C.4 Transient and Steady State Response Analysis
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Control Theory
Control theory S. Simrock DESY, Hamburg, Germany Abstract In engineering and mathematics, control theory deals with the behaviour of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain ref- erence over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system. Rapid advances in digital system technology have radically altered the control design options. It has become routinely practicable to design very complicated digital controllers and to carry out the extensive calculations required for their design. These advances in im- plementation and design capability can be obtained at low cost because of the widespread availability of inexpensive and powerful digital processing plat- forms and high-speed analog IO devices. 1 Introduction The emphasis of this tutorial on control theory is on the design of digital controls to achieve good dy- namic response and small errors while using signals that are sampled in time and quantized in amplitude. Both transform (classical control) and state-space (modern control) methods are described and applied to illustrative examples. The transform methods emphasized are the root-locus method of Evans and fre- quency response. The state-space methods developed are the technique of pole assignment augmented by an estimator (observer) and optimal quadratic-loss control. The optimal control problems use the steady-state constant gain solution. Other topics covered are system identification and non-linear control. System identification is a general term to describe mathematical tools and algorithms that build dynamical models from measured data. -
Systems Theory
1 Systems Theory BRUCE D. FRIEDMAN AND KAREN NEUMAN ALLEN iopsychosocial assessment and the develop - nature of the clinical enterprise, others have chal - Bment of appropriate intervention strategies for lenged the suitability of systems theory as an orga - a particular client require consideration of the indi - nizing framework for clinical practice (Fook, Ryan, vidual in relation to a larger social context. To & Hawkins, 1997; Wakefield, 1996a, 1996b). accomplish this, we use principles and concepts The term system emerged from Émile Durkheim’s derived from systems theory. Systems theory is a early study of social systems (Robbins, Chatterjee, way of elaborating increasingly complex systems & Canda, 2006), as well as from the work of across a continuum that encompasses the person-in- Talcott Parsons. However, within social work, sys - environment (Anderson, Carter, & Lowe, 1999). tems thinking has been more heavily influenced by Systems theory also enables us to understand the the work of the biologist Ludwig von Bertalanffy components and dynamics of client systems in order and later adaptations by the social psychologist Uri to interpret problems and develop balanced inter - Bronfenbrenner, who examined human biological vention strategies, with the goal of enhancing the systems within an ecological environment. With “goodness of fit” between individuals and their its roots in von Bertalanffy’s systems theory and environments. Systems theory does not specify par - Bronfenbrenner’s ecological environment, the ticular theoretical frameworks for understanding ecosys tems perspective provides a framework that problems, and it does not direct the social worker to permits users to draw on theories from different dis - specific intervention strategies. -
Control System Design Methods
Christiansen-Sec.19.qxd 06:08:2004 6:43 PM Page 19.1 The Electronics Engineers' Handbook, 5th Edition McGraw-Hill, Section 19, pp. 19.1-19.30, 2005. SECTION 19 CONTROL SYSTEMS Control is used to modify the behavior of a system so it behaves in a specific desirable way over time. For example, we may want the speed of a car on the highway to remain as close as possible to 60 miles per hour in spite of possible hills or adverse wind; or we may want an aircraft to follow a desired altitude, heading, and velocity profile independent of wind gusts; or we may want the temperature and pressure in a reactor vessel in a chemical process plant to be maintained at desired levels. All these are being accomplished today by control methods and the above are examples of what automatic control systems are designed to do, without human intervention. Control is used whenever quantities such as speed, altitude, temperature, or voltage must be made to behave in some desirable way over time. This section provides an introduction to control system design methods. P.A., Z.G. In This Section: CHAPTER 19.1 CONTROL SYSTEM DESIGN 19.3 INTRODUCTION 19.3 Proportional-Integral-Derivative Control 19.3 The Role of Control Theory 19.4 MATHEMATICAL DESCRIPTIONS 19.4 Linear Differential Equations 19.4 State Variable Descriptions 19.5 Transfer Functions 19.7 Frequency Response 19.9 ANALYSIS OF DYNAMICAL BEHAVIOR 19.10 System Response, Modes and Stability 19.10 Response of First and Second Order Systems 19.11 Transient Response Performance Specifications for a Second Order -
