An algorithm for obtaining the minimal realization of a linear time-invariant system and determining if a system is stabilizable-detectable
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Davison, E. J.↗
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An algorithm for obtaining the minimal realization of a linear time-invariant system and determining if a system is stabilizable-detectable
A definition of centralized fixed modes of a system, which is an adoption of the definition of fixed modes for a decentralized system is made. It is shown that the centralized fixed modes of a system can be easily and efficiently calculated in terms of the eigenvalues of the system, and that the calculation of such fixed modes enables one to determine, in a numerically efficient way, whether a system is controllable, observable, stabilizable, or detectable. An efficient algorithm for reducing a system to minimal realization form is then given. The algorithms have been effectively used on systems of order up to 100.
Davison, E. J.↗
A substructure coupling procedure applicable to general linear time-invariant dynamic systems
A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the non-self-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order model for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.
Howsman, T. G.↗
A substructure coupling procedure applicable to general linear time-invariant dynamic systems
A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the nonself-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order mode for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.
Howsman, T. G.↗
Control Reconfigurability of Linear Time-Invariant Systems
For any fault-tolerant control method to take effect, sufficient redundancy must exist in the plant (process) to be controlled. This paper is intended to establish a means of measuring the level of redundancy in connection with feedback control by borrowing the notion of the second-order modes. In particular, it is assumed that foreseeable faults of a process are parameterized in the model of the process. The smallest second-order mode is used as a measure of the potentiality of the process to maintain a certain performance through control reconfiguration at the occurrence of the worst faults over a prescribed set in the fault parameter space. This measure is called by the authors a control reconfigurability. The control reconfigurability is calculated for two process models to show its relevance to redundant actuating capabilities in the models.
Wu, N. Eva↗
AI-Batt (Autonomous Identification of Battery Life Models) [SWR 21-36]
Autonomous Identification of Battery Life Models (AI-Batt) AI-Batt is a MATLAB code base for developing lifetime models for batteries from accelerated aging data. The code base provides many functions for processing, visualizing, and modeling battery aging data, making the data processing, exploration, and modeling workflow substantially faster. These tools are tailored for working with battery aging data sets, which usually consist of many separate time-series for each cell, with many test conditions and possible replicates at each condition, which makes it difficult to simply process or visualize the data set. Complex modeling tasks, such as cross-validation, sensitivity analysis, and uncertainty quantification have been implemented to enable thorough statistical investigation of model predictions. Additionally, several machine-learning algorithms are implemented to autonomously identify suitable models via symbolic regression. Data processing functions automatically cast data from the struct data type, which is commonly used to store experimental data, but is not an acceptable input for most algorithms, to the table data type, which can be easily used as input to any optimization algorithm. Also, the data can be separated into time-invariant and time-variant data tables, which is helpful for exploring the data set as well as developing separate models for time-variant and time-invariant aging mechanisms. For example, in aging tests with constant temperature, temperature is a time-invariant experimental condition. Visualization tools enable plotting of data, model fits, and model simulations possible with single-line function calls, empowering data exploration of complex data sets with both time-varying and time-invariant trends. Plots can be automatically generated for the whole data set, or separated by data group (groups of test replicates) or individual data series. Data points or data series can be automatically colored by the value of a variable with a variety of color maps, and model predictions can also be colored by the value of a fit statistic. Comparisons between data sets and the predictions/simulations of different models on the same data set can be easily plotted as well. Distributions of parameter values from bootstrap resampling can be plotted to visualize the reliability of parameter estimation, or determine any correlations between parameters. Modeling tools handle the complex task of creating and parsing symbolic equations for modeling battery lifetime. Equations are parsed to grab relevant data variables, parameter values, or specified sub-models for input into optimization, evaluation, or simulation functions. Models can be optimized locally (one set of parameters for each data series), bi-level (some parameters shared across the data set), or globally (single set of parameters for all data). Functions implementing symbolic regression algorithms help users to discover effective model equations, even in poorly sampled, high-dimensional data.
Smith, Kandler [National Renewable Energy Lab. (NR↗
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↗
Stochastic Stability of Sampled Data Systems with a Jump Linear Controller
In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.
Gonzalez, Oscar R.↗
Mikhailov Stability Criterion for Time-delayed Systems
The valid and invalid application of the Mikhailov criterion to linear, time-invariant systems with time delays is discussed. The Mikhailov criterion is a graphical procedure which was developed to examine the stability of linear, time-invariant systems with no time delays. Two equivalent formulations of the criterion are discussed. Results indicate that the first formulation remains valid for time-delayed systems of the retared type, with the understanding that the Mikhailov curve need not necessarily always rotate in the counterclockwise direction for a stable system. Erroneous results in the second formulation are formed when there are time delays in the systems.
Barker, L. K.↗
An Angular Correlation Test of Time Reversal Invariance
Gamma-ray angular correlation experiment of time reversal invariance
ANGULAR CORRELATION↗
Tests of time-reversal invariance of strong interactions utilizing the Moessbauer effect.
Tests of time reversal invariance of strong interactions utilizing Mossbauer effect
Hannon, J. P.↗
Universal Fourier Attack for Time Series
A wide variety of adversarial attacks have been proposed and explored using image and audio data. These attacks are notoriously easy to generate digitally when the attacker can directly manipulate the input to a model, but are much more difficult to implement in the real world. In this paper we present a universal, time invariant attack for general time series data such that the attack has a frequency spectrum primarily composed of the frequencies present in the original data. The universality of the attack makes it fast and easy to implement as no computation is required to add it to an input, while time invariance is useful for real world deployment. Additionally, the frequency constraint ensures the attack can withstand filtering defenses. We demonstrate the effectiveness of the attack on two different classification tasks through both digital and real world experiments, and show that the attack is robust against common transform-and-compare defense pipelines.
