Adaptive time-delay command shaping filter for flexible manipulator control

In this paper, we introduce a new formulation of the time-delay command shaping filter using a commuted shaping order approach, which leads to the development of a simple and effective adaptive command shaping technique for both single- and multi-mode cases. The authors derived the conditions that the time-delay command shaping filter should satisfy to suppress the residual vibration. From the conditions, they calculated the minimum number of command shaping filter terms required to completely cancel the residual vibrations as a function of the number of elastic modes to be canceled. Using this new formula they also prove that the time-delay value is not a function of the system parameters and can be chosen freely even for multiple elastic modes. Making use of this freedom in choosing the time delay, the authors propose a direct adaptation of the time-delay command shaper for both single and multi-mode systems. Finally, the simulation and experimental results of the adaptation are included to show the effectiveness of the direct adaptive command shaping approach.