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begining of table of contents Contents Preface Chapter One: Qualitative Concepts in Control Engineering and Process Analysis 1.1 What is a Feedback Control? 1.2 What is a FeedForward Controller? 1.3 Process Disturbances 1.4 Comparing Feedback and FeedForward Controllers 1.5 Combining Feedback and FeedForward Controllers 1.6 Why is Feedback Control Difficult to Carry Out? 1.7 An Example of Controlling a Noisy Industrial Process 1.8 What is a Control Engineer? 1.9 Summary and Conclusions Chapter Two: Introduction to Developing Control Algorithms 2.1 Approaches to Developing Control Algorithms 2.1.1 Style, Massive Intelligence, Luck and Heroism (SMILH) 2.1.2 A Priori First Principles 2.1.3 A Common Sense, Pedestrian Approach 2.2 Dealing with the Existing Process 2.2.1 What is the Problem? 2.2.2 The Diamond Road Map Compartmentalization and Requirements Gathering Where to Start? Massive Cross Correlation Time Domain Analysis Frequency Domain Analysis Step Change Response Analysis Control Development 2.3 Dealing with Control Algorithms Bundled with the Process What is the Problem? Separation and Success Problem Solving and Bundling 2.4 Some Comments on Debugging Control Algorithms Rookie Fright When in Doubt, Simulate ¿ Not! At Last ¿ Busted! Surprise Sub Totally Covering my Derriere It¿s Too Complicated ¿ Use the Process for Debugging 2.5 Documentation and Indispensability 2.6 Summary and Conclusions Chapter Three: Basic Concepts in Process Dynamics 3.1 The First Order Process ¿ An Introduction The Process Gain and Time Constant 3.2 Mathematical Descriptions of the First Order Process 3.2.1 The Continuous-Time Domain Model Scaling 3.2.2 Solution of the Continuous-Time Domain Model Comments about the Solution 3.2.3 The First Order Model and Proportional Control Faster Response Offset from Set Point 3.2.4 The First Order Model and Proportional-Integral Control Showing that there is no Offset Trying a Partial Solution for the Transient Part Critical Damping Overdamped Response Underdamping So What? 3.3 The Laplace Transform 3.3.1 The Transfer Function and Block Diagram Algebra 3.3.2 Applying the New Tool to the First Order Model 3.3.4 The Laplace Transform of Derivatives 3.3.5 Applying the Laplace Transform to the Case with Proportional plus Integral Control 3.3.6 More Block Diagram Algebra and Some Useful Transfer Functions 3.3.7 Zeros and Poles Partial Fractions and Poles Poles and Time Domain Exponential Terms 3.4 Review and Summary Chapter Four: A New Domain and More Process Models 4.1 Onward to the Frequency Domain Sinusodially Disturbing the First Order Process A Little Mathematical Support in the Time Domain A Little Mathematical Support in the Laplace Transform Domain A Little Graphical Support A Graphing Trick 4.2 How Can Sinusoids Help Us with Understanding Feedback Control? 4.3 The First Order Process with Feedback Control in the Frequency Domain What¿s this about the Integral? What about adding P to the I? Partial Summary and a Rule of Thumb using Phase Margin and Gain Margin 4.4 A Pure Deadtime Process Proportional-Only Control of a Pure Deadtime Process Integral-Only Control of a Pure Deadtime Process 4.5 A First Order Process with Deadtime (FOWDT) Process The Concept of Minimum Phase Proportional-Only Control Proportional-Integral Control of the FOWDT Process 4.6 A Few Comments about Simulating Processes with Variable Deadtimes 4.7 Partial Summary and a Slight modification of the Rule of Thumb 4.8 Summary and Conclusions Chapter Five. Matrices and Higher Order Process Models 5.1 Third Order Processes without Back Flow The Laplace Transform Version The Frequency Domain Version The Matrix (State Space) Version 5.2 Third Order Process with Back Flow The State Space Version 5.3 Control of Three Tank System with No Back Flow Closed Loop Performance in the Frequency Domain 5.4 Critical Values and Finding the Poles 5.5 Multi-Tank Processes Matching the N-Tank Model with a FOWDT Model 5.6 Summary and Conclusions Chapter Six: An Underdamped Process 6.1 The Dynamics of the Mass/Spring/Dashpot Process 6.2 Solutions in Four Domains Time Domain Laplace Domain Solution Frequency Domain State Space