Holdings: Modeling and control of engineering systems

Modeling and control of engineering systems:

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Bibliographic Details
Main Author:	De Silva, Clarence W. (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] CRC Press 2009
Subjects:	Ingenieurwissenschaften Mathematisches Modell Automatic control Control theory Engineering > Mathematical models Systems engineering > Mathematical models Systemtheorie Regelungstechnik
Online Access:	Inhaltsverzeichnis Klappentext
Item Description:	Includes bibliographical references and index
Physical Description:	XXIX, 766 S. Ill., graph. Darst.
ISBN:	9781420076868

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adam_text	Contents Preface .............................................................................................................................xix Acknowledgments ........................................................................................................xxiii Author ............................................................................................................................xxv Further Reading ...........................................................................................................xxvii Units and Conversions (Approximate) .......................................................................xxix 1 Modeling and Control of Engineering Systems ...................................................1 1.1 Control Engineering .....................................................................................................1 1.2 Application Areas .........................................................................................................2 1.3 Importance of Modeling ..............................................................................................4 1.4 History of Control Engineering ..................................................................................5 1.5 Organization of the Book .............................................................................................7 Problems .................................................................................................................................9 2 Modeling of Dynamic Systems ............................................................................11 2.1 Dynamic Systems ........................................................................................................11 2.1.1 Terminology ......................................................................................................12 2.2 Dynamic Models .........................................................................................................12 2.2.1 Model Complexity ...........................................................................................13 2.2.2 Model Types .....................................................................................................13 2.2.3 Types of Analytical Models ............................................................................14 2.2.4 Principle of Superposition ..............................................................................15 2.2.5 Lumped Model of a Distributed System ......................................................16 2.2.5.1 Heavy Spring .....................................................................................17 2.2.5.2 Kinetic Energy Equivalence .............................................................18 2.2.5.3 Natural Frequency Equivalence ......................................................19 2.3 Lumped Elements and Analogies ............................................................................20 2.3.1 Across Variables and Through Variables .....................................................20 2.3.2 Mechanical Elements .......................................................................................20 2.3.2.1 Mass (Inertia) Element ......................................................................21 2.3.2.2 Spring (Stiffness) Element ................................................................22 2.3.2.3 Damping (Dissipation) Element ......................................................23 2.3.3 Electrical Elements ...........................................................................................23 2.3.3.1 Capacitor Element .............................................................................24 2.3.3.2 Inductor Element ...............................................................................25 2.3.3.3 Resistor (Dissipation) Element .........................................................26 2.3.4 Fluid Elements ..................................................................................................26 2.3.4.1 Fluid Capacitor or Accumulator (A-Type Element) ......................27 2.3.4.2 Fluid Inertor (Т -Type Element) ........................................................27 2.3.4.3 Fluid Resistor (D -Туре Element) ......................................................27 2.3.4.4 Derivation of Constitutive Equations .............................................27 2.3.5 Thermal Elements ............................................................................................32 2.3.5.1 Constitutive Equations .....................................................................32 vii viii Contents 2.3.5.2 Three Dimensional Conduction ......................................................36 2.3.5.3 Biot Number .......................................................................................37 2.3.6 Natural Oscillations ........................................................................................37 2.4 Analytical Model Development ................................................................................39 2.4.1 Steps of Model Development .........................................................................40 2.4.2 I/O Models ........................................................................................................40 2.4.3 State-Space Models ..........................................................................................40 2.4.3.1 State-Space ..........................................................................................41 2.4.3.2 Properties of State Models ...............................................................41 2.4.3.3 Linear State Equations ......................................................................42 2.4.4 Time-Invariant Systems ..................................................................................45 2.4.5 Systematic Steps for State Model Development ..........................................47 2.4.6 I/O Models f rom State-Space Models ...........................................................50 Problems ...............................................................................................................................53 Model Linearization ...............................................................................................63 3.1 Model Linearization ...................................................................................................63 3.1.1 Linearization about an Operating Point .......................................................64 3.1.2 Function of Two Variables ..............................................................................66 3.2 Nonlinear State-Space Models ..................................................................................66 3.2.1 Linearization ....................................................................................................67 3.2.2 Reduction of System Nonlinearities ..............................................................68 3.3 Nonlinear Electrical Elements ...................................................................................85 3.3.1 Capacitor ...........................................................................................................85 3.3.2 