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E-book: Optimal Reference Shaping for Dynamical Systems: Theory and Applications

  • Format: 416 pages
  • Pub. Date: 28-Oct-2009
  • Publisher: CRC Press Inc
  • Language: eng
  • ISBN-13: 9781439805633
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Optimal Reference Shaping for Dynamical Systems: Theory and ApplicationsLarger Image
  • Format: 416 pages
  • Pub. Date: 28-Oct-2009
  • Publisher: CRC Press Inc
  • Language: eng
  • ISBN-13: 9781439805633
Other books in subject:

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Integrating feedforward control with feedback control can significantly improve the performance of control systems compared to using feedback control alone. Focusing on feedforward control techniques, Optimal Reference Shaping for Dynamical Systems: Theory and Applications lucidly covers the various algorithms for attenuating residual oscillations that are excited by reference inputs to dynamical systems. The reference shaping techniques presented in the book require the system to be stable or marginally stable, including systems where feedback control has been used to stabilize the system.





Illustrates Techniques through Benchmark Problems





After developing models for applications in which the dynamics are dominated by lightly damped poles, the book describes the time-delay filter (input shaper) design technique and reviews the calculus of variations. It then focuses on four control problems: time-optimal, fuel/time-optimal, fuel limited time-optimal, and jerk limited time-optimal control. The author explains how the minimax optimization problem can help in the design of robust time-delay filters and explores the input-constrained design of open-loop control profiles that account for friction in the design of point-to-point control profiles. The final chapter presents numerical techniques for solving the problem of designing shaped inputs.





Supplying MATLAB® code and a suite of real-world problems, this book provides a rigorous yet accessible presentation of the theory and numerical techniques used to shape control system inputs for achieving precise control when modeling uncertainties exist. It includes up-to-date techniques for the design of command-shaped profiles for precise, robust, and rapid point-to-point control of underdamped systems.
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 αcr
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
C Parseval's Theorem 397
Index 399
Tarunraj Singh is a professor in the Department of Mechanical and Aerospace Engineering at the University at Buffalo. For more than twenty years, Dr. Singh has worked on the control of flexible structures at various institutions, including Texas A&M University, the University of Waterloo, IBM Almaden Research Center, the Technical University of Darmstadt, and the NASA Goddard Space Flight Center.
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