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1 | (24) |
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1.1 What is Active Vibration Control? |
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3 | (2) |
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1.2 The Choice of Strategy in Active Vibration Control |
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5 | (2) |
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1.3 The Role of Model Predictive Control in Active Vibration Control |
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7 | (1) |
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1.4 Model Predictive Vibration Control of Flexible and Lightly Damped Mechanical Systems |
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8 | (2) |
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10 | (15) |
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1.5.1 Structure of This Book |
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10 | (2) |
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1.5.2 Do I Have to Read the Whole Book? |
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12 | (1) |
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1.5.3 The Scope and Limitations of This Work |
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13 | (3) |
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1.5.4 Assumptions and Objectives of Part III |
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16 | (1) |
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17 | (8) |
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2 Basics of Vibration Dynamics |
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25 | (40) |
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2.1 Free Vibration Without Damping |
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26 | (4) |
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2.2 Free Vibration with Damping |
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30 | (3) |
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2.3 Forced Vibration of a Point Mass |
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33 | (2) |
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2.4 Multiple Degree of Freedom Systems |
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35 | (5) |
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2.4.1 The Eigenvalue Problem |
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37 | (1) |
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2.4.2 Modal Decomposition |
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38 | (2) |
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2.5 Distributed Parameter Systems |
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40 | (7) |
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40 | (6) |
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2.5.2 Damping in Distributed Systems Simulated by FEA |
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46 | (1) |
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2.6 Creating Models for Vibration Control |
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47 | (10) |
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2.6.1 Transfer Function Models |
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47 | (8) |
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2.6.2 Experimental Identification Procedures |
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55 | (2) |
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2.7 Identification via Software Packages |
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57 | (3) |
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2.8 FEM-Based Identification |
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60 | (5) |
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61 | (4) |
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3 Smart Materials in Active Vibration Control |
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65 | (40) |
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67 | (6) |
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3.1.1 SMA Materials and Properties |
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67 | (2) |
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3.1.2 Stress, Strain and Temperature |
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69 | (2) |
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3.1.3 SMA in Vibration Control |
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71 | (2) |
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3.2 Magneto- and Electrostrictive Materials |
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73 | (4) |
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3.2.1 Magnetostrictive Materials |
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74 | (1) |
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3.2.2 Electrostrictive Materials |
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75 | (1) |
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3.2.3 Magneto- and Electrostrictive Materials in Vibration Control |
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75 | (2) |
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3.3 Magneto- and Electrorheological Fluids |
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77 | (5) |
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3.3.1 Magnetorheological Fluids |
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77 | (1) |
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3.3.2 Electrorheological Fluids |
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78 | (1) |
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3.3.3 Magneto- and Electrorheological Materials in Vibration Control |
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79 | (3) |
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3.4 Piezoelectric Materials |
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82 | (7) |
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3.4.1 The Piezoelectric Effect and Materials |
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82 | (3) |
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3.4.2 Piezoelectric Transducers in Vibration Control |
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85 | (1) |
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3.4.3 Mathematical Description of the Piezoelectric Effect |
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86 | (2) |
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3.4.4 FEM Formulation for Piezoelectric Transducers |
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88 | (1) |
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3.5 Electrochemical Materials |
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89 | (4) |
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90 | (1) |
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91 | (1) |
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3.5.3 EAP in Vibration Control |
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92 | (1) |
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3.6 Other Types of Materials and Actuators |
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93 | (12) |
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94 | (11) |
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4 Algorithms in Active Vibration Control |
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105 | (36) |
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4.1 Classical Feedback Methods |
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107 | (5) |
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4.2 Proportional-Integral-Derivative Controllers |
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112 | (5) |
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4.3 Linear Quadratic Control |
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117 | (2) |
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119 | (4) |
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4.5 Soft Computing Approaches |
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123 | (6) |
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123 | (2) |
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125 | (2) |
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127 | (2) |
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129 | (12) |
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130 | (11) |
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5 Laboratory Demonstration Hardware for AVC |
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141 | (66) |
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142 | (8) |
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5.1.1 The Cantilever Beam as a Dynamic Model for a Class of Real-Life Applications |
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143 | (2) |
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5.1.2 Brief Device Description |
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145 | (2) |
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5.1.3 Functional Scheme of the Device |
