Vibration minimized design of trapezoidal acceleration input for semiconductor manufacturing systems

In this paper, we discuss about the design of the trapezoidal acceleration input which does not excite the mechanical vibration modes. We first obtain the spectrum of the trapezoidal acceleration input analytically, and the frequencies where the spectrum becomes zero are obtained. Since the zero spectrum frequencies are the function of the ramp-up and ramp-down time, they can be determined so as to coincide with the resonance frequencies of the mechanical vibration modes. The effectiveness of the proposed method is evaluated by simulations. The proposed method is very simple, and it is easy to apply not only to the stepper for semiconductor manufacturing systems but also to any other industrial systems that use trapezoidal acceleration input.