Vibration suppression of rotating long flexible mechanical arms based on harmonic input signals

The industrial long flexible arms usually have nonuniform cross sections and complex structures, leading to the difficulty of establishing accurate models. Moreover, the delay of dynamic response leads to the complexity of the state test and control. Correspondingly, the rotating residual vibration is difficult to control using existing feedback control methods. To this end, a feedforward strategy is presented in this paper to suppress the residual vibration of long flexible mechanical arms. Based on the Lagrange equation, an equivalent rotational flexible dynamic model is established. The model approximately describes the dynamic characteristics of long flexible arms, which exploits the existing mathematical foundation and extends it from the laboratory validation to the industrial application. It can be found that the starting and stopping signals are closely related with the residual vibration. According to harmonic response analysis, the input signals during the starting and stopping process are refined by using weighted Fourier series so as to suppress the residual vibration without considering input shaping filters. The performance is tested in the real industrial equipment that has long flexible arms, which validate the effectiveness of the proposed method.