Zero vibration derivative shaper with distributed delay for both feed-forward and feedback interconnections

Using a distributed delay as the key element, a novel zero vibration derivative (D^αZVD) shaper is introduced with the objective to suppress effectively and robustly an undesirable oscillatory mode of a controlled system. Compared to the classical ZVD shaper with a lumped delay, the D^αZVD shaper is less sensitive to system-model mismatch in higher frequency range. Various aspects of the novel shaper are studied, particularly the spectral patterns, time responses, and sensitivity features. Next, the closed loop architecture with an inverse implementation of the shaper is considered with the aim to suppress robustly the vibrations induced by both the set-point and disturbance changes.