Representation Scaling and Round-Off Error 6.3 PI Control of the Mass/Spring/Dashpot Process 6.4 Derivative Control (PID) Complete Cancellation Adding Sensor Noise Filtering the Derivative 6.5 Compensation Before Control-The Transfer Function Approach 6.6 Compensation Before Control-The State Space Approach 6.7 An Electrical Analog to the Mass-Dashpot-Spring Process 6.8. Summary and Conclusions Chapter Seven: Distributed Processes 7.1 The Tubular Energy Exchanger ¿ Steady State 7.2 The Tubular Energy Exchanger ¿ Transient Behavior Transfer by Diffusion 7.3 Solution of the Tubular Heat Exchanger Equation Inlet Temperature Transfer Function Steam Jacket Temperature Transfer Function 7.4 Response of Tubular Heat Exchanger to Step in Jacket Temperature The Large Diameter Case The Small Diameter Case 7.5 Studying the Tubular Energy Exchanger in the Frequency Domain. 7.6 Control of the Tubular Energy Exchanger 7.7 Lumping the Tubular Energy Exchanger Modeling an Individual Lump Steady State Solution Discretizing the Partial Differential Equation 7.8 Lumping and Axial Transport 7.9 State Space Version of the Lumped Tubular Exchanger 7.10 Summary and Review Chapter 8: Stochastic Process Disturbances and the Discrete Time Domain 8.1 The Discrete Time Domain 8.2 White Noise and Sample Estimates of Population Measures The Sample Average The Sample Variance The Histogram The Sample Autocorrelation The Line Spectrum The Cumulative Line Spectrum 8.3 Non-White Stochastic Sequences Positively Autoregressive Sequences Negatively Autoregressive Sequences Moving Average Stochastic Sequences Unstable Nonstationary Stochastic Sequences Multi-Dimensional Stochastic Processes and the Covariance 8.4 Populations, Realizations, Samples, Estimates and Expected Values Realizations Expected Value Ergodicity and Stationarity Applying the Expectation Operator 8.5 Comments on Stochastic Disturbances and Difficulty of Control White Noise Colored Noise 8.6 Summary and Conclusions Chapter Nine: The Discrete Time Domain and the Z-Transform 9.1 Discretizing the First Order Model 9.2 Moving to the Z-Domain via the Back Shift Operator 9.3 Sampling and Zero-Holding 9.4 Recognizing the First Order Model as a Discrete-Time Filter 9.5 Discretizing the FOWDT Model 9.6 The PI Control Equation in the Discrete Time Domain 9.7 Converting the PI Control Algorithm to Z-Transforms 9.8 The PIfD Control Equation in the Discrete Time Domain 9.9 Using the Laplace Transform to Design Control Algorithms ¿ The Q Method Developing the PI Control Algorithm Developing a PID-Like Control Algorithm 9.10 Using the Z-Transform to Design Control Algorithms 9.11 Designing a Control Algorithm for a Dead-Time process 9.12 Moving to the Frequency Domain The First Order Process Model The Ripple Sampling and Replication 9.13 Filters Autogressive Filters Moving Average Filters A Double Pass Filter High Pass Filters 9.14 Frequency Domain Filtering 9.15 The Discrete-Time State Space Equation 9.16 Determining Model Parameters from Experimental Data First Order Models Third Order Models A Practical Method 9.17 Process Identification with White Noise Inputs 9.18 Summary Chapter Ten: Estimating the State and Using It for Control 10.1 An Elementary Presentation of the Kalman Filter The Process Model The Pre-Measurement and Post-Measurement Equations The Scalar Case A Two-Dimensional Example The Propagation of the Covariances The Kalman Filter Gain 10.2 Estimating the Underdamped Process State 10.3 The Dynamics of the Kalman Filter and an Alternative Way to Find the Gain The Dynamics of a Predictor Estimator 10.4 Using the Kalman Filter for Control A Little Detour to Find the Integral Gain 10.5 Feeding Back the State for Control Integral Control? Duals 10.6 Integral and Multi-Dimensional Control Setting up the Example Process and Posing the Control Problem Developing the Discrete Time Version Finding the Open Loop Eigenvalues and Placing the Closed Loop Eigenvalues Implementing the Control Algorithm 10.7 PI Control Applied to the Three Tank Process 10.8 Control of the Lumped Tubular Energy Exchanger 10.9 Miscellaneous Issues Optimal Control Continuous-Time Domain Kalman Filter 10.10 Summary Chapter Eleven: A Review of Control Algorithms 