Advanced Techniques and Technology of Computer–Aided Feedback Control

Preface xi
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<br />Introduction xv
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Part 1. Advanced Elements and Test Bench of Computer–aided Feedback Control 1
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Chapter 1. Canonical Discrete State Models of Dynamic Processes 3
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<br />1.1. Interest and construction of canonical state models 3
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<br />1.2. Canonical realizations of a transfer function G(z) 4
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<br />1.2.1. Jordan canonical realization 4
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<br />1.2.2. Controllable canonical realization 7
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<br />1.2.3. Observable canonical realization 9
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<br />1.3. Canonical transformations of discrete state models 11
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<br />1.3.1. Jordan canonical transformation 12
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<br />1.3.2. Controllable canonical transformation 13
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<br />1.3.3. Observable canonical transformation 16
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<br />1.3.4. Kalman canonical transformation 19
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<br />1.4. Canonical decomposition diagram 19
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<br />1.5. Discretization and canonical transformations using Matlab 20
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<br />1.6. Exercises and solutions 21
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Chapter 2. Design and Simulation of Digital State Feedback Control Systems 27
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<br />2.1. Principle of digital state feedback control 27
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<br />2.2. Calculation of the gain K using pole placement 28
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<br />2.3. State feedback with complete order observer 29
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<br />2.3.1. Problem statement 29
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<br />2.3.2. Structure of the complete or full state observer 29
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<br />2.3.3. Synthesis diagram of the state feedback with complete observer 31
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<br />2.4. Discrete state feedback with partial observer 34
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<br />2.4.1. Problem statement 34
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<br />2.4.2. Structure of the partial state observer 34
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<br />2.4.3. Diagram of discrete state feedback with partial observer 37
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<br />2.5. Discrete state feedback with set point tracking 40
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<br />2.6. Block diagram of a digital control system 40
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<br />2.7. Computer–aided simulation of a servomechanism 41
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<br />2.7.1. Simulation of a speed servomechanism 41
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<br />2.7.2. Computer–aided simulation of a position servomechanism 46
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<br />2.8. Exercises and solutions 49
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Chapter 3. Multimedia Test Bench for Computer–aided Feedback Control 61
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<br />3.1. Context and interest 61
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<br />3.1.1. Context 61
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<br />3.1.2. Scientific/teaching interest 62
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<br />3.1.3. Platform presentation methodology 62
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<br />3.2. Hardware constituents of the platform 62
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<br />3.3. Design elements of the ServoSys software application 63
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<br />3.3.1. Fundamental elements 63
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<br />3.3.2. Elements of software programming 68
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<br />3.4. Design of the ServoSys software application 74
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<br />3.4.1. Architectural diagram of the software application 74
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<br />3.4.2. SFC of the ServoSys multimedia platform 75
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<br />3.5. Implementation of the ServoSys multimedia platform 80
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<br />3.5.1. Hardware implementation 80
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<br />3.5.2. Software implementation 81
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<br />3.6. Overall tests of the platform 84
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<br />3.6.1. Commissioning and procedures 84
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<br />3.6.2. Samples of results displayed on the Matlab/GUI panel 85
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<br />3.7. Exercises and solutions 90
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Part 2. Deterministic and Stochastic Optimal Digital Feedback Control 97
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Chapter 4. Deterministic Optimal Digital Feedback Control 99
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<br />4.1. Optimal control: context and historical background 99
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<br />4.1.1. Context 99
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<br />4.1.2. Historical background 99
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<br />4.2. General problem of discrete–time optimal control 102
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<br />4.2.1. Principle 102
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<br />4.2.2. Functional formulation 102
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<br />4.3. Linear quadratic regulator (LQR) 103
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<br />4.3.1. Definition, formulation and study methods 103
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<br />4.3.2. H J B equations 104
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<br />4.4. Translation in discrete time of continuous LQR problem 108
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<br />4.4.1. Discretization of state equation 109
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<br />4.4.2. Discretization of the cost function 109
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<br />4.4.3. Case study of a scalar LQR problem 110
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<br />4.5. Predictive optimal control 114
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<br />4.5.1. Basic principle 114
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<br />4.5.2. Recurrence equation of a process based on q 1 operator 116
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<br />4.5.3. General formulation of a prediction model 116
