Advanced Techniques and Technology of Computer-Aided Feedback Control

This book covers various modern theoretical, technical, practical and technological aspects of computerized numerical control and control systems of deterministic and stochastic dynamical processes.

Table of Contents:
Preface xi Introduction xv Part 1: Advanced Elements and Test Bench of Computer-aided Feedback Control 1 Chapter 1: Canonical Discrete State Models of Dynamic Processes 3 1.1. Interest and construction of canonical state models 3 1.2. Canonical realizations of a transfer function G(z) 4 1.2.1. Jordan canonical realization 4 1.2.2. Controllable canonical realization7 1.2.3. Observable canonical realization 9 1.3. Canonical transformations of discrete state models 11 1.3.1. Jordan canonical transformation 12 1.3.2. Controllable canonical transformation 13 1.3.3. Observable canonical transformation 16 1.3.4. Kalman canonical transformation 19 1.4. Canonical decomposition diagram 19 1.5. Discretization and canonical transformations using Matlab 20 1.6. Exercises and solutions 21 Chapter 2: Design and Simulation of Digital State Feedback Control Systems 27 2.1. Principle of digital state feedback control 27 2.2. Calculation of the gain K using pole placement 28 2.3. State feedback with complete order observer 29 2.3.1. Problem statement 29 2.3.2. Structure of the complete or full state observer 29 2.3.3. Synthesis diagram of the state feedback with complete observer 31 2.4. Discrete state feedback with partial observer 34 2.4.1. Problem statement 34 2.4.2. Structure of the partial state observer 34 2.4.3. Diagram of discrete state feedback with partial observer 37 2.5. Discrete state feedback with set point tracking 40 2.6. Block diagram of a digital control system 40 2.7. Computer-aided simulation of a servomechanism 41 2.7.1. Simulation of a speed servomechanism 41 2.7.2. Computer-aided simulation of a position servomechanism 46 2.8. Exercises and solutions 49 Chapter 3: Multimedia Test Bench for Computer-aided Feedback Control  61 3.1. Context and interest 61 3.1.1. Context 61 3.1.2. Scientific/teaching interest 62 3.1.3. Platform presentation methodology 62 3.2. Hardware constituents of the platform 62 3.3. Design elements of the ServoSys software application 63 3.3.1. Fundamental elements 63 3.3.2. Elements of software programming 68 3.4. Design of the ServoSys software application 74 3.4.1. Architectural diagram of the software application 74 3.4.2. SFC of the ServoSys multimedia platform 75 3.5. Implementation of the ServoSys multimedia platform 80 3.5.1. Hardware implementation 80 3.5.2. Software implementation 81 3.6. Overall tests of the platform 84 3.6.1. Commissioning and procedures 84 3.6.2. Samples of results displayed on the Matlab/GUI panel 85 3.7. Exercises and solutions 90 Part 2: Deterministic and Stochastic Optimal Digital Feedback Control 97 Chapter 4: Deterministic Optimal Digital Feedback Control 99 4.1. Optimal control: context and historical background 99 4.1.1. Context 99 4.1.2. Historical background 99 4.2. General problem of discrete-time optimal control 102 4.2.1. Principle 102 4.2.2. Functional formulation 102 4.3. Linear quadratic regulator (LQR) 103 4.3.1. Definition, formulation and study methods 103 4.3.2. H–J–B equations 104 4.4. Translation in discrete time of continuous LQR problem 108 4.4.1. Discretization of state equation 109 4.4.2. Discretization of the cost function 109 4.4.3. Case study of a scalar LQR problem 110 4.5. Predictive optimal control 114 4.5.1. Basic principle 114 4.5.2. Recurrence equation of a process based on q–1 operator 116 4.5.3. General formulation of a prediction model 116 4.5.4. Solution and structure of predictive optimal control 118 4.6. Exercises and solutions 119 Chapter 5: Stochastic Optimal Digital Feedback Control 127 5.1. Introduction to stochastic dynamic processes 127 5.2. Stochastic LQR 128 5.2.1. Formulation 128 5.2.2. Resolution of the stochastic H–J–B equation 129 5.2.3. Block diagram of stochastic LQR 133 5.2.4. Properties of stochastic LQR 134 5.3. Discrete Kalman filter 136 5.3.1. Scientific context and hypotheses 136 5.3.2. Notations 136 5.3.3. Closed-loop algorithmic diagram 137 5.4. Linear Quadratic Gaussian regulator 139 5.4.1. Context 139 5.4.2. Separation principle 140 5.4.3. Algorithmic diagram of LQG regulator 141 5.5. Exercises and solutions 142 Chapter 6: Deployed Matlab/GUI Platform for the Design and Virtual Simulation of Stochastic Optimal Control Systems 145 6.1. Introduction to OPCODE (Optimal Control Design) platform 145 6.1.1. Scientific context 145 6.1.2. Detailed presentation methodology 145 6.2. Fundamental OPCODE design elements 146 6.2.1. Elements of deterministic optimal control 146 6.2.2. Elements of stochastic optimal control 149 6.3. Design of OPCODE using SFC 152 6.3.1. Architectural diagram 152 6.3.2. Implementation of SFC 155 6.4. Software implementation 157 6.5. Examples of OPCODE use 159 6.5.1. Design of deterministic optimal control systems 159 6.5.2. Design of stochastic optimal control systems 159 6.6. Production of deployed OPCODE.EXE application 161 6.6.1. Interest of Matlab/GUI application deployment 161 6.6.2. Deployment methodology 162 6.6.3. Tests of deployed OPCODE.EXE application 162 6.7. Exercises and solutions 164 Part 3: Remotely Operated Feedback Control Systems via the Internet 169 Chapter 7: Elements of Remotely Operated Feedback Control Systems via the Internet 171 7.1. Problem statement 171 7.2. Infrastructural topologies 172 7.2.1. Basic topology 172 7.2.2. Advanced topologies 173 7.3. Remotely operated laboratories via the Internet 176 7.3.1. Comparison between classical and remotely operated laboratories 176 7.3.2. Infrastructures on the server side of a remotely operated laboratory 178 7.3.3. Criteria for the creation of a remotely operated laboratory 180 7.4. Exercises and solutions 180 Chapter 8: Remotely Operated Automation Laboratory via the Internet 187 8.1. Introduction to remotely operated automation laboratory 187 8.1.1. Creation context 187 8.1.2. Didactic context 188 8.1.3. Specifications 188 8.2. Design and implementation of the experimental system 189 8.2.1. Descriptive diagrams 189 8.2.2. Dynamic model of the real power lighting system 191 8.2.3. Dynamic model of the PID controller for power lighting 191 8.2.4. MMMI-aided Labview application 192 8.3. Topology of the remotely operated automation laboratory 193 8.3.1. Hardware infrastructure 194 8.3.2. Specialized infrastructure on the server side 194 8.3.3. Infrastructure on the remote operator side 196 8.4. Use of a remotely operated laboratory via the Internet 196 8.4.1. Procedure instruction sheet 196 8.4.2. Samples of test results obtained with REOPAULAB 197 8.5. Exercises and solutions 200 Appendices 207 Appendix 1. Table of z-transforms 209 Appendix 2. Matlab Elements Used in this Book 211 Appendix 3. Discretization of Transfer Functions 215 Bibliography 217 Index 219