Practical Control Engineering by Koenig, David M. -- Read -- Imperial Library of Trantor

Index

Cover Page Practical Control Engineering Copyright Page Contents Preface 1 Qualitative Concepts in Control Engineering and Process Analysis

1-1 What Is a Feedback Controller 1-2 What Is a Feedforward Controller 1-3 Process Disturbances 1-4 Comparing Feedforward and Feedback Controllers 1-5 Combining Feedforward and Feedback 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

2 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

2-3 Dealing with Control Algorithms Bundled with the Process 2-4 Some General Comments about Debugging Control Algorithms 2-6 Documentation and Indispensability 2-7 Summary

3 Basic Concepts in Process Analysis

3-1 The First-Order Process—an Introduction 3-2 Mathematical Descriptions of the First-Order Process

3-2-1 The Continuous Time Domain Model 3-2-2 Solution of the Continuous Time Domain Model 3-2-3 The First-Order Model and Proportional Control 3-2-4 The First-Order Model and Proportional-Integral Control

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 3-3-3 The Laplace Transform of Derivatives 3-3-4 Applying the Laplace Transform to the Case with Proportional plus Integral Control 3-3-5 More Block Diagram Algebra and Some Useful Transfer Functions 3-3-6 Zeros and Poles

3-4 Summary

4 A New Domain and More Process Models

4-1 Onward to the Frequency Domain

4-1-1 Sinusoidally Disturbing the First-Order Process 4-1-2 A Little Mathematical Support in the Time Domain 4-1-3 A Little Mathematical Support in the Laplace Transform Domain 4-1-4 A Little Graphical Support 4-1-5 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

4-3-1 What's This about the Integral? 4-3-2 What about Adding P to the I? 4-3-3 Partial Summary and a Rule of Thumb Using Phase Margin and Gain Margin

4-4 A Pure Dead-Time Process

4-4-1 Proportional-Only Control of a Pure Dead-Time Process 4-4-2 Integral-Only Control of a Pure Dead-Time Process

4-5 A First-Order with Dead-Time (FOWDT) Process

4-5-1 The Concept of Minimum Phase 4-5-2 Proportional-Only Control 4-5-3 Proportional-Integral Control of the FOWDT Process

4-6 A Few Comments about Simulating Processes with Variable Dead Times 4-7 Partial Summary and a Slight Modification of the Rule of Thumb 4-8 Summary

5 Matrices and Higher-Order Process Models

5-1 Third-Order Process without Backflow 5-2 Third-Order Process with Backflow 5-3 Control of Three-Tank System with No Backflow 5-4 Critical Values and Finding the Poles 5-5 Multitank Processes 5-6 Summary

6 An Underdamped Process

6-1 The Dynamics of the Mass/Spring/Dashpot Process 6-2 Solutions in Four Domains

6-2-1 Time Domain 6-2-2 Laplace Domain Solution 6-2-3 Frequency Domain 6-2-4 State-Space Representation 6-2-5 Scaling and Round-Off Error

6-3 PI Control of the Mass/Spring/Dashpot Process 6-4 Derivative Control (PID)

6-4-1 Complete Cancellation 6-4-2 Adding Sensor Noise 6-4-3 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

7 Distributed Processes

7-1 The Tubular Energy Exchanger—Steady State 7-2 The Tubular Energy Exchanger—Transient Behavior

7-2-1 Transfer by Diffusion

7-3 Solution of the Tubular Heat Exchanger Equation

7-3-1 Inlet Temperature Transfer Function 7-3-2 Steam Jacket Temperature Transfer Function

7-4 Response of Tubular Heat Exchanger to Step in Jacket Temperature

7-4-1 The Large-Diameter Case 7-4-2 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

7-7-1 Modeling an Individual Lump 7-7-2 Steady-State Solution 7-7-3 Discretizing the Partial Differential Equation

7-8 Lumping and Axial Transport 7-9 State-Space Version of the Lumped Tubular Exchanger 7-10 Summary

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

8-2-1 The Sample Average 8-2-2 The Sample Variance 8-2-3 The Histogram 8-2-4 The Sample Autocorrelation 8-2-5 The Line Spectrum 8-2-6 The Cumulative Line Spectrum

8-3 Non–White Stochastic Sequences

8-3-1 Positively Autoregressive Sequences 8-3-2 Negatively Autoregressive Sequences 8-3-3 Moving Average Stochastic Sequences 8-3-4 Unstable Nonstationary Stochastic Sequences 8-3-5 Multidimensional Stochastic Processes and the Covariance

8-4 Populations, Realizations, Samples, Estimates, and Expected Values

8-4-1 Realizations 8-4-2 Expected Value 8-4-3 Ergodicity and Stationarity 8-4-4 Applying the Expectation Operator

8-5 Comments on Stochastic Disturbances and Difficulty of Control

8-5-1 White Noise 8-5-2 Colored Noise

8-6 Summary

9 The Discrete Time Domain and the Z-Transform

9-1 Discretizing the First-Order Model 9-2 Moving to the Z-Domain via the Backshift Operator 9-3 Sampling and Zero-Holding 9-4 Recognizing the First-Order Model as a Discrete Time Filter 9-5 Descretizing the FOWDT Model 9-6 The Proportional-Integral Control Equation in the Discrete Time Domain 9-7 Converting the Proportional-Integral 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

