Modeling and Control of Engineering Systems

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 LabVIEWTM 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. 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. Cover......Page 1 Title Page......Page 4 Copyright......Page 5 Contents......Page 8 Preface......Page 20 Acknowledgments......Page 24 Author......Page 26 Further Reading......Page 28 Units and Conversions (Approximate)......Page 30 1.1 Control Engineering......Page 32 1.2 Application Areas......Page 33 1.3 Importance of Modeling......Page 35 1.4 History of Control Engineering......Page 36 1.5 Organization of the Book......Page 38 Problems......Page 40 2.1 Dynamic Systems......Page 42 2.2 Dynamic Models......Page 43 2.2.2 Model Types......Page 44 2.2.3 Types of Analytical Models......Page 45 2.2.4 Principle of Superposition......Page 46 2.2.5 Lumped Model of a Distributed System......Page 47 2.3.2 Mechanical Elements......Page 51 2.3.3 Electrical Elements......Page 54 2.3.4 Fluid Elements......Page 57 2.3.5 Thermal Elements......Page 63 2.3.6 Natural Oscillations......Page 68 2.4 Analytical Model Development......Page 70 2.4.3 State-Space Models......Page 71 2.4.4 Time-Invariant Systems......Page 76 2.4.5 Systematic Steps for State Model Development......Page 78 2.4.6 I/O Models from State-Space Models......Page 81 Problems......Page 84 3.1 Model Linearization......Page 94 3.1.1 Linearization about an Operating Point......Page 95 3.2 Nonlinear State-Space Models......Page 97 3.2.1 Linearization......Page 98 3.2.2 Reduction of System Nonlinearities......Page 99 3.3.1 Capacitor......Page 116 3.3.3 Resistor......Page 117 3.4.1 Torque-Speed Curves of Motors......Page 118 3.4.2 Linear Models for Motor Control......Page 119 Problems......Page 120 4.1.2 Sign Convention......Page 128 4.2.1 Single-Port Elements......Page 131 4.2.2 Two-Port Elements......Page 133 4.3.1 Compatibility (Loop) Equations......Page 138 4.3.2 Continuity (Node) Equations......Page 140 4.4 State Models from Linear Graphs......Page 141 4.4.2 Sign Convention......Page 142 4.4.4 General Observation......Page 143 4.4.5 Topological Result......Page 144 4.5.1 Amplifiers......Page 159 4.5.2 DC Motor......Page 161 4.5.3 Linear Graphs of Thermal Systems......Page 165 Problems......Page 169 5.1 Laplace and Fourier Transforms......Page 180 5.1.2 Laplace Transform of a Derivative......Page 181 5.1.4 Fourier Transform......Page 182 5.2 Transfer-Function......Page 183 5.2.1 Transfer-Function Matrix......Page 184 5.3.1 Frequency Transfer-Function (Frequency Response Function)......Page 190 5.3.2 Bode Diagram (Bode Plot) and Nyquist Diagram......Page 192 5.4.1 Significance of Transfer-Functions in Mechanical Systems......Page 193 5.4.2 Mechanical Transfer-Functions......Page 194 5.4.3 Interconnection Laws......Page 195 5.4.4 Transfer-Functions of Basic Elements......Page 197 5.4.5 Transmissibility Function......Page 201 5.5 Equivalent Circuits and Linear Graph Reduction......Page 206 5.5.1 Thevenin’s Theorem for Electrical Circuits......Page 207 5.5.2 Mechanical Circuit Analysis Using Linear Graphs......Page 210 5.5.3 Summary of Thevenin Approach for Mechanical Circuits......Page 219 5.6 Block Diagrams and State-Space Models......Page 220 5.6.2 Principle of Superposition......Page 222 5.6.3 Causality and Physical Realizability......Page 238 Problems......Page 239 6.1 Analytical Solution......Page 248 6.1.1 Homogeneous Solution......Page 249 6.1.3 