Inductor .............................................................................................................86 3.3.3 Resistor ..............................................................................................................86 3.4 Linearization Using Experimental Operating Curves ..........................................87 3.4.1 Torque-Speed Curves of Motors ....................................................................87 3.4.2 Linear Models for Motor Control ..................................................................88 Problems ...............................................................................................................................89 Linear Graphs .........................................................................................................97 4.1 Variables and Sign Convention .................................................................................97 4.1.1 Through Variables and Across Variables .....................................................97 4.1.2 Sign Convention ...............................................................................................97 4.2 Linear Graph Elements .............................................................................................100 4.2.1 Single-Port Elements ......................................................................................100 4.2.1.1 Source Elements ...............................................................................101 4.2.1.2 Effects of Source Elements .............................................................102 4.2.2 Two-Port Elements .........................................................................................102 4.2.2.1 Transformer ......................................................................................103 4.2.2.2 Electrical Transformer ....................................................................104 4.2.2.3 Gyrator ..............................................................................................105 4.3 Linear Graph Equations ...........................................................................................107 4.3.1 Compatibility (Loop) Equations ..................................................................107 4.3.1.1 Sign Convention ...............................................................................107 4.3.1.2 Number of Primary Loops .........................................................107 4.3.2 Continuity (Node) Equations .......................................................................109 4.3.3 Series and Parallel Connections ..................................................................110 Contents ix 4.4 State Models from Linear Graphs ...........................................................................HO 4.4.1 System Order..................................................................................................111 4.4.2 Sign Convention.............................................................................................111 4.4.3 Steps of Obtaining a State Model................................................................112 4.4.4 General Observation ......................................................................................112 4.4.5 Topological Result ..........................................................................................113 4.5 Miscellaneous Examples.......................................................................................... 128 4.5.1 Amplifiers .......................................................................................................128 4.5.1.1 Linear Graph Representation .........................................................129 4.5.2 DC Motor ........................................................................................................130 4.5.3 Linear Graphs of Thermal Systems .............................................................134 4.5.3.1 Model Equations ..............................................................................134 Problems .............................................................................................................................138 Transfer-Function and Frequency-Domain Models ........................................149 5.1 Laplace and Fourier Transforms .............................................................................149 5.1.1 Laplace Transform .........................................................................................150 5.1.2 Laplace Transform of a Derivative ..............................................................150 5.1.3 Laplace Transform of an Integral ................................................................151 5.1.4 Fourier Transform .........................................................................................151 5.2 Transfer-Function ......................................................................................................152 5.2.1 Transfer-Function Matrix .............................................................................153 5.3 Frequency Domain Models .....................................................................................159 5.3.1 Frequency Transfer-Function (Frequency Response Function) ..............159 5.3.1.1 Response to a Harmonic Input ......................................................159 5.3.1.2 Magnitude (Gain) and Phase .........................................................160 5.3.2 Bode Diagram (Bode Plot) and Nyquist Diagram .....................................161 5.4 Transfer-Functions of Electro-Mechanical Systems .............................................162 5.4.1 Significance of Transfer-Functions in Mechanical Systems .......................162 5.4.2 Mechanical Transfer-Functions ...................................................................163 5.4.2.1 Mechanical Impedance and Mobility ...........................................164 5.4.3 Interconnection Laws ....................................................................................164 5.4.3.1 Interconnection Laws for Mechanical Impedance and Mobility .............................................................................................164 5.4.3.2 Interconnection Laws for Electrical Impedance and Admittance .......................................................................................164 5.4.3.3 Л-Туре Transfer-Functions and T-Type Transfer-Functions ..........................................................................165 5.4.4 Transfer-Functions of Basic Elements .........................................................166 5.4.5 Transmissibility Function .............................................................................170 5.4.5.1 Force Transmissibility .....................................................................170 5.4.5.2 Motion Transmissibility .................................................................171 5.4.5.3 Single-Degree-of-Freedom System ...............................................171 5.4.5.4 Two-Degree-of-Freedom System ...................................................173 5.5 Equivalent Circuits and Linear Graph Reduction ................................................175 5.5.1 Thevenin s Theorem for Electrical Circuits ................................................176 5.5.2 Mechanical Circuit Analysis Using Linear Graphs ..................................179 5.5.3 Summary of Thevenin Approach for Mechanical Circuits .....................188 5.5.3.1 General Steps ....................................................................................188 Contents 5.6 Block Diagrams and State-Space Models..............................................................189 5.6.1 Simulation Block Diagrams ..........................................................................191 5.6.2 Principle of Superposition ............................................................................191 5.6.3 Causality