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147 | (2) |
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5.1.4 PZT Transducer Configuration and Usage |
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149 | (1) |
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5.2 Identification Procedure |
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150 | (7) |
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151 | (5) |
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5.2.2 Capacitive Sensor Feedback Model |
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156 | (1) |
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5.2.3 Piezoelectric Sensor Feedback Model |
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156 | (1) |
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157 | (15) |
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5.3.1 Actuator and Sensor Characteristics |
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157 | (5) |
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5.3.2 Noise and Disturbances |
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162 | (2) |
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5.3.3 Mechanical Properties |
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164 | (2) |
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5.3.4 Capacitive and Piezoelectric Sensor-Based Feedback |
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166 | (6) |
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172 | (10) |
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173 | (1) |
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174 | (2) |
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176 | (4) |
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180 | (1) |
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5.4.5 Control Prototyping |
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180 | (2) |
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182 | (25) |
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5.5.1 Piezoelectric Transducers |
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182 | (4) |
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5.5.2 Beam Material and Base |
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186 | (1) |
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5.5.3 Measurement of the Tip Displacement |
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187 | (5) |
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5.5.4 Real-Time Control Environment |
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192 | (2) |
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5.5.5 Electrodynamic Shaker and Amplifier |
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194 | (1) |
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195 | (12) |
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Part II Model Predictive Control |
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207 | (46) |
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209 | (4) |
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6.1.1 Historical Overview |
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211 | (2) |
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6.1.2 Nonlinear Model Predictive Control |
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213 | (1) |
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213 | (4) |
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217 | (2) |
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6.3.1 Building a Quadratic Cost Function |
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218 | (1) |
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6.4 State and Input Penalization |
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219 | (2) |
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6.5 Cost of the Future States and Inputs |
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221 | (3) |
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6.6 Unconstrained Model Predictive Control |
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224 | (1) |
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6.7 Constraint Formulation |
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225 | (4) |
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6.7.1 Hard Saturation Versus Constraint Handling |
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227 | (2) |
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6.8 Constrained Quadratic Programming-Based MPC |
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229 | (16) |
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6.8.1 Quadratic Programming |
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230 | (14) |
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6.8.2 MPC and Quadratic Programming |
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244 | (1) |
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6.9 Prediction and Control Horizon |
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245 | (1) |
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6.10 Fixed Target Tracking |
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246 | (1) |
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247 | (6) |
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249 | (4) |
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7 Stability and Feasibility of MPC |
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253 | (34) |
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7.1 Development of MPC with Stability Guarantees |
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256 | (3) |
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7.1.1 Equality Terminal Constraints |
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256 | (1) |
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7.1.2 Penalty on the Terminal State |
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257 | (1) |
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257 | (1) |
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7.1.4 Combination of Target Sets and Terminal Penalties |
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258 | (1) |
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7.1.5 State Contractility and Others |
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259 | (1) |
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7.2 Closed-Loop Stability of the Infinite Horizon MPC Law |
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259 | (4) |
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7.3 Stability Through Terminal Constraints |
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263 | (3) |
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7.4 Maximal Invariant Terminal Set |
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266 | (5) |
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7.4.1 Implementing the Terminal Constraints |
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269 | (2) |
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271 | (1) |
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7.5 Simplified Polyhedral Target Sets |
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271 | (4) |
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7.6 Elliptic Invariant Target Sets |
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275 | (4) |
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7.7 Infeasibility Handling |
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279 | (8) |
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283 | (4) |
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8 Efficient MPC Algorithms |
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287 | (38) |
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291 | (15) |
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8.1.1 Basic NRMPC Formulation |
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292 | (6) |
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8.1.2 Extension of the Newton-Raphson MPC |
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298 | (3) |
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8.1.3 Optimizing Prediction Dynamics for the Newton-Raphson MPC |
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301 | (4) |
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8.1.4 Warm Starting and Early Termination |
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305 | (1) |
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306 | (6) |
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8.2.1 Optimal Multi-Parametric MPC |
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306 | (5) |
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8.2.2 Multi-Parametric Programming-Based Minimum Time Suboptimal MPC |
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311 | (1) |
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8.3 Approximate Primal-Barrier Interior Point Method-Based MPC |
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312 | (1) |
