Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear systems”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 865 records · Page 48

Regions of stability with unequal saturation limits and non-zero set point

Constraints on the magnitudes of control variables limit the region where open-loop unstable systems can be stabilized using feedback control. Variations in regions of stability with unequal control saturation limits and non-zero set points are illustrated for single-input unstable linear systems which have one or two unstable eigenvalues. The regions of stability for saddle-point- and unstable-node-type singularities increase with the increase in one of the saturation limits, but they become invariant when the larger control limit exceeds a certain value; the stability regions vanish for non-zero set-points that saturate the controls. The unstable-focus-type singularity exhibits strikingly different characteristics. These results suggest guidelines for obtaining desired stability regions for different types of singularities.

Stengel, R. F.↗

Multidisciplinary analysis of actively controlled large flexible spacecraft

The control of Flexible Structures (COFS) program has supported the development of an analysis capability at the Langley Research Center called the Integrated Multidisciplinary Analysis Tool (IMAT) which provides an efficient data storage and transfer capability among commercial computer codes to aid in the dynamic analysis of actively controlled structures. IMAT is a system of computer programs which transfers Computer-Aided-Design (CAD) configurations, structural finite element models, material property and stress information, structural and rigid-body dynamic model information, and linear system matrices for control law formulation among various commercial applications programs through a common database. Although general in its formulation, IMAT was developed specifically to aid in the evaluation of the structures. A description of the IMAT system and results of an application of the system are given.

Cooper, Paul A.↗

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

Early Exploration of a Flexible Framework for Efficient Quantum Linear Solvers in Power Systems

The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there remain complex problems that classical computers cannot effectively address. Quantum computing, a promising technology, has the potential to fundamentally transform how we manage power systems, especially in scenarios with a higher proportion of renewable energy sources. One critical aspect is solving linear systems of equations, crucial for power system applications like power flow analysis, for which the Harrow-Hassidim-Lloyd (HHL) algorithm is a well-known quantum solution. However, HHL quantum circuits often exhibit excessive depth, making them impractical for current Noisy-Intermediate-Scale-Quantum (NISQ) devices. In this paper, we introduce a versatile framework, powered by NWQSim, that bridges the gap between power system applications and quantum linear solvers available in Qiskit. This framework empowers researchers to efficiently explore power system applications using quantum linear solvers. Through innovative gate fusion strategies, reduced circuit depth, and GPU acceleration, our simulator significantly enhances resource efficiency. Power flow case studies have demonstrated up to a eight-fold speedup compared to Qiskit Aer, all while maintaining comparable levels of accuracy.

quantum computing, Harrow-Hassidim-Lloyd, high-per↗

Development of a high stability microstrip-based L-band radiometer for ocean salinity measurements.

The development of a microstrip-based L-band Dicke radiometer with the long-term stability required for future ocean salinity measurements to an accuracy of 0.1 psu is presented. This will require the L-band radiometer requirements and configuration to achieve this objective. System configuration and component performance have been evaluated with radiometer test beds at both JPL and GSFC. The GSFC testbed uses a cryogenic chamber that al-lows long-term characterization at radiometric temperatures in the range of 70 - 120 K. The research has addressed several areas including component characterization as a function of temperature and bias, system linearity, optimum noise diode injection calibration and precision temperature control of components. A breadboard radiometer, utilizing microstrip-based technologies, has been built to demonstrate this long-term stability. This system is partially polarimetric providing V, H, -45 and +45 signals. Test results are compared to current and future ocean salinity radiometer requirements to show that the desire performance is possible.

Tanner, Alan B.↗

An Optimum Switching Criterion for a Third-order Contactor Acceleration Control System

A switching criterion for optimum performance of a third-order contractor acceleration control system having complex roots is presented. Analytical and analog-computer methods are utilized to determine this criterion. The resulting optimum transient responses are presented and compared with those of an equivalent linear system.

CONTROL, AUTOMATIC↗

Cascaded Control for Building HVAC Systems in Practice

Actuator hunting is a widespread and often neglected problem in the HVAC field. Hunting is typically characterized by sustained or intermittent oscillations, and can result in decreased efficiency, increased actuator wear, and poor setpoint tracking. Cascaded control loops have been shown to effectively linearize system dynamics and reduce the prevalence of hunting. This paper details the implementation of cascaded control architectures for Air Handling Unit chilled water valves at three university campus buildings. A framework for implementation the control in existing Building Automation software is developed that requires only a single line of additional code. Results gathered for more than a year show that cascaded control not only eliminates hunting in control loops with documented hunting issues, but provides better tracking and more consistent performance during all seasons. A discussion of efficiency losses due to hunting behavior is presented and illustrated with comparative data. Furthermore, an analysis of cost savings from implementing cascaded chilled water valve control is presented. Field tests show 2.2–4.4% energy savings, with additional potential savings from reduced operational costs (i.e., maintenance and controller retuning).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Magnetically Coupled Broadband Dual Magnetic Mass/Spring Vibrational Energy Harvesting Design

Self-powering sensors and networks are a reality. The ability to extract ambient energy from the surroundings to power electronic devices has a profound impact on the realization of smart adaptable sensor networks. In this study, a magnetically coupled dual spring and magnet design has been investigated to improve the efficiency and performance bandwidth of vibration energy harvesting (VEH) sensors. Using numerical models based on traditional systems of coupled ordinary differential equations (ODE), an optimized design was developed and compared to experimental measurements. Numerical and empirical results show good agreement. Results show improvement in the bandwidth over an equivalent linear system and corresponding improvement in output power conversion efficiency. The increased bandwidth allows improved conversion sensitivity and enhanced power harvesting capabilities. This operational bandwidth coincides with the expected input spectrum for in situ applications.

