An Impulse-time Perturbation Approach for a Symmetric Extra-insensitive Input Shaper

Abstract

In this study, symmetric perturbation extra-insensitive input shapers (SPEI-ISs) are proposed to enhance the robustness of the impulse-time perturbation approach, particularly toward the low-frequency range, with respect to the modeled natural frequency. These perturbation-based extra-insensitive input shapers (PEI-ISs) provide a wider range of robustness than the well-known robust input shapers, which include derivative input shapers (e.g., ZVD, ZVDD, and ZVDDD shapers) and extra-insensitive input shapers (EI-ISs). However, robustness may be lost, particularly at lower frequencies, as a result of asymmetric placement of the notch points on the sensitivity curve. To address this issue, an SPEI-IS is derived by placing the notch points symmetrically to enhance robustness, particularly in the low-frequency range. In single-, two-and three-hump cases, explicit solutions are presented to demonstrate the usability of the proposed shapers. The robustness and transient response are evaluated through simulation and experiment and are compared to the response of conventional robust input shapers. It is concluded that the proposed SPEI-IS improves robustness and transient response.