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8.4 Efficient MPC Based on Pontryagin's Minimum Principle |
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313 | (12) |
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318 | (7) |
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Part III Model Predictive Vibration Control |
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9 Applications of Model Predictive Vibration Control |
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325 | (36) |
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9.1 Concept Demonstration Examples |
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327 | (2) |
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327 | (1) |
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328 | (1) |
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328 | (1) |
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9.2 Manipulators in Robotics |
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329 | (1) |
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330 | (1) |
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331 | (1) |
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332 | (2) |
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334 | (3) |
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9.7 Manufacturing, Machinery and Tools |
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337 | (6) |
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338 | (1) |
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9.7.2 Active Mounts and Production Systems |
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339 | (1) |
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9.7.3 Anti-Sway Control for Cranes |
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339 | (3) |
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342 | (1) |
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9.8 Vibration Control in Aircraft and Spacecraft |
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343 | (18) |
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343 | (3) |
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9.8.2 Spacecraft Vibration |
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346 | (3) |
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349 | (12) |
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10 MPC Implementation for Vibration Control |
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361 | (30) |
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10.1 Implementation of the QPMPC Algorithm |
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364 | (4) |
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10.2 Implementation of the MPMPC Control Algorithm |
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368 | (7) |
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10.2.1 Optimal Multi-Parametric Programming-Based MPC |
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369 | (5) |
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10.2.2 Multi-Parametric Programming-Based Minimum-Time Suboptimal MPC |
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374 | (1) |
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10.3 Implementation of the NRMPC Control Algorithm |
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375 | (16) |
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10.3.1 SDP Problem Formulation and Solution |
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377 | (1) |
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10.3.2 Cost Transformation |
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378 | (2) |
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10.3.3 The Newton-Raphson Procedure |
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380 | (2) |
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382 | (1) |
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10.3.5 Code Implementation |
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382 | (3) |
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385 | (6) |
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11 Simulation Study of Model Predictive Vibration Control |
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391 | (36) |
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11.1 On the Horizon Length of Stable MPC |
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392 | (6) |
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11.1.1 Simulating Necessary Horizon Lengths |
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395 | (2) |
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11.1.2 NRMPC and Horizon Length |
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397 | (1) |
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11.2 Properties of MPMPC for Active Vibration Control |
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398 | (4) |
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11.2.1 MPMPC Computation Time |
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399 | (2) |
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401 | (1) |
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11.2.3 MPMPC Controller Size |
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402 | (1) |
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11.3 Issues with NRMPC Invariance |
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402 | (6) |
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11.3.1 Performance Bounds |
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405 | (2) |
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11.3.2 Solver Precision and Invariance |
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407 | (1) |
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11.4 Issues with NRMPC Optimality |
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408 | (6) |
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11.4.1 Penalization and Optimality |
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412 | (2) |
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11.5 Alternate NRMPC Extension |
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414 | (4) |
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11.6 Comparison of QPMPC, MPMPC and NRMPC in Simulation |
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418 | (9) |
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421 | (6) |
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12 Experimental Model Predictive Vibration Control |
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427 | (40) |
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12.1 Linear Quadratic Control |
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429 | (2) |
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12.2 Initial Deflection Test |
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431 | (5) |
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12.3 Frequency Domain Tests |
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436 | (6) |
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12.3.1 Disturbance by Modal Shaker |
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436 | (3) |
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12.3.2 Disturbance by PZT Actuation |
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439 | (3) |
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442 | (2) |
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12.4.1 Random Excitation by a Modal Shaker |
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442 | (1) |
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12.4.2 Pseudo-Random Excitation by a Medium Sized Fan |
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443 | (1) |
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444 | (6) |
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12.5.1 Initial Deflection |
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445 | (1) |
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446 | (2) |
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12.5.3 Pseudo-Random Binary Signal |
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448 | (2) |
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12.5.4 Possible Improvements on NRMPC Speed |
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450 | (1) |
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450 | (4) |
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454 | (13) |
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12.7.1 Summary of Main Points |
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454 | (3) |
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457 | (3) |
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460 | (7) |
Appendix A FE Modeling of the Active Structure |
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467 | (12) |
Appendix B MPC Code Implementation Details |
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479 | (28) |
Legal Information |
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507 | (4) |
Index |
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511 | |