Automatic Control with Experiments (Advanced Textbooks in Control and Signal Processing)

✍ Scribed by Victor Manuel Hernández-Guzmán, Ramón Silva-Ortigoza, Jorge Alberto Orrante-Sakanassi

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 987
• Edition: 2
• Category: Library

✦ Synopsis

This book offers an enhanced and comprehensive understanding of control theory and its practical applications. The theoretical chapters on control tools have been meticulously revised and improved to provide a clearer and more insightful exploration of the fundamental concepts and ideas. The explanations have been refined, and new examples have been added to aid comprehension. Additionally, a new chapter on discrete-time systems has been included, delving into an important aspect of control theory. Advanced topics in control are also covered in greater detail, ensuring a comprehensive treatment of the subject matter.

The section on experimental applications has been revamped to showcase the application of control ideas in various scenarios. Several chapters have been replaced with fresh content that focuses on controlling new and different experimental prototypes. These examples illustrate how control concepts can be effectively applied in real-world situations. Furthermore,this book introduces a new approach for control of non-minimum phase systems and explores the concept of differential flatness for multiple-input multiple-output systems. Additionally, a fascinating application involving a wheeled pendulum mobile robot has been included.

While some chapters have been replaced, the second edition retains the chapters on the control of DC motors and the control of a magnetic levitation system. However, the material in the former chapter is mostly new, and the latter chapter is entirely supported by new control concepts and ideas.

