Table of Contents
Preface vii
1 Introduction 1
1.1 Advanced Mechatronics Systems. Monitoring and Control of Distributed Parameters Systems 1
1.2 Signals versus Power Transmission. Lumped Parameters Modeling of Mechatronic Systems 3
1.2.1 Effort flow variables and two port models 6
1.2.2 Newton-Euler and Kirchhoff equations for a mixed electro-mechanical system 10
1.2.3 Lagrange equations for a mixed electro-mechanical system 14
1.3 Local Sensing and Actuation in Spatially Continuous Systems 30
1.3.1 Lumped parameters models with under-actuation and under-sensing 31
1.3.2 Distributed parameters models with under-actuation and under-sensing 32
1.4 Centralized versus Local Control 32
Problems 33
2 Examples of Direct and Inverse Problems for Mixed Systems 35
2.1 Modular Modeling and Control Issues for Mixed Systems 35
2.1.1 Effort-flow modeling of mechatronic systems 35
2.2 Modeling and Simulation of Distributed Parameters Systems 37
2.2.1 Examples of distributed parameters systems 37
2.2.1.1 Examples of models of vibrating flexible structures 37
2.2.1.2 Acoustic fields 40
2.2.1.3 Heat transfer 41
2.2.1.4 Fluid flow 41
2.2.1.5 Electric and magnetic fields 42
2.2.2 Direct and inverse problems. Well posed and ill posed problems 43
2.2.3 Classification of partial differential equations and methods of solving 44
2.3 Overview of Open Loop and Closed Loop Control of Distributed Parameters Systems 46
2.3.1 Direct and inverse problems 46
2.3.2 Inverse heat conduction problem 48
2.3.3 Open loop control of distributed parameters systems 51
2.3.4 Closed loop control of distributed parameters systems 53
2.4 Under-Actuated and Under-Sensed Mixed Systems 54
2.4.1General problem of multi DOF linear mechanical systems. Lumped parameters model 54
2.4.2 Two DOF mechanical system case 55
Problems 61
3 Overview of Integral Equations and Discrete Inverse Problems 63
3.1 Integral Equations and Continuous Inverse Problems 63
3.1.1 Integral equations 63
3.1.2 Discrete form 65
3.1.3 Other examples of discrete inverse problems 67
3.2 Discrete Problems for LTI Systems 70
3.2.1 Introduction 70
3.2.2 Lumped parameters systems 71
3.2.2.1 State space representation 71
3.2.2.2 Complex functions representation 72
3.2.2.3 Convolution integral representation 73
3.2.2.4 Matrix form representation 80
3.3 Discrete Inverse Problems Solved by Matrix Inversion 91
3.3.1 Types of methods for solving inverse problems 91
3.3.2 Inverse and pseudo-inverse. MATLAB solutions 94
3.3.3 Over-determined and under-determined problems 104
3.3.4 SVD method 113
3.3.5 Damped LS solution 119
3.3.6 Regularization method. Regularized LSS 119
Problems 126
4 Inverse Problems in Dynamic Calibration of Sensors 129
4.1 Introduction 129
4.2 First Order Instruments 130
4.2.1 Time and frequency response of forward Dynamics 130
4.2.2 Bandwidth of first order instruments 132
4.2.3 Static calibration of the sensor 132
4.2.4 Sinusoidal response of the sensor - MATLAB simulations 134
4.2.5 Analytical solutions for harmonic response of first order instruments 137
4.3 Second Order Instruments 140
4.3.1 Static calibration 140
4.3.2 Harmonic response of the second order sensor with ζ = 0.6. MATLAB simulations 148
4.3.3 Analytical solutions for harmonic response of a second order instrument 151
4.4 Calibration for Computer-Based Instrumentation 156
4.4.1 Calibration for computer based first order instruments 157
4.4.2 Phase lead compensation 160
4.4.3 Full and reduced order dynamic compensators 166
4.4.3.1 First order instrument 169
4.4.3.2 Second order instrument 170
4.5 Dynamic Calibration in Case of Noisy Measurements 173