11.1 The Strange Motel Shower Stall Control Problem 11.2 Identifying the Strange Motel Shower Stall Control Approach as Integral-Only 11.3 Proportional-Integral, Proportional-Only, and PID Control PI Control P-Only Control PID Control Modified PID Control 11.4 Cascade Control 11.5 Control of White Noise ¿ Conventional Feedback Control vs. SPC 11.6 Control Choices 11.7 Analysis and Design Tool Choices Appendix A: Rudimentary Calculus The Automobile Trip The Integral, Area and Distance Approximation of the Integral Integrals of Useful Functions The Derivative, Rate of Change and Acceleration Derivatives of Some Useful Functions The Relation between the Derivative and the Integral Some Simple Rules of Differentiation A Useful Test Function Summary Appendix B: Complex Numbers Complex Conjugates Complex Numbers as Vectors or Phasors Euler¿s Equation An Application to a Problem in Chapter Four The Full Monty Summary Appendix C: Spectral Analysis An Elementary Discussion of the Fourier Transform as a Data Fitting Problem Partial Summary Dectecting Periodic Components The Line Spectrum The Exponential Form of the Least Squares Fitting Equation Periodicity in the Time Domain Sampling and Replication Apparent Increased Frequency-Domain Resolution via Padding The Variance and the Discrete Fourier Transform Impact of Increased Frequency Resolution on Variability of the Power Spectrum Aliasing Summary Appendix D. Infinite and Taylor¿s Series Summary Appendix E. Application of the Exponential Function to Differential Equations First Order Differential Equations Partial Summary Partial Solution of a Second Order Differential Equation Summary Appendix F. The Laplace Transform Laplace Transform of a Constant (or a Step Change) Laplace Transform of a Step at a Time Greater than Zero Laplace Transform of a Delayed Quantity Laplace transform of the Impulse or Dirac Delta function Laplace Transform of the Exponential Function Laplace Transform of a Sinusoid Final Value Theorem Laplace Transform Tables Laplace Transform of the Time Domain Derivative Laplace Transform of Higher Derivatives Laplace Transform of an Integral The Laplace Transform Recipe Applying the Laplace Transform to the First Order Model: The Transfer Function Applying the Laplace Transform to the First Order Model: The Impulse Response Applying the Laplace Transform to the First Order Model: The Step Response Partial Fraction Expansions Applied to Laplace Transforms: The First Order Problem Partial Fraction Expansions Applied to Laplace Transforms: The Second Order Problem A Precursor to the Convolution Theorem Using the Integrating Factor to Obtain the Convolution Integral Application of the Laplace Transform to a First Order Partial Differential Equation Solving the Transformed Partial Differential Equation The Magnitude and Phase of the Transformed Partial Differential Equation A Brief History of the Laplace Transform Summary Appendix G. Vectors and Matrices Addition and Multiplication of Matrices Partitioning State Space Equations and Laplace Transforms Transposes and Diagonal Matrices Determinants, Cofactors and Adjoints of a Matrix The Inverse Matrix Some Matrix Calculus The Matrix Exponential Function and Infinite Series Eigenvalues of Matrices Eigenvalues of Transposes More on Operators The Cayley-Hamilton Theorem Summary Appendix H. Solving the State Space Equation Solving the State Space Equation in the Time Domain for a Constant Input Solution of the State Space Equation using the Integrating Factor Solving the State Space Equation in the Laplace Transform Domain The Discrete-Time State Space Equation Summary Appendix I. The Z-Transform The Sampling Process and the Laplace Transform of a Sampler The Zero-Order Hold Z-Transform of the Constant (Step Change) Z-Transform of the Exponential Function The Kronecker Delta and its Z-Transform Some Complex Algebra and the Unit Circle in the z-Plane A Partial Summary Developing Z-Transform Transfer Functions from Laplace Tranforms with Holds Poles and Associated Time Domain Terms Final Value Theorem Summary Appendix J: A Brief Exposure to Matlab Index

Library of Congress Subject Headings for this publication:

Automatic control.

Control theory.