Impulse Response Function......Page 250 6.1.4 Stability......Page 253 6.2 First-Order Systems......Page 254 6.3.1 Free Response of an Undamped Oscillator......Page 256 6.3.2 Free Response of a Damped Oscillator......Page 258 6.4.1 Impulse Response......Page 263 6.4.3 Step Response......Page 265 6.4.4 Response to Harmonic Excitation......Page 267 6.5 Response Using Laplace Transform......Page 272 6.5.1 Step Response Using Laplace Transforms......Page 273 6.5.2 Incorporation of ICs......Page 274 6.6 Determination of ICs for Step Response......Page 276 6.7 Computer Simulation......Page 284 6.7.1 Use of Simulink® in Computer Simulation......Page 285 Problems......Page 291 7.1 Control System Structure......Page 302 7.1.2 Feedforward Control......Page 303 7.1.3 Terminology......Page 307 7.1.4 Programmable Logic Controllers (PLCs)......Page 308 7.1.5 Distributed Control......Page 311 7.1.6 Hierarchical Control......Page 314 7.2 Control System Performance......Page 316 7.2.1 Performance Specification in Time-Domain......Page 317 7.2.2 Simple Oscillator Model......Page 319 7.3 Control Schemes......Page 322 7.3.1 Feedback Control with PID Action......Page 325 7.4 Steady-State Error and Integral Control......Page 327 7.4.2 Manual Reset......Page 328 7.4.4 Reset Windup......Page 330 7.5 System Type and Error Constants......Page 331 7.5.2 Error Constants......Page 332 7.5.4 Performance Specification Using s-Plane......Page 336 7.6 Control System Sensitivity......Page 340 7.6.1 System Sensitivity to Parameter Change......Page 341 Problems......Page 344 8.1.1 Natural Response......Page 360 8.2 Routh–Hurwitz Criterion......Page 362 8.2.1 Routh Array......Page 363 8.2.2 Auxiliary Equation (Zero-Row Problem)......Page 364 8.2.3 Zero Coefficient Problem......Page 365 8.2.4 Relative Stability......Page 366 8.3 Root Locus Method......Page 367 8.3.1 Rules for Plotting Root Locus......Page 369 8.3.2 Steps of Sketching Root Locus......Page 374 8.3.4 Variable Parameter in Root Locus......Page 387 8.4 Stability in the Frequency Domain......Page 389 8.4.1 Response to a Harmonic Input......Page 390 8.4.2 Complex Numbers......Page 391 8.4.3 Resonant Peak and Resonant Frequency......Page 392 8.4.4 Half-Power Bandwidth......Page 396 8.4.5 Marginal Stability......Page 398 8.4.6 PM and GM......Page 400 8.4.7 Bode and Nyquist Plots......Page 401 8.4.8 PM and Damping Ratio Relation......Page 403 8.5 Bode Diagram Using Asymptotes......Page 404 8.5.1 Slope-Phase Relationship for Bode Magnitude Curve......Page 406 8.5.2 Ambiguous Cases of GM and PM......Page 414 8.5.3 Destabilizing Effect of Time Delays......Page 415 8.6 Nyquist Stability Criterion......Page 416 8.6.1 Nyquist Stability Criterion......Page 417 8.6.3 Steps for Applying the Nyquist Criterion......Page 418 8.7.1 Graphical Tools for Closed-Loop Frequency Response......Page 425 8.7.2 M Circles and N Circles......Page 426 8.7.3 Nichols Chart......Page 429 Problems......Page 431 9.1 Controller Design and Tuning......Page 440 9.1.1 Design Specifications......Page 441 9.2 Conventional Time-Domain Design......Page 442 9.2.1 Proportional Plus Derivative Controller Design......Page 443 9.3 Compensator Design in the Frequency Domain......Page 445 9.3.1 Lead Compensation......Page 446 9.3.2 Lag Compensation......Page 451 9.3.3 Design Specifications in Compensator Design......Page 454 9.4.1 Design Steps Using Root Locus......Page 458 9.4.2 Lead Compensation......Page 459 9.4.3 Lag Compensation......Page 