and Physical Realizability ..........................................................207 Problems .............................................................................................................................208 Response Analysis and Simulation ...................................................................217 6.1 Analytical Solution ...................................................................................................217 6.1.1 Homogeneous Solution .................................................................................218 6.1.1.1 Repeated Poles .................................................................................218 6.1.2 Particular Solution .........................................................................................219 6.1.3 Impulse Response Function .........................................................................219 6.1.3.1 Convolution Integral .......................................................................221 6.1.4 Stability ............................................................................................................222 6.2 First-Order Systems ..................................................................................................223 6.3 Second-Order Systems .............................................................................................225 6.3.1 Free Response of an Undamped Oscillator ...............................................225 6.3.2 Free Response of a Damped Oscillator .......................................................227 6.3.2.1 Case 1: Underdamped Motion (ζ< ) ............................................228 6.3.2.2 Case 2: Overdamped Motion (ζ> 1)...............................................229 6.3.2.3 Case 3: Critically Damped Motion (ζ=ΐ) .....................................230 6.4 Forced Response of a Damped Oscillator .............................................................232 6.4.1 Impulse Response ..........................................................................................232 6.4.2 The Riddle of Zero ICs ..................................................................................234 6.4.3 Step Response .................................................................................................234 6.4.4 Response to Harmonic Excitation ...............................................................236 6.5 Response Using Laplace Transform .......................................................................241 6.5.1 Step Response Using Laplace Transforms .................................................242 6.5.2 Incorporation of ICs .......................................................................................243 6.5.2.1 Step Response of a First-Order System ........................................243 6.5.2.2 Step Response of a Second-Order System ...................................244 6.6 Determination of ICs for Step Response ...............................................................245 6.7 Computer Simulation ...............................................................................................253 6.7.1 Use of Simulink® in Computer Simulation ................................................254 6.7.1.1 Starting Simulink® ..........................................................................254 6.7.1.2 Basic Elements ..................................................................................255 6.7.1.3 Building an Application .................................................................255 6.7.1.4 Running a Simulation .....................................................................256 Problems .............................................................................................................................260 Control System Structure and Performance .....................................................271 7.1 Control System Structure .........................................................................................271 7.1.2 Feedforward Control .....................................................................................272 7.1.2.1 Computed-Input Control ................................................................274 7.1.3 Terminology ....................................................................................................276 7.1.4 Programmable Logic Controllers (PLCs) ...................................................277 7.1.4.1 PLC Hardware .................................................................................278 7.1.5 Distributed Control .......................................................................................280 7.1.5.1 A Networked Application ..............................................................281 Contents xi 7.1.6 Hierarchical Control ......................................................................................283 7.2 Control System Performance ...................................................................................285 7.2.1 Performance Specification in Time-Domain ..............................................286 7.2.2 Simple Oscillator Model ...............................................................................288 7.3 Control Schemes ........................................................................................................291 7.3.1 Feedback Control with PID Action .............................................................294 7.4 Steady-State Error and Integral Control ................................................................296 7.4.1 Final Value Theorem (FVT) ..........................................................................297 7.4.2 Manual Reset ..................................................................................................297 7.4.3 Automatic Reset (Integral Control) .............................................................299 7.4.4 Reset Windup .................................................................................................299 7.5 System Type and Error Constants ..........................................................................300 7.5.1 Definition of System Type .............................................................................301 7.5.2 Error Constants ..............................................................................................301 7.5.2.1 Position Error Constant Kp .............................................................302 7.5.2.2 Velocity Error Constant ίς .............................................................302 7.5.2.3 Acceleration Error Constant Ka ......................................................303 7.5.3 System Type as a Robustness Property ......................................................305 7.5.4 Performance Specification Using s-Plane ...................................................305 7.6 Control System Sensitivity .......................................................................................309 7.6.1 System Sensitivity to Parameter Change ....................................................310 Problems .............................................................................................................................313 Stability and Root Locus Method ......................................................................329 8.1 Stablility ......................................................................................................................329 8.1.1 Natural Response ...........................................................................................329 8.2 Routh-Hurwitz Criterion .........................................................................................331 8.2.1 Routh Array ....................................................................................................332 8.2.2 Auxiliary Equation (Zero-Row Problem) ...................................................333 8.2.3 Zero Coefficient Problem ..............................................................................334 8.2.4 Relative Stability ............................................................................................335 8.3 Root Locus Method ...................................................................................................336 8.3.1 Rules for Plotting Root Locus ......................................................................338 8.3.1.1 Complex Numbers ..........................................................................338 8.3.1.2 Root Locus Rules .............................................................................340 8.3.1.3 Explanation of the Rules .................................................................341 8.3.2 Steps of Sketching Root Locus .....................................................................343 8.3.4 Variable Parameter in Root Locus ...............................................................356 8.4 Stability in the Frequency Domain ........................................................................358 8.4.1 Response to a Harmonic Input ....................................................................359 8.4.2 Complex Numbers .........................................................................................360 8.4.3 Resonant Peak and Resonant Frequency ...................................................361 8.4.4.1 Damped Simple Oscillator .............................................................363 8.4.3.2 Peak Magnitude ...............................................................................365 8.4.4 Half-Power Bandwidth .................................................................................365 8.4.4.1 Damped Simple Oscillator .............................................................365 8.4.5 Marginal Stability ..........................................................................................367 8.4.5.1 The (1,0) Condition ..........................................................................367 8.4.6 PM and GM .....................................................................................................369 xii Contents 8.4.6.1 GM ..................................................................................................... 369 8.4.6.2 PM ......................................................................................................369 8.4.7 Bode and Nyquist Plots .................................................................................370 8.4.8 PM and Damping Ratio Relation .................................................................372 8.5 Bode Diagram Using Asymptotes .......................................................................... 373 8.5.1 Slope-Phase Relationship for Bode Magnitude Curve .............................375 8.5.1.1 Nonminimum-Phase Systems .......................................................376 8.5.2 Ambiguous Cases of GM and PM ...............................................................383 8.5.3 Destabilizing Effect of Time Delays ............................................................384 8.6 Nyquist Stability Criterion .......................................................................................385 8.6.1 Nyquist Stability Criterion ...........................................................................386 8.6.2 Loop Poles on the Imaginary Axis ..............................................................387 8.6.3 Steps for Applying the Nyquist Criterion ..................................................387 8.6.4 Relative Stability Specification .....................................................................394 8.7 Nichols Chart .............................................................................................................394 8.7.1 Graphical Tools for Closed-Loop Frequency Response ...........................394 8.7.2 M Circles and N Circles ................................................................................395 8.7.3 Nichols Chart ..................................................................................................398 Problems .............................................................................................................................400 9 Controller Design and Tuning ............................................................................409 9.1 Controller Design and Tuning ................................................................................409 9.1.1 Design Specifications ....................................................................................410 9.1.2 Time-Domain Design Techniques ...............................................................411 9.1.3 Frequency-Domain Design Techniques .....................................................411 9.2 Conventional Time-Domain Design ......................................................................411 9.2.1 Proportional Plus Derivative Controller Design .......................................412 9.2.2 Design Equations ...........................................................................................414 9.3 Compensator Design in the Frequency Domain ..................................................414 9.3.1 Lead Compensation .......................................................................................415 9.3.1.1 Design Steps for a Lead Compensator .........................................417 9.3.2 Lag Compensation .........................................................................................420 9.3.2.1 Design Steps for a Lag Compensator ............................................420 9.3.3 Design Specifications in Compensator Design .........................................423 9.4 Design Using Root Locus .........................................................................................427 9.4.1 Design Steps Using Root Locus ...................................................................427 9.4.2 Lead Compensation .......................................................................................428 9.4.3 Lag Compensation .........................................................................................431 9.5 Controller Tuning ......................................................................................................436 9.5.1 Ziegler-Nichols Tuning ................................................................................436 9.5.2 Reaction Curve Method ................................................................................437 9.5.3 Ultimate Response Method ..........................................................................439 Problems .............................................................................................................................441 10 Digital Control ......................................................................................................447 10.1 Digital Control .........................................................................................................447 10.1.1 Computer Control Systems .......................................................................447 10.1.2 Components of a Digital Control System ...............................................448 10.1.3 Advantages of Digital Control ..................................................................449 Contents xiii 10.2 Signal Sampling and Control Bandwidth ............................................................449 10.2.1 Sampling Theorem .....................................................................................450 10.2.2 Antialiasing Filter ......................................................................................450 10.2.3 Control Bandwidth .....................................................................................451 10.2.4 Bandwidth Design of a Control System ..................................................454 10.2.5 Control Cycle Time ....................................................................................455 