Modeling and Control of Engineering Systems 76868.indb 2 7/8/09 5:04:04 PM Modeling and Control of Engineering Systems Clarence W. de Silva Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business 76868.indb 3 7/8/09 5:04:04 PM MATLAB® and Simulink® are trademarks of The MathWorks, Inc. and are used with permission. The MathWorks does not warrant the accuracy of the text of exercises in this book.
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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.com and the CRC Press Web site at http://www.com To all my students, present and past “Education is just the progressive realisation of our ignorance” –Albert Einstein 76868.indb 6 7/8/09 5:04:05 PM Contents Preface. xxv Further Reading. xxvii Units and Conversions (Approximate).
xxix 1 Modeling and Control of Engineering Systems. Importance of Modeling. History of Control Engineering. Organization of the Book.9 2 Modeling of Dynamic Systems.
Types of Analytical Models. Principle of Superposition. Lumped Model of a Distributed System. Kinetic Energy Equivalence.
Natural Frequency Equivalence. Lumped Elements and Analogies. Across Variables and Through Variables. Fluid Capacitor or Accumulator (A-Type Element).
Derivation of Constitutive Equations.indb 7 7/8/09 5:04:05 PM viii Contents 2. Three Dimensional Conduction. Analytical Model Development. Steps of Model Development.
State-Space Models. Properties of State Models. Linear State Equations. Time-Invariant Systems.
Systematic Steps for State Model Development. I/O Models from State-Space Models. Linearization about an Operating Point. Function of Two Variables.
Nonlinear State-Space Models. Reduction of System Nonlinearities. Nonlinear Electrical Elements. Linearization Using Experimental Operating Curves.
Torque-Speed Curves of Motors. Linear Models for Motor Control. Variables and Sign Convention. Through Variables and Across Variables.
Linear Graph Elements. Single-Port Elements. Effects of Source Elements. Two-Port Elements.
Linear Graph Equations. Number of “Primary” Loops. Series and Parallel Connections.indb 8 7/8/09 5:04:05 PM Contents ix 4. State Models from Linear Graphs.
Steps of Obtaining a State Model. Linear Graph Representation. Linear Graphs of Thermal Systems. 138 5 Transfer-Function and Frequency-Domain Models.
Laplace and Fourier Transforms. Laplace Transform of a Derivative. Laplace Transform of an Integral. Transfer-Function Matrix.
Frequency Domain Models. Frequency Transfer-Function (Frequency Response Function). Response to a Harmonic Input. Magnitude (Gain) and Phase.
Bode Diagram (Bode Plot) and Nyquist Diagram. Transfer-Functions of Electro-Mechanical Systems.1 Significance of Transfer-Functions in Mechanical Systems. Mechanical Transfer-Functions. Mechanical Impedance and Mobility.
Interconnection Laws for Mechanical Impedance and Mobility. Interconnection Laws for Electrical Impedance and Admittance. A-Type Transfer-Functions and T-Type Transfer-Functions. Transfer-Functions of Basic Elements.
Single-Degree-of-Freedom System. Two-Degree-of-Freedom System. Equivalent Circuits and Linear Graph Reduction. Thevenin’s Theorem for Electrical Circuits.
Mechanical Circuit Analysis Using Linear Graphs. Summary of Thevenin Approach for Mechanical Circuits.indb 9 7/8/09 5:04:06 PM x Contents 5. Block Diagrams and State-Space Models. Simulation Block Diagrams.
Principle of Superposition. Causality and Physical Realizability. 208 6 Response Analysis and Simulation. Impulse Response Function.
First-Order Systems. Second-Order Systems. Free Response of an Undamped Oscillator. Free Response of a Damped Oscillator.
Case 1: Underdamped Motion (z < 1). Case 2: Overdamped Motion (z > 1). Case 3: Critically Damped Motion (z = 1). Forced Response of a Damped Oscillator.
The Riddle of Zero ICs. Response to Harmonic Excitation. Response Using Laplace Transform. Step Response Using Laplace Transforms.
Incorporation of ICs. Step Response of a First-Order System. Step Response of a Second-Order System. Determination of ICs for Step Response.
Use of Simulink® in Computer Simulation. Building an Application. 260 7 Control System Structure and Performance. Control System Structure.
