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Results for “Reduced order systems”

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At least 109 records · Page 6

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NASA NTRS2003

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Lucia, David J.↗

NASA NTRS2015

Application of Transfer Matrix Approach to Modeling and Decentralized Control of Lattice-Based Structures

This paper presents a modeling and control of aerostructure developed by lattice-based cellular materials/components. The proposed aerostructure concept leverages a building block strategy for lattice-based components which provide great adaptability to varying ight scenarios, the needs of which are essential for in- ight wing shaping control. A decentralized structural control design is proposed that utilizes discrete-time lumped mass transfer matrix method (DT-LM-TMM). The objective is to develop an e ective reduced order model through DT-LM-TMM that can be used to design a decentralized controller for the structural control of a wing. The proposed approach developed in this paper shows that, as far as the performance of overall structural system is concerned, the reduced order model can be as e ective as the full order model in designing an optimal stabilizing controller.

Transfer Matrix Method↗

NASA NTRSDate not supplied

On Computationally Efficient Radiative Transfer Calculations for Three-dimensional Entry Problems

The current work presents an efficient simulation framework for rigorously modeling radiative fields emanating from non-equilibrium planetary entry flows in complex three-dimensional domains. Key to this endeavor is adoption of finite-volume discretization in lieu of brute-force ray tracing. This change in conjunction with mesh sweeping and Lebedev-type quadrature for angular integration allows spatial-angular resolution of radiative transfer to be performed in a computationally tractable manner. Additionally, a new methodology has been established to build standalone reduced-order spectral databases for non-equilibrium radiative properties that can be applied to a broad range of hypersonic planetary entry problems with minimal loss in accuracy. The efficacy of the new framework has been demonstrated on the atomic nitrogen radiative system. The resulting reduced-order model requires three orders-of-magnitude fewer spectral evaluations and results in a 95% decrease in memory footprint. A comparative study for representative forebody and afterbody lines-of-sight from Stardust, FIRE II, and meteor entries into the Earth atmosphere indicates that both total intensity variation and detailed spectra can be retrieved with as few as 625 reduced-order groups (contrasting with the 100,000 frequencies in the original full set model). Similarly, three-dimensional predictions of radiative heating experienced by the Orion forebody are in excellent agreement with legacy radiation solvers while requiring only a sliver (roughly 0.5%) of computing wall time.

3D radiation↗

NASA NTRSDate not supplied

On Computationally Efficient Radiative Transfer Calculations for Three-Dimensional Entry Problems

3D radiation↗

NASA NTRS1992

A fundamental theorem for the model reduction of nonlinear systems

A simple, but fundamental, theorem is given on the extent to which a nonlinear system model can have its order reduced. Essentially, the result is that the order, or the dimension of the state space representation, cannot be reduced to, or below, the dimension of the system's attractor. Several examples are given to illustrate this point. The result is especially applicable to higher order systems such as the infinite dimensional systems arising from the modeling of distributed parameter systems.

Mossayebi, Faramarz↗

NASA NTRS1992

Linear adaptive control of a single-tether system

A control law for a single-tether orbiting satellite system based on a reduced order linear adaptive control technique is presented. The main advantages of this technique are its design simplicity and the facts that specific system parameters and model linearization are not required when designing the controller. Two controllers are developed: one which uses only tension in the tether as control actuation and one which uses both tension and in-plane thrusters as control actuation. Both a sixth-order nonlinear and an 11th-order bead model of a tethered satellite system are used for simulation purposes, demonstrating the ability of the controller to manage an uncertain system. Retrieval and stationkeeping results using these nonlinear models and the linear adaptive controller demonstrate the feasibility of the method. The robustness of the controller with respect to parameter uncertainties is also demonstrated by changing the nonlinear model and parameters within the model without redesigning the controller.

