Study on determining stability domains for nonlinear dynamical systems, II Quarterly progress report, 1 Aug. - 31 Oct. 1966
Stability domain determination for nonlinear dynamical system
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Stability domain determination for nonlinear dynamical system
Criterion for optimum design of quantizer imbedded in closed loop dynamic system is optimization of overall system performance expressed by variational criterion
Motion stability and instability of dynamic systems with many degrees of freedom, and relation between exact and approximate solutions
MOVER uses experimental data to verify mathematical models of "mixed" dynamic systems. The term "mixed" refers to interactive mechanical, hydraulic, electrical, and other components. Program compares analytical transfer functions with experiment.
A nonparametric identification technique for the identification of close coupled dynamic systems with arbitrary memoryless nonlinearities is presented. The method utilizes noisy recorded data (acceleration, velocity and displacement) to identify the restoring forces in the system. The masses in the system are assumed to be known (or fairly well estimated from the design drawings). The restoring forces are expanded in a series of orthogonal polnomials and the coefficients of these polynomial expansions are obtained by using least square fit method. A particularly simple and computationally efficient method is proposed for dealing with separable restoring forces. The identified results are found to be relatively insensitive to measurement noise. An analysis of the effects of measurement noise on the quality of the estimates is given. The computations are shown to be relatively quick (when compared say to the Wiener identification method) and the core storage required relatively small, making the method suitable for onboard identification of large space structures.
This report summarizes the overall history of the Flight Dynamics System (FDS) applications software conversion project. It describes the background and nature of the project; traces the actual course of conversion; assesses the process, product, and personnel involved; and offers suggestions for future projects. It also contains lists of pertinent reference material and examples of supporting data.
A framework to build simulation models for aircraft dynamic systems integration is described. The objective of the framework is increased simulation model fidelity and reduced time required to develop and modify these models. The equations of motion for an elastic aircraft and their impact on the framework are discussed in broad terms. A software tool which automatically generates FORTRAN routines for tabular data lookups, the language used to develop a simulation model, and the structures for passing information into a simulation are discussed. A simulation variable nomenclature is presented. The framework has been applied to build an open-loop F/A-18 simulation model. This example model is used to illustrate model reduction issues. Current deficiencies in the framework are identified as areas for future research.
Techniques of predicting and/or controlling the dynamic behavior of large scale systems are discussed in terms of decentralized decision making. Topics discussed include: (1) control of large scale systems by dynamic team with delayed information sharing; (2) dynamic resource allocation problems by a team (hierarchical structure with a coordinator); and (3) some problems related to the construction of a model of reduced dimension.
Algebraic methods for application to dynamic control systems
The problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.
The Small Modular Reactor (SMR) Dynamic System Modeling Tool project is in the third year of development. The project is designed to support collaborative modeling and study of various advanced SMR (non-light water cooled) concepts, including the use of multiple coupled reactors at a single site. The objective of the project is to provide a common simulation environment and baseline modeling resources to facilitate rapid development of dynamic advanced reactor SMR models, ensure consistency among research products within the Instrumentation, Controls, and Human-Machine Interface (ICHMI) technical area, and leverage cross-cutting capabilities while minimizing duplication of effort. The combined simulation environment and suite of models are identified as the Modular Dynamic SIMulation (MoDSIM) tool. The critical elements of this effort include (1) defining a standardized, common simulation environment that can be applied throughout the program, (2) developing a library of baseline component modules that can be assembled into full plant models using existing geometry and thermal-hydraulic data, (3) defining modeling conventions for interconnecting component models, and (4) establishing user interfaces and support tools to facilitate simulation development (i.e., configuration and parameterization), execution, and results display and capture.
This poster presents an assessment of the IEEE 1547 low-voltage ride-through criteria impact on bulk power system dynamics following the transmission path fault.
We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.
Measured effects of gaseous flow system dynamics on acoustic mode combustion instability
Synthesis of structural dynamic systems using digital computer and FORMA(FORTRAN Matrix Analysis)
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
Visual analytics supported by high performance computing (HPC) accelerates and enhances the discovery, exploration, and analysis of causal patterns in complex system dynamics (SD) models. We present a suite of visualization-assisted ensemble-based techniques for hypothesis generation and testing, and for sensitivity analysis. By employing HPC to provide parallel, on-demand simulation of SD models, one can “steer” an ensemble of simulated scenarios in real time as one first formulates and then informally tests those hypotheses: this provides rapid feedback for analysts to refine their understanding of the causal relationships emergent from a model. Such understandings can be followed and augmented by rigorous application of statistical methods, namely global variance-based sensitivity analysis, Monte-Carlo filtering, adaptive regional sensitivity analysis, and self-organized maps: here timely computation relies on HPC, while effective presentation emphasizes high-dimensional multivariate data visualization. Immersive visualization in virtual 3D environments provides an excellent adjunct to the traditional 2D graphics typically used for SD models, as it generates an embodied understanding of model behavior and facilitates an active, collaborative critique of model structure and output. Finally, we summarize prospects for HPC-enabled visual analytics applied to SD modeling.