42 ENGINEERING↗

Controls and guidance research

The objectives of the control group are concentrated on research and education. The control problem of the hypersonic space vehicle represents an important and challenging issue in aerospace engineering. The work described in this report is part of our effort in developing advanced control strategies for such a system. In order to achieve the objectives stated in the NASA-CORE proposal, the tasks were divided among the group based upon their educational expertise. Within the educational component we are offering a Linear Systems and Control course for students in electrical and mechanical engineering. Also, we are proposing a new course in Digital Control Systems with a corresponding laboratory.

Homaifar, Abdollah↗

Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems

Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.

Vanek, Petr↗

Centralized, decentralized, and independent control of a flexible manipulator on a flexible base

The dynamics and control of a flexible manipulator arm with payload mass on a flexible base in space are considered. The controllers are provided by one torquer at the center of the base and one torquer at the connection joint of the robot and the base. The nonlinear dynamics of the system is modeled by applying the finite element method and Lagrangian formula. Three control strategies are considered and compared, i.e., centralized control, decentralized control, and independent control. All these control designs are based on the linear quadratic regulator theory. A mathematical decomposition is used in the decentralization process so that the coupling between the subsystems is weak, while a physical decomposition is used in the independent control design process. For both the decentralized and the independent controls, the stability of the overall linear system is checked before a numerical simulations is initiated. Two numerical examples show that the response of the independent control system are close to those of the centralized control system, while the responses of the decentralized control system are not.

Li, Feiyue↗

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗

Regions of constrained maximum likelihood parameter identifiability

This short paper considers the parameter-identification problem of general discrete-time, nonlinear, multiple input-multiple output dynamic systems with Gaussian white distributed measurement errors. Knowledge of the system parameterization is assumed to be available. Regions of constrained maximum likelihood (CML) parameter identifiability are established. A computation procedure employing interval arithmetic is proposed for finding explicit regions of parameter identifiability for the case of linear systems.

Lee, C.-H.↗

Regions of constrained maximum likelihood parameter identifiability

This paper considers the parameter identification problem of general discrete-time, nonlinear, multiple-input/multiple-output dynamic systems with Gaussian-white distributed measurement errors. Knowledge of the system parameterization is assumed to be known. Regions of constrained maximum likelihood (CML) parameter identifiability are established. A computation procedure employing interval arithmetic is proposed for finding explicit regions of parameter identifiability for the case of linear systems. It is shown that if the vector of true parameters is locally CML identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the CML estimation sequence will converge to the true parameters.

Lee, C.-H.↗

Refinement and evaluation of helicopter real-time self-adaptive active vibration controller algorithms

A Real-Time Self-Adaptive (RTSA) active vibration controller was used as the framework in developing a computer program for a generic controller that can be used to alleviate helicopter vibration. Based upon on-line identification of system parameters, the generic controller minimizes vibration in the fuselage by closed-loop implementation of higher harmonic control in the main rotor system. The new generic controller incorporates a set of improved algorithms that gives the capability to readily define many different configurations by selecting one of three different controller types (deterministic, cautious, and dual), one of two linear system models (local and global), and one or more of several methods of applying limits on control inputs (external and/or internal limits on higher harmonic pitch amplitude and rate). A helicopter rotor simulation analysis was used to evaluate the algorithms associated with the alternative controller types as applied to the four-bladed H-34 rotor mounted on the NASA Ames Rotor Test Apparatus (RTA) which represents the fuselage. After proper tuning all three controllers provide more effective vibration reduction and converge more quickly and smoothly with smaller control inputs than the initial RTSA controller (deterministic with external pitch-rate limiting). It is demonstrated that internal limiting of the control inputs a significantly improves the overall performance of the deterministic controller.

Davis, M. W.↗

Nested subcritical flows within supercritical systems

In supercritical systems the design inlet and outlet pressures are maintained above the thermaodynamic critical pressure P sub C. Designers rely on this simple rule of thumb to circumvent problems associated with a subcritical pressure regime nested within the supercritical pressure system along with the uncertainties in heat transfer, fluid mechanics, and thermophysical property variations. The simple rule of thumb is adequate in many low-power designs but is inadequate for high-performance turbomachines and linear systems, where nested two-phase regions can exist. Examples for a free-jet expansion with backpressure greater than P sub C and a rotor (bearing) with ambient pressure greater than P sub C illustrate the existence of subcritical pressure regimes nested within supercritical systems.

Hendricks, R. C.↗

System balance analysis for vector computers

The availability of vector processors capable of sustaining computing rates of 10 to the 8th power arithmetic results pers second raised the question of whether peripheral storage devices representing current technology can keep such processors supplied with data. By examining the solution of a large banded linear system on these computers, it was found that even under ideal conditions, the processors will frequently be waiting for problem data.

Knight, J. C.↗