9-9-1 Developing the Proportional-Integral Control Algorithm 9-9-2 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

9-12-1 The First-Order Process Model 9-12-2 The Ripple 9-12-3 Sampling and Replication

9-13 Filters

9-13-1 Autogressive Filters 9-13-2 Moving Average Filters 9-13-3 A Double-Pass Filter 9-13-4 High-Pass Filters

9-14 Frequency Domain Filtering 9-15 The Discrete Time State-Space Equation 9-16 Determining Model Parameters from Experimental Data

9-16-1 First-Order Models 9-16-2 Third-Order Models 9-16-3 A Practical Method

9-17 Process Identification with White Noise Inputs 9-18 Summary

10 Estimating the State and Using It for Control

10-1 An Elementary Presentation of the Kalman Filter

10-1-1 The Process Model 10-1-2 The Premeasurement and Postmeasurement Equations 10-1-3 The Scalar Case 10-1-4 A Two-Dimensional Example 10-1-5 The Propagation of the Covariances 10-1-6 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

10-3-1 The Dynamics of a Predictor Estimator

10-4 Using the Kalman Filter for Control

10-4-1 A Little Detour to Find the Integral Gain

10-5 Feeding Back the State for Control

10-5-1 Integral Control 10-5-2 Duals

10-6 Integral and Multidimensional Control

10-6-1 Setting Up the Example Process and Posing the Control Problem 10-6-2 Developing the Discrete Time Version 10-6-3 Finding the Open-Loop Eigenvalues and Placing the Closed-Loop Eigenvalues 10-6-4 Implementing the Control Algorithm

10-7 Proportional-Integral Control Applied to the Three-Tank Process 10-8 Control of the Lumped Tubular Energy Exchanger 10-9 Miscellaneous Issues

10-9-1 Optimal Control 10-9-2 Continuous Time Domain Kalman Filter

10-10 Summary

11 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 Proportional-Integral-Derivative Control

11-3-1 Proportional-Integral Control 11-3-2 Proportional-Only Control 11-3-3 Proportional-Integral-Derivative Control 11-3-4 Modified Proportional-Integral-Derivative Control

11-4 Cascade Control 11-5 Control of White Noise—Conventional Feedback Control versus SPC 11-6 Control Choices 11-7 Analysis and Design Tool Choices

A Rudimentary Calculus

A-1 The Automobile Trip A-2 The Integral, Area, and Distance A-3 Approximation of the Integral A-4 Integrals of Useful Functions A-5 The Derivative, Rate of Change, and Acceleration A-6 Derivatives of Some Useful Functions A-7 The Relation between the Derivative and the Integral A-8 Some Simple Rules of Differentiation A-9 The Minimum/Maximum of a Function A-10 A Useful Test Function A-11 Summary

B Complex Numbers

B-1 Complex Conjugates B-2 Complex Numbers as Vectors or Phasors B-3 Euler's Equation B-4 An Application to a Problem in Chapter 4 B-5 The Full Monty B-6 Summary

C Spectral Analysis

C-1 An Elementary Discussion of the Fourier Transform as a Data-Fitting Problem C-2 Partial Summary C-3 Detecting Periodic Components C-4 The Line Spectrum C-5 The Exponential Form of the Least Squares Fitting Equation C-6 Periodicity in the Time Domain C-7 Sampling and Replication C-8 Apparent Increased Frequency Domain Resolution via Padding C-9 The Variance and the Discrete Fourier Transform C-10 Impact of Increased Frequency Resolution on Variability of the Power Spectrum C-11 Aliasing C-12 Summary

D Infinite and Taylor's Series

D-1 Summary

E Application of the Exponential Function to Differential Equations

E-1 First-Order Differential Equations E-2 Partial Summary E-3 Partial Solution of a Second-Order Differential Equation E-4 Summary

F The Laplace Transform

G Vectors and Matrices

G-1 Addition and Multiplication of Matrices G-2 Partitioning G-3 State-Space Equations and Laplace Transforms G-4 Transposes and Diagonal Matrices G-5 Determinants, Cofactors, and Adjoints of a Matrix G-6 The Inverse Matrix G-7 Some Matrix Calculus G-8 The Matrix Exponential Function and Infinite Series G-9 Eigenvalues of Matrices G-10 Eigenvalues of Transposes G-11 More on Operators G-12 The Cayley-Hamilton Theorem G-13 Summary

H Solving the State-Space Equation

H-1 Solving the State-Space Equation in the Time Domain for a Constant Input H-2 Solution of the State-Space Equation Using the Integrating Factor H-3 Solving the State-Space Equation in the Laplace Transform Domain H-4 The Discrete Time State-Space Equation H-5 Summary

I The Z-Transform

I-1 The Sampling Process and the Laplace Transform of a Sampler I-2 The Zero-Order Hold I-3 Z-Transform of the Constant (Step Change) I-4 Z-Transform of the Exponential Function I-5 The Kronecker Delta and Its Z-Transform I-6 Some Complex Algebra and the Unit Circle in the z-Plane I-7 A Partial Summary I-8 Developing Z-Transform Transfer Functions from Laplace Tranforms with Holds I-9 Poles and Associated Time Domain Terms I-10 Final Value Theorem I-11 Summary

J A Brief Exposure to Matlab Index

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