Design and Analysis of Control Systems: Driving the Fourth Industrial Revolution

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Key Features of the Book
Key Benefits for the User
Acknowledgements
Author
Chapter 1 An Introduction to Control Systems
	1.1 Introduction
		1.1.1 Background
	1.2 A Recent History of Control Systems
		1.2.1 Automatic Control
		1.2.2 Multivariable Control
	1.3 What Is a Control System?
	1.4 Open-Loop Control vs. Closed-Loop Control
		1.4.1 Open-Loop Control
		1.4.2 Closed-Loop Control
		1.4.3 Advantages of Closed-Loop Systems
		1.4.4 Disadvantages of Closed-Loop Systems
	1.5 Examples of Simple Control Systems
		1.5.1 Manual Car Direction of Travel Control
		1.5.2 Cruise Control for a Car
		1.5.3 Automatic Water Level Control
		1.5.4 Manual Water Level Control
		1.5.5 Feedback in Social, Economic, and Political Systems
	1.6 Classification of Control Systems
		1.6.1 Linear vs. Nonlinear Control Systems
		1.6.2 Time-Invariant vs. Time-Variant Control Systems
		1.6.3 Continuous-Data vs. Discrete-Data Control Systems
		1.6.4 Regulator vs. Tracking Control Systems
	1.7 Control System Design
	1.8 Advanced Applications of Control Systems
		1.8.1 Autonomous SpaceX Rocket Landing
		1.8.2 Boston Dynamics’ Atlas Robot
		1.8.3 Honda’s ASIMO Robot
		1.8.4 Sophia the Robot
	1.9 Computer-Aided Design and Analysis
		1.9.1 Overview of Automated Computational Tools
		1.9.2 MATLAB
		1.9.3 MATLAB Control System Toolbox
		1.9.4 Simulink Control Design
		1.9.5 LabVIEW
		1.9.6 SPICE-Based Simulation Software
		1.9.7 SimPowerSystems
		1.9.8 Stateflow
		1.9.9 Mathcad
	1.10 Control Systems in the 4IR
		1.10.1 The Fourth Industrial Revolution
		1.10.2 Control System Innovations in the 4IR
		1.10.3 Neural Networks
		1.10.4 Fuzzy Logic
		1.10.5 Intelligent Control System Structure
		1.10.6 Examples of Intelligent Control Systems
		1.10.7 Challenges of Intelligent Control Systems
	1.11 Book Outline
Chapter 2 Modelling of Dynamic Systems
	2.1 Introduction
		2.1.1 Chapter Objectives
	2.2 Dynamic Systems
	2.3 Dynamic System Models
		2.3.1 Modelling Concepts
		2.3.2 Summary of Model Derivation Procedure
		2.3.3 Different Dynamic System Models
	2.4 Overview of Different Dynamic Systems
		2.4.1 Translational Mechanical Systems
	2.5 Key Dynamic System Models
	2.6 Input-Output Differential Equation Form Model
	2.7 State-Variable Matrix Form (State-Space) Model
		2.7.1 Choice of State Variables
		2.7.2 Summary of the State-Variable Form Modelling
		2.7.3 Obtaining the State-Variable Matrix Model
		2.7.4 State-Variable Matrix Models for Nonlinear Systems
		2.7.5 Characteristics of State-Variable Models
		2.7.6 Comparison with the Input-Output Model
	2.8 Transfer Function Form Model
		2.8.1 Obtaining the Transfer Function Model
		2.8.2 The Laplace Transform
		2.8.3 Properties of Laplace Transforms
		2.8.4 Laplace Transform of Some Key Functions
		2.8.5 Determination of the Transfer Function Model
		2.8.6 The s-Operator Method
		2.8.7 The Component Transfer Function Method
		2.8.8 The Transfer Function in Pole-Zero Factored Form
	2.9 Block Diagram Form Model
		2.9.1 Networks of Blocks
		2.9.2 Negative Feedback in Op-Amp Circuits
		2.9.3 Positive Feedback in Op-Amp Circuits
		2.9.4 Simplifying Block Diagram Models
		2.9.5 Worked Examples of Simplifying Block Diagrams
	2.10 Examples of Dynamic System Modelling
		2.10.1 Translational Mechanical Systems
		2.10.2 Rotational Mechanical Systems
		2.10.3 Electrical Systems (RLC Networks)
		2.10.4 Electromechanical Systems
	2.11 Switching between Different System Models
