Jan Mikles Miroslav Fikar Process Modelling, Identification, and Control With 187 Figures and 13 Tables 4u Springer
Contents 1 Introduction 1 1.1 Topics in Process Control 1 1.2 An Example of Process Control 3 1.2.1 Process 3 1.2.2 Steady-State 3 1.2.3 Process Control 4 1.2.4 Dynamical Properties of the Process 4 1.2.5 Feedback Process Control 5 1.2.6 Transient Performance of Feedback Control 6 1.2.7 Block Diagram 8 1.2.8 Feedforward Control 9 1.3 Development of Process Control 10 1.4 References 11 2 Mathematical Modelling of Processes 13 2.1 General Principles of Modelling 13 2.2 Examples of Dynamic Mathematical Models 16 2.2.1 Liquid Storage Systems 16 2.2.2 Heat Transfer Processes 19 2.2.3 Mass Transfer Processes 26 2.2.4 Chemical and Biochemical Reactors 31 2.3 General Process Models 33 2.4 Linearisation 39 2.5 Systems, Classification of Systems 45 2.6 References 46 2.7 Exercises 47 3 Analysis of Process Models 51 3.1 The Laplace Transform 51 3.1.1 Definition of the Laplace Transform 51 3.1.2 Laplace Transforms of Common Functions 53
XIV Contents 3.1.3 Properties of the Laplace Transform 57 3.1.4 Inverse Laplace Transform 61 3.1.5 Solution of Linear Differential Equations by Laplace Transform Techniques 62 3.2 State-Space Process Models 66 3.2.1 Concept of State 67 3.2.2 Solution of State-Space Equations 67 3.2.3 Canonical Transformation 70 3.2.4 Stability, Controllability, and Observability of Continuous-Time Systems 71 3.2.5 Canonical Decomposition 83 3.3 Input-Output Process Models 84 3.3.1 SISO Continuous Systems with Constant Coefficients.. 84 3.3.2 Transfer Functions of Systems with Time Delays 93 3.3.3 Algebra of Transfer Functions for SISO Systems 96 3.3.4 Input Output Models of MIMO Systems - Matrix of Transfer Functions 100 3.3.5 BIBO Stability 103 3.3.6 Transformation of I/O Models into State-Space Models 104 3.3.7 I/O Models of MIMO Systems - Matrix Fraction Descriptions 107 3.4 References 112 3.5 Exercises 114 4 Dynamical Behaviour of Processes 117 4.1 Time Responses of Linear Systems to Unit Impulse and Unit Step 117 4.1.1 Unit Impulse Response 117 4.1.2 Unit Step Response 119 4.2 Computer Simulations 125 4.2.1 The Euler Method 126 4.2.2 The Runge-Kutta method 127 4.2.3 Runge-Kutta Method for a System of Differential Equations 129 4.2.4 Time Responses of Liquid Storage Systems 135 4.2.5 Time Responses of CSTR 137 4.3 Frequency Analysis 145 4.3.1 Response of the Heat Exchanger to Sinusoidal Input Signal 145 4.3.2 Definition of Frequency Responses 149 4.3.3 Frequency Characteristics of a First Order System 153 4.3.4 Frequency Characteristics of a Second Order System... 156 4.3.5 Frequency Characteristics of an Integrator 158 4.3.6 Frequency Characteristics of Systems in a Series 159 4.4 Statistical Characteristics of Dynamic Systems 162
Contents XV 4.4.1 Fundamentals of Probability Theory 162 4.4.2 Random Variables 163 4.4.3 Stochastic Processes 169 4.4.4 White Noise 176 4.4.5 Response of a Linear System to Stochastic Input 178 4.4.6 Frequency Domain Analysis of a Linear System with Stochastic Input 183 4.5 References 185 4.6 Exercises 187 5 Discrete-Time Process Models 189 5.1 Computer Controlled and Sampled Data Systems 189 5.2 Z - Transform 195 5.3 Discrete-Time Transfer Functions 200 5.4 Input-Output Discrete-Time Models - Difference Equations... 204 5.4.1 Direct Digital Control 205 5.5 State-Space Discrete-Time Models 207 5.6 Properties of Discrete-Time Systems 211 5.6.1 Stability 211 5.6.2 Controllability 212 5.6.3 Observability 212 5.6.4 Discrete-Time Feedback Systems - Control Performance 212 5.7 Examples of Discrete-Time Process Models 214 5.7.1 Discrete-Time Tank Model 214 5.7.2 Discrete-Time Model of Two Tanks in Series 215 5.7.3 Steady-State Discrete-Time Model of Heat Exchangers in Series 216 5.8 References 217 5.9 Exercises 218 6 Process Identification 221 6.1 Introduction 221 6.1.1 Models of Linear Dynamic Systems 223 6.2 Identification from Step Responses 225 6.2.1 First Order System 226 6.2.2 Underdamped Second Order System 227 6.2.3 System of a Higher Order 230 6.3 Least Squares Methods 233 6.3.1 Recursive Least Squares Method 235 6.3.2 Modifications of Recursive Lea-st Squares 241 6.3.3 Identification of a Continuous-time Transfer Function.. 245 6.4 References 250 6.5 Exercises 251
XVIII Contents 9.6.2 Explicit Solution 427 9.6.3 Multi-Parametric Toolbox 429 9.7 Tuning 431 9.7.1 Tuning based on the First Order Model 431 9.7.2 Multivariable Tuning based on the First Order Model.. 432 9.7.3 Output Horizon Tuning 433 9.7.4 A Tuning 434 9.7.5 Tuning based on Model Following 434 9.7.6 The C polynomial 435 9.8 Examples 436 9.8.1 A Linear Process 436 9.8.2 Neural Network based GPC 438 9.8.3 ph Control 439 9.9 References 442 9.10 Exercises 444 10 Adaptive Control 445 10.1 Discrete-Time Self-Tuning Control 446 10.2 Continuous-Time Self-Tuning Control 447 10.3 Examples of Self-Tuning Control 447 10.3.1 Discrete-Time Adaptive Dead-Beat Control of a Second Order System 448 10.3.2 Continuous-Time Adaptive LQ Control of a Second Order System 451 10.3.3 Continuous-Time Adaptive MIMO Pole Placement Control 456 10.3.4 Adaptive Control of a Tubular Reactor 459 10.4 References 463 References 465 Index 475