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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Robust Control Design for Uncertain Nonlinear Dynamic Systems

Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

Kenny, Sean P.↗
NASA NTRS2012

Nature's Autonomous Oscillators

Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.

Mayr, H. G.↗
NASA NTRS2012

Validation of Slosh Model Parameters and Anti-Slosh Baffle Designs of Propellant Tanks by Using Lateral Slosh Testing

The slosh dynamics of propellant tanks can be represented by an equivalent mass-pendulum-dashpot mechanical model. The parameters of this equivalent model, identified as slosh mechanical model parameters, are slosh frequency, slosh mass, and pendulum hinge point location. They can be obtained by both analysis and testing for discrete fill levels. Anti-slosh baffles are usually needed in propellant tanks to control the movement of the fluid inside the tank. Lateral slosh testing, involving both random excitation testing and free-decay testing, are performed to validate the slosh mechanical model parameters and the damping added to the fluid by the anti-slosh baffles. Traditional modal analysis procedures were used to extract the parameters from the experimental data. Test setup of sub-scale tanks will be described. A comparison between experimental results and analysis will be presented.

Perez, Jose G.↗
NASA NTRS2013

SparkJet Efficiency

A novel method for determining the thermal efficiency of the SparkJet is proposed. A SparkJet is attached to the end of a pendulum. The motion of the pendulum subsequent to a single spark discharge is measured using a laser displacement sensor. The measured displacement vs time is compared with the predictions of a theoretical perfect gas model to estimate the fraction of the spark discharge energy which results in heating the gas (i.e., increasing the translational-rotational temperature). The results from multiple runs for different capacitances of c = 3, 5, 10, 20, and 40 micro-F show that the thermal efficiency decreases with higher capacitive discharges.

Golbabaei-Asl, Mona↗
NASA NTRS2005

Advanced Method to Estimate Fuel Slosh Simulation Parameters

The nutation (wobble) of a spinning spacecraft in the presence of energy dissipation is a well-known problem in dynamics and is of particular concern for space missions. The nutation of a spacecraft spinning about its minor axis typically grows exponentially and the rate of growth is characterized by the Nutation Time Constant (NTC). For launch vehicles using spin-stabilized upper stages, fuel slosh in the spacecraft propellant tanks is usually the primary source of energy dissipation. For analytical prediction of the NTC this fuel slosh is commonly modeled using simple mechanical analogies such as pendulums or rigid rotors coupled to the spacecraft. Identifying model parameter values which adequately represent the sloshing dynamics is the most important step in obtaining an accurate NTC estimate. Analytic determination of the slosh model parameters has met with mixed success and is made even more difficult by the introduction of propellant management devices and elastomeric diaphragms. By subjecting full-sized fuel tanks with actual flight fuel loads to motion similar to that experienced in flight and measuring the forces experienced by the tanks these parameters can be determined experimentally. Currently, the identification of the model parameters is a laborious trial-and-error process in which the equations of motion for the mechanical analog are hand-derived, evaluated, and their results are compared with the experimental results. The proposed research is an effort to automate the process of identifying the parameters of the slosh model using a MATLAB/SimMechanics-based computer simulation of the experimental setup. Different parameter estimation and optimization approaches are evaluated and compared in order to arrive at a reliable and effective parameter identification process. To evaluate each parameter identification approach, a simple one-degree-of-freedom pendulum experiment is constructed and motion is induced using an electric motor. By applying the estimation approach to a simple, accurately modeled system, its effectiveness and accuracy can be evaluated. The same experimental setup can then be used with fluid-filled tanks to further evaluate the effectiveness of the process. Ultimately, the proven process can be applied to the full-sized spinning experimental setup to quickly and accurately determine the slosh model parameters for a particular spacecraft mission. Automating the parameter identification process will save time, allow more changes to be made to proposed designs, and lower the cost in the initial design stages.

Schlee, Keith↗
NASA NTRS2006

Educational Experiences of Embry-Riddle Students through NASA Research Collaboration

NASA's educational. programs benefit students and faculty while increasing the overall productivity of the organization. The NASA Graduate Student Research Program (GSRP) awards fellowships for graduate study leading to both masters and doctoral degrees in several technical fields. GSRP participants have the option to utilize NASA Centers andlor university research facilities. In addition, GSRP students can serve as mentors for undergrad students to provide a truly unique learning experience. NASA's Cooperative Education Program allows undergraduate students the chance to gain "real-world" work experience in the field. It also gives NASA a no risk capability to evaluate the true performance of a prospective new hire without relying solely on a "paper resume" while providing the students with a greater hiring potential upon graduation, at NASA or elsewhere. University faculty can also benefit by participating in the NASA Faculty Fellowship Program (NFFP). This program gives the faculty an opportunity to work with NASA peers. The Mission Analysis Branch of the Expendable Launch Vehicles Division at NASA Kennedy Space Center has utilized these two programs with students from Embry-Riddle Aeronautical University (ERAU) to conduct research in modeling and developing a parameter estimation method for spacecraft fuel slosh using simple pendulum analogs. Simple pendulum models are used to understand complicated spacecraft fuel slosh behavior. A robust parameter estimation process will help to identif' the parameters that will predict the response fairly accurately during the initial stages of design. These programs provide students with a unique opportunity to work on "real-world" aerospace problems, like spacecraft fuel slosh,. This in turn reinforces their problem solving abilities and their communication skills such as interviewing, resume writing, technical writing, and presentation. Faculty benefits by applying what they have learned to the classroom. Through university collaborations with NASA and industry help students to acquire skills that are vital for their success upon entering the workforce.

