of the four MMS spacecraft will be spin stabilized at 3 revolutions per minute (rpm), with the spin axis oriented near the ecliptic north pole but tipped approximately 2.5 deg towards the Sun line. The main body of each spacecraft will be an eight-sided platform with diameter of 3.4 m and height of 1.2 m. Several booms are attached to this central core: two axial booms of 14.9 m length, two radial magnetometer booms of 5 m length, and four radial -wire booms of 60 m length. Attitude and orbit control will use a set of axial and radial thrusters. A four-head star tracker and a slit-type digital Sun sensor (DSS) provide input for attitude determination. In addition, an accelerometer will be· used for closed-loop orbit maneuver control. The primary AGS product will be a daily definitive attitude history. Due to power limitations; the star tracker and accelerometer data will not be available at all times. However, tracker data from at least 10 percent of each orbit and continuous DSS data will be provided. An extended Kalman filter (EKF) will be used to estimate the three-axis attitude (i.e., spin axis orientation and spin phase) and rotation rate for all times when the tracker data is valid. For other times, the attitude is generated by assuming a constant angular momentum vector in the inertial frame. The DSS sun pulse will provide a timing signal to maintain an accurate spin phase. There will be times when the Sun is occulted and DSS data is not available. If this occurs at the start or end of a definitive attitude product, then the spin phase will be extrapolated using the mean rate determined by the EKF.

Sedlak, Joseph E.↗

NASA NTRS2010

Magnetospheric Multiscale (MMS) Mission Attitude Ground System Design

This paper describes the attitude ground system (AGS) design to be used for support of the Magnetospheric MultiScale (MMS) mission. The AGS exists as one component of the mission operations control center. It has responsibility for validating the onboard attitude and accelerometer bias estimates, calibrating the attitude sensors and the spacecraft inertia tensor, and generating a definitive attitude history for use by the science teams. NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland is responsible for developing the MMS spacecraft, for the overall management of the MMS mission, and for mission operations. MMS is scheduled for launch in 2014 for a planned two-year mission. The MMS mission consists of four identical spacecraft flying in a tetrahedral formation in an eccentric Earth orbit. The relatively tight formation, ranging from 10 to 400 km, will provide coordinated observations giving insight into small-scale magnetic field reconnection processes. By varying the size of the tetrahedron and the orbital semi-major axis and eccentricity, and making use of the changing solar phase, this geometry allows for the study of both bow shock and magnetotail plasma physics, including acceleration, reconnection, and turbulence. The mission divides into two phases for science; these phases will have orbit dimensions of 1.2 x 12 Earth radii in the first phase and 1.2x25 Earth radii in the second in order to study the dayside magnetopause and the nightside magnetotail, respectively. The orbital periods are roughly one day and three days for the two mission phases. Each of the four MMS spacecraft will be spin stabilized at 3 revolutions per minute (rpm), with the spin axis oriented near the ecliptic north pole but tipped approximately 2.5 deg towards the Sun line. The main body of each spacecraft will be an eight-sided platform with diameter of 3.4 m and height of 1.2 m. Several booms are attached to this central core: two axial booms of 14.9 m length, two radial magnetometer booms of 5 m length, and four radial wire booms of 60 m length. Attitude and orbit control will use a set of axial and radial thrusters. A four-head star tracker and a slit-type digital Sun sensor (DSS) provide input for attitude determination. In addition, an accelerometer will be used for closed-loop orbit maneuver control. The primary AGS product will be a daily definitive attitude history. Due to power limitations, the star tracker and accelerometer data will not be available at all times. However, tracker data from at least 10 percent of each orbit and continuous DSS data will be provided. An extended Kalman filter (EKF) will be used to estimate the three-axis attitude (i.e., spin axis orientation and spin phase) and rotation rate for all times when the tracker data is valid. For other times, the attitude is generated by assuming a constant angular momentum vector in the inertial frame. The DSS sun pulse will provide a timing signal to maintain an accurate spin phase. There will be times when the Sun is occulted and DSS data is not available. If this occurs at the start or end of a definitive attitude product, then the spin phase will be extrapolated using the mean rate determined by the EKF.

