كتاب Introduction to Control Engineering Modeling Analysis and Design

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Introduction to Control Engineering Modeling Analysis and Design

Contents
Preface
Introduction to Control Engineering
The Concept of Feedback and Closed Loop Control
Open-Loop Versus Closed-Loop Systems
Feedforward Control
Feedback Control in Nature
A Glimpse of the Areas where Feedback Control Systems have been
Employed by Man
Classification of Systems
Linear System
Time-Invariant System
Task of Control Engineers
Alternative Ways to Accomplish a Control Task
A Closer Look to the Control Task
Mathematical Modeling
Performance Objectives and Design Constraints
Controller Design
Performance Evaluation
The Laplace Transform
Complex Variables And Complex Functions
Complex Function
Laplace Transformation
Laplace Transform and Its Existence
Laplace Transform of Common Functions
Laplace Table
Properties of Laplace Transform
Inverse Laplace Transformation
Partial-Fraction Expansion Method
Partial-Fraction Expansion when F(s) has only Distinct Poles
Partial-Fraction Expansion of F(s) with Repeated Poles Concept of Transfer Function
Block Diagrams
Block Diagram Reduction
Signal Flow Graph Representation
Signal Flow Graphs
Properties of Signal Flow Graphs
Signal Flow Graph Algebra
Representation of Linear Systems by Signal Flow Graph
Mason’s Gain Formula
Vectors and Matrices
Minors, Cofactors and Adjoint of a Matrix
Inversion of a Nonsingular Matrix
Eigen Values and Eigen Vectors
Similarity Transformation
Diagonalization of Matrices
Jordan Blocks
Minimal Polynomial Function and Computation of Matrix Function Using
Sylvester’s Interpolation
MATLAB Scripts
Review Exercise
Problems
Introduction
System Representation in State-variable Form
Concepts of Controllability and Observability
Transfer Function from State-variable Representation
Computation of Resolvent Matrix from Signal Flow Graph
State Variable Representation from Transfer Function
Solution of State Equation and State Transition Matrix
Properties of the State Transition Matrix
Review Exercise
Problems
Time-Domain Performance of Control Systems
Typical Test Inputs
The Step-Function Input
The Ramp-Function Input
The Impulse-Function Input
The Parabolic-Function Input
Transient State and Steady State Response of Analog Control System Performance Specification of Linear Systems in Time-Domain
Transient Response Specifications
Transient Response of a Prototype Second-order System
Locus of Roots for the Second Order Prototype System
Constant wn Locus
Constant Damping Ratio Line
Constant Settling Time
Transient Response with Constant wn and Variable δ
Step Input Response
Impulse Response of a Transfer Function
The Steady-State Error
Steady-State Error Caused by Nonlinear Elements
Steady-State Error of Linear Control Systems
The Type of Control Systems
Steady-State Error of a System with a Step-Function Input
Steady-State Error of A System with Ramp-Function Input
Steady-State Error of A System with Parabolic-Function Input
Performance Indexes
Integral of Squared Error (ISE)
Integral of Time Multiplied Squared Error (ITSE) Criteria
Integral of Absolute Error (IAE) Criteria
Integral of Time Multiplied Absolute Error (ITAE)
Quadratic Performance Index
Frequency Domain Response
Frequency Response of Closed-Loop Systems
Frequency-Domain Specifications
Frequency Domain Parameters of Prototype Second-Order System
Peak Resonance and Resonant Frequency
Bandwidth
Bode Diagrams
Bode Plot
Principal Factors of Transfer Function
Procedure for Manual Plotting of Bode Diagram
Minimum Phase and Non-Minimum Phase Systems
MATLAB Scripts
Review Exercise
Problems
The Concept of Stability
The Routh-Hurwitz Stability Criterion
Relative Stability Analysis
Control System Analysis Using Routh’s Stability Criterion
Stability by the Direct Method of Lyapunov Introduction to the Direct Method of Lyapunov
System Representation
Stability by the Direct Method of Lyapunov
Definitions of Stability
Lyapunov Stability Theorems
Generation of Lyapunov Functions for Autonomous Systems
Generation of Lyapunov Functions for Linear Systems
Estimation of Settling Time Using Lyapunov Functions
MATLAB Scripts
Review Exercise
Problems