Greene, M. E.↗

NASA NTRS1991

Structural representation for analysis of a controlled structure

The purpose was to determine what reduced order structural representation is most appropriate for coupling with a control system. The goal was to choose a reduced order structural model which retains as closely as possible the characteristics of the closed loop model with a full order structural representation. By characteristics of the closed loop model, it is meant that the closed loop eigenvalues and the closed loop transfer functions from commands to loads and from commands to response. This process does not address the accuracy of the full order model (usually a finite element model) but only the loss of accuracy associated with reducing th model. For the purposes of this study, only collocated sensors and actuators are examined. The choice of a structural representation for noncollocated sensors and actuators is not so clear.

Blelloch, Paul A.↗

NASA NTRS1990

Mars outpost - System and operations challenges

The paper addresses the challenges inherent in establishing an outpost on the planet Mars. For background purposes, the unique, remote Martian environment and the developmental phases of a settlement in such an environment are discussed. Challenges are identified in terms of surface systems and operations. Due to its importance to habitability, the life support system (LSS) is highlighted with various options identified. Operations for the Mars outpost, earth-based and local, are characterized by a decentralized concept. The challenge of integrating logistics analysis early in system design and operations strategy is also addressed. In order to understand and reduce the system and operations challenges, the application of terrestrial and lunar testbeds is explained.

Roberts, Barney↗

NASA NTRS1973

A reduced adaptive observer for multivariable systems

An adaptive observer for multivariable systems is presented for which the dynamic order of the observer is reduced, subject to mild restrictions. The observer structure depends directly upon the multivariable structure of the system rather than a transformation to a single-output system. The number of adaptive gains is at most the sum of the order of the system and the number of input parameters being adapted. Moreover, for the relatively frequent specific cases for which the number of required adaptive gains is less than the sum of system order and input parameters, the number of these gains is easily determined by inspection of the system structure. This adaptive observer possesses all the properties ascribed to the single-input single-output adpative observer. Like the other adaptive observers some restriction is required of the allowable system command input to guarantee convergence of the adaptive algorithm, but the restriction is more lenient than that required by the full-order multivariable observer. This reduced observer is not restricted to cycle systems.

Carroll, R. L.↗

NASA NTRS1992

Model reduction using new optimal Routh approximant technique

An optimal Routh approximant of a single-input single-output dynamic system is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is determined by minimizing a time-response integral-squared-error (ISE) criterion. In this paper, a new elegant approach is presented for obtaining the optimal Routh approximants for linear time-invariant continuous-time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear Routh approximants of linear time-invariant discrete-time systems. The proposed technique is simple in formulation and is amenable to practical implementation.

Hwang, Chyi↗

DOE OSTI2026

Evaluation of a Reduced-Order Model for IBR Fault Response Representation via OEM Blackbox Models

This paper presents a fully implemented inverter reduced-order-model (ROM) in an EMT simulation (PSCAD) library component for direct user utilization in protection studies. The developed inverter ROM has the following features: Equivalent to a full inverter-based resource (IBR) inverter model with positive- and negative-sequence current formulation and representation. A Python script is developed to fully automate this process, including training data generation, ROM parameter training, updating parameters, and model verification and validation. The ROM is validated using both IEEE 2800-compliant and non-compliant OEM modes in a real-world system, building confidence of its usability by protection engineers.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1999

Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Ravindran, S. S.↗

NASA NTRS1996

Re-Engineering of the Hubble Space Telescope (HST) to Reduce Operational Costs

Satellite telemetry processing onboard the Hubble Space Telescope (HST) is carried out using dedicated software and hardware. The current ground system is expensive to operate and maintain. The mandate to reduce satellite ground system operations and maintenance costs by the year 2000 led NASA to upgrade the command and control systems in order to improve the data processing capabilities, reduce operator experience levels and increase system standardization. As a result, a command and control system product development team was formed to redesign and develop the HST ground system. The command and control system ground system development consists of six elements. The results of the prototyping phase carried out for the following of these elements are presented: the front end processor; middleware, and the graphical user interface.

