Optimal waveform design via control theoretic concepts.
Design of optimal waveforms for optimal estimation or prediction of state of linear dynamical system in presence of Markov and white noise
SYSTEMS DESIGN↗
SEARCH · Engineering Papers
Results for “Linear dynamics”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Compensating slice emittance growth in high brightness photoinjectors using sacrificial charge
Achieving maximum electron beam brightness in photoinjectors requires detailed control of the 3D bunch shape and precise tuning of the beam focusing. Even in state-of-the-art designs, slice emittance growth due to nonlinear space charge forces and partial nonlaminarity often remains non-negligible. In this work, we introduce a new means to linearize the transverse slice phase space: a sacrificial portion of the bunch’s own charge distribution, formed into a wavebroken shock front by highly nonlinear space charge forces within the gun, whose downstream purpose is to dynamically linearize the desired bunch core. We show that linearization of an appropriately prepared bunch can be achieved via strongly nonlaminar focusing of the sacrificial shock front, while the inner core focuses laminarly. This leads to a natural spatial separation of the two distributions: a dense core surrounded by a diffuse halo of sacrificial charge that can be collimated. Multiobjective genetic algorithm optimizations of the ultracompact x-ray free electron laser injector employ this concept, and we interpret it with an analytic model that agrees well with the simulations. In simulation, we demonstrate a final bunch charge of 100 pC, peak current ∼ 30 A, and a sacrificial charge of 150 pC (250 pC total emitted from cathode) with normalized emittance growth of < 20 nm rad due to space charge. This implies a maximum achievable brightness approximately an order of magnitude greater than existing free electron laser injector designs. Published by the American Physical Society 2024
43 PARTICLE ACCELERATORS↗
Multi-flexible-body dynamics capturing motion-induced stiffness
A multi-flexible-body dynamics formulation incorporating a recently developed theory for capturing motion induced stiffness for a arbitrary structure undergoing large rotation and translation accompanied by small vibrations is presented. In essence, the method consists of correcting prematurely linearized dynamical equations for an arbitrary flexible body with generalized active forces due to geometric stiffness corresponding to a system of twelve inertia forces and nine inertia couples distributed over the body. Equations of motion are derived by means of Kane's method. A useful feature of the formulation is its treatment of prescribed motions and interaction forces. Results of simulations of motions of three flexible spacecraft, involving stiffening during spinup motion, dynamic buckling, and a repositioning maneuver, demonstrate the validity and generality of the theory.
Banerjee, Arun K.↗
Wide Dynamic Range, 10 kHz Framing Detector for 4D-STEM
Hybrid pixel array detectors (PADs) have expanded the fidelity, frame rate and dynamic range for diffractive imaging in electron microscopes. With their high detective quantum efficiencies (DQE), the noise performance limited is by counting statistics. Consequently, improving the precision and quality of high-speed images requires increasing the linear dynamic range and the maximum usable beam current. Here we describe a new prototype hybrid PAD, our next-generation electron microscope pixel array detector (NG-EMPAD) that expands both the framing speed and dynamic range of our earlier EMPAD design. Like the EMPAD, electrons are detected directly in a 500 μm thick silicon sensor bonded pixel-by-pixel to a custom signal processing integrated circuit (IC). Each pixel in the IC integrates charge carriers produced by the high-energy incident electrons. Here, in-pixel circuitry uses a combination of techniques to extend the dynamic range, including adaptive gain switching and the quantitative excess charge dumping similar to the EMPAD. In-pixel buffering of signals during readout allows acquiring a new image while reading out the previously collected image, yielding an image collection duty cycle of nearly 100%.
36 MATERIALS SCIENCE↗
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↗
Space time neural networks for tether operations in space
A space shuttle flight scheduled for 1992 will attempt to prove the feasibility of operating tethered payloads in earth orbit. due to the interaction between the Earth's magnetic field and current pulsing through the tether, the tethered system may exhibit a circular transverse oscillation referred to as the 'skiprope' phenomenon. Effective damping of skiprope motion depends on rapid and accurate detection of skiprope magnitude and phase. Because of non-linear dynamic coupling, the satellite attitude behavior has characteristic oscillations during the skiprope motion. Since the satellite attitude motion has many other perturbations, the relationship between the skiprope parameters and attitude time history is very involved and non-linear. We propose a Space-Time Neural Network implementation for filtering satellite rate gyro data to rapidly detect and predict skiprope magnitude and phase. Training and testing of the skiprope detection system will be performed using a validated Orbital Operations Simulator and Space-Time Neural Network software developed in the Software Technology Branch at NASA's Lyndon B. Johnson Space Center.
