Modeling and Simulation for Automatic Control
|
|
- Elijah Booth
- 5 years ago
- Views:
Transcription
1 Modeling and Simulation for Automatic Control Olav Egeland and Jan Tommy Gravdahl Norwegian University of Science and Technology Trondheim, Norway MARINE CYBERNETICS Г~Т.! " " Trondheim, Norway
2 Contents I Modeling 1 1 Model representation Introduction State space methods State space models Second order models of mechanical systems Linearization of state space models Linearization of second order systems Stability with zero input Stability of linear systems Stability analysis using a linearized model Transfer function models Introduction The transfer function of a state-space model Rational transfer functions Impulse response and step response Loop transfer function Example: Actuator with dynamic compensation Stability of transfer functions Stability of closed loop systems Partial differential equations Network description Introduction Background Multiport Example: DC motor with flexible load Example: Voltage controlled DC motor Example: Diesel engine with turbocharger Assigning computational inputs and outputs Bond graphs Linear network theory Driving point impedance Linear two-ports Impedance of two-port with termination Example: Passive mechanical two-port Mechanical analog of PD controller Example: Transmission line model Introduction 33 ш
3 iv CONTENTS Introductory example Effort and flow model Transfer functions Transfer function for terminated transmission line Wave variables Lossless transmission line Line termination 38 2 Model analysis tools Frequency response methods The frequency response of a system Second order oscillatory system Performance of a closed loop system Stability margins Elimination of fast dynamics Example: The electrical time constant in a DC motor Nonlinear system Energy-based methods Introduction The energy function Second-order systems Example: Mass-spring-damper Lyapunov methods Contraction Energy flow in a turbocharged diesel engine Passivity Introduction Definition Examples Energy considerations Positive real transfer functions Positive real rational transfer functions Positive realness of irrational transfer functions Passivity and positive real transfer functions No poles on the imaginary axis Single poles at the imaginary axis Bounded real transfer functions Passivity of PID controllers Closed loop stability of positive real systems Storage function formulation Interconnections of passive systems Storage function for PID controller Passive plant with PID controller Example: Control of mass-spring-damper system Example: Active vibration damping Passive electrical one-port Electrical analog of PID controller Passive electrical two-port Termination of electrical two-port Passive electrical n-ports 70
4 CONTENTS v Example: Telemanipulation Passivity and gain Uncertainty in modeling General state space models Exact kinematic models Balance equations Passivity 76 II Motors and actuators 77 3 Electromechanical systems Introduction Electrical motors Introduction Basic equations Gear model Motor and gear Transformation of rotation to translation Torque characteristics The four quadrants of the motor The DC motor with constant field Introduction Model Energy function Laplace transformed model DC motor control Introduction Current controlled DC motor Velocity controlled DC motor Position controlled DC motor Motor and load with elastic transmission Introduction Equations of motion Transfer functions Zeros of the transfer function Energy analysis Motor with several resonances in the load Two motors driving an elastic load Energy analysis of two motors and load Motor and load with deadzone in the gear Introduction Elastic gear with deadzone Rigid gear with deadzone Two motors with deadzone and load Electromechanical energy conversion Introduction Inductive circuit elements Capacitive circuit elements Magnetic energy of a linear inductive element 103
5 3.7.5 Stored energy of a linear capacitive element Energy and coenergy Electromechanical two-port with inductive element Electromechanical two-port with linear flux linkage Magnetic levitation Voice coil Electromagnetic three-port Electromechanical capacitive element Ill Electromechanical two-port with linear charge Example: Capacitive microphone Piezoelectric actuator Actuator configuration DC motor with externally controlled field Model Network description DC motor with field weakening Dynamic model of the general AC motor Introduction Notation Dynamic model Induction motors Basic dynamic model Induction motor model in stator frame Dynamic model in the flux frame Lagrangian description of electromechanical systems Generalized coordinates Energy and coenergy Analogy of electrical and mechanical systems The Lagrangian Electromechanical systems Lagrange formulation of general AC motor Lagrange formulation of induction motor Lagrange formulation of DC motor 138 Hydraulic motors Introduction Valves Introduction Flow through a restriction Regularization of turbulent orifice flow Four-way valve Matched and symmetrical four-way valve Symmetric motor and valve with critical spool Symmetric motor and valve with open spool Flow control using pressure compensated valves Balance valve Motor models Mass balance Rotational motors Elastic modes in the load 154
6 CONTENTS vii Hydraulic eylinder Models for transfer function analysis Matched and symmetric valve and symmetric motor Valve controlled motor: Transfer function Hydraulic motor with P controller Symmetric cylinder with matched and symmetric valve Pump controlled hydraulic drive with P controller Transfer functions for elastic modes Mechanical analog Hydraulic transmission lines Introduction PDE Model Laplace transformed model Lossless model Linear friction Nonlinear friction Wave variables Example: Lossless pipe Linear network models of transmission lines Rational approximations of transfer function models Rational series expansion of impedance model Rational series expansion of admittance model Galerkin derivation of impedance model Galerkin derivation of the admittance model Galerkin derivation of the hybrid model Rational simulation models Lumped parameter model of hydraulic line Introduction Helmholtz resonator model Model formulation Admittance model Impedance model Hybrid model Natural frequencies Object oriented simulation models Introduction Pump controlled hydraulic motor Cylinder with balance valve Friction Introduction Background Static friction models Models for the individual phenomena Combination of individual models Problems with the static models Problems with signum terms at zero velocity Karnopp's model of Coulomb friction More on Karnopp's friction model Passivity of static models 199