Sedlak, Joseph E.↗

DOE OSTI2026

Development of a Test-Bed for Testing and Refining EarthEn’s Supercritical CO 2 Based Energy Storage System

EarthEn’s energy storage concept leverages supercritical carbon dioxide (sCO 2 ) as a working fluid and relies on compact, high-performance components operating at elevated pressures and temperatures. To accelerate component development and reduce technical risk prior to larger-scale demonstrations, Oak Ridge National Laboratory (ORNL) developed a 100 kW-scale sCO 2 test-bed under a Cooperative Research and Development Agreement with EarthEn (CRADA NO. NFE-24-10050). The objective of the work was to design and construct a flexible experimental facility capable of reproducing key thermodynamic state points and heat-transfer conditions relevant to EarthEn’s thermal energy storage (TES) cycle, with particular emphasis on enabling development and evaluation of next-generation heat exchangers and TES concepts. The test-bed consists of a closed-loop sCO 2 circulation system housed within an open-topped enclosure. In its as-installed configuration, dense-phase sCO 2 is recirculated through a printed circuit recuperator, an electrically heated section, a throttling device used to simulate turbine expansion, and a water-cooled printed circuit heat exchanger that rejects heat to the building chilled-water system before returning to the pump. The pump is driven by a variable frequency drive, enabling controlled adjustment of flow and operating point. A comprehensive instrumentation suite was integrated to support both safe operation and high-quality data collection. Installed sensors include Coriolis flow meters for sCO 2 flow rate and density, resistance temperature detectors and thermocouples distributed throughout the loop (including the heated section and key heat exchanger ports), and pressure transducers for absolute and differential pressure measurements. The facility was designed to support high-pressure (19 MPa nominal) and high-temperature (575°C nominal) operation with credited overpressure protection provided by a rupture disk. Nominal operating conditions were selected to support 100 kW-class testing while maintaining flexibility for non-heated and heated shakedown, control development, and future integration of advanced TES test sections. In parallel with facility development, a system-level thermal-hydraulic model was created using Modelica-based tools to support component sizing, anticipate performance over targeted test conditions, and establish a framework for future model calibration against experimental data. At the conclusion of the project performance period, the facility was in final assembly, and the pressure boundary was nearly completed. However, several practical challenges associated with high-pressure/high-temperature systems and specialized component procurement impacted schedule and prevented initial pump-driven operation and full commissioning within the available resources. This report documents the as-built design, operating capabilities, and instrumentation, and it summarizes key lessons learned related to heater fabrication and testing, first-of-a-kind assembly factors, specialty flange supply constraints, and fill pump corrective actions. Finally, it outlines a phased plan for future commissioning and experimental campaigns, including control and instrumentation shakedown, heater characterization, model calibration, and testing at state points representative of EarthEn’s TES cycle.

25 ENERGY STORAGE↗

NASA NTRS1979

Simulation evaluation of combined 4D RNAV and airborne traffic situation displays and procedures applied to terminal aerial maneuvers

Simulation scenarios were developed in which subject pilots must simultaneously follow a 3D terminal airspace structure and arrive at fixed waypoints within the structure precisely at pre-scheduled times in the presence of a full range of wind conditions aloft, and monitor nearby traffic on an airborne traffic situation display, especially during merging and spacing operations, and detect blunders and resolve conflicts in a safe manner. Open-loop simulator tests of the single-stage 4D RNAV algorithm indicate that a descending pilot can comply quite closely with an assigned time of arrival at a 3D waypoint simply by tracking a pre-calculated speed profile. Initial experiments show that the aircraft arrives at the 3D waypoint within a few seconds of the anticipated time. The presence of headwinds or tailwinds does not affect the arrival time error as long as the wind is accurately modeled in the descent algorithm. Results all but quarantee that a 5 second standard deviation in arrival time error can be realized in closed-loop descents at very moderate pilot workload levels.

Athans, M.↗

NASA NTRS2002

Development of Closed-Loop Simulation Methods for a Next-Generation Terminal Area Automation System

A next-generation air traffic decision support tool, known as the Active Final Approach Spacing Tool (aFAST), will generate heading, speed and altitude commands to achieve more precise separation of aircraft in the terminal area. The techniques used to analyze the performance of earlier generation decision support tools are not adequate to analyze the performance of aFAST. This paper summarizes the development of a new and innovative fully closed-loop testing method for aFAST. This method, called trajectory feedback testing, closes each aircraft's control loop inside of the aFAST scheduling algorithm. Validation of trajectory feedback testing by examination of the variation of aircraft time-of-arrival predictions between schedule updates and the variation of aircraft excess separation distances between simulation runs is presented.

