System Dynamics and Control
System Dynamics & Control Table of Contents
TABLE OF CONTENTS
PART I PHYSICAL MODELING AND MODEL CONSTRUCTION
Chapter 1 Introduction
1.1 CONCEPT OF DYNAMIC AND STATIC SYSTEMS
Basic Dynamic Operators
About Units and Dimensions
1.2 FEEDBACK CONTROL CONCEPT
Feedback Control Structure
Other Types of Control
Nature of Loop: Feed-forward Control System
Nature of Controller: Discontinuous versus Continuous Control
1.3 DEFINITION OF A SYSTEM
Purpose of a Dynamic Study
Stages of a Dynamic Study
Introducing the Block Diagram
1.4 STAGE ONE: PHYSICAL MODELING
Systems Concept: Illustration
1.5 PRACTICE PROBLEMS
Chapter 2 Specification of Dynamic Systems and Behavior
2.1 INTRODUCING MECHANICAL BEHAVIOR COMPONENTS
Compliance and Inertia
The Translational Spring
The Torsional Spring
The Translational Mass
Rotary Inertia
Mechanical Damping Other Types of Mechanical Resistance
2.2 SOME ELECTRICAL BEHAVIOR COMPONENTS
Ideal Resistor
Voltage and Current Sources
Ideal Capacitor and Inductor
2.3 PHYSICAL MODELING EXAMPLES
Simple Mechanical Systems
Some Examples of Electrical Networks
Series and Parallel Combinations of R, C, and L Elements
Practical R, RC, and RCL Networks
2.4 STAGE TWO: MODEL CONSTRUCTION: PRELIMINARIES
System Decomposition
Lumping, Linearity and Stationarity
Uncertainty, Continuous and Sampled Data
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2.5 PRACTICE PROBLEMS
Chapter 3 Engineering System Models in State Space
3.1 THE STATE SPACE APPROACH
The Concept and Definition of State
The State Modeling Procedure
Assigning State Variables and Causality
3.2 MECHANICAL SYSTEMS
One-dimensional Examples
Cables – Length and Stretch
Multi-dimensional Examples
Gyroscopic Action and Gyroscopes
3.3 INCOMPRESSIBLE FLUID SYSTEMS
Short and Long Constrictions
Fluid Storage and Fluid Inertia
Examples in Fluid Systems
3.4 ELECTRICAL SYSTEMS
Some Electronic Circuit Components
Further Examples in Electrical Engineering
3.5 PRACTICE PROBLEMS
Chapter 4 Other System Models in State Space
4.1 THERMAL SYSTEMS
Conduction, Convection, and Radiation
Heat Energy Storage
Examples in Thermal Systems
4.2 PROCESS ENGINEERING SYSTEMS
Simple Material Transport
Compressible, Mixing, and Reacting Systems
4.3 EXAMPLES OF DISTRIBUTED PARAMETER MODELS
Longitudinal and Torsional Vibration in Thin Rods
One-Dimensional Heat Conduction
Lumped-Parameter Alternatives
4.4 NON-ENGINEERING SYSTEM EXAMPLES
4.5 PRACTICE PROBLEMS
Chapter 5 Generalized System Models and Analogs
5.1 THE CONCEPT OF ENERGETIC SYSTEMS
Generalized Signal Variables and Elements
Kinetic and Potential Energy
Transformers and Gyrators, Transducers, and Example Systems
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5.2 ELECTROMECHANICAL SYSTEMS
Electrical Transducers
Introducing Electromechanical Energy Conversion Principles
DC Motor Control
Introducing Stepping Motors and Drives
5.3 OTHER HYBRID AND INTEGRATED SYSTEM EXAMPLES
Transducers in Mechanical Systems
Integrated System Examples
5.4 INTRODUCING MICROMACHINED DEVICES
Micro Sensors and Actuators
5.5 PRACTICE PROBLEMS
References for Part I
PART II MODEL SOLUTION
Chapter 6 Response of Lumped-Parameter Systems
6.1 STAGE THREE: MODEL SOLUTION
Free Response, Time Constant and Stability of First-Order-Systems
Forced Motion, Linearity and Superposition
Forced Response to Some Special Input Functions
Impulse Response and Convolution
6.2 REVIEW OF COMPLEX NUMBERS AND THEIR REPRESENTATIONS
The Complex Plane Exponential
Representation Sinusoids and Phasors
6.3 TIME DOMAIN SOLUTION OF THE VECTOR STATE EQUATION
State Vector and Vector Differential (or Difference) Equation
First-Order System Analogy and State Transition Matrix
Eigenvalues, Eigenvectors and Response Modes
Forced Response and Application of Linear Transformations
6.4 SOLUTION OF THE LINEAR DISCRETE-TIME MODEL
Response Modes Computation of Discrete-Time System Response