Computed-Input Control. Programmable Logic Controllers (PLCs).indb 10 7/8/09 5:04:06 PM Contents xi 7. Control System Performance. Performance Specification in Time-Domain.
Simple Oscillator Model. Feedback Control with PID Action. Steady-State Error and Integral Control. Final Value Theorem (FVT).
System Type and Error Constants. Definition of System Type. Position Error Constant Kp. Velocity Error Constant Kv.
Acceleration Error Constant Ka. System Type as a Robustness Property. Performance Specification Using s-Plane. Control System Sensitivity.
System Sensitivity to Parameter Change. 313 8 Stability and Root Locus Method. Routh–Hurwitz Criterion. Zero Coefficient Problem.
Root Locus Method. Rules for Plotting Root Locus. Root Locus Rules. Explanation of the Rules.
Steps of Sketching Root Locus. Variable Parameter in Root Locus. Stability in the Frequency Domain. Response to a Harmonic Input.
Resonant Peak and Resonant Frequency. Damped Simple Oscillator. Half-Power Bandwidth. Damped Simple Oscillator.
PM and GM.indb 11 7/8/09 5:04:06 PM xii Contents 8. Bode and Nyquist Plots. PM and Damping Ratio Relation. Bode Diagram Using Asymptotes.
Slope-Phase Relationship for Bode Magnitude Curve. Nonminimum-Phase Systems. Ambiguous Cases of GM and PM. Destabilizing Effect of Time Delays.
Nyquist Stability Criterion. Nyquist Stability Criterion. Loop Poles on the Imaginary Axis. Steps for Applying the Nyquist Criterion.
Relative Stability Specification. Graphical Tools for Closed-Loop Frequency Response. M Circles and N Circles.400 9 Controller Design and Tuning. Controller Design and Tuning.
Time-Domain Design Techniques. Frequency-Domain Design Techniques. Conventional Time-Domain Design. Proportional Plus Derivative Controller Design.
Compensator Design in the Frequency Domain. Design Steps for a Lead Compensator. Design Steps for a Lag Compensator. Design Specifications in Compensator Design.
Design Using Root Locus. Design Steps Using Root Locus. Ziegler–Nichols Tuning. Reaction Curve Method.
Ultimate Response Method. Computer Control Systems. Components of a Digital Control System. Advantages of Digital Control.indb 12 7/8/09 5:04:06 PM Contents xiii 10.
Signal Sampling and Control Bandwidth. Bandwidth Design of a Control System. Control Cycle Time. Digital Control Using z-Transform.
Discrete Transfer Functions. Stability of Discrete Models. Discrete Final Value Theorem (FVT). Pulse Response Function.
Unit Pulse and Unit Impulse. Direct Synthesis of Digital Compensators. Stability Analysis Using Bilinear Transformation. The Scalar Problem.
Time Response of a State-Space Model. Case of Constant System Matrix. Methods of Computing eAt. Time Response by Laplace Transform.
Transfer Function Matrix. State Response through Modal Response. Advantages of Modal Decomposition. Time-Varying Systems.
Properties of the State-Transition Matrix. Stability of Linear Systems. General Case of Repeated Eigenvalues. Stability from Modal Response for Repeated Eigenvalues.
Possibilities of Jordan Blocks and Modal Responses.indb 13 7/8/09 5:04:06 PM xiv Contents 11. Bounded-Input Bounded-State (BIBS) Stability. Bounded-Input Bounded-Output (BIBO) Stability. Stability of Linear Systems.
First Method of Lyapunov. Second Method (Direct Method) of Lyapunov. Controllability and Observability. Companion Form and Controllability.
Implication of Feedback Control. Controller Design by Pole Placement. Pole Placement in the Multiinput Case. Procedure of Pole Placement Design.
Placement of Repeated Poles. Placement of Some Closed-Loop Poles at Open-Loop Poles. Pole Placement with Output Feedback. Optimization through Calculus of Variations.
Cost Function having a Function of End State. Extension to the Vector Problem. General Optimal Control Problem. Pontryagin’s Minimum Principle.
Linear Quadratic Regulator (LQR). The Euler Equations. Infinite-Time LQR. Control System Design.
Other Advanced Control Techniques. Nonlinear Feedback Control. Sliding Mode Control. Linear Quadratic Gaussian (LQG) Control.
