Optimal Reference Shaping for Dynamical Systems: Theory and Applications

Tarunraj Singh

October 28, 2009 by CRC Press
Reference - 416 Pages - 242 B/W Illustrations
ISBN 9781439805626 - CAT# K10295


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  • Presents the frequency-domain approach for designing input-shaper/time-delay filters
  • Illustrates the design of optimal command shapers through gradient-based and convex programming-based approaches
  • Covers the minimax design of robust command shapers and state feedback controllers
  • Discusses the control of vibratory systems that are subject to Coulomb friction
  • Includes many example problems that represent actual engineering systems


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.