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At least 523 records · Page 29

Automated Generation of Fault Management Artifacts from a Simple System Model

Our understanding of off-nominal behavior - failure modes and fault propagation - in complex systems is often based purely on engineering intuition; specific cases are assessed in an ad hoc fashion as a (fallible) fault management engineer sees fit. This work is an attempt to provide a more rigorous approach to this understanding and assessment by automating the creation of a fault management artifact, the Failure Modes and Effects Analysis (FMEA) through querying a representation of the system in a SysML model. This work builds off the previous development of an off-nominal behavior model for the upcoming Soil Moisture Active-Passive (SMAP) mission at the Jet Propulsion Laboratory. We further developed the previous system model to more fully incorporate the ideas of State Analysis, and it was restructured in an organizational hierarchy that models the system as layers of control systems while also incorporating the concept of "design authority". We present software that was developed to traverse the elements and relationships in this model to automatically construct an FMEA spreadsheet. We further discuss extending this model to automatically generate other typical fault management artifacts, such as Fault Trees, to efficiently portray system behavior, and depend less on the intuition of fault management engineers to ensure complete examination of off-nominal behavior.

Spinup and Orient↗

An Introduction to Markov Modeling: Concepts and Uses

Kharkov modeling is a modeling technique that is widely useful for dependability analysis of complex fault tolerant systems. It is very flexible in the type of systems and system behavior it can model. It is not, however, the most appropriate modeling technique for every modeling situation. The first task in obtaining a reliability or availability estimate for a system is selecting which modeling technique is most appropriate to the situation at hand. A person performing a dependability analysis must confront the question: is Kharkov modeling most appropriate to the system under consideration, or should another technique be used instead? The need to answer this gives rise to other more basic questions regarding Kharkov modeling: what are the capabilities and limitations of Kharkov modeling as a modeling technique? How does it relate to other modeling techniques? What kind of system behavior can it model? What kinds of software tools are available for performing dependability analyses with Kharkov modeling techniques? These questions and others will be addressed in this tutorial.

Boyd, Mark A.↗

Creating Systems Engineering Products with Executable Models in a Model-Based Engineering Environment

Applying systems engineering across the life-cycle results in a number of products built from interdependent sources of information using different kinds of system level analysis. This paper focuses on leveraging the Executable System Engineering Method (ESEM) which automates requirements verification (e.g. power and mass budget margins and duration analysis of operational modes) using executable SysML models. The particular value proposition is to integrate requirements, and executable behavior and performance models for certain types of system level analysis. The models are created with modeling patterns that involve structural, behavioral and parametric diagrams, and are managed by an open source Model Based Engineering Environment (named OpenMBEE). This paper demonstrates how the ESEM is applied in conjunction with OpenMBEE to create key engineering products (e.g. operational concept document) for the Alignment and Phasing System (APS) within the Thirty Meter Telescope (TMT) project, which is under development by the TMT International Observatory (TIO).

MBSE↗

A comparison of two plasma models

The time dependent behavior of a plasma which surrounds a highly biased conducting sphere is considered. This plasma is treated as either a cold two component fluid or as a warm plasma whose time development can be found by solving the Vlasov equation. Both models demonstrate oscillatory behavior, but the electric fields predicted by the models are quantitatively quite different in regions close to the surface of the sphere and very similar otherwise. A broadening of the electron distribution function with time is observed indicating local heating of the plasma near the surface of the sphere.

Cottam, Russell↗

Computer-aided operations engineering with integrated models of systems and operations

CONFIG 3 is a prototype software tool that supports integrated conceptual design evaluation from early in the product life cycle, by supporting isolated or integrated modeling, simulation, and analysis of the function, structure, behavior, failures and operation of system designs. Integration and reuse of models is supported in an object-oriented environment providing capabilities for graph analysis and discrete event simulation. Integration is supported among diverse modeling approaches (component view, configuration or flow path view, and procedure view) and diverse simulation and analysis approaches. Support is provided for integrated engineering in diverse design domains, including mechanical and electro-mechanical systems, distributed computer systems, and chemical processing and transport systems. CONFIG supports abstracted qualitative and symbolic modeling, for early conceptual design. System models are component structure models with operating modes, with embedded time-related behavior models. CONFIG supports failure modeling and modeling of state or configuration changes that result in dynamic changes in dependencies among components. Operations and procedure models are activity structure models that interact with system models. CONFIG is designed to support evaluation of system operability, diagnosability and fault tolerance, and analysis of the development of system effects of problems over time, including faults, failures, and procedural or environmental difficulties.