	2.12 Input-Output Model to a Transfer Function Model
	2.13 Transfer Function Model to an Input-Output Model
	2.14 Block Diagram Model to a Transfer Function Model
	2.15 Transfer Function Model to a State-Variable Matrix Model
		2.15.1 General Controllable Canonical Form
		2.15.2 Special Controllable Canonical Form
		2.15.3 General Conversion to a State-Variable Matrix Model
	2.16 State-Variable Matrix Model to a Transfer Function Model
		2.16.1 Inverse of a General n × n Matrix
		2.16.2 Model Conversion Using Matrix Inversion
		2.16.3 State-Space to Transfer Function Using Laplace Transforms
	2.17 Linearisation of Nonlinear Models
		2.17.1 Small Signal Linearisation
		2.17.2 Linearisation of Element Laws
		2.17.3 Linearisation of Models
		2.17.4 Linearisation Concepts
		2.17.5 Examples of Nonlinear Dynamic Systems
		2.17.6 Modelling of Dynamic Systems with Time Delays
Chapter 3 Dynamic System Response
	3.1 Introduction
		3.1.1 Chapter Objectives
	3.2 Time Domain Solution of System Models
		3.2.1 Homogeneous Input-Output Equations
		3.2.2 Nonhomogeneous Input-Output Equations
		3.2.3 First-Order Systems
		3.2.4 Second-Order Systems
		3.2.5 Analogous Mechanical and Electrical Systems
		3.2.6 Solution of the State-Variable Matrix Model
	3.3 Frequency Domain Solution of System Models
		3.3.1 The Inverse Laplace Transform
		3.3.2 Partial Fractions
		3.3.3 General Second-Order Laplace Function
	3.4 Determination of the System Response
		3.4.1 Using the Input-Output Model
		3.4.2 Using the Transfer Function Model
		3.4.3 Impulse Response (Natural Response)
		3.4.4 Unit Step Response
		3.4.5 Impulse and Unit Step Responses: The Relationship
		3.4.6 Final Value Theorem (FVT)
		3.4.7 Initial Value Theorem
		3.4.8 System DC Gain
	3.5 First-Order Systems
	3.6 Second-Order Systems
		3.6.1 Impulse and Step Responses
		3.6.2 Stability of Second-Order Systems
		3.6.3 Response Characteristics of Second-Order Systems
		3.6.4 Effects of Pole-Zero Location on System Response
		3.6.5 Impact of Zeros on System Response
		3.6.6 Nonminimum Phase Systems
		3.6.7 Impact of Nonlinearities on System Response
		3.6.8 Impact of Time Delay on System Response
	3.7 Worked Examples of Dynamic System Response
Chapter 4 Characteristics of Feedback Control Systems
	4.1 Introduction
	4.2 Open-Loop vs. Closed-Loop Control: Analysis
		4.2.1 Open-Loop Control
		4.2.2 Closed-Loop Control
		4.2.3 Advantages of Closed-Loop Systems
		4.2.4 Disadvantages of Closed-Loop Systems
		4.2.5 Open-Loop Control Design
		4.2.6 The Case for Closed-Loop Control
		4.2.7 Closed-Loop Control Design
		4.2.8 Cascade and Feedback Controllers
		4.2.9 Control System Design Requirements
		4.2.10 Control Objectives and Specifications
	4.3 Feedback Control Systems
		4.3.1 Special Case I
		4.3.2 Special Case II
		4.3.3 Positive Feedback vs. Negative Feedback
	4.4 Steady-State Performance
		4.4.1 Expressions for Steady-State Error
	4.5 Disturbance Modelling
		4.5.1 Effective Disturbance Rejection
		4.5.2 Examples of Open- and Closed-Loop Systems
	4.6 Car Cruise Control System (Open-Loop)
		4.6.1 Input-Output Model
		4.6.2 Transfer Function Model
		4.6.3 Block Diagram Model
		4.6.4 State-Variable Matrix Model
	4.7 Car Cruise Control System (Closed-Loop)
		4.7.1 Input-Output Model
		4.7.2 Transfer Function Model
		4.7.3 Block Diagram Model
		4.7.4 State-Variable Matrix Model
	4.8 DC Motor Speed Control (Open-Loop)
		4.8.1 Input-Output Model
		4.8.2 Transfer Function Model
		4.8.3 Block Diagram Model (Open-Loop)
		4.8.4 State-Variable Matrix Model
	4.9 DC Motor Position Control (Open-Loop)