✦ Table of Contents

Series Editors’ Foreword
Foreword
Preface
Acknowledgments
Contents
1 Introduction
1.1 The Human Being as a Controller
1.1.1 Steering a Boat
1.1.2 Video Recording While Running
1.2 Feedback Is Omnipresent
1.2.1 A Predator-Prey System
1.2.2 Homeostasis
1.3 Real-Life Applications of Automatic Control
1.3.1 A Position Control System
1.3.2 A Velocity Control System
1.3.3 Robotic Arm
1.3.4 Automatic Steering of a Ship
1.3.5 A Gyro-Stabilized Video Camera
1.4 Nomenclature in Automatic Control
1.5 History of Automatic Control
1.6 Experimental Prototypes
1.7 Summary
1.8 Review Questions
References
2 Linear Ordinary Differential Equations
2.1 First-Order Differential Equation
2.1.1 The a not equals 0aneq0 Case
2.1.2 The a equals 0a= 0 Case
2.1.3 Transfer Function
2.2 Second-Order Differential Equation
2.2.1 Graphical Study of the Solution
2.2.2 Transfer Function
2.3 Arbitrary Order Differential Equations
2.3.1 Real and Different Roots
2.3.2 Real and Repeated Roots
2.3.3 Complex Conjugate and Nonrepeated Roots
2.3.4 Complex Conjugated and Repeated Roots
2.3.5 Conclusions
2.4 Poles and Zeros in Higher-Order Systems
2.4.1 Approximate Pole–Zero Cancelation and Reduced-Order Models
2.4.2 Dominant Poles and Reduced-Order Models
2.4.3 Approximating the Transient Response of Higher-Order Systems
2.5 The Case of Sinusoidal Excitations
2.6 The Superposition Principle
2.7 First- and Second-Order Control Systems
2.7.1 Proportional Control of Velocity in a DC Motor
2.7.2 Proportional Position Control Plus Velocity Feedback for a DC Motor
2.7.3 Proportional–Derivative Position Control of a DC Motor
2.7.4 Proportional–Integral Velocity Control of a DC Motor
2.7.5 Why Not to Use PID Control for First-Order Systems
2.8 Case Study: Electric Current Loops for Control of Electric Motors
2.9 Summary
2.10 Review Questions
2.11 Exercises
References
3 Basic Tools for Arbitrary-Order Systems
3.1 Block Diagrams
3.2 The Rule of Signs
3.2.1 Second Degree Polynomials
3.2.2 First Degree Polynomials
3.2.3 Polynomials with Degree Greater Than or Equal to 3
3.3 Routh's Stability Criterion
3.4 Steady-State Error
3.4.1 Step Desired Output
3.4.2 Ramp Desired Output
3.4.3 Parabola Desired Output
3.5 Case Study. An Electronic Oscillator
3.6 Summary
3.7 Review Questions
3.8 Exercises
References
4 Time Response-Based Design
4.1 An Introductory Example
4.2 Plotting Root Locus Diagrams
4.2.1 Rules to Plot the Root Locus Diagram
4.3 DC Motor Control
4.3.1 Proportional Control of Position
4.3.2 Proportional–Derivative (PD) Control of Position
4.3.3 Proportional–Integral (PI) Control of Velocity
4.3.4 Performance Limitations of Proportional–Integral (PI) Control of Velocity ch4FortinoIEEEtierlocus
4.3.5 Proportional–Integral–Derivative (PID) Control of Position
4.3.6 Performance Limitations of Classical Proportional–Integral–Derivative (PID) Control
4.4 Control of a Ball and Beam System
4.4.1 Assigning the Desired Closed-Loop Poles for a Ball and Beam System
4.5 Case Study. Additional Notes on PID Control of Position
4.6 Summary
4.7 Review Questions
4.8 Exercises
References
5 Frequency Response-Based Design
5.1 Frequency Response of Some Electric Circuits
5.1.1 A Series upper R upper CRC Circuit: Output at the Capacitance
5.1.2 A Series upper R upper CRC Circuit: Output at the Resistance
5.1.3 A Series upper R upper L upper CRLC Circuit: Output at the Capacitance
5.1.4 A Series upper R upper L upper CRLC Circuit: Output at the Resistance
5.2 The Relationship Between Frequency Response and Time Response
5.3 Common Graphical Representations
5.3.1 Bode Diagrams
5.3.2 Polar Plots
5.4 Frequency Response-Based Model Identification
5.4.1 DC Motor Velocity Model
5.4.2 DC Motor Position Model
5.4.3 A Mechanism with Flexibility
5.5 Nyquist Stability Criterion
5.5.1 Contours Around Poles and Zeros
5.5.2 Nyquist Path
5.5.3 Poles and Zeros
5.5.4 Nyquist Criterion. A Special Case
5.5.5 Nyquist Criterion—the General Case
5.6 Stability Margins for Minimum Phase Systems
5.7 The Relationship Between Frequency Response and Time Response Revisited
5.7.1 Closed-Loop Frequency Response and Closed-Loop Time Response
5.7.2 Open-Loop Frequency Response and Closed-Loop Time Response
5.8 Analysis and Design Examples
5.8.1 Velocity Control in a DC Motor
5.8.2 PD Position Control of a DC Motor
5.8.3 Redesign of the PD Position Control for a DC Motor
5.8.4 PID Position Control of a DC Motor
5.8.5 Time-Varying References and Disturbances
5.8.6 A Ball and Beam System
5.9 Case Study. PID Control of an Unstable Plant
5.10 Summary
5.11 Review Questions
5.12 Exercises
References
6 The State Variable Approach
6.1 Definition of State Variables
6.2 The Error Equation
6.3 Approximate Linearization of Nonlinear State Equations