10.3 Digital Control Using z-Transform .......................................................................456 10.3.1 z-Transform .................................................................................................457 10.3.2 Difference Equations .................................................................................458 10.3.3 Discrete Transfer Functions ......................................................................460 10.3.4 Time Delay ..................................................................................................461 10.3.5 s-z Mapping ................................................................................................462 10.3.6 Stability of Discrete Models ......................................................................464 10.3.7 Discrete Final Value Theorem (FVT) .......................................................464 10.3.8 Pulse Response Function ..........................................................................466 10.3.8.1 Unit Pulse and Unit Impulse ....................................................467 10.4 Digital Compensation .............................................................................................467 10.4.1 Hold Operation ...........................................................................................468 10.4.2 Discrete Compensator ...............................................................................469 10.4.3 Direct Synthesis of Digital Compensators ..............................................473 10.4.4 Causality Requirement ..............................................................................473 10.4.5 Stability Analysis Using Bilinear Transformation ................................474 10.4.6 Computer Implementation ........................................................................475 Problems .............................................................................................................................476 11 Advanced Control .................................................................................................483 11.1 Modern Control .......................................................................................................483 11.2 Time Response .........................................................................................................484 11.2.1 The Scalar Problem ....................................................................................484 11.2.1.1 Homogeneous Case (Input и = 0).............................................484 11.2.1.2 Nonhomogeneous (Forced) Case .............................................484 11.2.2 Time Response of a State-Space Model ...................................................486 11.2.2.1 Case of Constant System Matrix ..............................................486 11.2.2.2 Matrix Exponential ....................................................................486 11.2.2.3 Methods of Computing e4 ........................................................487 11.2.3 Time Response by Laplace Transform ....................................................494 11.2.4 Output Response ........................................................................................495 11.2.4.1 Transfer Function Matrix ..........................................................495 11.2.5 Modal Response .........................................................................................496 11.2.5.1 State Response through Modal Response ..............................497 11.2.5.2 Advantages of Modal Decomposition .....................................497 11.2.6 Time-Varying Systems ...............................................................................501 11.2.6.1 Properties of the State-Transition Matrix ................................503 11.3 System Stability ........................................................................................................503 11.3.1 Stability of Linear Systems ........................................................................503 11.3.1.1 General Case of Repeated Eigenvalues ...................................505 11.3.1.2 Generalized Eigenvectors .........................................................505 11.3.2 Stability from Modal Response for Repeated Eigenvalues ..................507 11.3.2.1 Possibilities of Jordan Blocks and Modal Responses ............508 xiv Contents 11.3.3 Equilibrium ................................................................................................. 508 11.3.3.1 Bounded-Input Bounded-State (BIBS) Stability .....................509 11.3.3.2 Bounded-Input Bounded-Output (BIBO) Stability ................509 11.3.4 Stability of Linear Systems ........................................................................509 11.3.4.1 Frobenius Theorem ...................................................................509 11.3.4.2 First Method of Lyapunov ........................................................510 11.3.5 Second Method (Direct Method) of Lyapunov ......................................513 11.3.5.1 Lyapunov Equation ....................................................................515 11.4 Controllability and Observability .........................................................................517 11.4.1 Minimum (Irreducible) Realizations .......................................................521 11.4.2 Companion Form and Controllability ....................................................525 11.4.3 Implication of Feedback Control ..............................................................525 11.4.4 State Feedback .............................................................................................526 11.4.5 Stabilizability ..............................................................................................527 11.5 Modal Control ..........................................................................................................528 11.5.1 Controller Design by Pole Placement ......................................................529 11.5.2 Pole Placement in the Multiinput Case ...................................................534 11.5.3 Procedure of Pole Placement Design .......................................................536 11.5.4 Placement of Repeated Poles ....................................................................538 11.5.5 Placement of Some Closed-Loop Poles at Open-Loop Poles ........................................................................................539 11.5.6 Pole Placement with Output Feedback ...................................................542 11.6 Optimal Control ......................................................................................................544 11.6.1 Optimization through Calculus of Variations .......................................544 11.6.2 Cost Function having a Function of End State .......................................555 11.6.3 Extension to the Vector Problem ..............................................................556 11.6.4 General Optimal Control Problem ..........................................................557 11.6.5 Boundary Conditions ................................................................................559 11.6.6 Hamiltonian Formulation .........................................................................559 11.6.7 Pontryagin s Minimum Principle ............................................................559 11.7 Linear Quadratic Regulator (LQR) .......................................................................560 11.7.1 The Euler Equations ...................................................................................560 11.7.2 Boundary Conditions ................................................................................561 11.7.3 Infinite-Time LQR ......................................................................................562 11.7.4 Control System Design ..............................................................................566 11.8 Other Advanced Control Techniques ...................................................................569 11.8.1 Nonlinear Feedback Control ....................................................................569 11.8.2 Adaptive Control ........................................................................................571 11.8.3 Sliding Mode Control ................................................................................573 11.8.4 Linear Quadratic Gaussian (LOG) Control ............................................574 11.8.5 Н„ Control ...................................................................................................576 11.9 Fuzzy Logic Control ................................................................................................577 11.9.1 Fuzzy Logic .................................................................................................578 11.9.2 Fuzzy Sets and Membership Functions ..................................................579 11.9.3 Fuzzy Logic Operations ............................................................................580 11.9.3.1 Complement (Negation, NOT) .................................................580 11.9.3.2 Union (Disjunction, OR) ............................................................580 11.9.3.3 Intersection (Conjunction, AND) .............................................581 11.9.3.4 Implication (If-Then) ..................................................................582 Contents xv 11.9.4 Compositional Rule of Inference .............................................................583 11.9.5 Extensions to Fuzzy Decision Making ....................................................584 11.9.6 Basics of Fuzzy Control .............................................................................585 11.9.7 Fuzzy Control Surface ...............................................................................589 Problems .............................................................................................................................593 12 Control System Instrumentation ........................................................................603 12.1 Control System Instrumentation ...........................................................................603 12.2 Component Interconnection ..................................................................................605 12.2.1 Cascade Connection of Devices ...............................................................605 12.2.2 Impedance Matching Amplifiers .............................................................607 12.2.3 Operational Amplifier ...............................................................................607 12.2.3.1 Use of Feedback in Op-Amps ...................................................609 12.2.4 Instrumentation Amplifiers ......................................................................609 12.2.4.1 Differential Amplifier ................................................................609 12.3 Motion Sensors ........................................................................................................610 12.3.1 Linear-Variable Differential Transformer (LVDT) .................................611 12.3.2 Signal Conditioning ...................................................................................612 12.3.3 DC Tachometer ...........................................................................................613 12.3.3.1 Electronic Commutation ...........................................................614 12.3.4 Piezoelectric Accelerometer ......................................................................614 12.3.4.1 Charge Amplifier .......................................................................616 12.3.5 Digital Transducers ....................................................................................616 12.3.6 Shaft Encoders ............................................................................................617 12.3.7 Optical Encoder ..........................................................................................618 12.4 Stepper Motors .........................................................................................................619 12.4.1 Stepper Motor Classification .....................................................................620 12.4.2 Driver and Controller ................................................................................620 12.4.3 Stepper Motor Selection ............................................................................623 12.4.3.1 Torque Characteristics and Terminology ...............................623 12.4.3.2 Stepper Motor Selection Process ..............................................625 12.5 dc Motors ..................................................................................................................630 12.5.1 Rotor and Stator..........................................................................................632 12.5.2 Commutation ..............................................................................................633 12.5.3 Brushless dc Motors ...................................................................................633 12.5.4 DC Motor Equations ..................................................................................634 12.5.4.1 Steady-State Characteristics ......................................................635 12.5.5 Experimental Model for dc Motor ...........................................................637 12.5.5.1 Electrical Damping Constant ...................................................637 12.5.5.2 Linearized Experimental Model ..............................................637 12.5.6 Control of dc Motors ..................................................................................638 12.5.6.1 Armature Control .......................................................................639 12.5.6.2 Motor Time Constants ...............................................................640 12.5.6.3 Field Control ................................................................................641 12.5.7 Feedback Control of dc Motors ................................................................642 12.5.7.1 Velocity Feedback Control ........................................................643 12.5.7.2 Position Plus Velocity Feedback Control ................................643 12.5.7.3 Position Feedback with PID Control .......................................644 12.5.8 Motor Driver ...............................................................................................644 xvi Contents 12.5.8.1 Interface Board ............................................................................645 12.5.8.2 Drive Unit ....................................................................................646 12.5.9 dc Motor Selection ......................................................................................648 12.5.9.1 Motor Data and Specifications .................................................648 12.5.9.2 Selection Considerations ...........................................................649 12.5.9.3 Motor Sizing Procedure ............................................................650 12.5.9.4 Inertia Matching .........................................................................651 12.5.9.5 Drive Amplifier Selection ..........................................................651 12.5.10 Summary of Motor Selection ....................................................................652 12.6 Control Experiments Using LabVIEW® ................................................................654 12.6.1 Experiment 1: Tank Level Display ...........................................................654 12.6.1.1 Procedure ....................................................................................654 12.6.1.2 Creating the Front Panel ...........................................................654 12.6.1.3 Creating the Block Diagram .....................................................656 12.6.1.4 Calibrating the VI .......................................................................658 12.6.1.5 Finding the Resistances of the Process Valves .......................659 12.6.2 Experiment 2: Process Control Using LabVIEW® ..................................660 12.6.2.1 Two-Tank System ........................................................................660 12.6.2.2 Description of the Front Panel ..................................................661 12.6.2.3 ON/OFF Control Algorithm .....................................................662 12.6.2.4 Proportional Control Algorithm ..............................................662 12.6.2.5 Single-Tank Process Control .....................................................662 Problems .............................................................................................................................666 Appendix A: Transform Techniques ...........................................................................677 A.I Laplace Transform ...................................................................................................677 A.I.I Laplace Transforms of Some Common Functions .................................678 A.I. 1.1 Laplace Transform of a Constant .............................................679 A.I. 1.2 Laplace Transform of the Exponential ....................................679 A.I. 1.3 Laplace Transform of Sine and Cosine ....................................679 A.l.l^ Laplace Transform of a Derivative ...........................................681 A.1.2 Table of Laplace Transforms .....................................................................682 A.2 Response Analysis ...................................................................................................682 A.3 Transfer Function ....................................................................................................689 A.4 Fourier Transform ...................................................................................................691 A.4.1 Frequency-Response Function (Frequency Transfer Function) ...........692 A.5 Thes-Plane ...............................................................................................................693 A.5.1 An Interpretation of Laplace and Fourier Transforms .........................693 A.5.2 Application in Circuit Analysis ................................................................693 Appendix B: Software Tools ........................................................................................695 B.I Simulink® ............................................................................................................. .695 B.2 MATLAB® .................................................... ľZZ ZZZZZZľľZZZZZ695 8.2.1 Computations ..............................................................................................695 8.2.2 Arithmetic ...................................................................................................6% 8.2.3 Arrays ...........................................................................................................697 8.2.4 Relational and Logical Operations ..........................................................698 B.2.5 Linear Algebra ............................................................................................698 B.2.6 M-Files ..........................................................................................................699 Contents xvii В.З Control Systems Toolbox ........................................................................................700 В.3.1 Compensator Design Example .................................................................700 B.3.1.1 Building the System Model .......................................................700 B.3.1.2 Importing Model into SISO Design Tool ................................700 B.3.1.3 Adding Lead and Lag Compensators .....................................703 B.3.2 PID Control with Ziegler-Nichols Tuning .............................................703 B.3.2.1 Proportional Control ..................................................................703 B.3.2.2 PI Control .....................................................................................705 B.3.2.3 PID Control .................................................................................707 B.3.3 Root Locus Design Example .....................................................................708 B.3.4 MATLAB® Modern Control Examples ....................................................708 B.3.4.1 Pole Placement of a Third Order Plant ....................................708 B.3.4.2 Linear Quadratic Regulator (LQR) for a Third Order Plant ..............................................................................................711 B.3.4.3 Pole Placement of an Inverted Pendulum on Mobile Carriage ..........................................................................712 B.3.4.4 LQG Controller for an Inverted Pendulum Mounted with Mobile Carriage .................................................................715 B.4 Fuzzy Logic Toolbox ...............................................................................................716 B.4.1 Graphical Editors ........................................................................................716 B.4.2 Command Line Driven FIS Design .........................................................717 B.4.3 Practical Stand-Alone Implementation in С ...........................................717 B.5 LabVIEW® .................................................................................................................719 B.5.1 Introduction ................................................................................................719 B.5.2 Some Key Concepts ....................................................................................719 B.5.3 Working with LabVIEW® ..........................................................................719 B.5.3.1 Front Panel ...................................................................................720 B.5.3.2 Block Diagrams ...........................................................................721 B.5.3.3 Tools Palette ................................................................................722 B.5.3.4 Controls Palette ..........................................................................723 B.5.3.5 Functions Palette ........................................................................723 B.6 LabVIEW® Sound and Vibration Tools .................................................................724 B.6.1 Sound and Vibration Toolkit ....................................................................724 B.6.2 Signal Acquisition and Simulation ..........................................................725 B.6.2.1 Integration ...................................................................................725 B.6.2.2 Vibration-Level Measurements ................................................725 B.6.2.3 Frequency Analysis ....................................................................726 B.6.2.4 Transient Analysis ......................................................................726 Appendix C: Review of Linear Algebra .....................................................................729 C.I Vectors and Matrices ...............................................................................................729 C.2 Vector-Matrix Algebra ...........................................................................................731 C.2.1 Matrix Addition and Subtraction .............................................................732 C.2.2 Null Matrix ..................................................................................................733 C.2.3 Matrix Multiplication .................................................................................733 C.2.4 Identity Matrix ............................................................................................734 C.3 Matrix Inverse ..........................................................................................................734 xvjj¡ Contents C.3.1 Matrix Transpose .......................................................................................735 C.3.2 Trace of a Matrix .........................................................................................736 C.3.3 Determinant of a Matrix ...........................................................................736 C.3.4 Adjoint of a Matrix .....................................................................................737 C.3.5 Inverse of a Matrix .....................................................................................738 C.4 Vector Spaces ............................................................................................................739 C.4.1 Field (F) ........................................................................................................739 C.4.2 Vector Space (L) ...........................................................................................739 C.4.3 Subspace S of L ...........................................................................................740 C.4.4 Linear Dependence ....................................................................................740 C.4.5 Bases and Dimension of a Vector Space ..................................................740 C.4.6 Inner Product ..............................................................................................741 C.4.7 Norm ............................................................................................................741 C.4.8 Gram-Schmidt Orthogonalization ..........................................................742 C.4.9 Modified Gram-Schmidt Procedure .......................................................742 C.5 Determinants ...........................................................................................................742 C.S.I Properties of Determinant of a Matrix ....................................................743 C.5.2 Rank of a Matrix .........................................................................................743 C.6 System of Linear Equations ...................................................................................743 C.7 Quadratic Forms ......................................................................................................744 C.8 Matrix Eigenvalue Problem ...................................................................................745 C.e.l Characteristic Polynomial .........................................................................745 C.8.2 Characteristic Equation .............................................................................745 C.8.3 Eigenvalues .................................................................................................745 C.8.4 Eigenvectors ................................................................................................745 C.9 Matrix Transformations ..........................................................................................745 C.9.1 Similarity Transformation ........................................................................745 C.9.2 Orthogonal Transformation ......................................................................746 CIO Matrix Exponential .................................................................................................746 C.lO.l Computation of Matrix Exponential .......................................................747 Index .............................................................................................................................................749 Modeling and Control of Engineering Systems Clarence W. de Silva Developed from the author s academic and industrial experiences, Modeling and Control of Engineering Systems provides a unified treatment of the modeling of mechanical, electrical, fluid, and thermal systems and then systematically covers conventional, advanced, and intelligent control, instrumentation, experimentation, and design. It includes theory, analytical techniques, popular computer tools, simulation details, and applications. Overcoming the deficiencies of other modeling and control books, this text relates the model to the physical system and addresses why a particular control technique is suitable for controlling the system. Although MATLAB®, Simulink®, and LabVIEW™ are used, the author fully explains the fundamentals and analytical basis behind the methods, the choice of proper tools to analyze a given problem, the ways to interpret and validate the results, and the limitations of the software tools. This approach enables readers to thoroughly grasp the core foundation of the subject and understand how to apply the concepts in practice. Features • Takes an integrated approach to modeling engineering systems that draws from equivalent circuits, Thevenin s theorem, and linear (line) graphs • Describes conventional and popular control techniques both in time domain and frequency domain • Covers intelligent control techniques, such as fuzzy logic control • Presents important aspects of laboratory experimentation, including control system instrumentation • Discusses the use of MATLAB, Simulink, LabVIEW, and the associated toolboxes • Includes a large number of real-world examples Control ensures accurate operation of a system. Proper control of an engineering system requires a basic understanding and a suitable representation (model) of the system. This book builds up expertise in modeling and control so that readers can further their analytical skills in hands-on settings.
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spelling	De Silva, Clarence W. Verfasser aut Modeling and control of engineering systems Clarence W. de Silva Boca Raton [u.a.] CRC Press 2009 XXIX, 766 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Ingenieurwissenschaften Mathematisches Modell Automatic control Control theory Engineering Mathematical models Systems engineering Mathematical models Systemtheorie (DE-588)4058812-9 gnd rswk-swf Regelungstechnik (DE-588)4076594-5 gnd rswk-swf Regelungstechnik (DE-588)4076594-5 s Systemtheorie (DE-588)4058812-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018013773&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018013773&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext
spellingShingle	De Silva, Clarence W. Modeling and control of engineering systems Ingenieurwissenschaften Mathematisches Modell Automatic control Control theory Engineering Mathematical models Systems engineering Mathematical models Systemtheorie (DE-588)4058812-9 gnd Regelungstechnik (DE-588)4076594-5 gnd
subject_GND	(DE-588)4058812-9 (DE-588)4076594-5
title	Modeling and control of engineering systems
title_auth	Modeling and control of engineering systems
title_exact_search	Modeling and control of engineering systems
title_full	Modeling and control of engineering systems Clarence W. de Silva
title_fullStr	Modeling and control of engineering systems Clarence W. de Silva
title_full_unstemmed	Modeling and control of engineering systems Clarence W. de Silva
title_short	Modeling and control of engineering systems
title_sort	modeling and control of engineering systems
topic	Ingenieurwissenschaften Mathematisches Modell Automatic control Control theory Engineering Mathematical models Systems engineering Mathematical models Systemtheorie (DE-588)4058812-9 gnd Regelungstechnik (DE-588)4076594-5 gnd
topic_facet	Ingenieurwissenschaften Mathematisches Modell Automatic control Control theory Engineering Mathematical models Systems engineering Mathematical models Systemtheorie Regelungstechnik
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