Schlee, Keith↗
NASA NTRS2007

Educational Experiences of Embry-Riddle Students through NASA Research Collaboration

NASA's educational programs benefit students while increasing the overall productivity of the organization. The NASA Graduate Student Research Program (GSRP) awards fellowships for graduate study leading to both masters and doctoral degrees in several technical fields, while the Cooperative Education program allows undergraduate and graduate students the chance to gain work experience in the field. The Mission Analysis Branch of the Expendable Launch Vehicles Division at NASA Kennedy Space Center has utilized these two programs with students from Embry-Riddle Aeronautical University to conduct research in modeling and developing a parameter estimation method for spacecraft fuel slosh using simple pendulum analogs. Simple pendulum models are used to understand complicated spacecraft fuel slosh behavior. A robust parameter estimation process will help to identiFy the parameters that will predict the response fairly accurately during the initial stages of design. NASA's Cooperative Education Program trains the next wave of new hires while allowing graduate and undergraduate college students to gain valuable "real-world" work experience. It gives NASA a no risk capability to evaluate the true performance of a prospective new hire without relying solely on a paper resume, while providing the students with a greater hiring potential upon graduation, at NASA or elsewhere. In addition, graduate students serve as mentors for undergrad students and provide a unique learning environment. Providing students with a unique opportunity to work on "real-world" aerospace problems ultimately reinforces their problem solving abilities and their communication skills (in terms of interviewing, resume writing, technical writing, presentation, and peer review) that are vital for the workforce to succeed.

Schlee, Keith↗
NASA NTRS2013

Parallel Plate System for Collecting Data Used to Determine Viscosity

A parallel-plate system collects data used to determine viscosity. A first plate is coupled to a translator so that the first plate can be moved along a first direction. A second plate has a pendulum device coupled thereto such that the second plate is suspended above and parallel to the first plate. The pendulum device constrains movement of the second plate to a second direction that is aligned with the first direction and is substantially parallel thereto. A force measuring device is coupled to the second plate for measuring force along the second direction caused by movement of the second plate.

Kaukler, William↗
NASA NTRS2016

NASA's Preparations for ESA's L3 Gravitational Wave Mission

Telescope Subsystem - Jeff Livas (GSFC): Demonstrate pathlength stability, straylight and manufacturability. Phase Measurement System - Bill Klipstein (JPL): Key measurement functions demonstrated. Incorporate full flight functionality. Laser Subsystem - Jordan Camp (GSFC): ECL master oscillator, phase noise of fiber power amplifier, demonstrate end-to-end performance in integrated system, lifetime. Micronewton Thrusters - John Ziemer (JPL): Propellant storage and distribution, system robustness, manufacturing yield, lifetime. Arm-locking Demonstration - Kirk McKenzie (JPL): Studying a demonstration of laser frequency stabilization with GRACE Follow-On. Torsion Pendulum - John Conklin (UF): Develop U.S. capability with GRS and torsion pendulum test bed. Multi-Axis Heterodyne Interferometry - Ira Thorpe (GSFC): Investigate test mass/optical bench interface. UV LEDs - John Conklin+ (UF): Flight qualify UV LEDs to replace mercury lamps in discharging system. Optical Bench - Guido Mueller (UF): Investigate alternate designs and fabrication processes to ease manufacturability. LISA researchers at JPL are leading the Laser Ranging Interferometer instrument on the GRACE Follow-On mission.

Midterm Assessment↗
NASA NTRS2020

X-56A Structural Dynamics Ground Testing Overview and Lessons Learned

The X-56A Multi-Utility Technology Testbed (MUTT) is a subscale, fixed-wing aircraft designed for high-risk aeroelastic flight demonstration and research. Structural dynamics ground testing for model validation was especially important for this vehicle because the structural model was directly used in the development of a flight control system with active flutter suppression capabilities. Structural dynamics ground tests of the X-56A MUTT with coupled rigid-body and structural modes provided a unique set of challenges. An overview of the ground vibration test (GVT) and moment of inertia (MOI) test setup and execution is presented. The series of GVTs included the wing by itself attached to a strongback and complete vehicle at two mass conditions: empty and full fuel. Two boundary conditions for the complete-vehicle test were studied: on landing gear and suspended free-free. Pitch MOI tests were performed using a compound pendulum method and repeated with two different pendulum lengths for independent verification. The original soft-support test configuration for the GVT used multiple bungees, resulting in unforeseen coupling interactions between the soft-support bungees and the vehicle structural modes. To resolve this problem, the soft-support test setup underwent multiple iterations. The various GVT configurations and boundary-condition modifications are highlighted and explained. Lessons learned are captured for future consideration when performing structural dynamics testing with similar vehicles.

