Optimal Reference Shaping for Dynamical Systems: Theory and Applications / Edition 1

by Tarunraj Singh

Overview

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.

Product Details

ISBN-13:	9780367384975
Publisher:	Taylor & Francis
Publication date:	10/29/2019
Pages:	416
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

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.

Table of Contents

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 Liner 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 α_cr 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 Lineal 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