6.5 DIGITAL COMPUTER SIMULATION OF DYNAMIC SYSTEMS
Introducing Some Math Packages
Digital Computer Solution of Continuous-Time Systems
6.6 PRACTICE PROBLEMS
Chapter 7 Solution of Higher-Order Scalar Systems
7.1 RESPONSE OF SECOND-ORDER-SYSTEMS
Free Response: Natural Frequency and Damping
Forced Response to Special Inputs
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7.2 PHASOR TRANSFORM SOLUTION AND SINUSOIDAL STEADY STATE
The Phasor Transform
Phasor Transfer Functions: Impedance/Admittance
Resonance, Quality Factor and Bandwidth
7.3 INTRODUCING MECHANICAL VIBRATIONS
Single-Degree-of-Freedom Examples
Eliminating Excess Vibration
Two-Degrees-of-Freedom Systems: Vibration Absorber
7.4 FORCED RESPONSE TO NON-SINUSOIDAL PERIODIC INPUTS
Introducing Fourier Series
The Complex Fourier Series
7.5 PRACTICE PROBLEMS
Chapter 8 Further Solution by Transformation
8.1 THE FOURIER TRANSFORM SOLUTION
Properties of the Fourier Transform
Signal Processing
Discrete Fourier Transform and Computation with Fast Fourier Transform
8.2 INTRODUCING THE LAPLACE TRANSFORM METHOD
Transform Properties: Initial- and Final-Value Theorems
Transfer Functions, Impulse Response, Convolution
The Inverse Transform and Partial Fraction Expansions
Applications to Non-stationary and Distributed Systems
8.3 LAPLACE DOMAIN SOLUTION OF THE VECTOR STATE EQUATION
The State Transition Matrix Revisited The Matrix Transfer Function
8.4 ɀ-DOMAIN SOLUTION OF DISCRETE-TIME SYSTEMS
Introducing the ɀ-Transform
Pulse Transfer Functions and Recurrence Solutions
ɀ-Domain to Discrete-time Domain
8.5 PRACTICE PROBLEMS
Chapter 9 Representation of System Dynamics
9.1 OPERATIONAL BLOCK DIAGRAMS AND RELATED ALGEBRA
Canonical Scalar Feedback
Application to Mixed Component Systems
Application to Reverse Reaction Processes
ɀ-Transform Block Diagrams
9.2 IDENTIFICATION AND FREQUENCY RESPONSE
Frequency Domain Identification
Bode and Nyquist Diagrams
Frequency Response Computation
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9.3 RELATIONS BETWEEN TRANSFER FUNCTIONS AND STATE MODELS Signal Flow Graphs
The Companion Form
9.4 CONCEPTS IN STATE SPACE
State Trajectories for Second-Order Systems
Application to Some Non-Linear Control Systems
Controllability and Observability of Dynamic Systems
9.5 PRACTICE PROBLEMS
Chapter 10 Stability of Dynamic Systems
10.1 STABILITY CONCEPTS IN STATE SPACE
Stability in the Sense of Lyapunov
Lyapunov Method of Stability Analysis
10.2 STABILITY AND EIGENVALUE PLACEMENT
The Root Locus Technique The Routh Stability Test
10.3 STABILITY OF DISCRETE-TIME SYSTEMS
Stability by Transformation to s-Plane Jury’s Inners Stability Test
10.4 STABILITY IN THE FREQUENCY DOMAIN
Closed Loop Frequency Response
Relative Stability and Gain and Phase Margins
Nyquist Stability Criterion
10.5 STABILITY AND NONLINEAR SYSTEMS
The Describing Function and Kochenburger Criterion
Stability of Limit Cycle of a Non-Linear System Circle Criterion
10.6 PRACTICE PROBLEMS
References for Part II
PART III SYSTEM DESIGN
Chapter 11 Introducing Automatic Control Systems Design
11.1 STAGE FOUR: DESIGN
Continuous-time Single-loop Feedback Control
Stability and Sensitivity
Time Response Performance and Design
11.2 CLASSICAL FEEDBACK CONTROLLERS
One-, Two- and Three-Mode Process Controllers
Controller Selection and Tuning
Computer-Assisted Design of A Nonlinear System
11.3 ROOT LOCUS AND ROUTH TEST DESIGN
Design Using the Root Locus Method
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Application to Dead Time and Other Nonlinear Systems
Second Order Dominance Design Using the Routh Criterion
11.4 PRACTICE PROBLEMS
Chapter 12 Design in the Frequency Domain
12.1 DESIGN FOR SPECIFIED PERFORMANCE
Design for Given Frequency/Bandwidth and Resonance Peak
Design based on Gain- and Phase-Margin Criteria
Correlation Between Transient and Frequency Response
12.2 DESIGN BY FREQUENCY DOMAIN COMPENSATION
The Problem of Pole-Zero Cancellation
Gain-Factor Compensation
