Identification and control of mechanical systems

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 15
1.1 Introduction......Page 19
1.2 Homogeneous ODE with Constant Coefficients......Page 20
CASE 1: REAL AND NONREPEATED ROOTS......Page 21
CASE 3: REPEATED REAL ROOTS......Page 22
1.2.2 Multiple Roots of…......Page 23
1.2.3 Determination of Coefficients......Page 25
1.3.1 General Solution......Page 26
1.3.2 Particular Solution......Page 27
1.4 Coupled Ordinary Differential Equations......Page 28
1.6 Problems......Page 29
BIBLIOGRAPHY......Page 31
2.2 Vectors and Matrices......Page 32
MATRIX MULTIPLICATION......Page 33
OUTER PRODUCT......Page 34
2.4 Special Matrices......Page 35
2.5 Determinants and Matrix Inverse......Page 36
2.6 Subspaces and Rank......Page 37
2.7 Quadratic Form of a Matrix......Page 38
2.9 Solving Linear Algebraic Equations......Page 39
2.10 Eigenvalues and Eigenvectors......Page 40
2.11 Diagonalization of a Matrix......Page 42
2.12.1 Basic Equations......Page 45
EFFECTIVE RANK AND CONDITIONED NUMBER......Page 46
LEAST SQUARES AND PSEUDOINVERSE......Page 47
2.13 Homogeneous First-Order Matrix Differential Equations......Page 48
COMPLEX-CONJUGATE PAIRS OF EIGENVALUES......Page 49
REPEATED EIGENVALUES......Page 50
2.14 Matrix Exponential......Page 52
METHOD OF UNDETERMINED COEFFICIENTS......Page 56
METHOD OF UNCOUPLING THE VARIABLES BY DIAGONALIZATION......Page 57
METHOD OF MATRIX EXPONENTIAL......Page 58
2.16 Concluding Remarks......Page 59
2.17 Problems......Page 60
BIBLIOGRAPHY......Page 62
SECOND LAW......Page 63
3.3 D’Alembert’s Principle......Page 64
3.4 Principle of Virtual Work......Page 65
3.5 Hamilton’s Principle......Page 67
3.6 Lagrange’s Equations......Page 76
3.6.1 Rayleigh’s Dissipation Function......Page 81
3.6.2 Constraint Equations......Page 82
3.7 Gibbs–Appell Equations......Page 87
3.8 Kane’s Equations......Page 91
3.9 Concluding Remarks......Page 92
3.10 Problems......Page 93
BIBLIOGRAPHY......Page 97
4.1 Introduction......Page 98
4.2.1 Interpolation Functions......Page 99
4.2.2 Matrix Equation of Motion for an Element......Page 101
4.2.3 Boundary Conditions......Page 107
4.3 Element Assembly......Page 110
4.3.1 Combined Matrix Equations of Motion......Page 111
4.3.2 Constraint Equations......Page 112
4.3.3 Assembled Matrix Equations of Motion......Page 114
4.4 Truss Structures......Page 118
4.4.1 Truss Element: Longitudinal Motion......Page 119
4.4.2 Truss Element: Rigid-Body Motion......Page 122
4.4.3 Coordinate Transformation......Page 126
4.5 Energy Method for Element Assembly......Page 128
4.7 Problems......Page 134
BIBLIOGRAPHY......Page 137
5.2 Single Degree of Freedom......Page 138
5.2.1 First-Order Systems......Page 139
FREQUENCY-RESPONSE FUNCTION......Page 141
5.2.2 Second-Order Systems......Page 143
5.3 Two-Degrees-of-Freedom Systems......Page 145
RESPONSE TO HARMONIC EXCITATION......Page 146
5.4 Multiple-Degrees-of-Freedom Systems......Page 149
5.5 Bending Vibration of Beams......Page 153
FREQUENCY EQUATION......Page 154
NATURAL MODES (MODE SHAPES)......Page 155
MODAL COORDINATES......Page 156
FORCED BENDING RESPONSE OF UNIFORM BEAMS......Page 158
5.7 Problems......Page 160
BIBLIOGRAPHY......Page 162
6.1 Introduction......Page 163
6.2 Direct Feedback......Page 164
6.3 Controller with Second-Order Dynamics......Page 167