Robinson, John E., III↗

NASA NTRS2004

Water for Two Worlds: Designing Terrestrial Applications for Exploration-class Sanitation Systems

At the United Nations Millennium Summit in September of 2000, the world leaders agreed on an ambitious agenda for reducing poverty and improving lives: the Millennium Development Goals (MDGs), a list of issues they consider highly pernicious, threatening to human welfare and, thereby, to global security and prosperity. Among the eight goals are included fundamental human needs such as the eradication of extreme poverty and hunger, the promotion of gender equality, the reduction of child mortality and improvement of maternal health, and ensuring the sustainability of our shared environment. In order to help focus the efforts to meet these goals, the United Nations (UN) has established a set of eighteen concrete targets, each with an associated schedule. Among these is Target 10: "By 2015, reduce by half the proportion of people without access to safe drinking water." A closely related target of equal dignity was agreed at the World Summit on Sustainable Development (Johannesburg, September 2002): "By 2015, reduce by half the proportion of people without access to basic sanitation." One of the greatest successes in the development of Exploration-class technologies for closed-loop, sustainable support of long-duration human space missions has been the work both ESA and NASA have done in bioregenerative water reclamation (WRS), and secondarily, in solid-waste management. Solid-waste and WRS systems tend to be combined in the commercial world into the field of sanitation, although as we will see, the most essential principles of sustainable terrestrial sanitation actually insist upon the separation of solid and liquid excreta. Seeing the potential synergy between the space program ALS technologies developed for Mars and the urgent needs of hundreds of millions of people for secure access to clean water here on Earth, we set out to organize the adaptation of these technologies to help the United Nations Development Programme (UNDP) meet Target 10. In this paper, we will summarize the issues and results of the first "Water for Two Worlds" summit held in January of this year, describe,the status of the sustainable sanitation systems that are on the table for adaptation to widespread terrestrial use, and present fundamental strategies for forward work.

Adams, Constance↗

NASA NTRS2006

Modeling the Scheduling of Eye Movements and Manual Responses in Performing a Sequence of Discrete Tasks

Common tasks in daily life are often accomplished by a sequence of actions that interleave information acquisition through the eyes and action execution by the hands. How are eye movements coordinated with the release of manual responses and how may their coordination be represented at the level of component mental operations? We have previously presented data from a typing-like task requiring separate choice responses to a series of five stimuli. We found a consistent pattern of results in both motor and ocular timing, and hypothesized possible relationships among underlying components. Here we report a model of that task, which demonstrates how the observed timing of eye movements to successive stimuli could be accounted for by assuming systems: an open-loop system generating saccades at a periodic rate, and a closed-loop system commanding a saccade based on stimulus processing. We relate this model to models of reading and discuss the motivation for dual control.

Wu, Shu-Chieh↗

NASA NTRS2010

Handling Qualities of a Capsule Spacecraft During Atmospheric Entry

A piloted simulation was conducted to study handling qualities for capsule spacecraft entering the Earth s atmosphere. Eight evaluation pilots, including six pilot astronauts, provided Cooper-Harper ratings, workload ratings, and qualitative comments. The simulation began after descending through the atmospheric entry interface point and continued until the drogue parachutes deployed. There were two categories of piloting tasks, both of which required bank angle control. In one task category, the pilot followed a closed-loop bank angle command computed by the backup guidance system to manage g-loads during entry. In the other task category, the pilot used intuitive rules to determine the desired bank angle independently, based on an open-loop schedule of vertical speed, Mach, and total energy specified at several range-to-target gates along the entry trajectory. Pilots were able to accurately track the bank angle guidance commands and steered the capsule toward the recovery site with essentially the same range error as the benchmark autopilot trajectory albeit with substantially higher propellant usage, and the handling qualities for this task were satisfactory. Another key result was that the complex piloting task of atmospheric entry could be performed satisfactorily, even in the presence of large dispersions, by controlling bank angle to follow a simple open-loop schedule.

Bilimoria, Karl D.↗

NASA NTRS2014

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC.

VanZwieten, Tannen↗