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<br />4.5.4. Solution and structure of predictive optimal control 118
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<br />4.6. Exercises and solutions 119
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Chapter 5. Stochastic Optimal Digital Feedback Control 127
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<br />5.1. Introduction to stochastic dynamic processes 127
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<br />5.2. Stochastic LQR 128
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<br />5.2.1. Formulation 128
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<br />5.2.2. Resolution of the stochastic H J B equation 129
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<br />5.2.3. Block diagram of stochastic LQR 133
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<br />5.2.4. Properties of stochastic LQR 134
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<br />5.3. Discrete Kalman filter 136
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<br />5.3.1. Scientific context and hypotheses 136
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<br />5.3.2. Notations 136
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<br />5.3.3. Closed–loop algorithmic diagram 137
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<br />5.4. Linear Quadratic Gaussian regulator 139
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<br />5.4.1. Context 139
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<br />5.4.2. Separation principle 140
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<br />5.4.3. Algorithmic diagram of LQG regulator 141
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<br />5.5. Exercises and solutions 142
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Chapter 6. Deployed Matlab/GUI Platform for the Design and Virtual Simulation of Stochastic Optimal Control&nbsp;
Systems 145
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<br />6.1. Introduction to OPCODE (Optimal Control Design) platform 145
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<br />6.1.1. Scientific context 145
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<br />6.1.2. Detailed presentation methodology 145
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<br />6.2. Fundamental OPCODE design elements 146
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<br />6.2.1. Elements of deterministic optimal control 146
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<br />6.2.2. Elements of stochastic optimal control 149
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<br />6.3. Design of OPCODE using SFC 152
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<br />6.3.1. Architectural diagram152
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<br />6.3.2. Implementation of SFC&nbsp; 155
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<br />6.4. Software implementation 157
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<br />6.5. Examples of OPCODE use 159
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<br />6.5.1. Design of deterministic optimal control systems 159
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<br />6.5.2. Design of stochastic optimal control systems 159
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<br />6.6. Production of deployed OPCODE.EXE application 161
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<br />6.6.1. Interest of Matlab/GUI application deployment 161
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<br />6.6.2. Deployment methodology 162
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<br />6.6.3. Tests of deployed OPCODE.EXE application 162
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<br />6.7. Exercises and solutions 164
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Part 3. Remotely Operated Feedback Control Systems via the Internet 169
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Chapter 7. Elements of Remotely Operate Feedback Control Systems via the Internet 171
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<br />7.1. Problem statement 171
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<br />7.2. Infrastructural topologies 172
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<br />7.2.1. Basic topology 172
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<br />7.2.2. Advanced topologies 173
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<br />7.3. Remotely operated laboratories via the Internet 176
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<br />7.3.1. Comparison between classical and remotely operated laboratories 176
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<br />7.3.2. Infrastructures on the server side of a remotely operated laboratory 178
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<br />7.3.3. Criteria for the creation of a remotely operated laboratory180
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<br />7.4. Exercises and solutions 180
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Chapter 8. Remotely Operated Automation Laboratory via the Internet 187
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<br />8.1. Introduction to remotely operated automation laboratory 187
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<br />8.1.1. Creation context 187
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<br />8.1.2. Didactic context 188
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<br />8.1.3. Specifications 188
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<br />8.2. Design and implementation of the experimental system 189
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<br />8.2.1. Descriptive diagrams 189
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<br />8.2.2. Dynamic model of the real power lighting system 191
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<br />8.2.3. Dynamic model of the PID controller for power lighting 191
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<br />8.2.4. MMMI–aided Labview application 192
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<br />8.3. Topology of the remotely operated automation laboratory 193
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<br />8.3.1. Hardware infrastructure 194
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<br />8.3.2. Specialized infrastructure on the server side 194
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<br />8.3.3. Infrastructure on the remote operator side 196
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<br />8.4. Use of a remotely operated laboratory via the Internet 196
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<br />8.4.1. Procedure instruction sheet 196
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<br />8.4.2. Samples of test results obtained with REOPAULAB 197
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<br />8.5. Exercises and solutions 200
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<br />Appendices 207
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<br />Appendix 1. Table of z–transforms 209
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<br />Appendix 2. Matlab Elements Used in this Book 211
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<br />Appendix 3. Discretization of Transfer Functions 215
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<br />Bibliography 217
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<br />Index 219