		4.9.1 Input-Output Model
		4.9.2 Transfer Function Model
		4.9.3 State-Variable Model
	4.10 DC Motor Speed Control (Closed-Loop)
		4.10.1 Input-Output Model
		4.10.2 Transfer Function Model
		4.10.3 Block Diagram Model (Closed-Loop)
		4.10.4 State-Variable Model
	4.11 Modelling PID Controllers
		4.11.1 Proportional Controller (P)
		4.11.2 Proportional and Integral Controller (PI)
		4.11.3 Proportional and Derivative Controller (PD)
		4.11.4 The General PID Controller
		4.11.5 The Standard PID Controller
		4.11.6 Summary of PID Controller Characteristics
		4.11.7 Performance of PID-Type Controllers
	4.12 MATLAB Implementation
		4.12.1 State-Variable Matrix Model
		4.12.2 Transfer Function Model
		4.12.3 Sample MATLAB Code: Motor Speed PID Control
	4.13 Further Analysis of PID-Type Controllers
		4.13.1 Poles and Zeros of PID-Type Controllers
	4.14 Tuning the General PID Controller
		4.14.1 Trial and Error Method
		4.14.2 Quarter Decay Ratio Method
		4.14.3 Stability Limit Method
	4.15 The Standard PID Controller
		4.15.1 Structure and Advantages
		4.15.2 Standard PI and PD Controllers
		4.15.3 Standard PID Controller: Performance Analysis
		4.15.4 Tuning the Standard PID Controller
	4.16 PID Controller Design and Implementation
		4.16.1 Implementation of PID Controllers
		4.16.2 Realisation Using an Operational Amplifier
		4.16.3 Windscreen Wiper Control System
	4.17 System Steady-State Tracking
		4.17.1 Steady-State Errors and System Type
		4.17.2 Illustrative Examples
	4.18 Sensitivity
		4.18.1 Definition of Sensitivity
		4.18.2 Open- and Closed-Loop Sensitivity
	4.19 System Stability
		4.19.1 Bounded Input-Bounded Output Stability
		4.19.2 Asymptotic Internal Stability
		4.19.3 Routh-Hurwitz Stability Criterion
	4.20 Worked Examples of System Stability
	4.21 System Type Based on Stability
		4.21.1 Absolutely Stable System
		4.21.2 Marginally Stable System
		4.21.3 Conditionally Stable System
	4.22 Time Delays in Control Systems
		4.22.1 Impact of Time Delay in Control Systems
		4.22.2 Time Delay and the Smith Predictor Controller
Chapter 5 Root Locus Design Methods
	5.1 Introduction
	5.2 Root Locus
		5.2.1 Background
		5.2.2 Definition
		5.2.3 Magnitude and Angle Criteria
		5.2.4 Breakpoint, Departure and Arrival Angles
	5.3 Constructing the Root Locus
		5.3.1 Summary of the Root Locus Steps
		5.3.2 Simple Rules for Constructing the Root Locus
		5.3.3 Details of the Root Locus Steps
		5.3.4 Determining the Root Locus Gain (Control Gain)
		5.3.5 Root Locus for Second-Order Systems
	5.4 Worked Examples of Root Locus Design
	5.5 Dynamic Compensation: Lead and Lag
	5.6 Extensions of Root Locus Method
		5.6.1 Time Delay
		5.6.2 Nonlinear Systems
	5.7 Computer-Aided Determination of the Root Locus
		5.7.1 MATLAB
Chapter 6 Frequency-Response Design Methods
	6.1 Introduction
	6.2 Definition of the Frequency Response
		6.2.1 Magnitude and Phase Angle
		6.2.2 Combining Magnitudes and Phase Angles
	6.3 Bode Plots
		6.3.1 Definition
		6.3.2 Background
		6.3.3 Advantages of Bode Plots
		6.3.4 Bode Plot Techniques
		6.3.5 Four Classes of Basic Factors
	6.4 Constant Factors (Gain)
		6.4.1 Magnitude
		6.4.2 Phase Angle
	6.5 A Simple Zero Factor
		6.5.1 Magnitude
		6.5.2 Phase Angle
	6.6 A Simple Pole Factor
		6.6.1 Magnitude
		6.6.2 Phase Angle
	6.7 An Integrator Factor
		6.7.1 Magnitude
		6.7.2 Phase Angle
	6.8 A Derivative Factor
		6.8.1 Magnitude
		6.8.2 Phase Angle
	6.9 A Complex Pole Factor
		6.9.1 Magnitude
		6.9.2 Phase Angle
	6.10 A Complex Zero Factor
		6.10.1 Magnitude
		6.10.2 Phase Angle
	6.11 Drawing Bode Plots of Complex Systems
