Phase space methods for the analysis and design of discontinuous systems by Kuang-Wei Han

Cover of: Phase space methods for the analysis and design of discontinuous systems | Kuang-Wei Han

Published by Naval Postgraduate School in Monterey, California .

Written in English

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ContributionsNaval Postgraduate School (U.S.)
The Physical Object
Pagination1 v. :$bill. ;
ID Numbers
Open LibraryOL25167073M

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Thesis (Ph. D.)--Naval Postgraduate School, Search metadata Search text contents Search TV news captions Search archived web sites Advanced SearchPages: Phase space methods for the analysis and design of discontinuous systems.

Han, Kuang-Wei PN /T Paperback Book / Textbook Details Add to Comparison Cart. Discontinuous control systems are one of the most important and oldest types of nonlinear systems; however, the available methods of analysis of Author: Igor Boiko.

In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.

For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann.

phase space reconstruction discontinuous map smooth flow spectral analysis nonlinear time series analysis many physical application example impacting oscillator chosen poincar low-dimensional nonlinear behaviour false nearest neighbour statistical one main aim much recent research scalar measurement dynamical information linear method nonlinear.

Abhay ASHTEKAR, Oscar REULA, in Mechanics, Analysis and Geometry: Years After Lagrange, 1 INTRODUCTION. The phase space description of classical systems has proved to be a powerful tool in the analysis of their physical properties. The key reason is that phase spaces naturally arise as symplectic manifolds.

The availability of the symplectic structure enormously simplifies the. NASA SYSTEMS ENGINEERING HANDBOOK viii Preface S ince the initial writing of NASA/SP in and the following revision (Rev 1) insystems engineering as a discipline at the National Aeronautics and Space Administration (NASA) has undergone rapid and continued evolution.

Changes include using Model-Based Systems Engineering to improve. 12 Cellular Automata II: Analysis. Sizes of Rule Space and Phase Space.

Phase Space Visualization. Mean-Field Approximation. Renormalization Group Analysis to Predict Percolation Thresholds. 13 Continuous Field Models I: Modeling.

Continuous Field Models with Partial Differential Equations. Fundamentals of Vector. The cell mapping methods have also been applied to global analysis and control design of deterministic, stochastic and fuzzy dynamical systems.

Representative examples of new applications are. State space analysis. State space analysis is an excellent method for the design and analysis of control systems.

The conventional and old method for the design and analysis of control systems is the transfer function method. The transfer function method for design and analysis had many drawbacks. Advantages of state variable analysis. This video gives a high level overview of the Design Phase.

The video corresponds to Chapter 7 of "Systems Analysis & Design", 6th Ed. by Dennis, Wixom, & Roth.

Endeve E, Hauck C, Xing Y and Mezzacappa A () Bound-preserving discontinuous Galerkin methods for conservative phase space advection in curvilinear coordinates, Journal of Computational Physics, C, (), Online publication date: Apr Discontinuous Galerkin methods are developed for solving the Vlasov--Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy.

Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov--Maxwell system. • Phase C (Detailed Design) – detailed design and drawings, purchase or manufacture parts and components, code software.

• Phase D (System Assembly, Integration, Test and Launch) Assemble subsystems, integrate subsystems to create systems, test. In this survey we consider the development and mathematical analysis of numerical methods for kinetic partial differential equations.

C.-W. (), ‘ Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system ’, Kinet. Relat. ‘ Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. CONCEPT OF PHASE PLANE ANALYSIS phase portraits:The phase plane method is concerned with the graphical study of second-order autonomous systems described by ˙x1 = f1(x1, x2) (1) ˙x2 = f2(x1, x2) (2) where x1, x2: states of the system f1, f2 nonlinear functions of the states Geometrically, the state space of this system is a plane having x1.

The goal of the analysis phase is to truly understand the requirements of the new system and develop a system that addresses them -- or decide a new system isn’t needed. The System Proposal is presented to the approval committee via a system walk-through.

Systems analysis incorporates initial systems design. Requirements determination is the. Compared to the traditional analytic control design methods, the phase-space based control synthesis and evaluation rely on high-performance computational techniques and are applicable to physical systems operating in large nonlinear regimes.

Singular perturbations and time-scale techniques were introduced to control engineering in the late s and have since become common tools for the modeling, analysis and design of control systems.

The edition of this book, reprinted here in its original form, provides the theoretical foundation for representative control applications.

• Allows the use of graphical methods to predict system performance without solving the differential equations of the system.

These include response, steady state behavior, and transient behavior. • Mainly used in control system analysis and design. The simple inclined straight line boundary in phase space is considered as a control law for the dynamical system to switch.

The normal vector-field product for flow switching on the separation boundary is introduced, and the passability condition of flow to the discontinuous boundary is presented.

Phase Space Probability Density. Consider a tiny volume of phase space, defined by position \(i\) being between \(x_i\) and \(x_i+\delta x_i\), and momentum \(i\) being between \(p_i\) and \(p_i+\delta p_i\).If there are a total of \(N\) positions and momenta, then this is a \(2N\) dimensional phase space.

