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At least 1,207 records · Page 67

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NASA NTRS1999

Dynamical Signatures of Living Systems

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Zak, M.↗

DOE OSTI2023

Model-based predictive control of multi-stage air-source heat pumps integrated with phase change material-embedded ceilings

This paper presents a model-based predictive control strategy to optimize the operations of phase change material (PCM) ceiling panels coupled with a multi-stage air-source heat pump. A three-stage prototype heat pump unit has been built and tested in the laboratory, with the low and medium stages designed for space heating/cooling and the high compression stage dedicated to charging of the PCM energy storage. To facilitate optimal control of the integrated heat pump system, a mixed-integer linear programming formulation is derived through linearization of the heat pump model and a mixed-integer reformulation of the PCM dynamic governing equations. A predictive control strategy is synthesized based on the resultant control formulation and implemented in a receding horizon scheme that optimizes the PCM charging and the zone temperature schedules simultaneously to leverage both the passive (associated with building construction materials) and active (PCM) storage capacities of a building. The control strategy has been tested along with three benchmarking control scenarios using a co-simulation platform for a prototypical detached house in Atlanta, GA. In this study, test results showed that application of the proposed control strategy to the PCM-integrated heat pump could provide 27.1% electricity cost savings while a fine tuned rule-based control strategy could achieve cost savings of 20.4%, compared to a baseline case without PCM storage, under a time-of-use rate tariff.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Dynamically reconfigurable topological routing in nonlinear photonic systems

The propagation path of topologically protected states is bound to the interface between regions with different topology, and as such, the functionality of linear photonic devices leveraging these states is fixed during fabrication. Here, we propose a mechanism for dynamic control over a driven dissipative system’s local topology, yielding reconfigurable topological interfaces and thus tunable paths for protected routing. We illustrate our approach in non-resonantly pumped polariton lattices, where the nonlinear interaction between the polaritons and the exciton reservoir due to non-resonant pumping can yield picosecond-scale changes in the propagation paths of the chiral edge states. To analytically confirm the numerically observed topological dynamics, we generalize the spectral localizer framework to non-linear non-Hermitian Chern materials and apply this framework to a continuous model of the polariton system based on a driven-dissipative Gross-Pitaevskii equation. In doing so, we show that the local changes in the polariton lattice’s topology are captured by a local Chern marker. Looking forward, we anticipate such reconfigurable topological routing will enable the realization of novel classes of topological photonic devices.

Wong, Stephan [Sandia National Laboratories (SNL-N↗

NASA NTRS1972

Random gravitational encounters and the evolution of spherical systems. III - Halo.

The accumulation of stars in the halo of a spherical stellar system, together with the escape of stars from the system, result from stellar encounters within a dense central core. The resultant halo structure is studied both analytically and numerically for an isolated system. On the assumption that conditions in the central core remain constant with time, a simple steady-state solution is obtained for the outermost halo, or 'fringe', defined as the region from which stars may escape after a few additional orbits through the central core of the system. In this steady-state solution the density in phase space, obtained from a simple integral equation for the fringe region, is found to vary nearly linearly with the total energy of a star per unit mass for energies which are less than the energy of escape.

Spitzer, L., Jr.↗

NASA NTRS1976

Gaussian ideal impulsive loading of rigid viscoplastic plates

The response of a thin, rigid, viscoplastic plate subjected to a spatially axisymmetric Gaussian ideal impulse loading was studied analytically. The Gaussian ideal impulse distribution instantaneously imparts a Gaussian initial velocity distribution to the plate, except at the fixed boundary. The plate deforms with monotonically increasing deflections until the initial dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid, viscoplastic materials. For the small deflection bending response of the plate, neglecting the transverse shear stress in the yield condition and rotary inertia in the equations of dynamic equilibrium, the governing system of equations is essentially nonlinear. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and obtain analytical solution in the form of eigenvalue expansions. The linearized governing equations required the knowledge of the collapse load of the corresponding static problem.

Hayduk, R. J.↗

NASA NTRS1976

NASA Ames potential flow analysis (POTFAN) geometry program (POTGEM), version 1

A computer program known as POTGEM is reported which has been developed as an independent segment of a three-dimensional linearized, potential flow analysis system and which is used to generate a panel point description of arbitrary, three-dimensional bodies from convenient engineering descriptions consisting of equations and/or tables. Due to the independent, modular nature of the program, it may be used to generate corner points for other computer programs.