Malin, Jane T.↗

Reducing Risk of InSight Surface Operations Through High-Fidelity Command Sequence Modeling

Simulating spacecraft behavior is crucial for the success of deep space missions, and failure to do so may result in damages to or the loss of the spacecraft. Many previous deep space missions have made use of ground-simulation of sequenced commanding, at speeds far greater than real time, to predict spacecraft state over time through the execution of onboard sequences. This type of modeling can be done at any fidelity, and most missions have opted to decrease fidelity to reduce cost and complexity. However, NASA’s Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) mission expanded the scope of ground modeling considerably, which has led to numerous benefits over past implementations. This paper will discuss the process and products that InSight created, as well as the lessons learned from successfully operating the spacecraft on Mars. InSight is the first JPL mission to expand the scope of ground modeling to include the uplink of files from Earth to the spacecraft, rather than making the simplification that any command sequences already exist onboard the spacecraft. The advantages of modeling the uplink of files are numerous. First, it allows for accurate modeling of the onboard filesystem of the spacecraft at all points in time, meaning that all file loads and deletions throughout the mission are modeled at the exact moment they are predicted to actually happen. Second, operators can be more certain that dependencies between sequences are not broken due to the dynamic nature of the filesystem as files are deleted, copied, and uplinked. Lastly, spacecraft filesystem tracking allows for management of sequences prior to uplink, limiting the uplink to only new sequences. The onboard filesystem model became crucial to mission success, emphasizing the importance of investing in accurate models before the need for them arises. During daily tactical operations of a spacecraft on Mars, a model is only useful if the results can be interpreted quickly. In this fast-paced environment, it is essential that command products are modeled and reviewed, errors are found and diagnosed, and new command products are redelivered, remodeled, re-reviewed in a timely manner. It is impossible to review the entire model and therefore the results of the model must be condensed and presented in a fashion that is intuitive, easy-to-navigate, complete, and trustworthy. InSight developed a number of innovative sequence review products that are designed to provide operators with the information required to quickly assess the validity of command products and diagnose potential issues. Together, these products provide a complete, yet succinct picture of the command and sequence model to the operators and facilitate a quick assessment of all sequence command products. This paper will cover planning and sequencing innovations made during InSight surface operations, and will compare the tools, processes, and results to those on other missions. Additionally, the paper will cover the flexible, yet robust nature of the planning and sequencing system architecture and how that flexibility allowed for rapid development and response to the unpredictability of Mars.

Cloutier, Kyle↗

Impact of Variations on 1-D Flow in Gas Turbine Engines via Monte Carlo Simulations

The unsteady compressible inviscid flow is characterized by the conservations of mass, momentum, and energy; or simply the Euler equations. In this paper, a study of the subsonic one-dimensional Euler equations with local preconditioning is presented using a modal analysis approach. Specifically, this study investigates the behavior of airflow in a gas turbine engine using the specified conditions at the inflow and outflow boundaries of the compressor, combustion chamber, and turbine, to determine the impact of variations in pressure, velocity, temperature, and density at low Mach numbers. Two main questions motivate this research: 1) Is there any aerodynamic problem with the existing gas turbine engines that could impact aircraft performance? 2) If yes, what aspect of a gas turbine engine could be improved via design to alleviate that impact and to optimize aircraft performance? This paper presents an initial attempt to model the flow behavior in terms of their eigenfrequencies subject to the assumption of the uncertainty or variation (perturbation). The flow behavior is explored using simulation outputs from a customer-deck model obtained from Pratt & Whitney. Variations of the main variables (i.e., pressure, temperature, velocity, density) about their mean states at the inflow and outflow boundaries of the compressor, combustion chamber, and turbine are modeled. Flow behavior is analyzed for the high-pressure compressor and combustion chamber utilizing the conditions on their left and right boundaries. In the same fashion, similar analyses are carried out for the high-pressure and low-pressure turbines. In each case, the eigenfrequencies that are obtained for different boundary conditions are examined closely based on their probabilistic distributions, a result of a Monte Carlo 10,000 sample simulation. Furthermore, the characteristic waves and wave response are analyzed and contrasted among different cases, with and without preconditioners. The results reveal the existence of flow instabilities due to the combined effect of variations and excessive pressures in the case of the combustion chamber and high-pressure turbine. Finally, a discussion is presented on potential impacts of the instabilities and what can be improved via design to alleviate them for a better aircraft performance.