Robust Steady State Analysis of Power Grid with Equivalent Circuit
Robust Steady-State Analysis of Power Grid using Equivalent Circuit Formulation with Circuit Simulation Methods Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Department of Electrical and Computer Engineering Amritanshu Pandey B.S., Electrical and Electronics Engineering, Visvesvaraya Technological University M.S., Electrical and Computer Engineering, Carnegie Mellon University Carnegie Mellon University Pittsburgh, PA December 2018 © Amritanshu Pandey 2018 All rights reserved ACKNOWLEDGEMENTS To my advisors, Larry Pileggi and Gabriela Hug, without their guidance this research would not have materialized and this dissertation would be incomplete. To my committee members, Granger Morgan and Soummya Kar, for their guidance towards achieving the goals stipulated within this thesis. To my colleagues, Marko, Martin, David, Aayushya, Dimitrios, Joe and others, for being the most helpful corroborators and for enabling a welcoming and productive working environment. To my friends, Jolly, Naveen, Akhilesh, Panickos, and many others, for being the most amazing friends and company when the chips were low, and the research was hard. To my girlfriend, Deirdre, for being by my side throughout the whole journey and for uplifting my spirits when I needed it the most. Finally, to my wonderful family, Mom, Dad and Anshu, to whom I owe everything I have achieved in my life so far. Thesis Statement: Develop robust methods to obtain the steady-state operating point of the transmission and distribution power grid independently or jointly using equivalent circuit approach and circuit simulation methods Abstract v 1. Abstract A robust framework for steady-state analysis (power flow and three-phase power flow problem) of transmission as well as distribution networks is essential for operation and planning of the electric power grid. -
Systems Theory"
General By the same author: System Modern Theories of Development (in German, English, Spani~h) Nikolaus von Kues Theory Lebenswissenschaft und Bildung Theoretische Biologie J Foundations, Development, Applications Das Gefüge des Lebens Vom Molekül zur Organismenwelt Problems of Life (in German, English, French, Spanish, Dutch, Japanese) Auf den Pfaden des Lebens I by Ludwig von Bertalanffy Biophysik des Fliessgleichgewichts t Robots, Men and Minds University of Alberta Edmonton) Canada GEORGE BRAZILLER New York MANIBUS Nicolai de Cusa Cardinalis, Gottfriedi Guglielmi Leibnitii, ]oannis Wolfgangi de Goethe Aldique Huxleyi, neenon de Bertalanffy Pauli, S.J., antecessoris, cosmographi Copyright © 1968 by Ludwig von Bertalanffy All rights in this hook are reserved. For information address the publisher, George Braziller, lnc. One Park Avenue New York, N.Y. 10016 Foreword The present volume appears to demand some introductory notes clarifying its scope, content, and method of presentation. There is a large number of texts, monographs, symposia, etc., devoted to "systems" and "systems theory". "Systems Science," or one of its many synonyms, is rapidly becoming part of the estab lished university curriculum. This is predominantly a develop ment in engineering science in the broad sense, necessitated by the complexity of "systems" in modern technology, man-machine relations, programming and similar considerations which were not felt in yesteryear's technology but which have become im perative in the complex technological and social structures of the modern world. Systems theory, in this sense, is preeminently a mathematica! field, offering partly novel and highly sophisti cated techniques, closely linked with computer science, and essentially determined by the requirement to cope with a new sort of problem that has been appearing. -
Far-From-Equilibrium Attractors and Nonlinear Dynamical Systems Approach to the Gubser flow
Prepared for submission to JHEP Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Alireza Behtash1;2 C. N. Cruz-Camacho3 M. Martinez1 1 Department of Physics, North Carolina State University, Raleigh, NC 27695, USA 2Kavli Institute for Theoretical Physics University of California, Santa Barbara, CA 93106, USA 3Universidad Nacional de Colombia, Sede Bogot´a,Facultad de Ciencias, Departamento de F´ısica, Grupo de F´ısica Nuclear, Carrera 45 N o 26-85, Edificio Uriel Guti´errez, Bogot´a D.C. C.P. 1101, Colombia E-mail: [email protected], [email protected], [email protected] Abstract: The non-equilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed non-planar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansion diverge and use resurgence techniques to perform the resummation of these divergences. -
Jun 27 2013 Libraries