	6.12 Worked Examples of Bode Plots
	6.13 Nonminimum Phase Systems
		6.13.1 Magnitude and Phase
	6.14 Impact of Time Delay on Bode Plots
		6.14.1 Bode Plots of a Time Delay
		6.14.2 Impact of Time Delay on Bode Plots
	6.15 Bode Plots Using MATLAB
		6.15.1 A Single Plot
		6.15.2 Several Plots on the Same Curve
		6.15.3 System in State-Space
	6.16 Models from Experimental Frequency Data
	6.17 Compensation
		6.17.1 PD and Lead Compensators
		6.17.2 PI and Lag Compensators
		6.17.3 Generic Compensator
		6.17.4 PID Compensator
		6.17.5 Lead-Lag Compensator
		6.17.6 Summary of Compensation Characteristics
Chapter 7 State-Space Design Methods
	7.1 Introduction
	7.2 Definitions
	7.3 Block Diagram and the Transfer Function
		7.3.1 State-Space Description and the Block Diagram
		7.3.2 Transfer Function Model: A Revisit
	7.4 System Response by State-Transition Matrix
		7.4.1 Direct Solution of the Differential Equation
		7.4.2 Direct State-Transition Matrix Method
		7.4.3 Diagonalisation
		7.4.4 System Response by Laplace Transform Method
	7.5 System Controllability and Observability
		7.5.1 Summary of Definitions
		7.5.2 Implication of Pole-Zero Cancellation
		7.5.3 Worked Examples of Controllability & Observability
	7.6 Canonical State-Space Models
		7.6.1 Controllable Canonical State-Space Model
		7.6.2 Observable Canonical State-Space Model
		7.6.3 Diagonal Canonical State-Space Model
		7.6.4 Jordan Canonical State-Space Model
		7.6.5 Matrix Eigenvalues and Eigenvectors
		7.6.6 Matrix Diagonalisation
	7.7 Similarity Transformations
	7.8 Canonical State-Space Models: Revisited
		7.8.1 Controllable Canonical State-Space Model
		7.8.2 Observable Canonical State-Space Model
		7.8.3 Jordan Canonical State-Space Model
	7.9 Transfer Function Direct Decomposition
		7.9.1 Decomposition to Controllable Canonical Form
		7.9.2 Decomposition to Observable Canonical Form
	7.10 Full State Feedback Control
		7.10.1 Pole Placement Design Method
		7.10.2 Pole Placement Using Ackermann’s Formula
	7.11 Introduction to Optimal Control
		7.11.1 Overview of Optimisation Theory
		7.11.2 Basic Optimal Control Problem
	7.12 Estimator Design
		7.12.1 Full-Order State Estimator
		7.12.2 Duality of Estimation and Control
		7.12.3 Reduced-Order Estimator
		7.12.4 Compensator Design: Control Law and Estimator
		7.12.5 A Robust Tracking Control System
Chapter 8 Digital Control Systems
	8.1 Introduction
	8.2 Digitisation: Sampled Data Systems
		8.2.1 General Structure
		8.2.2 Data Sampling
		8.2.3 Characteristics of Discrete Time Signals
		8.2.4 The Z-Transform
		8.2.5 Z-Transform in Digital Control: A Summary
		8.2.6 Use of the System DC Gain
	8.3 Key Digital Control Design Methods
		8.3.1 Equivalent Digital Control Design
		8.3.2 Assessment and Comparison of EDCD Methods
		8.3.3 Direct Digital Control Design
		8.3.4 State-Space Analysis
		8.3.5 System Transfer Function
		8.3.6 Controllability and Observability
		8.3.7 Stability of Digital Control Systems
	8.4 Worked Examples of Digital Control Systems
	8.5 MATLAB Implementation of Digital Systems
		8.5.1 Mass-Spring-Damper System
		8.5.2 Ball and Beam Control System
		8.5.3 Digitising a PID Controller and the Plant
		8.5.4 The Digital PID Controller
		8.5.5 Time Delay in Digital Control System
		8.5.6 Implementation of Digital Control Systems
Chapter 9 Advanced Control Systems
	9.1 Introduction
	9.2 State-Space Estimation
		9.2.1 System Description
		9.2.2 Kalman Filter Algorithm
	9.3 The Information Filter
		9.3.1 Information Space
		9.3.2 Information Filter Derivation
		9.3.3 Filter Characteristics