Ngo, Khiem Viet↗

Vegetation clutter model

The statistical behavior of the radar backscattering coefficient of agricultural crops is examined. The data used were obtained by the microwave active spectrometer (MAS) systems in 1975 and 1976. Based on an evaluation of the angular and spectral variation of the mean, median, and 90-percent dynamic range of the coefficient (dB) histograms, empirical expressions describing the joint angular and frequency dependence of the mean and median were generated for each linear polarization configuration. The clutter model thus generated covers the angular range between 0 deg (nadir) and 80 deg and the frequency range between 1 GHz and 18 GHz. Decorrelation of the coefficient with frequency spacing was also evaluated and modeled.

Ulaby, F. T.↗

Monitoring with Trackers Based on Semi-Quantitative Models

In three years of NASA-sponsored research preceding this project, we successfully developed a technology for: (1) building qualitative and semi-quantitative models from libraries of model-fragments, (2) simulating these models to predict future behaviors with the guarantee that all possible behaviors are covered, (3) assimilating observations into behaviors, shrinking uncertainty so that incorrect models are eventually refuted and correct models make stronger predictions for the future. In our object-oriented framework, a tracker is an object which embodies the hypothesis that the available observation stream is consistent with a particular behavior of a particular model. The tracker maintains its own status (consistent, superceded, or refuted), and answers questions about its explanation for past observations and its predictions for the future. In the MIMIC approach to monitoring of continuous systems, a number of trackers are active in parallel, representing alternate hypotheses about the behavior of a system. This approach is motivated by the need to avoid 'system accidents' [Perrow, 1985] due to operator fixation on a single hypothesis, as for example at Three Mile Island. As we began to address these issues, we focused on three major research directions that we planned to pursue over a three-year project: (1) tractable qualitative simulation, (2) semiquantitative inference, and (3) tracking set management. Unfortunately, funding limitations made it impossible to continue past year one. Nonetheless, we made major progress in the first two of these areas. Progress in the third area as slower because the graduate student working on that aspect of the project decided to leave school and take a job in industry. I enclosed a set of abstract of selected papers on the work describe below. Several papers that draw on the research supported during this period appeared in print after the grant period ended.

Kuipers, Benjamin↗

HyDE Framework for Stochastic and Hybrid Model-Based Diagnosis

Hybrid Diagnosis Engine (HyDE) is a general framework for stochastic and hybrid model-based diagnosis that offers flexibility to the diagnosis application designer. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. Several alternative algorithms are available for the various steps in diagnostic reasoning. This approach is extensible, with support for the addition of new modeling paradigms as well as diagnostic reasoning algorithms for existing or new modeling paradigms. HyDE is a general framework for stochastic hybrid model-based diagnosis of discrete faults; that is, spontaneous changes in operating modes of components. HyDE combines ideas from consistency-based and stochastic approaches to model- based diagnosis using discrete and continuous models to create a flexible and extensible architecture for stochastic and hybrid diagnosis. HyDE supports the use of multiple paradigms and is extensible to support new paradigms. HyDE generates candidate diagnoses and checks them for consistency with the observations. It uses hybrid models built by the users and sensor data from the system to deduce the state of the system over time, including changes in state indicative of faults. At each time step when observations are available, HyDE checks each existing candidate for continued consistency with the new observations. If the candidate is consistent, it continues to remain in the candidate set. If it is not consistent, then the information about the inconsistency is used to generate successor candidates while discarding the candidate that was inconsistent. The models used by HyDE are similar to simulation models. They describe the expected behavior of the system under nominal and fault conditions. The model can be constructed in modular and hierarchical fashion by building component/subsystem models (which may themselves contain component/ subsystem models) and linking them through shared variables/parameters. The component model is expressed as operating modes of the component and conditions for transitions between these various modes. Faults are modeled as transitions whose conditions for transitions are unknown (and have to be inferred through the reasoning process). Finally, the behavior of the components is expressed as a set of variables/ parameters and relations governing the interaction between the variables. The hybrid nature of the systems being modeled is captured by a combination of the above transitional model and behavioral model. Stochasticity is captured as probabilities associated with transitions (indicating the likelihood of that transition being taken), as well as noise on the sensed variables.