Systems of Valuation by Irina Chernyakova Bachelor of Architecture Cornell University, 2010 Submitted to the Department of Architecture in Partial Fulfillment of the Requirements for the Degree of -NS MA SSCHUSETTS INSTITUTE OF TECHNOLOGY Master of Science in Architecture Studies at the Massachusetts Institute of Technology JUN 27 2013 June 2013 LIBRARIES @2013 Irina Chernyakova. All Rights Reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature of Author: Department of Architecture May 24, 2013 Certified by: Arindam Dutta, Associate Professor of the History of Architecture Thesis Co-Supervisor Certified by: Mark Jarzombek, Profesor of the History and Theory of Architecture ,1- Thesis Co-Supervisor Accepted by: Takehiko Nagakura, Associate Professor of Design and Computation, Chair of the Department Committee on Graduate Students Committee Arindam Dutta Associate Professor of the History of Architecture Co-Supervisor Mark Jarzombek Professor of History and Theory of Architecture Co-Supervisor Kristel Smentek Assistant Professor of the History of Art Reader Systems of Valuation by Irina Chernyakova Submitted to the Department of Architecture on May 24, 2013 in partial fulfillment of the requirements for the Degree of Master of Science in Architecture Studies Abstract The 1972 publication of The Limits to Growth marked a watershed moment in ongoing environmental debates among politicians, economists, scientists, and the public in the postwar period. Sponsored by the Club of Rome, an influential think-tank established in 1968, the report was published against the backdrop of the progressive activism of the 1960s, and prefigured the neo-conservative politics of the 1980s. -
Review Vibrations of SDOF Mechanical Systems
ME459/659 Notes# 1 A Review to the Dynamic Response of SDOF Second Order Mechanical System with Viscous Damping by Luis San Andrés Mast-Childs Chair Professor ME 459/659 Sound & Vibration Measurements Reproduced from material in ME 363 and ME617 http://rotorlab.tamu.edu ME459/659 Notes# 1a (pp. 1-31) Dynamic Response of SDOF Second Order Mechanical System: Viscous Damping d2 X d X MDKXF d t2 d t ext() t Free Response to F(t) = 0 + initial conditions and Underdamped, Critically Damped and Overdamped Systems Forced Response to a Step Loading F(t) = Fo MEEN 459/659 Notes 1a © Luis San Andrés (2019) 1-1 Second Order Mechanical Translational System: d2 X d X Fundamental equationMDKXF of motion about equilibrium position (X=0) d t2 d t ext() t dX2 FMFFF Xdt2 ext() t D K dX FD : Viscous Damping Force D dt FKXk : Elastic restoring Force ( M, D ,K ) represent the system equivalent mass, viscous damping coefficient, and stiffness coefficient, respectively. equation of motion + Initial Conditions in velocity and displacement; at t=0: X(0) Xoo and X (0) V MEEN 459/659 Notes 1a © Luis San Andrés (2019) 1-2 Second Order Mechanical Torsional System: Fundamental equation of motion about equilibrium position, θ=0 d Torques I Text() t T D T K ; dt Tθ D = D : Viscous dissipation torque T θ K = K : Elastic restoring torque ( I, D ,K ) are the system equivalent mass moment of inertia, rotational viscous damping coefficient, and rotational (torsional) stiffness coefficient, respectively. dd2 Equation of motion IDKT2 ext() t d t d t + Initial Conditions in angular velocity and displacement at t=0: (0) ooand (0) MEEN 459/659 Notes 1a © Luis San Andrés (2019) 1-3 (a) Free Response of Second Order SDOF Mechanical System Let the external force Fext=0 and the system has an initial displacement Xo and initial velocity Vo. -
An Application of General Systems Theory to the Determination of the Nature of Accounting
Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1970 An Application of General Systems Theory to the Determination of the Nature of Accounting. Robert Eldon Bailey Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Bailey, Robert Eldon, "An Application of General Systems Theory to the Determination of the Nature of Accounting." (1970). LSU Historical Dissertations and Theses. 1819. https://digitalcommons.lsu.edu/gradschool_disstheses/1819 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. 71-6539 BAILEY, Eldon Robert, 1935- AN APPLICATION OF GENERAL SYSTEMS THEORY TO THE DETERMINATION OF THE NATURE OF ACCOUNTING. The Louisiana State University and Agricultural and Mechanical College, Ph.D., 1970 Accounting University Microfilms, Inc., Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED AN APPLICATION OF GENERAL SYSTEMS THEORY TO THE DETERMINATION OF THE NATURE OF ACCOUNTING A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Accounting by, Eldon R. Bailey B.S., McNeese State College, 1957 M.B.A., Louisiana State University, i960 August, 1970 ACKNOWLEDGEMENT The writer wishes to express appreciation to Dr. Fritz A. Me Cameron, Professor and. Head of the Department of Accounting, Loui siana State University, and Dr. -
Time Response 4