6.3.1 Displacement Feedback......Page 168
PHYSICAL INTERPRETATION......Page 171
CASE 2:......Page 172
CASE 3:......Page 173
6.3.2 Acceleration Feedback......Page 175
6.3.3 Frequency-Matched Virtual Passive Controller......Page 177
6.4 Concluding Remarks......Page 178
6.5 Problems......Page 179
SUGGESTED READING......Page 181
7.1 Introduction......Page 182
7.2 Continuous-Time State–Space Model......Page 183
7.2.1 Direct-Transmission Term......Page 187
7.2.2 Coordinate Transformation......Page 188
7.2.3 Dynamic Response to General Input......Page 189
7.3.2 Continuous-Time to Discrete-Time Conversion......Page 191
7.3.3 Coordinate Transformation......Page 194
7.3.4 Dynamic Response of a Discrete-Time Model......Page 195
7.4 Sampling and Aliasing......Page 196
7.5 System Eigenvalues......Page 198
7.7 Problems......Page 199
BIBLIOGRAPHY......Page 201
8.2 Controllability and Observability......Page 202
8.2.1 Controllability in the Discrete-Time Domain......Page 203
8.2.2 Observability in the Discrete-Time Domain......Page 206
8.3 Continuous-Time State Feedback......Page 209
8.4 Discrete-Time State Feedback......Page 210
8.5 Placement of Closed-Loop Eigenvalues......Page 211
8.5.1 Null-Space Technique......Page 218
8.5.2 Gain Minimization......Page 222
8.6 Optimal Control......Page 223
8.6.1 Continuous-Time Technique......Page 226
8.6.2 Discrete-Time Technique......Page 229
8.7 Concluding Remarks......Page 230
8.8 Problems......Page 231
BIBLIOGRAPHY......Page 234
9.1 Introduction......Page 235
9.2 Continuous-Time State Estimation......Page 236
9.3 Discrete-Time State Estimation......Page 238
9.4.1 Definition Based on the First-Order Model......Page 240
9.4.2 Second-Order Formulation......Page 243
9.5 Continuous-Time Observer-Based State Feedback......Page 250
9.6 Discrete-Time Observer-Based State Feedback......Page 256
9.7 Static Output Feedback......Page 261
9.8 Dynamic Output Feedback......Page 262
CONTINUOUS-TIME DYNAMIC OUTPUT FEEDBACK......Page 263
DISCRETE-TIME DYNAMIC OUTPUT FEEDBACK......Page 264
A SPECIAL CASE: OBSERVER-BASED STATE-FEEDBACK CONTROL......Page 266
9.10 Problems......Page 270
BIBLIOGRAPHY......Page 273
10.2 Finite-Difference Model......Page 274
10.3 Multistep Output Prediction......Page 282
10.4 System Markov Parameters......Page 290
10.5 Eigensystem Realization Algorithm......Page 294
10.6 Observable Canonical-Form Realization......Page 298
10.7 Relationship with an Observer Model......Page 302
10.7.1 State–Space Observer Model......Page 303
10.7.2 Relationship with State–Space System Matrices......Page 304
10.7.3 Computation of Observer Gain......Page 307
10.9 Problems......Page 309
10.10 Appendix: Efficient Computation of Data Correlation Matrix......Page 311
BIBLIOGRAPHY......Page 312
11.2 Generalized Predictive Control......Page 313
11.3 Deadbeat Predictive Control......Page 319
11.4.1 Direct GPC Algorithm......Page 324
11.4.2 Direct DPC Algorithm......Page 325
GPC Controller......Page 328
COMPUTATIONAL STEPS......Page 329
11.5 State–Space Representation......Page 330
11.5.1 Observable Canonical-Form Realization......Page 331
11.5.3 DPC Controller......Page 334
GPC Controller......Page 337
DPC Controller......Page 340
11.6 Concluding Remarks......Page 344
11.7 Problems......Page 346
BIBLIOGRAPHY......Page 348
SUGGESTED READING......Page 349
Index......Page 351