Narasimhan, Sriram↗

Acquisition of Long-Duration, Low-Gravity Slosh Data Utilizing Existing ISS Equipment (SPHERES) for Calibration of CFD Models of Coupled Fluid-Vehicle Behavior

Accurate prediction of coupled fluid slosh and launch vehicle or spacecraft dynamics (e.g., nutation/precessional movement about various axes, attitude changes, ect.) requires Computational Fluid Dynamics (CFD) models calibrated with low-gravity, long duration slosh data. Recently completed investigations of reduced gravity slosh behavior have demonstrated the limitations of utilizing parabolic flights on specialized aircraft with respect to the specific objectives of the experiments. Although valuable data was collected, the benefits of longer duration low-gravity environments were clearly established. The proposed research provides the first data set from long duration tests in zero gravity that can be directly used to benchmark CFD models, including the interaction between the sloshing fluid and the tank/vehicle dynamics. To explore the coupling of liquid slosh with the motion of an unconstrained tank in microgravity, NASA's Kennedy Space Center, Launch Services Program has teamed up with the Florida Institute of Technology (FIT), Massachusetts Institute of Technology (MIT) and the Office of the Chief Technologist (OCT) to perform a series of slosh dynamics experiments on the International Space Station using the SPHERES platform. The Synchronized Position Hold Engage Reorient Experimental Satellites (SPHERES) testbed provides a unique, free-floating instrumented platform on ISS that can be utilized in a manner that would solve many of the limitations of the current knowledge related to propellant slosh dynamics on launch vehicle and spacecraft fuel tanks. The six degree of freedom (6-DOF) motion of the SPHERES free-flyer is controlled by an array of cold-flow C02 thrusters, supplied from a built-in liquid C02 tank. These SPHERES can independently navigate and re-orient themselves within the ISS. The intent of this project is to design an externally mounted tank to be driven inside the ISS by a set of two SPHERES devices (Figure 1 ). The tank geometry simulates a launch vehicle upper stage propellant tank and the maneuvers replicate those of real vehicles. The design includes inertial sensors, data acquisition, image capture and data storage interfaces to the SPHERES VERTIGO computer system on board the flight article assembly. The design also includes mechanical and electronic interfaces to the existing SPHERES hardware, which include self-contained packages that can operate in conjunction with the existing SPHERES electronics.

Schallhorn, Paul↗

Acquisition of Long-Duration, Low-Gravity Slosh Data Utilizing Existing ISS Equipment (SPHERES) for Calibration of CFD Models of Coupled Fluid-Vehicle Behavior

Accurate prediction of coupled fluid slosh and launch vehicle or spacecraft dynamics (e.g., nutation/precessional movement about various axes, attitude changes, ect.) requires Computational Fluid Dynamics (CFD) models calibrated with low-gravity, long duration slosh data. Recently completed investigations of reduced gravity slosh behavior have demonstrated the limitations of utilizing parabolic flights on specialized aircraft with respect to the specific objectives of the experiments. Although valuable data was collected, the benefits of longer duration low-gravity environments were clearly established. The proposed research provides the first data set from long duration tests in zero gravity that can be directly used to benchmark CFD models, including the interaction between the sloshing fluid and the tank/vehicle dynamics. To explore the coupling of liquid slosh with the motion of an unconstrained tank in microgravity, NASA's Kennedy Space Center, Launch Services Program has teamed up with the Florida Institute of Technology (FIT), Massachusetts Institute of Technology (MIT) and the NASA Game Changing Development Program (GCD) to perform a series of slosh dynamics experiments on the International Space Station using the SPHERES platform. The Synchronized Position Hold Engage Reorient Experimental Satellites (SPHERES) testbed provides a unique, free-floating instrumented platform on ISS that can be utilized in a manner that would solve many of the limitations of the current knowledge related to propellant slosh dynamics on launch vehicle and spacecraft fuel tanks. The six degree of freedom (6-DOF) motion of the SPHERES free-flyer is controlled by an array of cold-flow C02 thrusters, supplied from a built-in liquid C02 tank. These SPHERES can independently navigate and re-orient themselves within the ISS. The intent of this project is to design an externally mounted tank to be driven inside the ISS by a set of two SPHERES devices (Figure 1). The tank geometry simulates a launch vehicle upper stage propellant tank and the maneuvers replicate those of real vehicles. The design includes inertial sensors, data acquisition, image capture and data storage interfaces to the SPHERES VERTIGO computer system on board the flight article assembly. The design also includes mechanical and electronic interfaces to the existing SPHERES hardware, which include self-contained packages that can operate in conjunction with the existing SPHERES electronics