Time Response 4 Chapter Learning Outcomes After completing this chapter the student will be able to: • Use poles and zeros of transfer functions to determine the time response of a control system (Sections 4.1 –4.2) • Describe quantitatively the transient response of first-order systems (Section 4.3) • Write the general response of second-order systems given the pole location (Section 4.4) • Find the damping ratio and natural frequency of a second-order system (Section 4.5) • Find the settling time, peak time, percent overshoot, and rise time for an underdamped second-order system (Section 4.6) • Approximate higher-order systems and systems with zeros as first- or second- order systems (Sections 4.7 –4.8) • Describe the effects of nonlinearities on the system time response (Section 4.9) • Find the time response from the state-space representation (Sections 4.10 –4.11) Case Study Learning Outcomes You will be able to demonstrate your knowledge of the chapter objectives with case studies as follows: • Given the antenna azimuth position control system shown on the front endpapers, you will be able to (1) predict, by inspection, the form of the open-loop angular velocity response of the load to a step voltage input to 157 158 Chapter 4 Time Response the power ampli fier; (2) describe quantitatively the transient response of the open-loop system; (3) derive the expression for the open-loop angular velocity output for a step voltage input; (4) obtain the open-loop state-space representation; (5) plot the open-loop velocity step response using a computer simulation. -
Economics, Steady State
Economics, Steady State The “steady state” economy is rooted in the nineteenth- application of the entropy law to economic processes and to century economic theory of John Stuart Mill. Little used the emergence of the limits-to-growth argument in the until after World War II, the idea is a foundational con- early 1970s. (Entropy is a concept taken from the sub-dis- cept in sustainability science. It can be considered an cipline of physics called thermodynamics. A basic defi nition intellectual fabric with strands from classical econom- of entropy is the process whereby energy moves from a state ics to neo-Malthusianism, including growth limits, eco- of being able to do work—a state of high organization logical economics, and degrowth. Whether a steady termed “low entropy”—to a state of being unable to do state economy is desirable and achievable remains an work—a state of lower organization termed “high entropy.” unanswered question for sustainability science. Entropy is roughly synonymous with lack of organization.) It is embraced by the US ecological economist Herman he “steady state” economy (also called the “stationary Daly and thus is basic to the development of the discipline T state” economy) is a 150-year-old economic concept of ecological economics. Th ere are elements of the steady that became central to debates over the meaning of sus- state within the sustainable development paradigm, and it tainability or sustainable development in the twentieth leads logically to its most radical form, sustainable degrowth. century. Th ere are several views on what the steady state Nonetheless, there remain unanswered questions as to how actually would be, as well as on the process of economic a steady state economy might be achieved, whether it is still and social change that might lead to it, and whether or relevant in today’s economic environment, and whether it is not it is even a desirable vision of a sustainable society a desirable part of the sustainability paradigm. -
Time Response of First Order Systems
Time Response of First Order Systems Consider a general first order transfer function (strictly proper) G(s) b G(s) = = 0 R(s) s + a0 It is common also to write G(s) as K b G(s) = = 0 τs + 1 s + a0 i.e., 1 K a = ; b = 0 τ 0 τ Example: 3 1:5 G(s) = = s + 2 0:5s + 1 a0 = 2 ; b0 = 3 τ = 0:5 ;K = 1:5 The pole of the system is at s = −a0 or s = −1/τ. τ is called the time constant. K is called the DC-gain or steady state gain. What is the differential equation corresponding to the input/output system K c(s) = R(s) τs + 1 becomes (s + 1/τ)C(s) = K/τR(s) which is equivalent to 1 c_(t) + c(t) = K/τr(t) τ Let us consider the effect of both the input r(t) and the initial condition c(0). Taking Laplace Transform of the differentiation equation | this time including the initial condition yields 1 K sC(s) − c(0) + c(s) = R(s) τ τ 1 or c(0) K/τ c(s) = + R(s): s + 1/τ s + 1/τ Note that the initial condition could be represented in the differential equation by an input c(0)δ(t) where δ is the unit impulse function 1 K c_(t) + c(t) = r(t) + c(0)δ? τ τ In block diagram from we have By superposition the response of the system is the sum of the response due to the initial condition alone (the free response) and the response due to the input R(s) (the forced response).