Garvis, Michael↗

NASA NTRS2018

Assessment of the Mars Helicopter Thermal Design Sensitivities Using the Veritrek Software

The Mars Helicopter will be a technology demonstration conducted during the Mars 2020 mission. The primary mission objective is to achieve several 90-second flights and capture visible light images via forward and nadir mounted cameras. These flights could possibly provide reconnaissance data for sampling site selection for other Mars surface missions. The helicopter is powered by a solar array, which stores energy in secondary batteries for flight operations, imaging, communications, and survival heating. The helicopter thermal design is driven by minimizing survival heater energy while maintaining compliance with allowable flight temperatures in a variable thermal environment. Due to the small size of the helicopter and its complex geometries, along with the fact that it operates with very low power and small margins, additional care had to be paid while planning thermal tests and designing the thermal system. A Thermal Desktop® model has been developed to predict the thermal system’s performance. A reduced-order model (ROM) created with the Veritrek software has been utilized to explore the sensitivities of the thermal system’s drivers, such as electronics dissipations, gas gaps, heat transfer coefficients, etc., as well as to assess and verify the final thermal design. This paper presents the performance of the Veritrek software products and the details of the ROM creation process. The results produced by Veritrek were utilized to study the effect of the major thermal design drivers and Mars environment on the Mars Helicopter in as little as 10 days, an effort that would have taken over 4 months using traditional thermal analysis techniques.

Hengeveld, Derek W.↗

DOE OSTI2025

An Optimization-Based Coupling of Reduced Order Models with an Efficient Reduced Adjoint Basis Generation Approach

Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.

coupled problems↗

DOE OSTI2024

Effect of parallel flow on resonant layer responses in high beta plasmas

Abstract Resonant layers in a tokamak respond to non-axisymmetric magnetic perturbations by amplifying the mode amplitude and balancing the plasma rotation through magnetic reconnection and force balance, respectively. This resonant response can be characterized by local layer parameters and especially by a single quantity in the linear regime, the so-called inner-layer Δ. The computation of Δ under two-fluid drift-MHD formalism has been progressed by reducing the order of the system in the phase space, where the shielding current is approximated as being only carried by electrons, a posteriori . In this study, we relax the approximation and compute Δ accounted for by the parallel flow associated with the ion shielding current. The posteriori is numerically verified in great agreement with the original SLAYER developed in a previous paper (J.-K. Park 2022 Phys. Plasmas 29 072506). Extending the resonant layer response theory to high β plasmas, our research findings answer two important questions: how the parallel flow influences the resonant layer response and why the parallel flow effect appears in high β plasmas. The complicated plasma compression in high β regime allows the parallel flow response to give rise to the ion shielding current, which not only shifts the zero-crossing condition of the ExB flow but also enhances the field penetration threshold. Technically, the Riccati matrix transformation method is adapted to handle the numerical stiffness due to the increased order of the system. The high fidelity of this numerical method makes use of further extension of the model to higher-order systems to take other physical phenomena into account. This work is envisaged to predict the resonant layer response under high β fusion reactor conditions.

Lee, Yeongsun (ORCID:000000034474416X)↗

NASA NTRS1988

Application of the Thurston bifurcation solution strategy to problems with modal interaction

The solution of bifurcation problems with closely-spaced critical points is achieved by first separating the singular part of the equation system encountered during a Newton iteration and carrying the Taylor expansion of the reduced system out to higher order. This separation is accomplished by transforming the equation system into an equivalent system in which some of the original unknowns are replaced with an equal number of modal amplitude coefficients. This method was used to continue the analysis of two significant example problems well past multiple fiburcation points, allowing a detailed examination of postbuckling behavior in the presence of modal interaction.

Rankin, C. C.↗

NASA NTRS1990

Optimal model reduction and frequency-weighted extension

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. The existence of globally optimal stable solutions to the optimization problem is established, and convergence of the algorithm to stationary values of the cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