Schallhorn, Paul↗

System monitoring and diagnosis with qualitative models

A substantial foundation of tools for model-based reasoning with incomplete knowledge was developed: QSIM (a qualitative simulation program) and its extensions for qualitative simulation; Q2, Q3 and their successors for quantitative reasoning on a qualitative framework; and the CC (component-connection) and QPC (Qualitative Process Theory) model compilers for building QSIM QDE (qualitative differential equation) models starting from different ontological assumptions. Other model-compilers for QDE's, e.g., using bond graphs or compartmental models, have been developed elsewhere. These model-building tools will support automatic construction of qualitative models from physical specifications, and further research into selection of appropriate modeling viewpoints. For monitoring and diagnosis, plausible hypotheses are unified against observations to strengthen or refute the predicted behaviors. In MIMIC (Model Integration via Mesh Interpolation Coefficients), multiple hypothesized models of the system are tracked in parallel in order to reduce the 'missing model' problem. Each model begins as a qualitative model, and is unified with a priori quantitative knowledge and with the stream of incoming observational data. When the model/data unification yields a contradiction, the model is refuted. When there is no contradiction, the predictions of the model are progressively strengthened, for use in procedure planning and differential diagnosis. Only under a qualitative level of description can a finite set of models guarantee the complete coverage necessary for this performance. The results of this research are presented in several publications. Abstracts of these published papers are presented along with abtracts of papers representing work that was synergistic with the NASA grant but funded otherwise. These 28 papers include but are not limited to: 'Combined qualitative and numerical simulation with Q3'; 'Comparative analysis and qualitative integral representations'; 'Model-based monitoring of dynamic systems'; 'Numerical behavior envelopes for qualitative models'; 'Higher-order derivative constraints in qualitative simulation'; and 'Non-intersection of trajectories in qualitative phase space: a global constraint for qualitative simulation.'

Kuipers, Benjamin↗

Prediction of active control of subsonic centrifugal compressor rotating stall

A mathematical model is developed to predict the suppression of rotating stall in a centrifugal compressor with a vaned diffuser. This model is based on the employment of a control vortical waveform generated upstream of the impeller inlet to damp weak potential disturbances that are the early stages of rotating stall. The control system is analyzed by matching the perturbation pressure in the compressor inlet and exit flow fields with a model for the unsteady behavior of the compressor. The model was effective at predicting the stalling behavior of the Purdue Low Speed Centrifugal Compressor for two distinctly different stall patterns. Predictions made for the effect of a controlled inlet vorticity wave on the stability of the compressor show that for minimum control wave magnitudes, on the order of the total inlet disturbance magnitude, significant damping of the instability can be achieved. For control waves of sufficient amplitude, the control phase angle appears to be the most important factor in maintaining a stable condition in the compressor.

Lawless, Patrick B.↗

Role of the Polar Oceans in Global Climate

The project focused on ice-ocean model development and in particular on the assimilation of ice motion data and ice concentration data into both regional and global models. Many of the resulting publications below deal with improvements made in the physics treated by the model and the procedures for assimilating data. Several papers examine how the ability of the model to simulate the past behavior of the ice cover, especially to represent the ice thickness and ice deformation, is improved by data assimilation. A second aspect of the work involved interpretation of modeled behavior. Resulting papers treat the decline of arctic ice thickness over the last thirty years, and how that decline was caused by a slight warming of the near-surface atmosphere, and also how large variation in ice thickness are due to changes in wind patterns associated with a well- known oscillation of the atmospheric circulation. The research resulted in over 20 published papers on these topics.