Lea, Robert N.↗
A Guide to Forced Oscillation Data Processing and Analysis
The NASA Langley Research Center Flight Dynamics Branch has a long history of experimental testing of aircraft and spacecraft flight dynamics. One of the frequently used wind tunnel test methods is forced oscillation testing. This method involves a model mounted on a specialized dynamic test rig in a tunnel and oscillated about a body axis, typically at a fixed sinusoidal frequency and amplitude. This report provides the derivation of two commonly used data reduction methods and introduces one new method to extract the linear dynamic derivatives from forced oscillation wind tunnel data.
Flight Dynamics↗
Revising the dynamic energy budget theory with a new reserve mobilization rule and three example applications to bacterial growth
Dynamic energy budget (DEB) theory has been applied to model a wide range of organisms, including microbes. In the standard DEB model, biomass is partitioned into reserve and structural compartments, where reserve biomass is mobilized in a pseudolinear manner (while the reserve biomass density, defined as the ratio between reserve and structural biomass, decays linearly) to drive maintenance and the growth of structural biomass (and extracellular enzyme production if it is considered). However, the linear dynamics of the reserve biomass density makes the standard DEB model incapable of explaining the slowdown of microbial growth at high reserve density that is caused by macromolecular crowding effect which reduces biochemical reaction rates (a typical situation occurs when microbes are experiencing severe moisture stress) and is inconsistent with the observation that intracellular enzymatic reactions generally follow non-linear kinetics. By partitioning biomass into reserve, kinetic, and structural compartments, we show here that the Equilibrium Chemistry Approximation (ECA) kinetics can be used to represent enzymatically catalyzed reserve biomass mobilization that can then drive the kinetic and structural biomass synthesis. This revised DEB model better represents the tradeoff in ribosome allocation for structural growth and internal enzyme production, is structurally compatible with metabolic models of cell individuals, and includes the standard DEB model and the popular compromise model as special cases for representing population growth. We then applied the revised DEB model to interpret components of bacterial respiration, their dependence on substrate availability, and emergent microbial carbon use efficiency dynamics for an exponentially growing population. We found that the revised DEB model enables a better understanding of bacterial substrates use (carbon in our examples) than that can be derived from a few other models in the literature. In particular, the revised DEB model explains why carbon use efficiency may first increase, then plateau, and finally decrease with growth rate (and substrate uptake rate), as a function of proteomics. Additionally, the revised DEB model explains why the kinetic biomass compartment needs to be divided to reasonably incorporate proteomic control of microbial growth.
59 BASIC BIOLOGICAL SCIENCES↗
An optimal discrete control strategy for interplanetary guidance.
Guiding one state of linear dynamical system to prescribed rms terminal accuracy in presence of injection, measurement and engine-mechanization error
ROOT-MEAN-SQUARE ERROR↗
Robustness of extended-Kalman-type observers
Robustness properties of extended-Kalman-type observers are investigated for linear plants when actuators and sensors have non-linearities or linear dynamics. Sufficient conditions for the stability of the estimation error are obtained for time-varying extended Kalman filters (EKF) for time-varying plants, and for constant-gain, exponentially weighted EKF for time-invariant plants. When the non-linearities are known only within bands of uncertainty, it is proved that the observer is non-divergent.
Joshi, S. M.↗
Exact Linearization For Control Of Robots
Equivalence of several theoretical approaches discussed. Report comments on application of geometric control theory (GCT), resolved-acceleration control (RAC), operational-space control (OSC), and nonlinear-decoupling theory (NDT) to remote manipulator consisting of multiple rigid links. Principal concern, search for nonlinear feedback law making end effector behave, for purposes of control, as though its dynamics linear and decoupled.
