Preface ........................................................ xi
Acknowledgments ................................................ xv
1 Introduction ................................................. 1
1.1 Hard Disk Drives ........................................ 1
1.2 High-Speed Tape Drives .................................. 4
1.3 High-Speed Elevator ..................................... 6
1.4 Cranes .................................................. 8
1.5 Slosh Modeling ......................................... 10
1.6 Vehicle Platooning ..................................... 14
1.7 Summary ................................................ 16
2 Time-Delay Filter/Input Shaping ............................. 19
2.1 Time-Delay Filters ..................................... 24
2.1.1 Proportional Plus Delay (PPD) Control ........... 24
2.1.2 Proportional Plus Multiple Delay (PPMD)
Control ......................................... 27
2.2 Proportional Plus User Selected Multiple Delay
Control ................................................ 32
2.2.1 Signs of the Time-Delay Gains ................... 34
2.2.2 Periodicity ..................................... 35
2.3 Time-Delay Control of Multi-Mode Systems ............... 37
2.3.1 Concurrent Time-Delay Filter Design for Multi-
Mode Systems .................................... 38
2.3.2 User Selected Time-Delay ........................ 39
2.3.3 Minimum Time-Delay .............................. 41
2.4 Jerk Limited Input Shapers ............................. 42
2.4.1 Undamped Systems ................................ 43
2.4.2 Damped Systems .................................. 45
2.5 Robust Jerk Limited Time-Delay Filter .................. 46
2.6 Jerk Limited Time-Delay Filters for Multi-Mode
Systems ................................................ 47
2.7 Filtered Input Shapers ................................. 50
2.7.1 First-Order Filtered Input Shaper ............... 50
2.7.2 Sinusoid Filtered Input Shaper .................. 50
2.7.3 Jerk Limits ..................................... 51
2.8 Discrete-Time Time-Delay Filters ....................... 54
2.9 Summary ................................................ 59
3 Optimal Control ............................................. 67
3.1 Calculus of Variations ................................. 68
3.1.1 Beltrami Identity ............................... 70
3.1.2 Differential Equation Constraints ............... 73
3.2 Hamiltonian Formulation ................................ 77
3.2.1 Linear Quadratic Regulator (LQR) ................ 83
3.2.2 LQR without State Penalty ....................... 94
3.2.3 Desensitized LQR Control ........................ 96
3.3 Minimum Power Control ................................. 100
3.3.1 Minimum Power Control of Maneuvering
Structures ..................................... 100
3.3.2 Robust Minimum Power Control of Maneuvering
Structures ..................................... 105
3.3.3 Minimum Time/Power Control ..................... 109
3.4 Frequency-Shaped LQR Controller ....................... 114
3.5 LQR Control with Noisy Input .......................... 121
3.6 Summary ............................................... 126
4 Saturating Control ......................................... 133
4.1 Benchmark Problem ..................................... 134
4.2 Minimum-Time Control .................................. 135
4.2.1 Singular Time-Optimal Control .................. 136
4.2.2 Rigid Body ..................................... 137
4.2.3 Time-Optimal Rest-to-Rest Maneuvers ............ 139
4.2.4 Implications of Pole-Zero Cancelation .......... 142
4.2.5 Sufficiency Condition .......................... 144
4.2.6 Benchmark Problem .............................. 145
4.2.7 Effect of Damping .............................. 147
4.2.8 Example ........................................ 147
4.3 Fuel/Time Optimal Control ............................. 150
4.3.1 Singular Fuel/Time Optimal Control ............. 152
4.3.2 Rigid Body ..................................... 155
4.3.3 Fuel/Time Optimal Rest-to-Rest Maneuver ........ 157
4.3.4 Sufficiency Conditions ......................... 159
4.3.5 Benchmark Problem .............................. 159
4.3.6 Determination of acr ........................... 165
4.3.7 Effect of Damping .............................. 168
4.4 Fuel Limited Minimum/Time Control ..................... 170
4.4.1 Singular Fuel Constrained Time-Optimal
Control ........................................ 172
4.4.2 Rigid Body ..................................... 172
4.4.3 Fuel Constrained Time-Optimal Rest-to-Rest
Maneuver ....................................... 174
4.4.4 Sufficiency Conditions ......................... 175
4.4.5 Benchmark Problem .............................. 176
4.4.6 Effect of Damping .............................. 179
4.5 Jerk Limited Time-Optimal Control ..................... 182
4.5.1 Rigid Body ..................................... 184
4.5.2 Jerk Limited Time-Optimal Rest-to-Rest
Maneuver ....................................... 192
4.5.3 Sufficiency Conditions ......................... 194
4.5.4 Benchmark Problem .............................. 196
4.5.5 Summary ........................................ 208
5 Minimax Control ............................................ 219
5.1 Minimax Time-Delay Filters ............................ 220
5.1.1 Cost Function .................................. 221
5.1.2 Van Loan Identity .............................. 222
5.1.3 Pre-Filter Design .............................. 224
5.1.4 Minimax Filter Design for Multi-Input
Systems ........................................ 228
5.2 Minimax Feedback Controllers .......................... 233
5.2.1 Exponentially Weighted LQR Cost ................ 240
5.2.2 Minimax Output Feedback Controller ............. 244
5.3 Summary ............................................... 249
6 Friction Control ........................................... 255
6.1 Time-Optimal Rest-to-Rest Maneuvers ................... 255
6.1.1 Rigid Body ..................................... 256
6.1.2 Flexible Structure ............................. 264
6.2 Pulse-Width Pulse-Amplitude Control ................... 282
6.2.1 Rigid Body ..................................... 283
6.2.2 Benchmark Problem .............................. 294
6.3 Summary ............................................... 305
7 Numerical Approach ......................................... 311
7.1 Parameter Optimization ................................ 311
7.1.1 Minimax Control ................................ 318
7.1.2 Analytic Gradients ............................. 321
7.2 Linear Programming .................................... 324
7.2.1 Minimum Time Control ........................... 325
7.2.2 Minimum Fuel Control ........................... 332
7.2.3 Fuel/Time Optimal Control ...................... 335
7.2.4 Minimax Control ................................ 337
7.3 Linear Matrix Inequality .............................. 367
7.3.1 Time-Delay Filter .............................. 369
7.3.2 Minimax Time-Delay Filters ..................... 374
7.3.3 Modal Weighted Minimax Time-Delay Filters ...... 378
7.4 Summary ............................................... 385
A Van Loan Exponential ....................................... 393
B Differential Lyapunov Equation ............................. 395
С Parseval's Theorem ......................................... 397
Index ......................................................... 399
| 