7 Vlll 5.3 Dynamic friction models Introduction The Dahl model Passivity of the Dahl model The Bristle and LuGre model Passivity of the LuGre model The Elasto-Plastic model Passivity of the Elasto-Plastic model 206 III Dynamics Rigid body kinematics Introduction Vectors Vector description The scalar product The vector cross product Dyadics Introduction Introductory example: The inertia dyadic Matrix representation of dyadics The rotation matrix Coordinate transformations for vectors Properties of the rotation matrix Composite rotations Simple rotations Coordinate transformations for dyadics Homogeneous transformation matrices Euler angles Introduction Roll-pitch-yaw Classical Euler angles Angle-axis description of rotation Introduction Angle-axis parameters Derivation of rotation dyadic The rotation dyadic Rotation matrix Euler parameters Definition Quaternions Unit quaternions The quaternion product for unit quaternions Rotation by the quaternion product Euler parameters from the rotation matrix The Euler rotation vector Euler-Rodrigues parameters Angular velocity Introduction 239
8 CONTENTS ix Definition Simple rotations Composite rotations Differentiation of coordinate vectors Differentiation of vectors Kinematic differential equations Introduction Attitude deviation Homogeneous transformation matrices Euler angles Euler parameters Normalization for numerical integration Euler rotation Euler-Rodrigues parameters Passivity of kinematic differential equations Angle-axis representation The Serret-Frenet frame Kinematics Control deviation Navigational kinematics Introduction Coordinate frames Acceleration Kinematics of a rigid body Configuration Velocity Acceleration The center of mass System of particles Rigid body Newton-Euler equations of motion Introduction Forces and torques Resultant force Torque Equivalent force and torque Forces and torques on a rigid body Example: Robotic link Newton-Euler equations for rigid bodies Equations of motion for a system of particles Equations of motion for a rigid body Equations of motion about a point The inertia dyadic The inertia matrix Expressions for the inertia matrix The parallel axes theorem The equations of motion for a rigid body Satellite attitude dynamics Example: Ball and beam dynamics 278
9 7.5 Example: Inverted pendulum Equations of motion Double inverted pendulum Example: The Furuta pendulum Principle of virtual work Introduction Generalized coordinates Virtual displacements d'alembert's principle Principle of virtual work for a rigid body Virtual displacements for a rigid body Force and torque of constraint Multi-body dynamics and virtual work Introduction Equations of motion Equations of motion about a point Ball and beam Single and double inverted pendulum Furuta pendulum Planar two-link manipulator: Derivation Planar two-link manipulator: Derivation Kane's computational scheme for two-link manipulator Manipulator dynamics in coordinate form Spacecraft and manipulator Recursive Newton-Euler Inverse dynamics Simulation 311 Analytical mechanics Introduction Lagrangian dynamics Introduction Lagrange's equation of motion Generalized coordinates and generalized forces Pendulum Mass-spring system Ball and beam Furuta pendulum Manipulator Passivity of the manipulator dynamics Example: Planar two-link manipulator Example: Planar two-link manipulator Limitations of Lagrange's equation of motion Calculus of variations Introduction Variations versus differentials The variation of a function The Euler-Lagrange equation for a general integral The variation of the rotation matrix The variation of the homogeneous transformation matrix 330
10 CONTENTS xi 8.4 The adjoint formulation Introduction Rotations Rigid motion The Euler-Poincare equation A central equation Rotating rigid body Free-floating rigid body Mechanism with n degrees of freedom Hamilton's principle Introduction The extended Hamilton principle Derivation of Lagrange's equation of motion Hamilton's principle Rotations with the Euler-Poincare equation Rigid motion with the Euler-Poincare equation Lagrangian dynamics for PDE's Flexible beam dynamics Euler-Bernoulli beam Lateral vibrations in a string Hamilton's equations of motion Introduction Hamilton's equation of motion The energy function Change of generalized coordinates Control aspects Passivity of Hamilton's equation of motion Example: Manipulator dynamics Example: The restricted three-body problem Example: Attitude dynamics for a satellite Example: Gravity gradient stabilization The Hamilton-Jacobi equation Mechanical vibrations Introduction Lumped elastic two-ports Hybrid two-port Displacement two-port Three masses in the hybrid formulation Three masses in the displacement formulation Four masses Vibrating string Linearized model Orthogonal shape functions Galerkin's method for orthogonal shape functions Finite element shape functions String element Assembling string elements Nonlinear string dynamics Kirchhoff's nonlinear string model 371
11 Xll CONTENTS Marine cables Euler Bernoulli beam Model Boundary conditions Energy Orthogonal shape functions Clamped-free Euler Bernoulli beam Beam fixed to an inertia and a mass Orthogonality of the eigenfunctions Galerkin's method for orthogonal mode shapes Finite element model of Euler Bernoulli beam Introduction Beam element Assembling a structure Finite element model and Galerkin's method Motor and Euler Bernoulli beam Equations of motion Assumed mode shapes Finite elements Irrational transfer functions for beam dynamics Introduction Clamped-free beam Motor and beam 395 IV Balance equations Kinematics of Flow Introduction Kinematics The material derivative The nabla operator Divergence Curl Material coordinates The dilation Orthogonal curvilinear coordinates General results Cylindrical coordinates Reynolds' transport theorem Introduction Basic transport theorem The transport theorem for a material volume The transport theorem and balance laws Mass, momentum and energy balances The mass balance Differential form Integral form Control volume with compressible fluid 418
