Carefully separating the essential from the ornamental, Essentials of Control Techniques and Theory presents the nuts and bolts for designing a successful controller. It discusses the theory required to support the art of designing a working controller as well as the various aspects to convince a client, employer, or examiner of your expertise.
A Compelling Account of the Basics of Control Theory
Control solutions for practicing engineers
Using the author’s own Javascript On-Line Learning Interactive Environment for Simulation (Jollies), the text relies on computer-based graphical analysis methods, such as Nyquist, Nichols, root locus, and phase-plane, to illustrate how useful computer simulation can be for analyzing both linear and nonlinear systems. It explains step-by-step the design and modeling of various control systems, including discrete time systems and an inverted pendulum. Along with offering many web-based simulations, the book shows how mathematics, such as vectors, matrices, and the differential equations that govern state variables, can help us understand the concepts that underpin the controller’s effects.
From frequency domain analysis to time-domain state-space representation, this book covers many aspects of classical and modern control theory. It presents important methods for designing and analyzing linear systems and controllers.
ESSENTIALS OF CONTROL TECHNIQUES—WHAT YOU NEED TO KNOW
Introduction: Control in a Nutshell, History, Theory, Art, and Practice
The Origins of Control
Early Days of Feedback
The Origins of Simulation
Discrete Time
Modeling Time
Introduction
A Simple System
Simulation
Choosing a Computing Platform
An Alternative Platform
Solving the First Order Equation
A Second Order Problem
Matrix State Equations
Analog Simulation
Closed Loop Equations
Simulation with JavaScript "On-Line Learning Interactive Environment for Simulation" (Jollies)Introduction
How a Javascript On-Line Learning Interactive Environment for Simulation (Jollies) Is Made Up
Moving Images without an Applet
A Generic Simulation
Practical Control Systems
Introduction
The Nature of Sensors
Velocity and Acceleration
Output Transducers
A Control Experiment
Adding Control
Introduction
Vector State Equations
Feedback
Another Approach
A Change of Variables
Systems with Time Delay and the PID Controller
Simulating the Water Heater Experiment
Systems with Real Components and Saturating Signals—Use of the Phase Plane
An Early Glimpse of Pole Assignment
The Effect of Saturation
Meet the Phase Plane
Phase Plane for Saturating Drive
Bang-Bang Control and Sliding Mode
Frequency Domain Methods
Introduction
Sine-Wave Fundamentals
Complex Amplitudes
More Complex Still-Complex Frequencies
Eigenfunctions and Gain
A Surfeit of Feedback
Poles and Polynomials
Complex Manipulations
Decibels and Octaves
Frequency Plots and Compensators
Second Order Responses
Excited Poles
Discrete Time Systems and Computer Control
Introduction
State Transition
Discrete Time State Equations and Feedback
Solving Discrete Time Equations
Matrices and Eigenvectors
Eigenvalues and Continuous Time Equations
Simulation of a Discrete Time System
A Practical Example of Discrete Time Control
And There’s More
Controllers with Added Dynamics
Controlling an Inverted Pendulum
Deriving the State Equations
Simulating the Pendulum
Adding Reality
A Better Choice of Poles
Increasing the Realism
Tuning the Feedback Pragmatically
Constrained Demand
In Conclusion
ESSENTIALS OF CONTROL THEORY—WHAT YOU OUGHT TO KNOW
More Frequency Domain Background Theory
Introduction
Complex Planes and Mappings
The Cauchy–Riemann Equations
Complex Integration
Differential Equations and the Laplace Transform
The Fourier Transform
More Frequency Domain Methods
Introduction
The Nyquist Plot
Nyquist with M-Circles
Software for Computing the Diagrams
The "Curly-Squares" Plot
Completing the Mapping
Nyquist Summary
The Nichols Chart
The Inverse-Nyquist Diagram
Summary of Experimental Methods
The Root Locus
Introduction
Root Locus and Mappings
A Root Locus Plot
Plotting with Poles and Zeroes
Poles and Polynomials
Compensators and Other Examples
Conclusions
Fashionable Topics in Control
Introduction
Adaptive Control
Optimal Control
Bang-Bang, Variable Structure, and Fuzzy Control
Neural Nets
Heuristic and Genetic Algorithms
Robust Control and H-infinity
The Describing Function
Lyapunov Methods
Conclusion
Linking the Time and Frequency Domains
Introduction
State-Space and Transfer Functions
Deriving the Transfer Function Matrix
Transfer Functions and Time Responses
Filters in Software
Software Filters for Data
State Equations in the Companion Form
Time, Frequency, and Convolution
Delays and the Unit Impulse
The Convolution Integral
Finite Impulse Response Filters
Correlation
Conclusion
More about Time and State Equations
Introduction
Juggling the Matrices
Eigenvectors and Eigenvalues Revisited
Splitting a System into Independent Subsystems
Repeated Roots
Controllability and Observability
Practical Observers, Feedback with Dynamics
Introduction
The Kalman Filter
Reduced-State Observers
Control with Added Dynamics
Conclusion
Digital Control in More Detail
Introduction
Finite Differences—The Beta-Operator
Meet the z-Transform
Trains of Impulses
Some Properties of the z-Transform
Initial and Final Value Theorems
Dead-Beat Response
Discrete-Time Observers
Relationship between z- and Other Transforms
Introduction
The Impulse Modulator
Cascading Transforms
Tables of Transforms
The Beta and w Transforms
Design Methods for Computer Control
Introduction
The Digital-to-Analog Convertor (DAC) as Zero Order Hold
Quantization
A Position Control Example, Discrete Time Root Locus
Discrete Time Dynamic Control-Assessing Performance
Errors and Noise
Disturbances
Practical Design Considerations
Delays and Sample Rates
Conclusion
Optimal Control—Nothing but the Best
Introduction: The End Point Problem
Dynamic Programming
Optimal Control of a Linear System
Time Optimal Control of a Second Order System
Optimal or Suboptimal?
Quadratic Cost Functions
In Conclusion
Index
Biography
John Billingsley is Chair of Mechatronic Engineering at the University of Southern Queensland in Toowoomba, Australia, and directs technology research in the National Centre for Engineering in Agriculture (NCEA).
…a valuable and much-needed demystification of control theory … The role of the blackboard is assumed by a well-matched and balanced Web site, on which JavaScript-based simulations of the book’s examples and experiments can be run (and rerun with changed parameters). … The complement of the lucid and reasoned thinking out loud is, along with coherent excerpts of JavaScript, in the hard copy. … Forgetting for the moment that this is an intrinsically excellent book, it is also the right control theory book at the right time. … This book has my highest recommendation among control theory books.
—George Hacken, Computing Reviews, August 2010This book contains some basic notions and techniques from the control theory presented from the point of view of an engineer. Special attention is paid to the classical frequency-domain methods, practical observers, and different principles of controller design. Using the author's own Javascript On-Line Learning Interactive Environment for Simulation (Jollies), the design and modeling of various control systems is explained step-by-step (as the inverted pendulum). ... The book contains a large number of illustrative examples (including the corresponding Javascript codes and simulation results) helping to understand the application of the control theory to design of working controllers. … very useful as a complementary reading for a course in control theory.
— Mikhail I. Krastanov, in Zentralblatt MATH, 1198-1