97 MATHEMATICS AND COMPUTING↗
Elastic Model Transitions: A Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)
A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes a hybrid approach for determining physical displacements by augmenting the original quadratically constrained least squares (LSQI) algorithm with Direct Shape Mapping (DSM) and modifying the energy constraints. The approach presented is applicable to simulation of the elastic behavior of launch vehicles and other structures that utilize discrete LTI finite element model (FEM) derived mode sets (eigenvalues and eigenvectors) that are propagated throughout time. The time invariant nature of the elastic data presents a problem of how to properly transition elastic states from the prior to the new model while preserving motion across the transition and ensuring there is no truncation or excitation of the system. A previous approach utilizes a LSQI algorithm with an energy constraint to effect smooth transitions between eigenvector sets with no requirement that the models be of similar dimension or have any correlation. This approach assumes energy is conserved across the transition, which results in significant non-physical transients due to changing quasi-steady state energy between mode sets, a phenomenon seen when utilizing a truncated mode set. The computational burden of simulating a full mode set is significant so a subset of modes is often selected to reduce run time. As a result of this truncation, energy between mode sets may not be constant and solutions across transitions could produce non-physical transients. In an effort to abate these transients an improved methodology was developed based on the aforementioned approach, but this new approach can handle significant changes in energy across mode set transitions. It is proposed that physical velocities due to elastic behavior be solved for using the LSQI algorithm, but solve for displacements using a two-step process that independently addresses the quasi-steady-state and non-steady-state contributions to the elastic displacement. For structures subject to large external forces, such as thrust or atmospheric drag, it is imperative to capture these forces when solving for elastic displacement. To simplify the mathematical formulation, assumptions are made regarding mass matrix normalization, constant external forcing, and constant viscous damping. These simplifications allow for direct solutions to the quasi-steady-state displacements through a process titled Direct Shape Mapping. DSM solves for the displacements using the eigenvalues of the elastic modes and the external forcing and returns a set of elastic displacements dictated by the eigenvectors of the post-transition mode set. For the non-steady-state contributions to displacement we formulate a LSQI problem that is constrained by energy of the non-steady state terms. The contributions from the quasi-steady-state and non-steady state solutions are then combined to obtain the physical displacements associated with the new set of eigenvectors. Results for the LSQI-DSM approach show significant reduction/complete removal of transients across mode set transitions while maintaining elastic motion from the prior state. For time propagation applications employing discrete elastic models that need to be transitioned in time and where running with full a full mode set is not feasible, the method developed offers a practical solution to simulating vehicle elasticity.
Hannan, Mike R.↗
Modern control concepts in hydrology
Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.
Duong, N.↗
The application of charge-coupled device processors in automatic-control systems
The application of charge-coupled device (CCD) processors to automatic-control systems is suggested. CCD processors are a new form of semiconductor component with the unique ability to process sampled signals on an analog basis. Specific implementations of controllers are suggested for linear time-invariant, time-varying, and nonlinear systems. Typical processing time should be only a few microseconds. This form of technology may become competitive with microprocessors and minicomputers in addition to supplementing them.
Mcvey, E. S.↗
On reliable control system designs
A mathematical model for use in the design of reliable multivariable control systems is discussed with special emphasis on actuator failures and necessary actuator redundancy levels. The model consists of a linear time invariant discrete time dynamical system. Configuration changes in the system dynamics are governed by a Markov chain that includes transition probabilities from one configuration state to another. The performance index is a standard quadratic cost functional, over an infinite time interval. The actual system configuration can be deduced with a one step delay. The calculation of the optimal control law requires the solution of a set of highly coupled Riccati-like matrix difference equations. Results can be used for off-line studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.
Birdwell, J. D.↗
Aerodynamic Parameters of High Performance Aircraft Estimated from Wind Tunnel and Flight Test Data
A concept of system identification applied to high performance aircraft is introduced followed by a discussion on the identification methodology. Special emphasis is given to model postulation using time invariant and time dependent aerodynamic parameters, model structure determination and parameter estimation using ordinary least squares an mixed estimation methods, At the same time problems of data collinearity detection and its assessment are discussed. These parts of methodology are demonstrated in examples using flight data of the X-29A and X-31A aircraft. In the third example wind tunnel oscillatory data of the F-16XL model are used. A strong dependence of these data on frequency led to the development of models with unsteady aerodynamic terms in the form of indicial functions. The paper is completed by concluding remarks.
Klein, Vladislav↗
Aerodynamic Parameters of High Performance Aircraft Estimated from Wind Tunnel and Flight Test Data
A concept of system identification applied to high performance aircraft is introduced followed by a discussion on the identification methodology. Special emphasis is given to model postulation using time invariant and time dependent aerodynamic parameters, model structure determination and parameter estimation using ordinary least squares and mixed estimation methods. At the same time problems of data collinearity detection and its assessment are discussed. These parts of methodology are demonstrated in examples using flight data of the X-29A and X-31A aircraft. In the third example wind tunnel oscillatory data of the F-16XL model are used. A strong dependence of these data on frequency led to the development of models with unsteady aerodynamic terms in the form of indicial functions. The paper is completed by concluding remarks.
Klein, Vladislav↗