Optimal Reference Shaping for Dynamical Systems: Theory and Applications, 1st Edition (Hardback) book cover

Optimal Reference Shaping for Dynamical Systems

Theory and Applications, 1st Edition

By Tarunraj Singh

CRC Press

416 pages | 242 B/W Illus.

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pub: 2009-10-28
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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.

Table of Contents


Hard Disk Drives

High Speed Tape Drives

High Speed Elevator


Slosh Modeling

Vehicle Platooning

Time-Delay Filter/Input Shaping

Time-Delay Filters

Proportional Plus User-Selected Multiple Delay Control

Time-Delay Control of Multi-Mode Systems

Jerk Limited Input Shapers

Robust Jerk Limited Time-Delay Filter

Jerk Limited Time-Delay Filters for Multi-Mode Systems

Filtered Input Shapers

Discrete-Time Time-Delay Filters

Optimal Control

Calculus of Variations

Hamiltonian Formulation

Minimum Power Control

Frequency Shaped LQR Controller

LQR Control with Noisy Input

Saturating Control

Benchmark Problem

Minimum Time Control

Fuel/Time Optimal Control

Fuel Limited Minimum Time Control

Jerk Limited Time Optimal Control

Minimax Control

Minimax Time-Delay Filters

Minimax Feedback Controllers

Friction Control

Time-Optimal Rest-to-Rest Maneuvers

Pulse-Width Pulse-Amplitude Control

Numerical Approach

Parameter Optimization

Linear Programming

Linear Matrix Inequality

Appendix A: Van Loan Exponential

Appendix B: Differential Lyapunov Equation

Appendix C: Parseval’s Theorem


A Summary appears at the end of each chapter.

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.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General