Introduction
Poles and Zeros of Open Loop and Closed Loop Systems
Mapping Contour and the Principle of the Argument
The Nyquist Criterion
The Nyquist Path
The Nyquist Plot Using a Part of Nyquist Path
Nyquist Plot of Transfer Function with Time Delay
Relative Stability: Gain Margin and Phase Margin
Analytical Expression for Phase Margin and Gain Margin
of a Second Order Prototype
Gain-Phase Plot
Constant Amplitude (M) and Constant Phase (N) Circle
Nichols Plot
Linear System Response Using Graphical User Interface in
MATLAB
MATLAB Scripts
Review Exercise
Problems
Correlation of System-Roots with Transient Response
The Root Locus Diagram–A Time Domain Design Tool
Root Locus Technique
Properties of Root Loci
Step by Step Procedure to Draw the Root Locus Diagram
Root Locus Design Using Graphical Interface in MATLAB
Root Locus Technique for Discrete Systems
Sensitivity of the Root Locus
MATLAB Scripts
Review Exercise
Problems
Introduction
Approaches to System Design
Structure of the Compensated System
Cascade Compensation Networks
Design Concept for Lag or Lead Compensator in Frequency-Domain
Design Steps for Lag Compensator
Design Steps for Lead Compensator
Design Examples
Design of Compensator by Root Locus Technique
Design of Phase-lead Compensator Using Root Locus Procedure
Design of Phase-lag Compensator Using Root Locus Procedure
PID Controller
Ziegler-Nichols Rules for Tuning PID Controllers
First Method
Second Method
Design of Compensators for Discrete Systems
Design Steps for Lag Compensator
Design Steps for Lead Compensator
MATLAB Scripts
Review Exercise
Problems
Pole Assignment Design and State Estimation
Ackerman’s Formula
Guidelines for Placement of Closed Loop System Poles
Linear Quadratic Regulator Problem
State Estimation
Sources of Error in State Estimation
Computation of the Observer Parameters
Equivalent Frequency-Domain Compensator
Combined Plant and Observer Dynamics of the Closed Loop System
Incorporation of a Reference Input
Reduced-Order Observer
Some Guidelines for Selecting Closed Loop Poles in Pole Assignment
Design
MATLAB Scripts
Review Exercise
Problems
Advantage of Digital Control
Disadvantages
Representation of Sampled Process
The Z-Transform
The Residue Method
Some Useful Theorems
Inverse Z-Transforms
Partial Fraction Method
Residue Method
Block Diagram Algebra for Discrete Data System
Limitations of the Z-Transformation Method
Frequency Domain Analysis of Sampling Process
Data Reconstruction
Zero Order Hold
First Order Hold
Discrete State Equation
State Equations of Systems with Digital Components
The Solution of Discrete State Equations
The Recursive Method
Stability of Discrete Linear Systems
Jury’s Stability Test
Steady State Error for Discrete System
State Feedback Design for Discrete Systems
Predictor Estimator
Current Estimator
Reduced-order Estimator for Discrete Systems
Provision for Reference Input
MATLAB Scripts
Review Exercise
Problems
Introduction
Optimal Control Problem
Performance Index
Calculus of Variations
Functions and Functionals
A Closeness of Functions
B Increment of a Functional
C The Variation of a Functional
The Fundamental Theorem of the Calculus of Variations
Extrema of Functionals of a Single Function
Variational Problems and the Euler Equation
Extrema of Functionals of n Functions
Variable End Point Problems
Optimal Control Problem
Pontryagin’s Minimum Principle
The LQ Problem
The Hamilton-Jacobi Approach
The Matrix Riccati Equation
Finite Control Horizon
Linear Regulator Design (Infinite-time Problem)
Optimal Controller for Discrete System
Linear Digital Regulator Design (Infinite-time Problem)
MATLAB Scripts
Review Exercise
Problems
The Concept of Fuzzy Logic and Relevance of Fuzzy Control
Industrial and Commercial Use of Fuzzy Logic-based Systems
Fuzzy Modeling and Control
Advantages of Fuzzy Controller
When to Use Fuzzy Control
Potential Areas of Fuzzy Control
Summary of Some Benefits of Fuzzy Logic and Fuzzy Logic Based
Control System
When Not to Use Fuzzy Logic
Fuzzy Sets and Membership
Introduction to Sets
Classical Sets
Fuzzy Sets
Basic Definitions of Fuzzy Sets and a Few Terminologies
Commonly Used Fuzzy Set Terminologies
Set-Theoretic Operations
Classical Operators on Fuzzy Sets
Generalized Fuzzy Operators