Chin, Alexander W.↗
NASA NTRSDate not supplied

A Low-Cost and Low-Risk Testbed for Control Design of Launch Vehicles and Landing Systems

This research seeks to bridge the gap between the simulation/theory and the flight-testing phases of control algorithmdesign for launch vehicles (LVs) and landing systems (LSs). Thispaper reviews contemporary testbeds for LV and LS control sys-tem design with an emphasis on reducing costs and risks. Also, anew low-cost and low-risk testbed utilizing a quadcopter, flexibleinverted pendulum, and a hanging pendulum is proposed. It is shown that the planar dynamic response of this proposed testbedcan match the planar dynamic response of an LV. As mission objectives for frequent cislunar and interplanetary travel become more complex, the algorithms that control LVs and LSs need to become more advanced to ensure mission safety and success. These control systems are slow to mature because it is difficult to perform experiments in an environment relevant to the mission in a safe and cost-effective manner. A solution to this problem frequently leveraged in the aviation andsatellite industries involves mimicking the dynamic response ofthe vehicle with a test platform that is low-cost and low-risk.

William J Elke III↗
NASA NTRSDate not supplied

Modeling and Simulation of Rotary Sloshing in Launch Vehicles

The nonlinear dynamics of propellant sloshing during orbital ascent are usually neglected in the flight control analysis of large boost vehicles under the assumption that the viscous damping of the fluid is sufficient to suppress nonlinear phenomena and confine the fluid to small, planar free surface displacements. In this case, the sloshing dynamics can be modeled using a spring-mass-damper or linearized pendulum mechanical analog. However, large, smooth-wall tanks without significant internal hardware or ring baffles are still susceptible to nonlinear effects. In particular, rotary sloshing can present a risk to flight control as it involves the formation of a stable limit cycle which can lead to undesirable roll coupling. The underlying phenomena of jump resonance does not manifest in linear models, but can be reproduced using a nonlinear spherical pendulum or the Bauer paraboloid model developed during the Apollo/Saturn program. In this paper, a detailed analysis of the rotary sloshing dynamics of these mechanical analogs is presented, and discussed in the context of flight control stability. High-fidelity simulations of a representative boost vehicle are used to verify the semi-analytical predictions of the nonlinear dynamic response.

Modeling↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Wave energy converter buoy for Arctic observations

Ocean observation buoys are currently powered-constrained by battery storage capacity or available solar power. Power constraints limit the number of measurements that can be made and the lifetime of the buoys. Ocean surface wave energy could be used for power production, but wave energy converters are not yet commercially available for ocean observation buoys. Here we present the design and testing of a drifting wave energy converter buoy using a pendulum transmission system (PTS). The wave energy converter buoy was designed to operate in Arctic temperatures and wave conditions, but it could be used in areas with warmer temperatures and larger waves. Field tests measured a maximum power production of 5 watts in waves with a significant wave height of 0.42 meters and a ten minute average power production of 37 milliwatts. Power production increased with the energy period and significant wave height. The energy harvesting capabilities of the PTS showed the utility of adding a wave energy conversion device to a drifting ocean observation buoy.

Arctic observations↗
DOE OSTI2024

Emergent actin flows explain distinct modes of gliding motility

During host infection, Toxoplasma gondii and related unicellular parasites move using gliding, which differs fundamentally from other known mechanisms of eukaryotic cell motility. Gliding is thought to be powered by a thin layer of flowing filamentous (F)-actin sandwiched between the plasma membrane and a myosin-covered inner membrane complex. How this surface actin layer drives the various gliding modes observed in experiments—helical, circular, twirling and patch, pendulum or rolling—is unclear. Here we suggest that F-actin flows arise through self-organization and develop a continuum model of emergent F-actin flow within the confines provided by Toxoplasma geometry. In the presence of F-actin turnover, our model predicts the emergence of a steady-state mode in which actin transport is largely directed rearward. Removing F-actin turnover leads to actin patches that recirculate up and down the cell, which we observe experimentally for drug-stabilized actin bundles in live Toxoplasma gondii parasites. These distinct self-organized actin states can account for observed gliding modes, illustrating how different forms of gliding motility can emerge as an intrinsic consequence of the self-organizing properties of F-actin flow in a confined geometry.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