Table of Contents
Preface v
Acknowledgments ix
1 Introduction 1
1.1 Mechatronics 1
1.2 Systems 2
1.3 Units of Measurement 4
2 Model and Modeling 7
2.1 Modeling in Dimensional Analysis and Criteria of Similarity 9
2.2 Modeling by Analogy 14
2.3 Theory of Similarity 16
2.3.1 Introduction 16
2.3.2 Scaling of Equations by Similarity 17
2.3.3 Characteristic Scale Units 20
3 Magnetic and Electromagnetic Phenomena 23
3.1 Electric Charge and its Quantization 23
3.2 Capacitance, Resistance and Electric Laws 32
3.2.1 Electric Flux 32
3.2.2 Capacitance and Capacitors 41
3.2.3 Resistance 44
3.2.4 Electric Laws 46
3.2.5 Poisson's and Laplace's Equation 51
3.3 Induced Electric Fields 55
3.3.1 Electromotive Force 55
3.3.2 Rectangular Loop with a Conductor Moving in a Magnetic Field 60
3.3.3 Alternating Current 65
3.4 Magnetic and Electromagnetic Phenomena 67
3.4.1 Magnets and Magnetic Fields 67
3.4.2 Magnetic Charge and a Dipole 69
3.4.3 Magnetic Effect of Current 71
3.4.4 The Law of Ampére and its Generalization 79
3.4.5 Magnetic Dipole Moment of a Closed Planar Current-Carrying Loop 83
3.4.6 Electromagnetic Induction 86
3.4.7 Electric and Magnetic Susceptibility and Permeability 98
3.4.8 Permeability and Susceptibility as Tensors and Dyadics 104
3.4.9 Diamagnetic Materials 108
3.4.10 Paramagnetic Materials 109
3.4.11 Ferromagnetic Materials 111
3.5 An Introduction to Electromagnetic Fields 112
4 Modeling of Piezoelectric Phenomena 123
4.1 Piezoelectric Materials, Materials Laws and Constitutive Equations 123
4.2 One-dimensional Rod Polarized Along its Axis an Example of an Actuator 133
5 Modeling of Mechanical Fluid Systems 143
5.1 The Balance of Fluid Flow 146
5.2 Description of the Dynamics of a Mechanical System 152
5.3 Modeling of an Open Hydromechanical System of Linear Displacement 153
5.4 Modeling of a Hydraulic Electromechanical Servomechanism of Rotational Motion 155
5.5 A Proportional Valve in the Drive and Control of a Hydromechanical System 159
5.6 Physical and Mathematical Model of the Pneumatic Hydromechanical System 163
6 Modeling of Electro hydraulic Servomechanisms 169
6.1 Simplified Model of a Servo With a Proportional Valve 173
6.2 Torque Motor 175
6.3 Piezoelectric Plate Transducer 177
6.4 Control System of Load Positioning Using a Hydraulic Servo Valve 179
6.5 Numerical Simulations of the Dynamics of an Electrohydraulic Servo Subjected to Dynamic Loading 185
7 Atom Modeling 195
7.1 Newtonian Model 195
7.2 Wave Model 200
7.3 Magnetic Field vs. Free Atom 207
7.4 Electron Orbital Perturbation by a Proton Moving in a Magnetic Field 211
7.5 Planar Dynamics of a Particle in a Magnetic Field 213
7.6 3D Dynamics of a Charge 214
8 Maxwell's Equations 217
9 Optimization 223
9.1 Introduction 223
9.2 Methods of Optimization 224
9.2.1 Experimental Methods 224
9.2.2 Mathematical Methods 225
9.3 Examples 226
9.3.1 Linear and Nonlinear-Programming 226
9.3.2 Dynamic Programming 234
9.3.3 Geometric Programming Methods 236
9.3.4 Stiffness Optimization of a Spindle System 242
9.3.5 Minimization of Total Power Loss in a Hydrostatic Bearing 245
10 Fuzzy Logic in Numerical Algorithms 249
10.1 Basic Concepts 252
10.1.1 Membership Functions of Fuzzy Sets 253
10.1.2 Operations on Fuzzy Sets 255
10.1.3 Construction of a Fuzzy Controller 256
10.1.4 Mamdani Model 257
10.1.5 Takagi-Sugeno Model 259
10.2 Experimental Stand 260
10.3 Control Algorithms 264
10.3.1 PID Controller 264
10.3.2 Fuzzy Logic PI Controller 265
10.3.3 Modification of the Rule Base 268
10.3.4 Test Results 269
11 Tracking Control of an Electromechanical System 275
11.1 Problem Statement 277
11.2 Control Strategy 278
11.2.1 Estimation of Linear and Nonlinear Parameters 279
11.2.2 Voltage Input for Control of Rotational Velocity 280
11.3 Numerical Simulation 282
12 Numerical Modeling of a Shock Response 287
12.1 Variation of an Air-Blast Overpressure Wave 288
12.2 The Foam-Based Armor With a Buffer Plate 290
12.3 Physical Model of the System 292
12.3.1 Formulation of the Large-Scale Problem 294
12.3.2 Uncertainties and the Switching Matrices 296
12.4 Semi-Analytical Estimation of the Optimal Parameter 298
12.5 Numerical Experiments 301
13 Control of a Multibody System Response to a Suddenly Applied Force 305
13.1 Introduction 305
13.2 Dynamical Modeling of the Analyzed Problem 306
13.3 Control Methodology 308
13.4 Numerical Simulation 312
Bibliography 315
Index 325
