Process Modelling, Identification, and Control

✍ Scribed by Mikles J., Fikar M.

• Year: 2002
• Tongue: English
• Leaves: 170
• Category: Library

✦ Synopsis

This publication is the first part of a book that deals with mathematical modelling of processes, their dynamical properties and dynamical characteristics. The need of investigation of dynamical characteristics of processes comes from their use in process control. The second part of the book will deal with process identi♀cation, optimal, and adaptive control. The aim of this part is to demonstrate the development of mathematical models for process control. Detailed explanation is given to state-space and input-output process models. In the chapter Dynamical properties of processes, process responses to the unit step, unit impulse, harmonic signal, and to a random signal are explored.

✦ Table of Contents

1.1 Topics in Process Control......Page 11
1.2.2 Steady-State......Page 12
1.2.3 Process Control......Page 13
1.2.5 Feedback Process Control......Page 14
1.2.6 Transient Performance of Feedback Control......Page 15
1.2.7 Block Diagram......Page 16
1.3 Development of Process Control......Page 18
1.4 References......Page 19
2.1 General Principles of Modelling......Page 21
2.2.1 Liquid Storage Systems......Page 23
2.2.2 Heat Transfer Processes......Page 26
2.2.3 Mass Transfer Processes......Page 32
2.2.4 Chemical and Biochemical Reactors......Page 37
2.3 General Process Models......Page 39
2.4 Linearisation......Page 44
2.5 Systems, Classification of Systems......Page 48
2.6 References......Page 49
2.7 Exercises......Page 50
3.1.1 Definition of The Laplace Transform......Page 55
3.1.2 Laplace Transforms of Common Functions......Page 56
3.1.3 Properties of the Laplace Transform......Page 58
3.1.4 Inverse Laplace Transform......Page 63
3.1.5 Solution of Linear Differential Equations by Laplace Transform Techniques......Page 64
3.2.2 Solution of State-Space Equations......Page 67
3.2.3 Canonical Transformation......Page 70
3.2.4 Stability, Controllability, and Observability of Continuous-Time Systems......Page 71
3.2.5 Canonical Decomposition......Page 80
3.3.1 SISO Continuous Systems with Constant Coefficients......Page 81
3.3.2 Transfer Functions of Systems with Time Delays......Page 89
3.3.3 Algebra of Transfer Functions for SISO Systems......Page 92
3.3.4 Input Output Models of MIMO Systems - Matrix of Transfer Functions......Page 94
3.3.6 Transformation of I/O Models into State-Space Models......Page 97
3.3.7 I/O Models of MIMO Systems - Matrix Fraction Descriptions......Page 101
3.4 References......Page 104
3.5 Exercises......Page 105
4.1.1 Unit Impulse Response......Page 109
4.1.2 Unit Step Response......Page 111
4.2 Computer Simulations......Page 116
4.2.1 The Euler Method......Page 117
4.2.2 The Runge-Kutta method......Page 118
4.2.3 Runge-Kutta method for a System of Differential Equations......Page 119
4.2.4 Time Responses of Liquid Storage Systems......Page 123
4.2.5 Time Responses of CSTR......Page 125
4.3.1 Response of the Heat Exchanger to Sinusoidal Input Signal......Page 133
4.3.2 Definition of Frequency Responses......Page 134
4.3.3 Frequency Characteristics of a First Order System......Page 139
4.3.4 Frequency Characteristics of a Second Order System......Page 141
4.3.6 Frequency Characteristics of Systems in a Series......Page 143
4.4.2 Random Variables......Page 146
4.4.3 Stochastic Processes......Page 152
4.4.4 White Noise......Page 157
4.4.5 Response of a Linear System to Stochastic Input......Page 159
4.4.6 Frequency Domain Analysis of a Linear System with Stochastic Input......Page 162
4.5 References......Page 164
4.6 Exercises......Page 165
Index......Page 166