12 CONTENTS xiii Mass flow through a pipe Continuity equation and Reynolds' transport theorem Multi-component systems The momentum balance Euler's equation of motion The momentum equation for a control volume Example: Waterjet Example: Sand dispenser and conveyor Irrotational Bernoulli equation Bernoulli's equation along a streamline Example: Transmission line Liquid mass flow through a restriction Example: Water turbine Example: Waterhammer Angular momentum balance General expression Centrifugal pump with radial blades Euler's turbomachinery equation Pump instability The energy balance Material volume Fixed volume General control volume The heat equation Transfer function for the heat equation Viscous flow Introduction Tensor notation The velocity gradient tensor Example: The velocity gradient for a rigid body The stress tensor Cauchy's equation of motion Newtonian fluids The Navier-Stokes equation The Reynolds number The equation of kinetic energy The energy balance for a viscous fluid Fixed volume General control volume Gas dynamics Introduction Energy, enthalpy and entropy Energy Enthalpy Specific heats Entropy The entropy equation Internal energy equation in terms of temperature Energy balance in terms of pressure 471
13 xiv CONTENTS Piston motion Isentropic conditions Isentropic processes Stagnation state Energy balance for isentropic processes The speed of sound Helmholtz resonator Acoustic resonances in pipes Dynamic model Pipe closed at both ends Pipe closed at one end Pressure measurement in diesel engine cylinder Gas flow Gas flow through a restriction Example: Discharge of gas from tank The Euler equation around sonic speed Compressor dynamics Introduction Compressors Surge and rotating stall Centrifugal Compressors Introduction Shaft dynamics Compressor system Mass balance Momentum equation Compressor characteristic Derivation The compressor characteristic at zero mass flow Compressor surge The Greitzer surge model Linearization Passivity of the Greitzer surge model Curvefitting of compressor characteristic Compression systems with recycle 504 V Simulation Simulation Introduction The use of simulation in automatic control The Moore Greitzer model The restricted three-body problem Mass balance of chemical reactor Preliminaries Notation Computation error The order of a one-step method 517
14 CONTENTS xv Linearization The linear test function Euler methods Euler's method The improved Euler method The modified Euler method Explicit Runge-Kutta methods Introduction Numerical scheme Order conditions Some explicit Runge-Kutta methods Case study: Pneumatic spring Stability function FSAL methods Implicit Runge-Kutta methods Stiff systems Implicit Runge-Kutta methods Implicit Euler method Trapezoidal rule Implicit midpoint rule The theta method Stability function Some implicit Runge-Kutta methods Case study: Pneumatic spring revisited Stability of Runge-Kutta methods Aliasing A-stability, L-stability Stiffly accurate methods Pade approximations Stability for Pade approximations Example: Mechanical vibrations Frequency response AN-stability B-stability Algebraic stability Properties of Runge-Kutta methods Automatic adjustment of step size Estimation of the local error for Runge-Kutta methods Adjustment algorithm Implementation aspects Solution of implicit equations Dense outputs Event detection Systems with inertia matrix Invariants Introduction Linear invariants Quadratic functions Quadratic invariants 569
15 xvi CONTENTS Symplectic Runge-Kutta methods Rosenbrock methods Multistep methods Explicit Adams methods Implicit Adams methods Predictor-Corrector implementation Backwards differentiation methods Linear stability analysis Stability of Adams methods Stability of BDF methods Frequency response Adams methods BDF methods Differential-algebraic equations Implicit Runge-Kutta methods for index 1 problems Multistep methods for index 1 problems Computational fluid dynamics Introduction Governing equations Classification Hyperbolic equations Parabolic equations Elliptic equations Diffusion Introduction Finite volume method for stationary diffusion Solution of equations Worked example on stationary diffusion Stability issues Finite volume method for diffusion dynamics Finite volumes for Convection-Diffusion Introduction Finite volume method for ID diffusion and convection dynamics Pressure-velocity coupling Introduction The staggered grid The momentum equations The transient SIMPLE algorithm Von Neuman stability method 620
Index. Index. More information. in this web service Cambridge University Press
A-type elements, 4 7, 18, 31, 168, 198, 202, 219, 220, 222, 225 A-type variables. See Across variable ac current, 172, 251 ac induction motor, 251 Acceleration rotational, 30 translational, 16 Accumulator,
More informationDynamic Systems. Modeling and Analysis. Hung V. Vu. Ramin S. Esfandiari. THE McGRAW-HILL COMPANIES, INC. California State University, Long Beach
Dynamic Systems Modeling and Analysis Hung V. Vu California State University, Long Beach Ramin S. Esfandiari California State University, Long Beach THE McGRAW-HILL COMPANIES, INC. New York St. Louis San
More informationPiezoelectric Multilayer Beam Bending Actuators
R.G. Bailas Piezoelectric Multilayer Beam Bending Actuators Static and Dynamic Behavior and Aspects of Sensor Integration With 143 Figures and 17 Tables Sprin ger List of Symbols XV Part I Focus of the
More informationFluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition
Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow
More informationThe written qualifying (preliminary) examination covers the entire major field body of knowledge
Dynamics The field of Dynamics embraces the study of forces and induced motions of rigid and deformable material systems within the limitations of classical (Newtonian) mechanics. The field is intended
More informationContents. Dynamics and control of mechanical systems. Focus on
Dynamics and control of mechanical systems Date Day 1 (01/08) Day 2 (03/08) Day 3 (05/08) Day 4 (07/08) Day 5 (09/08) Day 6 (11/08) Content Review of the basics of mechanics. Kinematics of rigid bodies
More informationDetailed Outline, M E 320 Fluid Flow, Spring Semester 2015
Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous
More informationClass XI Physics Syllabus One Paper Three Hours Max Marks: 70
Class XI Physics Syllabus 2013 One Paper Three Hours Max Marks: 70 Class XI Weightage Unit I Physical World & Measurement 03 Unit II Kinematics 10 Unit III Laws of Motion 10 Unit IV Work, Energy & Power
More informationDynamics and control of mechanical systems
Dynamics and control of mechanical systems Date Day 1 (03/05) - 05/05 Day 2 (07/05) Day 3 (09/05) Day 4 (11/05) Day 5 (14/05) Day 6 (16/05) Content Review of the basics of mechanics. Kinematics of rigid
More informationPHYSICS. Course Structure. Unit Topics Marks. Physical World and Measurement. 1 Physical World. 2 Units and Measurements.