Kreutz, Kenneth K.↗
Gain optimization with non-linear controls
An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.
Slater, G. L.↗
The structure of robust observers
Conventional observers for linear time-invariant systems are shown to be structurally inadequate from a sensitivity standpoint. It is proved that if a linear dynamic system is to provide observer action despite arbitrary small perturbations in a specified subset of its parameters, it must: (1) be a closed loop system, be driven by the observer error, (2) possess redundancy, the observer must be generating, implicitly or explicitly, at least one linear combination of states that is already contained in the measurements, and (3) contain a perturbation-free model of the portion of the system observable from the external input to the observer. The procedure for design of robust observers possessing the above structural features is established and discussed.
Bhattacharyya, S. P.↗
Magnetic reconnection in incompressible fluids
The paper investigates the dynamical relaxation of a disturbed X-type magnetic neutral point in a periodic geometry, with an ignorable coordinate, for an incompressible fluid. It is found that the properties of the current sheet cannot be understood in terms of steady state reconnection theory or more recent linear dynamical solutions. Accordingly, a new scaling law for magnetic reconnection is presented, consistent with fast energy dissipation (i.e., the dissipation rate at current maximum is approximately independent of magnetic diffusivity (eta)). The flux annihilation rate, however, scales at eta exp 1/4, faster than the Sweet-Parker rate of sq rt eta but asymptotically much slower than the dissipation rate. These results suggest a flux pile-up regime in which the bulk of the free magnetic energy is released as heat rather than as kinetic energy of mass motion. The implications of our results for reconnection in the solar atmosphere and interior are discussed.
Deluca, Edward E.↗
Dynamics of Permanent-Magnet Biased Active Magnetic Bearings
Active magnetic radial bearings are constructed with a combination of permanent magnets to provide bias forces and electromagnets to generate control forces for the reduction of cost and the operating energy consumption. Ring-shaped permanent magnets with axial magnetization are attached to a shaft and share their magnet stators with the electromagnets. The magnet cores are made of solid iron for simplicity. A simplified magnetic circuit of the combined magnet system is analyzed with linear circuit theory by approximating the characteristics of permanent magnets with a linear relation. A linearized dynamical model of the control force is presented with the first-order approximation of the effects of eddy currents. Frequency responses of the rotor motion to disturbance inputs and the motion for impulsive forces are tested in the non-rotating state. The frequency responses are compared with numerical results. The decay of rotor speed due to magnetic braking is examined. The experimental results and the presented linearized model are similar to those of the all-electromagnetic design.
Fukata, Satoru↗
Helistat simulation studies
An analysis of the flight dynamics and piloted control characteristics of the Helistat, a quadrotor heavy-lift airship, was completed using the HYBRDS airship simulation facility. The analysis covered the full operating flight envelope, including likely ranges of altitude, airspeed, sideslip, and loading variations. Particular areas of study were performance, trim, power requirements, linearized dynamics, handling qualities, and mooring operations. The key assumptions were: a rigid vehicle, no control system dynamics, fixed rotor and propeller RPM, and no ballonet dynamics. The nominal cruise speed for the H34 engines operating at 1275 HP was found to be 40-50 kts, depending on the loading condition. The maximum payload capability was calculated as 45,000 lbs for sea level-based operations. The crosswind capability in hover is 5-10 kts depending on the loading conditions, but this requires excessive roll angle due to the roll-to-translate control gearing. Sideslip angles of 110-135 degrees (wind from aft quarters) are critical for directional trim and stability, and should be avoided.
Tischler, M. B.↗
Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria
The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Analysis and simulation of a magnetic bearing suspension system for a laboratory model annular momentum control device
A linear analysis and the results of a nonlinear simulation of a magnetic bearing suspension system which uses permanent magnet flux biasing are presented. The magnetic bearing suspension is part of a 4068 N-m-s (3000 lb-ft-sec) laboratory model annular momentum control device (AMCD). The simulation includes rigid body rim dynamics, linear and nonlinear axial actuators, linear radial actuators, axial and radial rim warp, and power supply and power driver current limits.
Groom, N. J.↗