A vibration minimized input design based on a polynomial input

We have proposed a frequency-shaped final-state control method that can reduce a residual vibration after positioning by minimizing Fourier gain of feedforward input at desired frequency points. In this method, the feedforward input is obtained as a time series data, therefore, it requires a large memory size to store them in an embedded controller. In this paper, we propose a final-state control method based on a polynomial input. It only requires to store the coefficient of the polynomial, and the required memory size can be drastically reduced. Furthermore, by considering the time symmetry of input, a method to reduce the order of the polynomial without a performance degradation is proposed. The effectiveness is verified by simulations.