Fractional Order Control of Vibration in Flexible Electronic Moving Thin Films

Flexible printed electronic films are susceptible to vibration caused by external interference due to their minor stiffness, thus affecting the quality of printed matter, so active vibration control is necessary. An integer order controlled vibration method containing a model of fractional order terms is employed for active control over flexible printed electronic films. Firstly, a fractional order damping term on top of the integer order dynamics equation is introduced and the spatial equation of state is obtained by equating the fractional order transfer function with that of the integer order by using the Oustaloup filter. Secondly, the optimal controller for active control is designed using the LQR control method, and the vibration control of flexible printed electronic films is realized. Finally, the control emulation indicates that the LQR control can decrease the amplitude without changing the resonance frequency of the flexible printed electronic films. The effects of fractional order control on the vibration control of flexible electronic films are shown to be able to achieve the desired control effect.