PHYSICS Course Structure Unit Topics Marks I Physical World and Measurement 1 Physical World 2 Units and Measurements II Kinematics 3 Motion in a Straight Line 23 4 Motion in a Plane III Laws of Motion
More informationSTATICS Chapter 1 Introductory Concepts
Contents Preface to Adapted Edition... (v) Preface to Third Edition... (vii) List of Symbols and Abbreviations... (xi) PART - I STATICS Chapter 1 Introductory Concepts 1-1 Scope of Mechanics... 1 1-2 Preview
More informationHYDRAULIC CONTROL SYSTEMS
HYDRAULIC CONTROL SYSTEMS Noah D. Manring Mechanical and Aerospace Engineering Department University of Missouri-Columbia WILEY John Wiley & Sons, Inc. vii Preface Introduction xiii XV FUNDAMENTALS 1 Fluid
More informationENGI9496 Modeling and Simulation of Dynamic Systems Bond Graphs
ENGI9496 Modeling and Simulation of Dynamic Systems Bond Graphs Topics covered so far: Analogies between mechanical (translation and rotation), fluid, and electrical systems o Review of domain-specific
More informationINDEX 363. Cartesian coordinates 19,20,42, 67, 83 Cartesian tensors 84, 87, 226
INDEX 363 A Absolute differentiation 120 Absolute scalar field 43 Absolute tensor 45,46,47,48 Acceleration 121, 190, 192 Action integral 198 Addition of systems 6, 51 Addition of tensors 6, 51 Adherence
More informationCOPYRIGHTED MATERIAL. Index
Index A Admissible function, 163 Amplification factor, 36 Amplitude, 1, 22 Amplitude-modulated carrier, 630 Amplitude ratio, 36 Antinodes, 612 Approximate analytical methods, 647 Assumed modes method,
More informationModeling of Electromechanical Systems
Page 1 of 54 Modeling of Electromechanical Systems Werner Haas, Kurt Schlacher and Reinhard Gahleitner Johannes Kepler University Linz, Department of Automatic Control, Altenbergerstr.69, A 4040 Linz,
More information1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
More informationD.A.V. PUBLIC SCHOOL, UPPAL S SOUTHEND, SECTOR 49, GURUGRAM CLASS XI (PHYSICS) Academic plan for
D.A.V. PUBLIC SCHOOL, UPPAL S SOUTHEND, SECTOR 49, GURUGRAM CLASS XI (PHYSICS) Academic plan for 2017-2018 UNIT NAME OF UNIT WEIGHTAGE 1. 2. 3. Physical World and Measurement Kinemetics Laws of Motion
More informationAnalytical Mechanics for Relativity and Quantum Mechanics
Analytical Mechanics for Relativity and Quantum Mechanics Oliver Davis Johns San Francisco State University OXPORD UNIVERSITY PRESS CONTENTS Dedication Preface Acknowledgments v vii ix PART I INTRODUCTION:
More informationVideo 2.1a Vijay Kumar and Ani Hsieh
Video 2.1a Vijay Kumar and Ani Hsieh Robo3x-1.3 1 Introduction to Lagrangian Mechanics Vijay Kumar and Ani Hsieh University of Pennsylvania Robo3x-1.3 2 Analytical Mechanics Aristotle Galileo Bernoulli
More informationDIVIDED SYLLABUS ( ) - CLASS XI PHYSICS (CODE 042) COURSE STRUCTURE APRIL
DIVIDED SYLLABUS (2015-16 ) - CLASS XI PHYSICS (CODE 042) COURSE STRUCTURE APRIL Unit I: Physical World and Measurement Physics Need for measurement: Units of measurement; systems of units; SI units, fundamental
More informationGAME PHYSICS SECOND EDITION. дяййтаййг 1 *
GAME PHYSICS SECOND EDITION DAVID H. EBERLY дяййтаййг 1 * К AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO MORGAN ELSEVIER Morgan Kaufmann Publishers
More informationContents. Part I Vector Analysis
Contents Part I Vector Analysis 1 Vectors... 3 1.1 BoundandFreeVectors... 4 1.2 Vector Operations....................................... 4 1.2.1 Multiplication by a Scalar.......................... 5 1.2.2
More informationSTATICS & DYNAMICS. Engineering Mechanics. Gary L. Gray. Francesco Costanzo. Michael E. Plesha. University of Wisconsin-Madison
Engineering Mechanics STATICS & DYNAMICS SECOND EDITION Francesco Costanzo Department of Engineering Science and Mechanics Penn State University Michael E. Plesha Department of Engineering Physics University
More informationNCEES Fundamentals of Engineering (FE) Examination OTHER DISCIPLINES EXAM SPECIFICATIONS. Effective Beginning with the April 2010 Examinations
NCEES Fundamentals of Engineering (FE) Examination OTHER DISCIPLINES EXAM SPECIFICATIONS Effective Beginning with the April 2010 Examinations The FE examination is an 8-hour supplied-reference examination:
More informationMETHODS OF THEORETICAL PHYSICS
METHODS OF THEORETICAL PHYSICS Philip M. Morse PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY Herman Feshbach PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY PART II: CHAPTERS 9
More informationENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids
CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific
More information202 Index. failure, 26 field equation, 122 force, 1
Index acceleration, 12, 161 admissible function, 155 admissible stress, 32 Airy's stress function, 122, 124 d'alembert's principle, 165, 167, 177 amplitude, 171 analogy, 76 anisotropic material, 20 aperiodic
More informationBasic. Theory. ircuit. Charles A. Desoer. Ernest S. Kuh. and. McGraw-Hill Book Company
Basic C m ш ircuit Theory Charles A. Desoer and Ernest S. Kuh Department of Electrical Engineering and Computer Sciences University of California, Berkeley McGraw-Hill Book Company New York St. Louis San
More informationMETHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS
METHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS V.I. Agoshkov, P.B. Dubovski, V.P. Shutyaev CAMBRIDGE INTERNATIONAL SCIENCE PUBLISHING Contents PREFACE 1. MAIN PROBLEMS OF MATHEMATICAL PHYSICS 1 Main
More informationPassivity-based Control of Euler-Lagrange Systems
Romeo Ortega, Antonio Loria, Per Johan Nicklasson and Hebertt Sira-Ramfrez Passivity-based Control of Euler-Lagrange Systems Mechanical, Electrical and Electromechanical Applications Springer Contents
More informationLecture Module 5: Introduction to Attitude Stabilization and Control
1 Lecture Module 5: Introduction to Attitude Stabilization and Control Lectures 1-3 Stability is referred to as a system s behaviour to external/internal disturbances (small) in/from equilibrium states.
More informationVibration Dynamics and Control
Giancarlo Genta Vibration Dynamics and Control Spri ringer Contents Series Preface Preface Symbols vii ix xxi Introduction 1 I Dynamics of Linear, Time Invariant, Systems 23 1 Conservative Discrete Vibrating
More informationENGINEERING MECHANICS
ENGINEERING MECHANICS BASUDEB BHATTACHARYYA Assistant Professor Department of Applied Mechanics Bengal Engineering and Science University Shibpur, Howrah OXJFORD UNIVERSITY PRESS Contents Foreword Preface
More informationContents. I Introduction 1. Preface. xiii
Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................
More informationMeasurement p. 1 What Is Physics? p. 2 Measuring Things p. 2 The International System of Units p. 2 Changing Units p. 3 Length p. 4 Time p. 5 Mass p.
Measurement p. 1 What Is Physics? p. 2 Measuring Things p. 2 The International System of Units p. 2 Changing Units p. 3 Length p. 4 Time p. 5 Mass p. 7 Review & Summary p. 8 Problems p. 8 Motion Along
More informationHigh School. Prentice Hall. Conceptual Physics South Carolina Science Academic Standards - Physics High School
Prentice Hall Conceptual Physics 2009 High School C O R R E L A T E D T O High School Scientific Inquiry Standard P-1: The student will demonstrate an understanding of how scientific inquiry and technological
More informationContents. 1 Introduction to Gas-Turbine Engines Overview of Turbomachinery Nomenclature...9
Preface page xv 1 Introduction to Gas-Turbine Engines...1 Definition 1 Advantages of Gas-Turbine Engines 1 Applications of Gas-Turbine Engines 3 The Gas Generator 3 Air Intake and Inlet Flow Passage 3
More informationTable of Contents. Preface... xiii
Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...
More informationMathematical Theory of Control Systems Design
Mathematical Theory of Control Systems Design by V. N. Afarias'ev, V. B. Kolmanovskii and V. R. Nosov Moscow University of Electronics and Mathematics, Moscow, Russia KLUWER ACADEMIC PUBLISHERS DORDRECHT
More informationModeling of Dynamic Systems: Notes on Bond Graphs Version 1.0 Copyright Diane L. Peters, Ph.D., P.E.
Modeling of Dynamic Systems: Notes on Bond Graphs Version 1.0 Copyright 2015 Diane L. Peters, Ph.D., P.E. Spring 2015 2 Contents 1 Overview of Dynamic Modeling 5 2 Bond Graph Basics 7 2.1 Causality.............................
