Process Modelling, Identification, and Control

Transcription

1 Jan Mikles Miroslav Fikar 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Process Modelling, Identification, and Control With 187 Figures and 13 Tables A \ ^J Springer

2 Contents 1 Introduction Topics in Process Control An Example of Process Control Process Steady-State : Process Control Dynamical Properties of the Process Feedback Process Control Transient Performance of Feedback Control.. : Block Diagram Feedforward Control.' Development of Process Control References 11 2 Mathematical Modelling of Processes General Principles of Modelling Examples of Dynamic Mathematical Models Liquid Storage Systems Heat Transfer Processes Mass Transfer Processes Chemical and Biochemical Reactors General Process Models Linearisation Systems, Classification of Systems References Exercises 47 3 Analysis of Process Models The Laplace Transform Definition of the Laplace Transform Laplace Transforms of Common Functions 53

3 XIV Contents Properties of the Laplace Transform Inverse Laplace Transform Solution of Linear Differential Equations by Laplace Transform Techniques State-Space Process Models Concept of State Solution of State-Space Equations Canonical Transformation Stability, Controllability, and Observability of Continuous-Time Systems Canonical Decomposition Input-Output Process Models SISO Continuous Systems with Constant Coefficients Transfer Functions of Systems with Time Delays Algebra of Transfer Functions for SISO Systems Input Output Models of MIMO Systems - Matrix of Transfer Functions BIBO Stability Transformation of I/O Models into State-Space Models I/O Models of MIMO Systems - Matrix Fraction Descriptions References Exercises Dynamical Behaviour of Processes Time Responses of Linear Systems to Unit Impulse and Unit Step Unit Impulse Response Unit Step Response Computer Simulations The Euler Method The Runge-Kutta method Runge-Kutta Method for a System of Differential Equations Time Responses of Liquid Storage Systems Time Responses of CSTR Frequency Analysis Response of the Heat Exchanger to Sinusoidal Input Signal Definition of Frequency Responses Frequency Characteristics of a First Order System Frequency Characteristics of a Second Order System Frequency Characteristics of an Integrator Frequency Characteristics of Systems in a Series Statistical Characteristics of Dynamic Systems 162

4 Contents Fundamentals of Probability Theory Random Variables Stochastic Processes White Noise Response of a Linear System to Stochastic Input Frequency Domain Analysis of a Linear System with Stochastic Input References Exercises Discrete-Time Process Models Computer Controlled and Sampled Data Systems Z - Transform Discrete-Time Transfer Functions Input-Output Discrete-Time Models - Difference Equations Direct Digital Control State-Space Discrete-Time Models Properties of Discrete-Time Systems Stability Controllability Observability Discrete-Time Feedback Systems - Control Performance Examples of Discrete-Time Process Models Discrete-Time Tank Model Discrete-Time Model of Two Tanks in Series Steady-State Discrete-Time Model of Heat Exchangers in Series References Exercises Process Identification Introduction Models of Linear Dynamic Systems Identification from Step Responses First Order System Underdamped Second Order System System of a Higher Order Least Squares Methods Recursive Least Squares Method Modifications of Recursive Least Squares Identification of a Continuous-time Transfer Function References Exercises 251 XV

5 XVI Contents 7 The Control Problem and Design of Simple Controllers Closed-Loop System Feedback Control Problem Definition SteadyrState Behaviour Control Performance Indices Time Domain Integral Criteria Control Quality and Frequency Indices Poles PID Controller Description of Components PID Controller Structures Setpoint Weighting Simple Rules for Controller Selection Practical Aspects Controller Tuning References Exercises Optimal Process Control Problem of Optimal Control and Principle of Minimum Feedback Optimal Control Optimal Tracking, Servo Problem, and Disturbance Rejection Tracking Problem Servo Problem LQ Control with Integral Action Dynamic Programming Continuous-Time Systems Dynamic Programming for Discrete-Time Systems Optimal Feedback Observers and State Estimation State Observation Kalman Filter Analysis of State Feedback with Observer and Polynomial Pole Placement ' Properties of State Feedback with Observer Input-Output Interpretation of State Feedback with Observer Diophantine Equations Polynomial Pole Placement Control Design Integrating Behaviour of Controller Polynomial Pole Placement Design for Multivariable Systems The Youla-Kucera Parametrisation Fractional Representation 366

6 Contents XVII Parametrisation of Stabilising Controllers Parametrised Controller in the State-Space Representation Parametrisation of Transfer Functions of the Closed-Loop System Dual Parametrisation Parametrisation of Stabilising Controllers for Multivariable Systems Parametrisation of Stabilising Controllers for Discrete-Time Systems Observer LQ Control, State-Space and Polynomial Interpretations Polynomial LQ Control Design with Observer for Singlevariable Systems Polynomial LQ Design with State Estimation for Multivariable Systems LQG Control, State-Space and Polynomial Interpretation Singlevariable Polynomial LQG Control Design Multivariable Polynomial LQG Control Design H 2 Optimal Control...'... : References.'. ; Exercises 400 Predictive Control Introduction : : Ingredients of MBPC Models Cost Function : Derivation and Implementation of Predictive Control Derivation of the Predictor Calculation of the Optimal Control Closed-Loop Relations Derivation of the Predictor from State-Space Models Multivariable Input-Output Case Implementation Relation to Other Approaches Continuous-Time Approaches Constrained Control Stability Results Stability Results in GPC Terminal Constraints Infinite Horizons Finite Terminal Penalty Explicit Predictive Control Quadratic Programming Definition 426

7 XVIII Contents Explicit Solution : Multi-Parametric Toolbox Tuning Tuning based on the First Order Model Multivariable Tuning based on the First Order Model Output Horizon Tuning A Tuning Tuning based on Model Following The C polynomial Examples A Linear Process Neural Network based GPC ph Control References Exercises Adaptive Control Discrete-Time Self-Tuning Control Continuous-Time Self-Tuning Control Examples of Self-Tuning Control Discrete-Time Adaptive Dead-Beat Control of a Second Order System Continuous-Time Adaptive LQ Control of a Second Order System Continuous-Time Adaptive MIMO Pole Placement Control Adaptive Control of a Tubular Reactor References 463 References 465 Index 475