Lead and Lag Compensation
Lag-Lead and Cascade Compensation
12.3 CLASSICAL MODE CONTROLLERS AND NONLINEAR EXAMPLES
Proportional, Reset, and Rate Compensation
Rate Feedback Compensation
12.4 PRACTICE PROBLEMS
Chapter 13 Multi-Loop and Other Control Configurations
13.1 FEEDFORWARD AND CASCADE CONFIGURATIONS
Introducing Feedforward Control Systems
Comparative Design Examples of Feedforward Control
Cascade Control Systems
Tuning the Cascade Controller
13.2 MULTIVARIABLE CONTROL SYSTEMS
The Concept of Decoupling Control
State Vector Feedback and Eigenvalue Assignment
Scalar Controlling Input and Integral Action
Extension to a Vector Controlling Input
13.3 INTRODUCING STATE OBSERVERS AND ADAPTIVE CONTROL
Design of State Observers
Application to State Vector Feedback Systems
Adaptive Control Concepts
Signal-Synthesis MRAS Design Illustration
13.4 INTRODUCING CONTINUOUS-TIME OPTIMAL CONTROL AND THE H∞ CONTROL CONCEPT
Nature of the Optimal Control Problem
Some Basic Concepts of Calculus of Variations
The Maximum (Minimum) Principle and Time-Optimal Control
Optimal Linear Quadratic Regulator
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Performance-Robustness and the H∞ Norm
An H∞ Control Problem and Solution
13.5 PRACTICE PROBLEMS
Chapter 14 Discrete-Time Control Systems
14.1 DIGITAL COMPUTER IN CONTROL LOOPS
Supervisory Control
Hierarchical and Distributed Controls
Sequence and Numerical Control Systems
Direct Digital Control Systems
14.2 SINGLE-LOOP DIGITAL CONTROLLERS
Two-term (PI) and Three-term (PID) Control
Sampled-Data Systems and Parameter Tuning
Minimal Response Algorithms in the ɀ-Domain
14.3 DISCRETE-TIME STATE SPACE DESIGN
Finite-Time Settling State Vector Feedback Control
State Vector Feedback with Eigenvalue Assignment Method
Finite-Time Settling Observer
14.4 INTRODUCING DISCRETE-TIME OPTIMAL CONTROL
Elements of Dynamic Programming
Discrete-Time Optimal Control Problem
Computing a Solution
The Discrete-Time Linear Quadratic Problem
14.5 PRACTICE PROBLEMS
Chapter 15 Realization of Microcomputer Control Systems
15.1 INTERFACING WITH EXTERNAL EQUIPMENT
Digital-to-Analog Conversion
Analog-to-Digital Conversion
Digital Input/Output
15.2 COMPUTER DATA ACQUISITION AND CONTROL
Pulse Measurements and Commands
Pulse Outputs and the Stepping Motor
Features of Analog Data Acquisition
Analog Outputs and Pulse Modulation
15.3 ILLUSTRATION OF A COMPUTER IMPLEMENTATION: PRELIMINARIES
Process Control Valves Revisited
Commercial Interface and Signal Conditioning
Instrument Modules
The Implemented Interface Hardware and Software
15.4 MICROCOMPUTER REALIZATION OF A LIQUID LEVEL/FLOW CONTROL SYSTEM
Physical Elements and Configuration of Control System
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Component Calibrations
Analytical Design and Computer Simulation
Main Control Experiment
15.5 PRACTICE PROBLEMS
References for Part III
Appendix A Selected Constants, Properties and Conversion Factors
SELECTED CONSTANTS
Table A1 Some Fundamental Constants
TYPICAL VALUES OF SELECTED PROPERTIES
Table A2 Selected Properties of Some Gases
Table A3 Selected Properties of Some Liquids
Table A4 Selected Properties of Some Solids
SELECTED CONVERSION FACTORS
Table A5 Conversion Factors from SI to US Customary Units
Table A6 Conversion Factors from US Customary to SI Units
Appendix B Some Elements of Linear Algebra
B.1 MATRICES: DEFINITIONS
Vectors Other Special Types of Matrices
B.2 MATRIX ALGEBRA
Equality, Addition and Multiplication of Matrices
Determination of Rank (and Inverse) of a Matrix
B.3 EIGENVALUES AND DIAGONALIZATION
Eigenvalue Problem
Diagonalization
Quadratic and Definite Forms
B.4 FUNCTIONS OF A SQUARE MATRIX
Conversion of Continuous Vector State Model to Discrete-Time
Cayley-Hamilton Theorem and Sylvester’s Formula
Zeros of a Polynomial Matrix
Appendix C Answers to Selected (*) Problems
Index
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