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Essentials of Control Techniques and Theory

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Table of Contents

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

About the Author

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 2010 This 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

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