6.3.1 Procedure for First-Order State Equations Without Input
6.3.2 General Procedure for Arbitrary Order State Equations with Arbitrary Number of Inputs
6.4 Some Results from Linear Algebra
6.5 Solution of a Linear Time-Invariant Dynamical Equation
6.6 Stability of a Dynamical Equation
6.7 Linearly Independent Functions of Time ch6chitsongchenestado
6.8 Controllability and Observability
6.8.1 Controllability
6.8.2 Observability
6.9 Transfer Function of a Dynamical Equation
6.10 A Realization of a Transfer Function
6.11 Equivalent Dynamical Equations
6.12 State Feedback Control
6.13 State Observers
6.14 The Separation Principle
6.15 Case Study: Output-Feedback Control of a DC Motor
6.16 Summary
6.17 Review Questions
6.18 Exercises
References
7 Advanced Topics in Control
7.1 Trade-Offs in Classical Control
7.1.1 Time-Domain Design Limitations
7.1.2 Frequency-Domain Design Limitations. Bode's Integral Constraints
7.2 Internal Model Principle
7.2.1 Simulation Example
7.3 Nonminimum Phase Systems
7.3.1 Linear Nonminimum Phase Systems
7.3.2 Nonlinear Nonminimum Phase Systems
7.4 Differential Flatness
7.4.1 Linear Single-Input Single-Output Systems
7.4.2 Linear Multiple-Input Multiple-Output Systems ch7SiraDCT
7.5 Describing Function Analysis
7.5.1 The Dead Zone Nonlinearity ch7DCTslotine,ch7Cagliari
7.5.2 The Saturation Nonlinearity ch7DCTslotine,ch7Cagliari
7.6 Summary
7.7 Review Questions
7.8 Exercises
References
8 Discrete-Time Systems
8.1 The Sampling Process
8.2 Reconstructing Continuous-Time Functions from Discrete-Time Functions
8.2.1 Aliasing
8.2.2 Folding
8.2.3 Hidden Oscillation
8.2.4 Zero-Order Hold
8.3 script upper ZmathcalZ Transform
8.3.1 Transfer Functions of Sampled Systems
8.3.2 Transfer Function of Systems Including a Zero-Order Hold
8.4 Inverse script upper ZmathcalZ Transform
8.5 Stability of Discrete-Time Systems
8.6 Performance Limitations
8.7 Is upper X left parenthesis s right parenthesisX(s) the Limit of upper X left parenthesis z right parenthesisX(z) When upper T Subscript s Baseline right arrow 0Tsto0?
8.7.1 An Introductory Example
8.7.2 Result in ch8astrom84Discreto
8.7.3 The Proposed Procedure
8.7.4 A Different Approach. An Example
8.7.5 Conclusions
8.7.6 Result in ch8astrom84Discreto Revisited
8.8 The Frequency Response Method
8.8.1 Nyquist Stability Criterion
8.8.2 Sensitivity Function for Discrete-Time Systems
8.8.3 An Illustrative Example
8.9 Effect of Sampling Period on Closed-Loop Response …
8.10 State Space Representation of Discrete-Time Systems
8.10.1 Stability
8.11 Summary
8.12 Review Questions
8.13 Exercises
References
9 Control of PM Brushed DC Motor
9.1 Mathematical Model
9.2 Identification
9.2.1 Velocity Model. Step Response-Based Identification
9.2.2 Position Model—Step Response-Based Identification
9.3 Velocity Control
9.3.1 Proportional Control
9.3.2 Proportional-Integral (PI) Control of Velocity
9.4 Position Control
9.4.1 Proportional Position Control Plus Velocity Feedback
9.4.2 Proportional-Derivative (PD) Position Control
9.4.3 Proportional-Integral-Derivative (PID) Position Control
9.5 Trajectory Tracking
9.6 Control of a Mechanism with Flexibility
9.6.1 System Modeling
9.6.2 Controller Design
9.7 Experimental Prototype Construction
9.7.1 Microcontroller PIC16F877A C Program
9.7.2 Personal Computer Builder C++ Program
9.7.3 Other Experiments
9.8 Internal Model Principle
9.8.1 Experimental Results
9.9 PC Program Used in Experiments of Sect.9.8
9.10 Inverted Pendulum Control
9.10.1 The Experimental Prototype
9.10.2 Limit Cycles
9.10.3 PID Control
9.11 Microcontroller Program Used for Experiments in Sect. 9.10
9.12 Summary
9.13 Review Questions
References
10 Control of a Ball and Beam System
10.1 Mathematical Model
10.1.1 Nonlinear Model
10.1.2 Linear Approximate Model
10.2 Prototype Construction
10.2.1 Ball Position xx Measurement System
10.2.2 Beam Angle thetaθ Measurement System
10.3 Parameter Identification
10.3.1 Motor-Beam Subsystem
10.3.2 Ball Dynamics
10.4 Controller Design
10.5 Experimental Results
10.6 Control System Implementation
10.6.1 Dead Zone Reduction in Complementary Symmetry Power Amplifier
10.6.2 Control System Electric Diagram
10.7 Builder 6Cplus plus++ Code used to Implement Control Algorithms
10.8 PIC C Code Used to Program the Microcontroller PIC16F877A
10.9 Control Based on a PIC16F877A Microcontroller
10.9.1 Prototype Construction
10.9.2 Controller Design
10.9.3 Experimental Results
10.9.4 PIC16F877A Microcontroller Programming
10.10 Summary
10.11 Review Questions
References
11 Control of a Magnetic Levitation System
11.1 The Complete Nonlinear Mathematical Model
11.2 Approximate Linear Model
11.2.1 A State Variables Representation Model
11.2.2 Linear Approximation
11.3 Experimental Prototype Construction
11.3.1 Ball
11.3.2 Electromagnet