	9.4 The Extended Kalman Filter (EKF)
		9.4.1 Nonlinear State-Space
		9.4.2 EKF Derivation
		9.4.3 Summary of the EKF Algorithm
	9.5 The Extended Information Filter (EIF)
		9.5.1 Nonlinear Information Space
		9.5.2 EIF Derivation
		9.5.3 Summary of the EIF Algorithm
		9.5.4 Filter Characteristics
		9.5.5 Decentralised Estimation
	9.6 Optimal Stochastic Control
		9.6.1 Stochastic Control Problem
		9.6.2 Optimal Stochastic Solution
		9.6.3 Nonlinear Stochastic Control
		9.6.4 Centralised Control
	9.7 Nonlinear Control Systems
		9.7.1 Nonlinear Dynamic Systems
	9.8 Analysis of Nonlinear Control Systems
		9.8.1 Describing Function Analysis
		9.8.2 Phase Plane Methods
	9.9 Design of Nonlinear Control Systems
		9.9.1 Linearisation Methods
		9.9.2 Introduction to Adaptive Control
		9.9.3 Introduction to Robust Control
		9.9.4 Nonlinear Control for a Solar PV Power System
Chapter 10 AI-Based Design and Analysis of Control Systems
	10.1 Introduction
	10.2 Data-Driven Dynamic System Modelling
		10.2.1 AI-Based Approaches to Control Systems
	10.3 Introduction to Artificial Intelligence
		10.3.1 Traditional (Single-Task) Artificial Intelligence
		10.3.2 Artificial General Intelligence
		10.3.3 Machine Learning
		10.3.4 Deep Learning
		10.3.5 Deep Reinforcement Learning
		10.3.6 Generative AI
		10.3.7 Machine Learning Workflow
	10.4 Applying AI Techniques to Control Systems
		10.4.1 Classification of PID Control Systems
		10.4.2 Machine Learning and PID Control
		10.4.3 Deep Reinforcement Learning Agents
		10.4.4 MATLAB Reinforcement Learning Environments
	10.5 Fuzzy Logic Control Systems
		10.5.1 Fuzzy PID Control System
		10.5.2 Tank Water Level Control System
		10.5.3 Advanced Fuzzy Logic Control Systems
	10.6 Artificial Neural Networks-Driven Control Systems
	10.7 The Fourth Industrial Revolution
		10.7.1 History of Industrial Revolutions
		10.7.2 Key 4IR Technologies
	10.8 A 4IR Example: An Intelligent Fleet Management System
		10.8.1 System Components
		10.8.2 Summary of Intelligent Capabilities
	10.9 Design and Analysis of a Drone’s Control System
		10.9.1 Components of the Control System
		10.9.2 Designing the Drone Control System
		10.9.3 Advanced Drone Control Systems
	10.10 Design and Analysis of a Driverless Car’s Control System
		10.10.1 Automation Levels for a Driverless Car
		10.10.2 Designing the Control System
		10.10.3 Objective Functions for a Driverless Car
	10.11 Artificial Intelligence and Robotics: Great Expectations and Daunting Existential Risks
		10.11.1 Definitions
		10.11.2 Opportunities and Challenges in Equal Measure
		10.11.3 AI Risk Mitigation and Management
		10.11.4 The Way Forward
Appendix A Laplace and Z-Transforms
	A.1 Properties of Laplace Transforms
	A.2 Table of Laplace Transforms
	A.3 Properties of Z-Transforms
	A.4 Table of Z-Transforms
Appendix B MATLAB: Basics and Exercises
	B.1 Getting Started
	B.2 Creating MATLAB Files
	B.3 Commands
		B.3.1 Vectors
		B.3.2 Functions
		B.3.3 Plotting
		B.3.4 Polynomials
		B.3.5 Matrices
	B.4 Printing
		B.4.1 Macintosh
		B.4.2 Windows
		B.4.3 Unix
		B.4.4 Plots
	B.5 Using M-files in MATLAB
		B.5.1 Macintosh
		B.5.2 PC Windows
		B.5.3 Unix
	B.6 Saving Workspace
	B.7 Getting Help in MATLAB
	B.8 Control Functions
		B.8.1 Step
		B.8.2 Impulse
	B.9 More Commands
	B.10 LABWORK I
	B.11 LABWORK II
	B.12 LABWORK III
	B.13 LABWORK IV
	B.14 LABWORK V
	B.15 LABWORK VI
	B.16 LABWORK VII
	B.17 LABWORK VIII
	B.18 LABWORK IX
	B.19 LABWORK X
		B.19.1 Control Using Artificial Intelligence and MATLAB
		B.19.2 DC Motor Control Using Arduino
Bibliography
Index