Medan, R. T.↗

NASA NTRS1979

Bilinear tangent yaw guidance

This paper presents a parametric yaw steering law which has been used to provide closed-loop yaw guidance for the launch of the HEAO (High Energy Astronomy Observatory) satellite mission using the Atlas/Centaur launch vehicle. This bilinear tangent steering law provides near optimal yaw steering for maneuvers requiring insertion into orbits with a specified inclination and node. Bilinear tangent steering is shown to be optimal in both the pitch and yaw planes when a uniform gravitational field is assumed. The conditions under which the general bilinear tangent laws degenerate into linear tangent and constant attitude laws are presented. The flight computer implementation of these laws in a rotating coordinate system using real-time integration of the equations of motion is detailed. Explicit solution of the parametric guidance equations requires the inflight solution of (2x2) two-point boundary value problems in the pitch and yaw planes. Excellent results are obtained even for very large (greater than 50 deg) out-of-plane steering angles.

Brusch, R. G.↗

NASA NTRS1981

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

Magnus, A. E.↗

NASA NTRS1984

Goertler instability of compressible boundary layers

The instability of the laminar compressible boundary-layer flows along concave surfaces is investigated. The linearized disturbance equations for the three-dimensional, counter-rotating, longitudinal-type vortices in two-dimensional boundary layers are presented in an orthogonal curvilinear system of coordinates. The basic approximation of the disturbance equations, which includes the effect of the growth of the boundary layer, is considered and solved numerically.

El-Hady, N. M.↗

NASA NTRS1984

Electron precipitation in solar flares - Collisionless effects

A large fraction of the electrons which are accelerated during the impulsive phase of solar flares stream towards the chromosphere and are unstable to the growth of plasma waves. The linear and nonlinear evolution of plasma waves as a function of time is analyzed with a set of rate equations that follows, in time, the nonlinearly coupled system of plasma waves-ion fluctuations. As an outcome of the fast transfer of wave energy from the beam to the ambient plasma, nonthermal electron tails are formed which can stabilize the anomalous Doppler resonance instability responsible for the pitch angle scattering of the beam electrons. The non-collisional losses of the precipitating electrons are estimated, and the observational implication of these results are discussed.

Vlahos, L.↗

NASA NTRS1985

Exact spacecraft detumbling and reorientation maneuvers with gimbaled thrusters and reaction wheels

The equations of rotational motion for a spacecraft equipped with external jets and internal reaction wheels are shown to be feedback-equivalent to those of a linear system in attitude parameter space. Reorientation maneuvers are thereby formulated as linear optimal control problems with least mean square acceleration in attitude parameter space, solved in closed form and implementable either with internal or external torque commands, the choice depending on power and throttling requirements. For prior detumbling, an alternative solution with least mean square torque by angular momentum feedback is also given, that is implementable with gimbaled pairs of thrusters at constant throttle. Such a detumbling maneuver may then be followed by an acceleration-commanded rest-to-rest maneuver by means of the reaction wheels.

Dwyer, T. A. W., III↗

NASA NTRS1985

On-three time scale analysis

In the present consideration of a three-timescale system, a block diagonalization employing three-stage linear transformations is used to decouple the original system into slow, fast, and faster subsystems. A numerical algorithm is given to solve the resulting Ricatti-type equations, and the technique is verified for the case of a ninth-order example. The technique yields substantial computational requirment reductions, since it involves subsystems that are of a lower order than the original system.

Naidu, D. S.↗

NASA NTRS1992

Derivation and application of hard deadlines for real-time control systems

The computation-time delay in the feedback controller of a real-time control system may cause failure to update the control input during one or more sampling periods. If this delay exceeds a certain limit called a hard deadline, either the necessary conditions for system stability are violated or the system leaves the allowed state-space. In such a case a dynamic failure is said to occur to the system. A method for calculating the hard deadlines in linear time-invariant control systems by considering system stability and the allowed state-space is presented. To derive necessary conditions for (asymptotic) system stability, the state difference equation is modified based on an assumed maximum delay and the probability distribution of delays whose magnitudes are less than, or equal to, the assumed maximum delay. Moreover, the allowed state-space - which is derived from given input and state constraints - is used to calculate the hard deadline as a function of time and the system state. A one-shot delay model in which a single event causes a dynamic failure is also considered. The knowledge of hard deadline is then applied to the design of error recovery in a triple modular redundant (TMR) controller computer.

Shin, Kang G.↗

NASA NTRS1999

Real-Time Simulation of the X-33 Aerospace Engine

This paper discusses the development and performance of the X-33 Aerospike Engine RealTime Model. This model was developed for the purposes of control law development, six degree-of-freedom trajectory analysis, vehicle system integration testing, and hardware-in-the loop controller verification. The Real-Time Model uses time-step marching solution of non-linear differential equations representing the physical processes involved in the operation of a liquid propellant rocket engine, albeit in a simplified form. These processes include heat transfer, fluid dynamics, combustion, and turbomachine performance. Two engine models are typically employed in order to accurately model maneuvering and the powerpack-out condition where the power section of one engine is used to supply propellants to both engines if one engine malfunctions. The X-33 Real-Time Model is compared to actual hot fire test data and is been found to be in good agreement.