More informationAdvanced Vibrations. Elements of Analytical Dynamics. By: H. Ahmadian Lecture One
Advanced Vibrations Lecture One Elements of Analytical Dynamics By: H. Ahmadian ahmadian@iust.ac.ir Elements of Analytical Dynamics Newton's laws were formulated for a single particle Can be extended to
More informationDissipative Systems Analysis and Control
Bernard Brogliato, Rogelio Lozano, Bernhard Maschke and Olav Egeland Dissipative Systems Analysis and Control Theory and Applications 2nd Edition With 94 Figures 4y Sprin er 1 Introduction 1 1.1 Example
More informationScience. Circular Motion. Atomic Structure and Nuclear Chemistry. Kinematics; Motion in One and Two Dimensions
Inquiry -P-1.1 -P-1.2 -P-1.3 -P-1.4 -P-1.5 -P-1.6 -P-1.7 -P-1.8 -P-1.9 -P-2.1 -P-1.1 -P-2.1 -P-2.2 -P-2.3 Circular Motion Use appropriate safety procedures when conducting investigations. Use appropriate
More informationANSWERS 403 INDEX. Bulk modulus 238 Buoyant force 251
ANSWERS 403 INDEX A Absolute scale temperature 276 Absolute zero 276 Acceleration (linear) 45 Acceleration due to gravity 49,189 Accuracy 22 Action-reaction 97 Addition of vectors 67 Adiabatic process
More informationDetailed Outline, M E 521: Foundations of Fluid Mechanics I
Detailed Outline, M E 521: Foundations of Fluid Mechanics I I. Introduction and Review A. Notation 1. Vectors 2. Second-order tensors 3. Volume vs. velocity 4. Del operator B. Chapter 1: Review of Basic
More informationTurbomachinery Flow Physics and Dynamic Performance
Turbomachinery Flow Physics and Dynamic Performance Bearbeitet von Meinhard T Schobeiri 1. Auflage 2004. Buch. XXI, 522 S. Hardcover ISBN 978 3 540 22368 9 Format (B x L): 15,5 x 23,5 cm Gewicht: 2070
More informationChemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017
Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering
More information2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity
2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity Energy 7 4 Kinematics Free fall Collisions 3 5 Dynamics
More informationSAMCEF For ROTORS. Chapter 1 : Physical Aspects of rotor dynamics. This document is the property of SAMTECH S.A. MEF A, Page 1
SAMCEF For ROTORS Chapter 1 : Physical Aspects of rotor dynamics This document is the property of SAMTECH S.A. MEF 101-01-A, Page 1 Table of Contents rotor dynamics Introduction Rotating parts Gyroscopic
More informationAP Physics 1. Course Overview
Radnor High School Course Syllabus AP Physics 1 Credits: Grade Weighting: Yes Prerequisites: Co-requisites: Length: Format: 1.0 Credit, weighted Honors chemistry or Advanced Chemistry Honors Pre-calculus
More informationECEN 420 LINEAR CONTROL SYSTEMS. Lecture 6 Mathematical Representation of Physical Systems II 1/67
1/67 ECEN 420 LINEAR CONTROL SYSTEMS Lecture 6 Mathematical Representation of Physical Systems II State Variable Models for Dynamic Systems u 1 u 2 u ṙ. Internal Variables x 1, x 2 x n y 1 y 2. y m Figure
More informationOKLAHOMA SUBJECT AREA TESTS (OSAT )
CERTIFICATION EXAMINATIONS FOR OKLAHOMA EDUCATORS (CEOE ) OKLAHOMA SUBJECT AREA TESTS (OSAT ) FIELD 014: PHYSICS September 2011 Subarea Range of Competencies I. Scientific and Engineering Processes 0001
More informationTable of Contents. Preface... 13
Table of Contents Preface... 13 Chapter 1. Vibrations of Continuous Elastic Solid Media... 17 1.1. Objective of the chapter... 17 1.2. Equations of motion and boundary conditions of continuous media...
More informationFrank Y. Wang. Physics with MAPLE. The Computer Algebra Resource for Mathematical Methods in Physics. WILEY- VCH WILEY-VCH Verlag GmbH & Co.
Frank Y. Wang Physics with MAPLE The Computer Algebra Resource for Mathematical Methods in Physics WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA k Preface Guide for Users Bibliography XI XVII XIX 1 Introduction
More informationStructure of the Comprehensive Examination in the ME Department. For circulation to students
Structure of the Comprehensive Examination in the ME Department For circulation to students i. The qualifying exams will be held up to 3 times every year. ii. Generally, the qualifying examination will
More informationEngineering Fluid Mechanics
Engineering Fluid Mechanics Eighth Edition Clayton T. Crowe WASHINGTON STATE UNIVERSITY, PULLMAN Donald F. Elger UNIVERSITY OF IDAHO, MOSCOW John A. Roberson WASHINGTON STATE UNIVERSITY, PULLMAN WILEY
More informationKINETIC BOOKS PHYSICS CORRELATED TO SOUTH CAROLINA PHYSICS STANDARDS CORRELATION
Virtual Standard P-1: The student will demonstrate an understanding of how scientific inquiry and technological design, including mathematical analysis, can be used appropriately to pose questions, seek
More informationADVANCED ENGINEERING MATHEMATICS
ADVANCED ENGINEERING MATHEMATICS DENNIS G. ZILL Loyola Marymount University MICHAEL R. CULLEN Loyola Marymount University PWS-KENT O I^7 3 PUBLISHING COMPANY E 9 U Boston CONTENTS Preface xiii Parti ORDINARY
More informationFor any use or distribution of this textbook, please cite as follows:
MIT OpenCourseWare http://ocw.mit.edu Electromechanical Dynamics For any use or distribution of this textbook, please cite as follows: Woodson, Herbert H., and James R. Melcher. Electromechanical Dynamics.
More informationFor any use or distribution of this textbook, please cite as follows:
IT OpenCourseWare http://ocw.mit.edu Electromechanical Dynamics For any use or distribution of this textbook, please cite as follows: Woodson, Herbert H., and James R. elcher. Electromechanical Dynamics.
More informationNORCO COLLEGE SLO to PLO MATRIX
SLO to PLO MATRI CERTIFICATE/PROGRAM: Math ADT COURSE: MAT-1A Calculus I Calculate the limit of a function. SLO 2 Determine the continuity of a function. Find the derivatives of algebraic and transcendental
More informationThe... of a particle is defined as its change in position in some time interval.