Fuzzy Logic Control. Fuzzy Sets and Membership Functions. Fuzzy Logic Operations.indb 14 7/8/09 5:04:07 PM Contents xv 11. Compositional Rule of Inference.
Extensions to Fuzzy Decision Making. Basics of Fuzzy Control. Fuzzy Control Surface. 593 12 Control System Instrumentation.
Control System Instrumentation. Cascade Connection of Devices. Impedance Matching Amplifiers. Use of Feedback in Op-Amps.
Linear-Variable Differential Transformer (LVDT). Stepper Motor Classification. Driver and Controller. Stepper Motor Selection.
Torque Characteristics and Terminology. Stepper Motor Selection Process. Rotor and Stator. Brushless dc Motors.
DC Motor Equations. Steady-State Characteristics. Experimental Model for dc Motor. Electrical Damping Constant.
Linearized Experimental Model. Control of dc Motors. Motor Time Constants. Feedback Control of dc Motors.
Velocity Feedback Control. Position Plus Velocity Feedback Control. Position Feedback with PID Control.indb 15 7/8/09 5:04:07 PM xvi Contents 12. dc Motor Selection.
Motor Data and Specifications. Motor Sizing Procedure. Drive Amplifier Selection. Summary of Motor Selection.
Control Experiments Using LabVIEW®. Experiment 1: Tank Level Display. Creating the Front Panel. Creating the Block Diagram.
Calibrating the VI. Finding the Resistances of the Process Valves. Experiment 2: Process Control Using LabVIEW®. Two-Tank System.
Description of the Front Panel. ON/OFF Control Algorithm. Proportional Control Algorithm. Single-Tank Process Control.
666 Appendix A: Transform Techniques. Laplace Transforms of Some Common Functions. Laplace Transform of a Constant. Laplace Transform of the Exponential.
Laplace Transform of Sine and Cosine. Laplace Transform of a Derivative. Table of Laplace Transforms. Frequency-Response Function (Frequency Transfer Function).
An Interpretation of Laplace and Fourier Transforms. Application in Circuit Analysis. 693 Appendix B: Software Tools. Relational and Logical Operations.indb 16 7/8/09 5:04:07 PM Contents xvii B.
Control Systems Toolbox. Compensator Design Example. Building the System Model. Importing Model into SISO Design Tool.
Adding Lead and Lag Compensators. PID Control with Ziegler–Nichols Tuning. Root Locus Design Example. MATLAB® Modern Control Examples.
Pole Placement of a Third Order Plant. Linear Quadratic Regulator (LQR) for a Third Order Plant. Pole Placement of an Inverted Pendulum on Mobile Carriage. LQG Controller for an Inverted Pendulum Mounted with Mobile Carriage.
Fuzzy Logic Toolbox. Command Line Driven FIS Design. Practical Stand-Alone Implementation in C. Some Key Concepts.
Working with LabVIEW®. LabVIEW® Sound and Vibration Tools. Sound and Vibration Toolkit. Signal Acquisition and Simulation.
Vibration-Level Measurements. 726 Appendix C: Review of Linear Algebra. Vectors and Matrices. Vector–Matrix Algebra.
Matrix Addition and Subtraction.indb 17 7/8/09 5:04:07 PM xviii Contents C. Trace of a Matrix. Determinant of a Matrix. Adjoint of a Matrix.
Inverse of a Matrix. Bases and Dimension of a Vector Space. Gram–Schmidt Orthogonalization. Modified Gram–Schmidt Procedure.
Properties of Determinant of a Matrix. Rank of a Matrix. System of Linear Equations. Matrix Eigenvalue Problem.
Computation of Matrix Exponential.indb 18 7/8/09 5:04:07 PM Preface This is an introductory book in the subject of modeling and control of engineering systems. It serves as both a textbook for undergraduate engineering students and entry-level gradu- ate students, and a reference book for practicing professionals. As a textbook, it is suitable for courses in: modeling of dynamic systems, feedback control systems, control engineer- ing, and design and instrumentation of control systems. There is adequate material in the book for two 14-week courses, one at the junior (third-year undergraduate) or senior (fourth- year undergraduate) level and the other at the first-year graduate level.