Title Details

Preface ix

Chapter 1. Control, Servo-mechanisms and System Regulation 1

1.1. Introduction  1

1.1.1. Generalities and definitions 1

1.1.2. Control law synthesis 5

1.1.3. Comprehension and application exercises  7

1.2. Process control 11

1.2.1. Correction in the frequency domain 11

1.2.2. Phase advance controller and PD controller  12

1.2.3. Phase delay controller and integrator compensator 14

1.2.4. Proportional, integral and derivative (PID) control 17

1.3. Some application exercises  23

1.3.1. Identification of the transfer function and control 23

1.3.2. PI control  30

1.3.3. Phase advance control 33

1.4. Some application exercises  36

1.5. Application 1: stabilization of a rigid robot with pneumatic actuator 39

1.5.1. Conventional approach  41

1.6. Application 2: temperature control of an oven 51

1.6.1. Modeling and identification study  51

Chapter 2. System Process Control  55

2.1. Introduction  55

2.2. Modeling  55

2.2.1. Introduction  55

2.3. Governability, controllability and observability 56

2.3.1. Characteristic polynomial, minimal polynomial and Cayley–Hamilton theorem  56

2.3.2. Governability or controllability 56

2.3.3. Observability  63

2.3.4. Observer  68

2.3.5. Observer for state reconstruction 69

2.3.6. Minimal state–space representation 76

2.4. State feedback, control by poles placement and stability 79

2.4.1. State feedback control 79

2.4.2. Poles placement and stabilizability 80

2.4.3. Finite-time response for a discrete system, deadbeat response  83

2.4.4. Use of observers in control: separation principle  85

2.5. Linear quadratic (LQ) control  86

2.5.1. Linear quadratic regulator  89

2.6. Optimal control (LQ) 90

2.7. Comprehension and application exercises  94

Chapter 3. Actuators: Modeling and Analysis 117

3.1. Introduction: electric, hydraulic and pneumatic actuators 117

3.1.1. Representation methods for physical systems 118

3.1.2. Modeling of a few constituents of physical systems  120

3.2. Transmission chains, actuators and sensors 126

3.2.1. Electric actuators in robotics 126

3.2.2. Motor speed torque characteristic  131

3.2.3. Dynamic behavior or transient behavior 131

3.2.4. Electric systems motor load 134

3.3. Pneumatic actuators  137

3.3.1. Pneumatic system modeling 137

3.3.2. Frictions model  145

3.4. Hydraulic actuators  149

3.4.1. System description  149

3.4.2. Mechanical model 151

3.4.3. Hydraulic actuator model 152

3.5. Application exercises 155

Chapter 4. Digital Control and Polynomial Approach 161

4.1. Introduction to digital control  161

4.1.1. Digital controller synthesis by transposition  162

4.1.2. Euler’s transposition  164

4.1.3. Choice of the sampling period (Shannon’s theorem)  170

4.2. PID controller synthesis and its equivalent digital RST  171

4.2.1. Standard controllers  171

4.2.2. Study of digital PIDs 172

4.2.3. Digital RST controller synthesis 178

4.2.4. Choice of poles and zeros to compensate  179

4.2.5. Computation of polynomials R, S and T  180

4.2.6. Additional objectives for synthesis 181

4.3. Digital control by poles placement  182

4.3.1. Choice of the sampling period  183

4.4. Diophantine, Bézout, greatest common divisor, least common multiple and division 183

4.4.1. Polynomial arithmetic 183

4.4.2. Diophantine equation ax + by = c and Bachet–Bézout theorem 184

4.4.3. Bézout’s identity  185

4.4.4. Greatest common divisor 185

4.4.5. Least common multiple  185

4.5. A few comprehension and application exercises  186

Chapter 5. NAO Robot 193

5.1. Introduction  193

5.2. Home care project 194

5.2.1. Choregraphe software 194

5.2.2. Nao Matlab SDK research  199

5.2.3. Nao and home care  206

5.2.4. The actions to be made  207

5.3. Details of the various programs 208

5.3.1. Ask for news  208

5.3.2. CallFirefighters box  212

5.3.3. CallNeighbor box 213

5.3.4. CallFamily box  215

5.3.5. Collision detection 215

5.3.6. Special actions: waking-up  216

5.3.7. Morning hygiene 220

5.3.8. Gymnastics 221

5.3.9. Nurse call  225

5.3.10. Memory game  227

5.3.11. Drugs reminder  232

5.3.12. Reading  233

5.3.13. Listening to music  235

5.3.14. Multiplication game 239

5.3.15. Nao’s dance  243

5.3.16. Memory game  245

5.3.17. Detect person on the ground  247

5.3.18. At any time  251

5.4. Conclusion 253

5.4.1. Nao’s limitations and possible improvements 253

Chapter 6. Application Problems with Solutions  255

6.1. Exercise 6.1: car suspension 255

6.1.1. Modeling  256

6.1.2. Analysis  257

6.2. Exercise 6.2: electromechanical system 259

6.2.1. Modeling  260

6.2.2. Analysis  262

6.3. Exercises: identification and state–space representation  263

6.3.1. Exercise 6.3  263

6.3.2. Exercise 6.4  265

6.3.3. Exercise 6.5  268

6.3.4. Exercise 6.6  270

6.3.5. Exercise 6.7  276

6.4. Exercises: observation and control of nonlinear systems 278

6.4.1. Exercise 6.8  278

6.4.2. Exercise 6.9  280

6.4.3. Exercise 6.10 288

6.4.4. Exercise 6.11 291

6.4.5. Exercise 6.12 293

6.4.6. Exercise 6.13 296

6.4.7. Exercise 6.14 300

6.4.8. Exercise 6.15 300

Bibliography 307

Index  313