Distance is the. of a path followed by a particle. Distance is a quantity. The... of a particle is defined as its change in position in some time interval. Displacement is a.. quantity. The... of a particle
More informationElastic Multibody Dynamics
H. Bremer Elastic Multibody Dynamics A Direct Ritz Approach Springer TABLE OF CONTENTS 1. INTRODUCTION 1 1.1 Background 1 1.2 Contents 5 2. AXIOMS AND PRINCIPLES 7 2.1 Axioms 7 2.2 Principles - the "Differential"
More informationVibrations and Waves in Continuous Mechanical Systems
Vibrations and Waves in Continuous Mechanical Systems Peter Hagedorn TU Darmstadt, Germany Anirvan DasGupta IIT Kharagpur, India BICENTENNIAL John Wiley & Sons, Ltd Preface xi 1 Vibrations of strings and
More informationNCEES Fundamentals of Engineering (FE) Examination ELECTRICAL EXAM SPECIFICATIONS
NCEES Fundamentals of Engineering (FE) Examination ELECTRICAL EXAM SPECIFICATIONS Effective Beginning with the April 2009 Examinations The FE examination is an 8-hour supplied-reference examination: 120
More informationELECTRICAL ENGINEERING
ELECTRICAL ENGINEERING Subject Code: EE Course Structure Sections/Units Section A Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Section B Section C Section D Section E Section F Section G Section H
More informationMonth. March APRIL. The Orchid School Baner Weekly Syllabus Overview Std : XI Subject : Physics. Activities/ FAs Planned.
The Orchid School Baner Weekly Syllabus Overview 2015-2016 Std : XI Subject : Physics Month Lesson / Topic Expected Learning Objective Activities/ FAs Planned Remark March Physical World and Measurement
More informationGeneral procedure for formulation of robot dynamics STEP 1 STEP 3. Module 9 : Robot Dynamics & controls
Module 9 : Robot Dynamics & controls Lecture 32 : General procedure for dynamics equation forming and introduction to control Objectives In this course you will learn the following Lagrangian Formulation
More information2002 Prentice Hall, Inc. Gene F. Franklin, J. David Powell, Abbas Emami-Naeini Feedback Control of Dynamic Systems, 4e
u Figure 2.1 Cruise-control model x Friction force bx m x u Figure 2.2 Free-body diagram for cruise control S P 278 Figure 2.3 Automobile suspension y m 2 k s b v car x m 1 k w Road surface r Inertial
More information1 2 Models, Theories, and Laws 1.5 Distinguish between models, theories, and laws 2.1 State the origin of significant figures in measurement
Textbook Correlation Textbook Correlation Physics 1115/2015 Chapter 1 Introduction, Measurement, Estimating 1.1 Describe thoughts of Aristotle vs. Galileo in describing motion 1 1 Nature of Science 1.2
More informationModeling and Simulation Revision III D R. T A R E K A. T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N
Modeling and Simulation Revision III D R. T A R E K A. T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N 0 1 4 Block Diagrams Block diagram models consist of two fundamental objects:
More informationAn Introduction to the Finite Element Method
An Introduction to the Finite Element Method Third Edition J. N. REDDY Department 01 Mechanical Engineering Texas A&M University College Station, Texas, USA 77843 11 Boston Burr Ridge, IL Dubuque, IA Madison,
More informationMETHODS OF THEORETICAL PHYSICS
METHODS OF THEORETICAL PHYSICS Philip M. Morse PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY Herman Feshbach PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY PART I: CHAPTERS 1 TO
More informationFor any use or distribution of this textbook, please cite as follows:
IT OpenCourseWare http://ocw.mit.edu Electromechanical Dynamics For any use or distribution of this textbook, please cite as follows: Woodson, Herbert H., and James R. elcher. Electromechanical Dynamics.
More informationStructural Dynamics Lecture 4. Outline of Lecture 4. Multi-Degree-of-Freedom Systems. Formulation of Equations of Motions. Undamped Eigenvibrations.
Outline of Multi-Degree-of-Freedom Systems Formulation of Equations of Motions. Newton s 2 nd Law Applied to Free Masses. D Alembert s Principle. Basic Equations of Motion for Forced Vibrations of Linear
More informationAPPLICATIONS OF VIBRATION TRANSDUCERS
APPLICATIONS OF VIBRATION TRANSDUCERS 1) Measurements on Structures or Machinery Casings: Accelerometers and Velocity Sensors Used in gas turbines, axial compressors, small and mid-size pumps. These sensors
More informationAnalytical Mechanics. of Space Systems. tfa AA. Hanspeter Schaub. College Station, Texas. University of Colorado Boulder, Colorado.
Analytical Mechanics of Space Systems Third Edition Hanspeter Schaub University of Colorado Boulder, Colorado John L. Junkins Texas A&M University College Station, Texas AIM EDUCATION SERIES Joseph A.