462 9.5.1 Ziegler–Nichols Tuning......Page 467 9.5.2 Reaction Curve Method......Page 468 9.5.3 Ultimate Response Method......Page 470 Problems......Page 472 10.1.1 Computer Control Systems......Page 478 10.1.2 Components of a Digital Control System......Page 479 10.2 Signal Sampling and Control Bandwidth......Page 480 10.2.2 Antialiasing Filter......Page 481 10.2.3 Control Bandwidth......Page 482 10.2.4 Bandwidth Design of a Control System......Page 485 10.2.5 Control Cycle Time......Page 486 10.3 Digital Control Using z-Transform......Page 487 10.3.1 z-Transform......Page 488 10.3.2 Difference Equations......Page 489 10.3.3 Discrete Transfer Functions......Page 491 10.3.4 Time Delay......Page 492 10.3.5 s–z Mapping......Page 493 10.3.7 Discrete Final Value Theorem (FVT)......Page 495 10.3.8 Pulse Response Function......Page 497 10.4 Digital Compensation......Page 498 10.4.1 Hold Operation......Page 499 10.4.2 Discrete Compensator......Page 500 10.4.4 Causality Requirement......Page 504 10.4.5 Stability Analysis Using Bilinear Transformation......Page 505 10.4.6 Computer Implementation......Page 506 Problems......Page 507 11.1 Modern Control......Page 514 11.2.1 The Scalar Problem......Page 515 11.2.2 Time Response of a State-Space Model......Page 517 11.2.3 Time Response by Laplace Transform......Page 525 11.2.4 Output Response......Page 526 11.2.5 Modal Response......Page 527 11.2.6 Time-Varying Systems......Page 532 11.3.1 Stability of Linear Systems......Page 534 11.3.2 Stability from Modal Response for Repeated Eigenvalues......Page 538 11.3.3 Equilibrium......Page 539 11.3.4 Stability of Linear Systems......Page 540 11.3.5 Second Method (Direct Method) of Lyapunov......Page 544 11.4 Controllability and Observability......Page 548 11.4.1 Minimum (Irreducible) Realizations......Page 552 11.4.3 Implication of Feedback Control......Page 556 11.4.4 State Feedback......Page 557 11.4.5 Stabilizability......Page 558 11.5 Modal Control......Page 559 11.5.1 Controller Design by Pole Placement......Page 560 11.5.2 Pole Placement in the Multiinput Case......Page 565 11.5.3 Procedure of Pole Placement Design......Page 567 11.5.4 Placement of Repeated Poles......Page 569 11.5.5 Placement of Some Closed-Loop Poles at Open-Loop Poles......Page 570 11.5.6 Pole Placement with Output Feedback......Page 573 11.6.1 Optimization through Calculus of Variations......Page 575 11.6.2 Cost Function having a Function of End State......Page 586 11.6.3 Extension to the Vector Problem......Page 587 11.6.4 General Optimal Control Problem......Page 588 11.6.7 PontryaginŁfs Minimum Principle......Page 590 11.7.1 The Euler Equations......Page 591 11.7.2 Boundary Conditions......Page 592 11.7.3 Infinite-Time LQR......Page 593 11.7.4 Control System Design......Page 597 11.8.1 Nonlinear Feedback Control......Page 600 11.8.2 Adaptive Control......Page 602 11.8.3 Sliding Mode Control......Page 604 11.8.4 Linear Quadratic Gaussian (LQG) Control......Page 605 11.8.5 H_Control......Page 607 11.9 Fuzzy Logic Control......Page 608 11.9.1 Fuzzy Logic......Page 609 11.9.2 Fuzzy Sets and Membership Functions......Page 610 11.9.3 Fuzzy Logic Operations......Page 611 11.9.4 Compositional Rule of Inference......Page 614 11.9.5 Extensions to Fuzzy Decision Making......Page 615 11.9.6 Basics of Fuzzy Control......Page 616 11.9.7 Fuzzy Control Surface......Page 620 Problems......Page 624 12.1 Control System Instrumentation......Page 634 12.2.1 Cascade