Suppose the system has a probability \(P\) of being inside this particular volume. The phase-space representation of the bundle of rays going from the source to the target is discontinuous between channels.

This phase-space ray-bundle flow is divided in as many branches as channels there are but it is a single trunk at the source and at the target. SMS design method in 3D geometry: examples and applications Proceedings of.

a simple graphical method for analysis of 2nd-order nonlinear systems. Its main idea is to construct motion trajectories of a 2nd-order system corresponding to different initial conditions in phase plane and determine qualitative features of the system – number, types and stability of its equilibrium points and/or limit cycles – by their.

8 Chapter 1: Network Design Requirements: Analysis and Design Principles Building A Building B Building C Core Module Figure Flexible Design Similarly, a flexible network design must support the capability to integrate with other networks (for examples, when mergers and acquisitions occur).

With mergers and acqui. Phase B: Preliminary Design & Technology Completion. Phase C: Final Design & Fabrication Approval for Implementatio n. FORMULATION IMPLEMENTATION Project. KDP C.

Life Cycle. Gates & Major Events. Pre-Systems Acquisition. Systems Acquisition Operations Phase E: Operations. KDP A. Launch KDP D System Assembly, Int & Test, Launch. KDP B. methods, available operation time, farm labor, cultural practices, and management skills must be noted for selecting and planning the type and method of irrigation.

The most opportune time to discuss and review problems and revise management plans that affect design and operation of the irrigation system is during the planning and design phase.

Discontinuous Dynamical Systems A tutorial on notions of solutions, nonsmooth analysis, and stability Jorge Cort´es Janu This article considers discontinuous dynamical systems.

By discontinuous we mean that the vector field defining the dynamical system can be a discontinuous function of the state. In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method.

The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the. can be viewed as 2-D space vectors. In this common frame the inductances become constant independent of position.

Figure 1 illustrates various reference frames (coordinate systems): the triplet [As Bs Cs] denotes a three-phase system attached to the stator while the pair [as bs] corresponds to an equivalent two-phase system (zero.

Requirements: The first phase involves understanding what needs to design and what is its function, purpose, etc. Here, the specifications of the input and output or the final product are studied and marked. System Design: The requirement specifications from the first phase are studied in this phase and system design is prepared.

System Design. In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent differential equations. The method consists of first rewriting the equations as a system of differential equations that are first-order in time, by introducing additional variables.

space frequencies (hertz) Figure a shows in the time domain the binary input to an FSK modulator and the corresponding FSK output. When the binary input (f b) changes from a logic 1 to a logic 0 and vice versa, the FSK output frequency shifts from a mark (f m) to a space (f s) frequency and vice versa.

Each step in the 5S process has an associated goal that can be specifically outlined to help guide efforts. For the step of Sort, the goal is to remove unnecessary items from the room, station, or space being organized. Furthermore, the sorting phase also aims to provide a clean slate on which to build and carry out the other four steps.

Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theory.

Inverter Mode of Operation. Continuous and discontinuous modes, Effect of source inductance assuming constant load current. Effect of freewheeling diode. Three phase bridge converters for different types of load with constant load current, different waveforms.

and degree operations. MODULE-III. systems, even these trace resistances and simple wire interconnections can have degrading effects. Copper is not a superconductor—and too many engineers appear to think it is. Figure illustrates a method of calculating the sheet resistance R of a copper. Section 5 shows the advantages of full phase-space analysis, with respect to more classical approaches such as the proxy Q=ρ/σ 3.

Finally, Section 6 wraps up. 2 PHASE-SPACE DENSITY ESTIMATION. There are a few common approaches to measure 6D phase-space density, f(x, v), for unrelaxed systems. Design Decisions in Research 6. The Analytic Phase.

In all research, the analytic phase is closely aligned with the empirical phase. After data are collected, the data is prepared for analysis. Quantitative data is typically entered into a statistical software program and qualitative data is often transcribed verbatim to facilitate data analysis.

Ideation is the process where you generate ideas and solutions through sessions such as Sketching, Prototyping, Brainstorming, Brainwriting, Worst Possible Idea, and a wealth of other ideation techniques.

Ideation is also the third stage in the Design Thinking process. Although many people might have experienced a “brainstorming” session before, it is not easy to facilitate a truly.

Let’s work on an example. Consider a one-dimensional binary CA model with neighborhood radius \(r = 2\).

We assume the space is made of nine cells with periodic boundary conditions(i.e., the space is a ring made of nine cells). In this setting, the size of its phase space is .Zhao and S. Osher, Visualization, Analysis and Shape Reconstruction of Unorganized Data Sets, book chapter in Geometric Level Set Methods in Imaging, Vision and Graphics, S.

Osher and N. Paragios Editors, Springer, Traditionally, IT departments had a(n) _____ group composed of systems analysis and programmers who handled information system design, development, and implementation. histogram A common tool for showing the distribution of a questionaire or sampling results is a vertical bar chart called a(n) _____.

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