4.6 State Estimation for Indirect Sensing 179
4.6.1 Derivation of the estimator for indirect states estimation using matrix inversion approach 179
4.6.2 Luenberger observers and Kalman filters 183
4.6.3 Indirect estimation of states and inputs for LTI ODE systems using matrix inversion 185
Problems 187
5 Active Vibration Control in Flexible Structures 189
5.1 Active Vibration Suppression for Lumped Parameters Mechanical Systems Using Force and Position Control 189
5.1.1 Direct problem 189
5.1.2 Force control for SISO mechanical system 192
5.1.3 Position feedback control approach 194
5.2 Direct Problem and Under-Actuated Control of a Non-Minimum Phase Flexible Shaft 197
5.3 Control of Vibrations in Beams 202
5.3.1 Perturbation cancellation control in MIMO linear systems 202
5.3.2 Direct problem in beam vibration modeling 206
5.3.3 Feedback control of transversal vibrations in beams 210
5.3.4 Feedback modal control 216
5.3.5 Modal control in beam vibration 224
5.4 Direct Problem in Free Vibrations in Membranes 225
5.4.1 Membrane vibration solution plotting 227
5.4.2 Simulation of membrane using FEMLAB 230
Problems 232
6 Acousto-Mechatronics 235
6.1 Acousto-Mechatronic Systems 235
6.1.1 Recording studio 235
6.1.2 Active sound control in halls 236
6.1.3 Active noise control 237
6.2 Distributed Parameters Models of Sound Transmission 238
6.2.1 Wave equation for planer sound wave 1D propagation in a free sound field 238
6.2.2 Wave equation for planar sound wave 3D propagation a free sound field 243
6.2.3 Sound wave propagation in an enclosed sound field 245
6.3 Calculation of Eigenvalues and Eigenvectors for a Rectangular Cavity 246
6.4 Experimental and Simulation Study of Room Acoustics 254
6.4.1 Introduction 254
6.4.2 Proposed approach 255
6.4.3 Simulation model 256
6.4.4 Simulation results based on ray propagation approach 258
6.4.5 Experimental results 260
6.5 Discrete Inverse Problems based on Direct and Reflected Ray Propagation 264
6.5.1 Parameters estimation using direct ray propagation 264
6.5.2 Other inverse problems using ray propagation 271
Problems 271
7 Themo-Mechatronics 273
7.1 Direct Problem: Heat Flow Modeling and Simulation 273
7.1.1 Direct problem solving for 2-Dimentional (2D) heat conduction from a distributed heat source 273
7.1.2 Direct problem simulation of 2D heat flow for a continuous point-heat source input using MAPLETM 276
7.1.3 Simulation of 2D heat flow for a short temperature pulse input using FEMLABTM 278
7.1.4 Direct problem formulation for 3-D heat flow 282
7.2 Inverse Problem Solution for Remote Temperature Monitoring 283
7.2.1 Introduction 283
7.2.2 Inverse problem for heat flux input remote estimation from temperature measurements 284
Problems 286
8 Magneto-Mechatronics 287
8.1 Introduction 287
8.2 Direct Model 288
8.3 Simulation Results for Linear Control 290
8.4 State-Input Linearization of a Magnetic Levitation System 293
8.4.1 Feedback linearization 293
8.4.2 State-Input linearization and linear feedback control 295
8.5 Nonlinear Controller of a Magnetic Suspension System 297
Problems 300
9 Inverse Problems Issues for Non-Minimum Phase Systems 301
9.1 Direct and Inverse Problems for Non-Minimum Phase Nonlinear Systems 301
9.1.1 Introduction 301
9.1.2 Direct problem for non-minimum phase systems 301
9.1.3 Neural network approach to inverse dynamics 303
9.2 Feedback Linearization of a Non-Minimum Phase UAV 303
9.3 Mathematical Model for UAV Direct Problem 305
9.4 Simulation Results for the Neural Controller and Output Redefinition 312
References 317
Index 325