11.3.3 Position Sensor
11.3.4 Power Amplifier
11.4 Experimental Identification of Model Parameters
11.4.1 Electromagnet Internal Resistance, upper RR
11.4.2 Electromagnet Inductance, upper L left parenthesis y right parenthesisL(y)
11.4.3 Position Sensor Gain, upper A Subscript sAs
11.4.4 Ball Mass, mm
11.5 Electric Diagram
11.6 Control System Structure
11.7 Controller Design
11.7.1 PID Position Controller Design
11.7.2 Design of the PI Electric Current Controller
11.7.3 More on Noise Effects
11.7.4 Sampling Period Selection
11.7.5 A Modified Closed-Loop Strategy
11.7.6 Discrete-Time Analysis
11.7.7 Controller Design Summary
11.8 Experimental Results
11.8.1 The TMS320F28377S Program
11.9 Some Additional Observations
11.9.1 Reasons to Employ an Internal Electric Current Loop
11.9.2 Warming-Up of the Magnetic Levitation System
11.10 Comparison with Control of an Inverted Pendulum
11.10.1 Limit Cycles
11.10.2 Conclusions
11.11 Summary
11.12 Review Questions
References
12 Control of Pendubot
12.1 Pendubot Dynamical Model
12.2 Linear Approximate Model
12.3 Stabilization at the Top Configuration
12.3.1 Pendubot Prototype
12.3.2 Experimental Results
12.4 Differential Flatness-Based Model
12.4.1 Experimental Results
12.5 Stabilization at Some Out-the-Top Configuration
12.5.1 Experimental Results
12.5.2 Numerical Computations for Controller Design
12.6 Controller Program Codes
12.6.1 Computer Program
12.6.2 Microcontroller Program
12.7 Summary
12.8 Review Questions
References
13 Tilt Angle Estimation
13.1 State Observers
13.2 Kalman Filter
13.3 Complementary Filter
13.4 Estimating Tilt Angle
13.4.1 State Observer
13.4.2 Kalman Filter
13.4.3 Complementary Filter
13.4.4 Experimental Results
13.5 Summary
13.6 Review Questions
References
14 Control of Wheeled Pendulum
14.1 Basic Mathematical Tools for Robot Modeling
14.1.1 Rotation Matrices
14.1.2 Skew-Symmetric Matrices
14.1.3 Angular Velocity
14.1.4 The Jacobian
14.1.5 Robot Dynamics
14.2 Mathematical Modeling of Wheeled Pendulum
14.2.1 Kinetic and Potential Energies of Robot
14.2.2 Robot Equations of Motion
14.2.3 Nonholonomic Constraints in the Wheeled Pendulum
14.2.4 Including Nonholonomic Constraints in the Wheeled Pendulum Model
14.2.5 Checking Properties of Model
14.3 Linear Approximate Model
14.4 Experimental Prototype
14.4.1 Prototype Description
14.4.2 Task to Be Solved
14.4.3 Tilt Angle alphaα Estimation
14.4.4 Robot Parameter Computation
14.4.5 Model Parameter Computation
14.5 Controller Design Based on Linear Approximation
14.5.1 Design Based on Differential Flatness
14.5.2 Experimental Results
14.6 Computer Program
14.7 Numerical Computations for Controller Design
14.8 Another Simpler Differential Flatness-Based Controller
14.8.1 Model Reduction Using Nonholonomic Constraints
14.8.2 Controller Design
14.8.3 Experimental Results
14.9 Summary
14.10 Review Questions
References
15 Control of Mechanical Systems with Flexibility
15.1 Introduction
15.2 Dynamic Model of Robot Manipulators with Flexible Joints
15.3 The Regulation Control Problem
15.3.1 Simulation Results
15.3.2 Experimental Results
15.4 The Trajectory Tracking Control Problem
15.4.1 Simulation Results
15.4.2 Experimental Results
15.5 Experimental Prototype Construction
15.6 Microcontroller PIC16F877A C Program
15.7 Laptop Builder C++ Program
15.8 Summary
15.9 Review Questions
References
16 Control of DC/DC Power Electronic Converters
16.1 The Boost Converter
16.1.1 Nonminimum Phase Property
16.1.2 Partial Feedback Linearization Control
16.1.3 A Controller Inspired by Passivity
16.1.4 Controller in ch16ZengshiChenDCDC
16.1.5 Boost Converter Prototype Used in Experiments
16.2 The Buck-Boost Converter
16.2.1 Nonminimum Phase Property
16.2.2 Partial Feedback Linearization Control
16.2.3 A Controller Inspired by Passivity
16.2.4 Buck-Boost Converter Prototype Used in Experiments
16.3 Summary
16.4 Review Questions
References
Appendix A Fourier and Laplace Transforms
A.1 Fourier Series
A.2 Fourier Transform
A.3 Laplace Transform
Appendix B Bode Diagrams
B.1 First-Order Terms
B.1.1 A Differentiator
B.1.2 An Integrator
B.1.3 A First-Order Pole
B.1.4 A First-Order Zero
B.2 A Second-Order Transfer Function
B.3 A Second-Order Zero
Appendix C Decibels, dB
Appendix D Euler–Lagrange Equations Subject to Constraints
D.1 General Method to Include Nonholonomic Constraints in System Dynamics
Appendix E Numerical Implementation of Controllers
E.1 Numerical Computation of an Integral
E.2 Numerical Differentiation
E.3 Lead Compensator
E.4 Controller in Fig. 10.8a
E.5 Controller in (9.75)
Appendix F Background on Complex Variable
F.1 Residue at normal infinityinfty
F.1.1 Definition [2]
F.1.2 Computing the Residue
F.2 Inverse script upper ZmathcalZ Transform: The Inversion Integral Method
Index