An impulse-time perturbation approach for enhancing the robustness of extra-insensitive input shapers

In this paper, perturbation-based extra-insensitive input shapers (PEI-ISs) are proposed to enhance the robustness of the input shaping technique. The extra-insensitive input shaper (EI-IS) has been known to be more robust than the so-called derivative input shapers such as ZVD, ZVDD, and ZVDDD shapers. However, the robustness of the known EI-IS is restricted by the symmetric property in the sensitivity curve. To address this, the PEI-IS is devised by multiplying a series of input shapers in the Laplace domain, of which the impulse times are slightly perturbed from those of the zero vibration (ZV) shaper. For a single-hump case, a closed-form solution to the PEI-IS is provided. For two- and three-hump cases, the approximate solutions are presented. The robustness is evaluated by simulations and assessed by means of the insensitivity. It will be shown that the proposed PEI-IS does improve the robustness and that it can be easily designed.