Aguilar, Robert↗

NASA NTRS2006

An Empirical Comparison between Two Recursive Filters for Attitude and Rate Estimation of Spinning Spacecraft

The advantages of inducing a constant spin rate on a spacecraft are well known. A variety of science missions have used this technique as a relatively low cost method for conducting science. Starting in the late 1970s, NASA focused on building spacecraft using 3-axis control as opposed to the single-axis control mentioned above. Considerable effort was expended toward sensor and control system development, as well as the development of ground systems to independently process the data. As a result, spinning spacecraft development and their resulting ground system development stagnated. In the 1990s, shrinking budgets made spinning spacecraft an attractive option for science. The attitude requirements for recent spinning spacecraft are more stringent and the ground systems must be enhanced in order to provide the necessary attitude estimation accuracy. Since spinning spacecraft (SC) typically have no gyroscopes for measuring attitude rate, any new estimator would need to rely on the spacecraft dynamics equations. One estimation technique that utilized the SC dynamics and has been used successfully in 3-axis gyro-less spacecraft ground systems is the pseudo-linear Kalman filter algorithm. Consequently, a pseudo-linear Kalman filter has been developed which directly estimates the spacecraft attitude quaternion and rate for a spinning SC. Recently, a filter using Markley variables was developed specifically for spinning spacecraft. The pseudo-linear Kalman filter has the advantage of being easier to implement but estimates the quaternion which, due to the relatively high spinning rate, changes rapidly for a spinning spacecraft. The Markley variable filter is more complicated to implement but, being based on the SC angular momentum, estimates parameters which vary slowly. This paper presents a comparison of the performance of these two filters. Monte-Carlo simulation runs will be presented which demonstrate the advantages and disadvantages of both filters.

Harman, Richard R.↗

NASA NTRSDate not supplied

Electromagnetic Modeling of Wind tunnel Magnetic Suspension and Balance Systems

An analytical framework for the open-loop behavior of a permanent magnet element levitated within an applied magnetic field are shown, in the context of application to wind tunnel Magnetic Suspension and Balance Systems (MSBS). Various modes of motion are identified, which correlate with observed behavior of the NASA/ODU 6-inch MSBS. This system is being developed as a technology demonstrator for dynamic stability testing of atmospheric entry capsules, with possible application to a supersonic wind tunnel. The analytic equations are populated with field information from experimental measurements and a finite element model. Finally, a system simulation can provide alternative estimates of system dynamic behavior via model linearization, with preliminary comparisons presented. Taken together, the analytical framework, experimental measurement, finite element analysis, and dynamic simulation provide a complete understanding of the characteristics and behavior of the MSBS.

magnetic suspension↗

NASA NTRS1984

A degree of controllability definition - Fundamental concepts and application to modal systems

Starting from basic physical considerations, this paper develops a concept of the degree of controllability of a control system, and then develops numerical methods to generate approximate values of the degree of controllability for any linear time-invariant system. In many problems, such as the control of future, very large, flexible spacecraft and certain chemical process control problems, the question of how to choose the number and locations of the control system actuators is an important one. The results obtained here offer the control system designer a tool which allows him to rank the effectiveness of alternative actuator distributions, and hence to choose the actuator locations on a rational basis. The degree of controllability is shown to take a particularly simple form when the dynamic equations of a satellite are in second-order modal form. The degree of controllability concept has still other fundamental uses - it allows one to study the system structural relations between the various inputs and outputs of a linear system, which has applications to decoupling and model reduction.

Viswanathan, C. N.↗

NASA NTRS1985

On the factorization of block-tridiagonals without storage constraints

In many programs solving difference equations, problem size is restricted by the number of available memory cells. A strategy has been developed to permit trade-offs between the number of floating point operations required and storage requirements for the solution of certain problems such as block tridiagonal systems of equations. This is done by recomputing some intermediate results instead of storing them. Reducing the storage to the square root of the current requirement will roughly double the number of computations. In theory, if m is the order of each sub-matrix in the block tridiagonal matrix, one can solve any linear system with only 5 sq m + 1 temporary storage cells. This method lends itself to efficient use on computers with parallel processing or vector processing architectures. On these computers the larger number of floating point operations is more than offset by the decrease in I/O and the increased percentage of vector operations made possible by this algorithm.

Merriam, M. L.↗