Connection of Devices......Page 636 12.2.3 Operational Amplifier......Page 638 12.2.4 Instrumentation Amplifiers......Page 640 12.3 Motion Sensors......Page 641 12.3.1 Linear-Variable Differential Transformer (LVDT)......Page 642 12.3.2 Signal Conditioning......Page 643 12.3.3 DC Tachometer......Page 644 12.3.4 Piezoelectric Accelerometer......Page 645 12.3.5 Digital Transducers......Page 647 12.3.6 Shaft Encoders......Page 648 12.3.7 Optical Encoder......Page 649 12.4 Stepper Motors......Page 650 12.4.2 Driver and Controller......Page 651 12.4.3 Stepper Motor Selection......Page 654 12.5 dc Motors......Page 661 12.5.1 Rotor and Stator......Page 663 12.5.3 Brushless dc Motors......Page 664 12.5.4 DC Motor Equations......Page 665 12.5.5 Experimental Model for dc Motor......Page 668 12.5.6 Control of dc Motors......Page 669 12.5.7 Feedback Control of dc Motors......Page 673 12.5.8 Motor Driver......Page 675 12.5.9 dc Motor Selection......Page 679 12.5.10 Summary of Motor Selection......Page 683 12.6.1 Experiment 1: Tank Level Display......Page 685 12.6.2 Experiment 2: Process Control Using LabVIEW®......Page 691 Problems......Page 697 A.1 Laplace Transform......Page 708 A.1.1 Laplace Transforms of Some Common Functions......Page 709 A.2 Response Analysis......Page 713 A.3 Transfer Function......Page 720 A.4 Fourier Transform......Page 722 A.4.1 Frequency-Response Function (Frequency Transfer Function)......Page 723 A.5.2 Application in Circuit Analysis......Page 724 B.2.1 Computations......Page 726 B.2.2 Arithmetic......Page 727 B.2.3 Arrays......Page 728 B.2.5 Linear Algebra......Page 729 B.2.6 M-Files......Page 730 B.3.1 Compensator Design Example......Page 731 B.3.2 PID Control with Ziegler–Nichols Tuning......Page 734 B.3.4 MATLAB® Modern Control Examples......Page 739 B.4.1 Graphical Editors......Page 747 B.4.3 Practical Stand-Alone Implementation in C......Page 748 B.5.3 Working with LabVIEW®......Page 750 B.6.1 Sound and Vibration Toolkit......Page 755 B.6.2 Signal Acquisition and Simulation......Page 756 C.1 Vectors and Matrices......Page 760 C.2 Vector–Matrix Algebra......Page 762 C.2.1 Matrix Addition and Subtraction......Page 763 C.2.3 Matrix Multiplication......Page 764 C.3 Matrix Inverse......Page 765 C.3.1 Matrix Transpose......Page 766 C.3.3 Determinant of a Matrix......Page 767 C.3.4 Adjoint of a Matrix......Page 768 C.3.5 Inverse of a Matrix......Page 769 C.4.2 Vector Space (L)......Page 770 C.4.5 Bases and Dimension of a Vector Space......Page 771 C.4.7 Norm......Page 772 C.5 Determinants......Page 773 C.6 System of Linear Equations......Page 774 C.7 Quadratic Forms......Page 775 C.9.1 Similarity Transformation......Page 776 C.10 Matrix Exponential......Page 777 C.10.1 Computation of Matrix Exponential......Page 778 Index......Page 780

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.

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.

"Proper control of any part of an engineering system requires an overall understanding of the system. This volume provides engineers with an accessible introduction to the modeling, analysis, control, instrumentation, and design of engineering systems. It presents a wide range of analytical techniques, computer tools, instrumentation details, and design methods; it also addresses important aspects of laboratory instrumentation; and provides practical applications of various models. A special chapter is devoted to control system instrumentation."--Pub. desc