More informationOPTIMAL SPACECRAF1 ROTATIONAL MANEUVERS
STUDIES IN ASTRONAUTICS 3 OPTIMAL SPACECRAF1 ROTATIONAL MANEUVERS JOHNL.JUNKINS Texas A&M University, College Station, Texas, U.S.A. and JAMES D.TURNER Cambridge Research, Division of PRA, Inc., Cambridge,
More informationEXPERIENCE COLLEGE BEFORE COLLEGE
Mechanics, Heat, and Sound (PHY302K) College Unit Week Dates Big Ideas Subject Learning Outcomes Assessments Apply algebra, vectors, and trigonometry in context. Employ units in problems. Course Mathematics
More informationShigeji Fujita and Salvador V Godoy. Mathematical Physics WILEY- VCH. WILEY-VCH Verlag GmbH & Co. KGaA
Shigeji Fujita and Salvador V Godoy Mathematical Physics WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XIII Table of Contents and Categories XV Constants, Signs, Symbols, and General Remarks
More informationTEACHER CERTIFICATION STUDY GUIDE
Table of Contents Pg. Domain I. Mechanics Vectors (properties; addition and subtraction)... 129H1 Vector multiplication (dot and cross product)... 130H3 Motion along a straight line (displacement, velocity,
More informationModeling and Simulation Revision IV D R. T A R E K A. T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N
Modeling and Simulation Revision IV D R. T A R E K A. T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N 2 0 1 7 Modeling Modeling is the process of representing the behavior of a real
More informationApplied Numerical Analysis
Applied Numerical Analysis Using MATLAB Second Edition Laurene V. Fausett Texas A&M University-Commerce PEARSON Prentice Hall Upper Saddle River, NJ 07458 Contents Preface xi 1 Foundations 1 1.1 Introductory
More information41514 Dynamics of Machinery
41514 Dynamics of Machinery Theory, Experiment, Phenomenology and Industrial Applications Ilmar Ferreira Santos 1. Recapitulation Mathematical Modeling & Steps 2. Example System of Particle 3. Example
More informationTopic wise Tests. Complex Variables, Numerical Methods and Probability and Statistics.
ME-01 ME-02 ME-03 ME-04 GEM-1 GEM-2 GMC 1 Mechanics) GHT 1 Topic wise Tests Each test carries 25 marks and 45 minutes duration Test consists of 5 one mark questions and 10 two marks questions Tests will
More informationMathematica. 1? Birkhauser. Continuum Mechanics using. Fundamentals, Methods, and Applications. Antonio Romano Addolorata Marasco.
Antonio Romano Addolorata Marasco Continuum Mechanics using Mathematica Fundamentals, Methods, and Applications Second Edition TECHNISCHE INFORM ATIONSB IBLIOTHEK UNIVERSITATSBtBLIOTHEK HANNOVER 1? Birkhauser
More informationvii Preface ix Acknowledgements
Series Preface vii Preface ix Acknowledgements xi Chapter 1: Introduction 1 1.1 Brief History of Underwater Sound Transducers..... 2 1.2 Underwater Transducer Applications... 9 1.3 General Description
More informationPublic Service Commission, West Bengal
Public Service Commission, West Bengal Syllabus for the Written Test for recruitment to the posts of ASSISTANT ENGINEER (Agri - Mechanical) in West Bengal Service of Agricultural Engineers Mechanical Engineering
More informationFoundations of Ultraprecision Mechanism Design
Foundations of Ultraprecision Mechanism Design S.T. Smith University of North Carolina at Charlotte, USA and D.G. Chetwynd University of Warwick, UK GORDON AND BREACH SCIENCE PUBLISHERS Switzerland Australia
More informationANALYTICAL MECHANICS. LOUIS N. HAND and JANET D. FINCH CAMBRIDGE UNIVERSITY PRESS
ANALYTICAL MECHANICS LOUIS N. HAND and JANET D. FINCH CAMBRIDGE UNIVERSITY PRESS Preface xi 1 LAGRANGIAN MECHANICS l 1.1 Example and Review of Newton's Mechanics: A Block Sliding on an Inclined Plane 1
More informationAnalysis and Control of Multi-Robot Systems. Elements of Port-Hamiltonian Modeling
Elective in Robotics 2014/2015 Analysis and Control of Multi-Robot Systems Elements of Port-Hamiltonian Modeling Dr. Paolo Robuffo Giordano CNRS, Irisa/Inria! Rennes, France Introduction to Port-Hamiltonian
More informationCHIEF ENGINEER REG III/2 APPLIED MECHANICS
CHIEF ENGINEER REG III/2 APPLIED MECHANICS LIST OF TOPICS A B C D E F G H I J Vector Representation Statics Friction Kinematics Dynamics Machines Strength of Materials Hydrostatics Hydrodynamics Control
More informationNonlinear Problems of Elasticity
Stuart S. Antman Nonlinear Problems of Elasticity With 105 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Contents Preface vn Chapter I. Background
More informationDepartment of Mechanical Engineering
UNDERGRADUATE COURSE DESCRIPTIONS 15102 Statics 3 Cr. Basic concepts. Forces, moments, and couples. Equilibrium of particles and rigid bodies. First and second moments. Structures (trusses, frames, machines).
More informationCOURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics
COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid
More informationAEROSPACE ENGINEERING
AEROSPACE ENGINEERING Subject Code: AE Course Structure Sections/Units Topics Section A Engineering Mathematics Topics (Core) 1 Linear Algebra 2 Calculus 3 Differential Equations 1 Fourier Series Topics
More informationMassachusetts Tests for Educator Licensure (MTEL )
Massachusetts Tests for Educator Licensure (MTEL ) FIELD 11: PHYSICS TEST OBJECTIVES Subarea Multiple-Choice Range of Objectives Approximate Test Weighting I. Nature of Science 01 05 12% II. Force and
More informationHistory of Physics: History of Physics: - Identify the contributions of key figures in the history of physics.
Texas University Interscholastic League Contest Event: Science (Physics) The contest challenges students to read widely in physics, to understand the significance of experiments rather than to recall obscure
More information