Fuzzy Complement
Fuzzy Union and Intersection
Fuzzy Intersection: The T-Norm
Fuzzy Union: The T-Conorm (or S-Norm)
MF Formulation and Parameterization
MFs of One Dimension
From Numerical Variables to Linguistic Variables
Term Sets of Linguistic Variables
Classical Relations and Fuzzy Relations
Cartesian Product
Crisp Relations
Fuzzy Relations
Operation on Fuzzy Relations Extension Principle
Logical Arguments and Propositions
Logical Arguments
Modus Ponens
Modus Tollens
Hypothetical Syllogism
Interpretations of Fuzzy If-then Rules
Fuzzy Relation Equations
Basic Principles of Approximate Reasoning
Generalized Modus Ponens
Generalized Modus Tollens
Generalized Hypothetical Syllogism
Representation of a Set of Rules
Approximate Reasoning with Multiple Conditional Rules
MATLAB Scripts
Problems
The Structure of Fuzzy Logic-based Controller
Knowledge Base
Rule Base
Choice of Sate Variables and Controller Variables
Contents of Antecedent and Consequent of Rules
Derivation of Production Rules
Membership Assignment
Cardinality of a Term Set
Completeness of Rules
Consistency of Rules
Inference Engine
Special Cases of Fuzzy Singleton
Reasoning Types
Fuzzification Module
Fuzzifier and Fuzzy Singleton
Defuzzification Module
Defuzzifier
Center of Area (or Center of Gravity) Defuzzifier
Center Average Defuzzifier (or Weighted Average Method)
Design Consideration of Simple Fuzzy Controllers
Design Parameters of General Fuzzy Controllers
Examples of Fuzzy Control System Design: Inverted Pendulum
Design of Fuzzy Logic Controller on Simulink and MATLAB Environment
Iterative Design Procedure of a PID Controller in MATLAB
Environment
Simulation of System Dynamics in Simulink for PID Controller
Design
Simulation of System Dynamics in Simulink for Fuzzy Logic Controller
Design
Problems
Introduction
Some Phenomena Peculiar to Nonlinear Systems
Approaches for Analysis of Nonlinear Systems: Linearization
Describing Function Method
Procedure for Computation of Describing Function
Describing Function of Some Typical Nonlinear Devices
Describing Function of an Amplifying Device with Dead Zone and
Saturation
Describing Function of a Device with Saturation but without any
Dead Zone
Describing Function of a Relay with Dead Zone
Describing Function of a Relay with Dead Zone and Hysteresis
Describing Function of a Relay with Pure Hysteresis
Describing Function of Backlash
Stability Analysis of an Autonomous Closed Loop System by Describing
Function
Graphical Analysis of Nonlinear Systems by Phase-Plane Methods
Phase-Plane Construction by the Isocline Method
Pell’s Method of Phase-Trajectory Construction
The Delta Method of Phase-Trajectory Construction
Construction of Phase Trajectories for System with Forcing Functions
Singular Points
The Aizerman and Kalman Conjectures
Popov’s Stability Criterion
The Generalized Circle Criteria
Simplified Circle Criteria
Finding Sectors for Typical Nonlinearities
S-function SIMULINK Solution of Nonlinear Equations
MATLAB Scripts
Problems
Series or Direct Form
Direct Form (Canonical)
Cascade Realization
Parallel Realization
Effects of Finite Bit Size on Digital Controller Implementation
Sign Magnitude Number System (SMNS)
Truncation Quantizer
Round-off Quantizer
Mean and Variance
Dynamic Range of SMNS
Overflow
Two’s Complement Number System
Truncation Operation
Round-off Quantizer in Two’s CNS
Mean and Variance
Dynamic Range for Two’s CNS
Overflow
Propagation of Quantization Noise Through the Control System
Very High Sampling Frequency Increases Noise
Propagation of ADC Errors and Multiplication Errors through the
Controller
Propagated Multiplication Noise in Parallel Realization
Propagated Multiplication Noise in Direct Form Realization
Coefficient Errors and Their Influence on Controller Dynamics
Sensitivity of Variation of Coefficients of a Second Order
Controller
Word Length in A/D Converters, Memory, Arithmetic Unit and D/A
Converters
Quantization gives Rise to Nonlinear Behavior in Controller
Avoiding the Overflow
Pole Zero Pairing
Amplitude Scaling for Avoiding Overflow
Design Guidelines
MATLAB Scripts
Problems
Appendex A
Appendex B
Appendex C
Notes on MATLAB Use
Bibliography
Index

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