Rothrock, D. A.↗

Fault diagnosis based on continuous simulation models

The results are described of an investigation of techniques for using continuous simulation models as basis for reasoning about physical systems, with emphasis on the diagnosis of system faults. It is assumed that a continuous simulation model of the properly operating system is available. Malfunctions are diagnosed by posing the question: how can we make the model behave like that. The adjustments that must be made to the model to produce the observed behavior usually provide definitive clues to the nature of the malfunction. A novel application of Dijkstra's weakest precondition predicate transformer is used to derive the preconditions for producing the required model behavior. To minimize the size of the search space, an envisionment generator based on interval mathematics was developed. In addition to its intended application, the ability to generate qualitative state spaces automatically from quantitative simulations proved to be a fruitful avenue of investigation in its own right. Implementations of the Dijkstra transform and the envisionment generator are reproduced in the Appendix.

Feyock, Stefan↗

Gimbal Bearing Friction in the SLS Core Stage Thrust Vector Control System

The Space Launch System (SLS) Core Stage Thrust Vector Control (TVC) system is comprised of eight mechanical feedback Shuttle heritage Type III TVC actuators that vector the four Shuttle heritage RS-25 engines about a Shuttle heritage gimbal block/bearing. The MSFC Controls community has long regarded gimbal friction to be a negligible effect on the overall control of gimbaled RS-25 engines. This is corroborated by Space Shuttle test and flight data that does not appear to show degraded effects, nor limit cycling at the end of the shuttle flight. For this reason, friction was not expected to be a driving factor of performance and control of the reused RS-25 engines aboard the SLS. However, after test data showed a large shift in frequency behavior and a highly damped step-response in the time series, there was further investigation into what could have caused this behavior. Heritage friction models used in previous gimbal and ball bearings were evaluated such as Coulomb, Dahl and LuGre, but the single degree of freedom friction models alone were not enough to explain the behavior and shifts seen in the test data. This paper presents the additional findings and modeling efforts regarding friction on the RS-25 engines. Using the Two Actuator Operational Simulation (TAOS), the difference from modeling separate friction degrees of freedom to coupled degrees of freedom was investigated to deduce the effects of one axis’s movement on the other. Next, due to the vibration environment, a modified LuGre model has been proposed that adds an additional term to decrease the friction coefficient at low engine velocity amplitudes. Lastly, the addition of the stiffness in each half of the gimbal bearing has increased modeling fidelity by also adding the effect on the gimbal bearing bending in compliance to both the friction torque on the surface of the gimbal bearing and the actuator force that is forcing the engine in a specified direction. Through these effects, the time and frequency domain behavior seen in test can be characterized accurately.

Friction↗

Gimbal Bearing Friction in the SLS Core Stage Thrust Vector Control System

The Space Launch System (SLS) Core Stage Thrust Vector Control (TVC) system is comprised of eight mechanical feedback Shuttle heritage Type III TVC actuators that vector the four Shuttle heritage RS-25 engines about a Shuttle heritage gimbal block/bearing. The MSFC Controls community has long regarded gimbal friction to be a negligible effect on the overall control of gimbaled RS-25 engines. This is corroborated by Space Shuttle test and flight data that does not appear to show degraded effects, nor limit cycling at the end of the shuttle flight. For this reason, friction was not expected to be a driving factor of performance and control of the reused RS-25 engines aboard the SLS. However, after test data showed a large shift in frequency behavior and a highly damped step-response in the time series, there was further investigation into what could have caused this behavior. Heritage friction models used in previous gimbal and ball bearings were evaluated such as Coulomb, Dahl and LuGre, but the single degree of freedom friction models alone were not enough to explain the behavior and shifts seen in the test data. This paper presents the additional findings and modeling efforts regarding friction on the RS-25 engines. Using the Two Actuator Operational Simulation (TAOS), the difference from modeling separate friction degrees of freedom to coupled degrees of freedom was investigated to deduce the effects of one axis’s movement on the other. Next, due to the vibration environment, a modified LuGre model has been proposed that adds an additional term to decrease the friction coefficient at low engine velocity amplitudes. Lastly, the addition of the stiffness in each half of the gimbal bearing has increased modeling fidelity by also adding the effect on the gimbal bearing bending in compliance to both the friction torque on the surface of the gimbal bearing and the actuator force that is forcing the engine in a specified direction. Through these effects, the time and frequency domain behavior seen in test can be characterized accurately.

Friction↗