Model-based piezoelectric hysteresis and creep compensation for highly-dynamic feedforward rest-to-rest motion control of piezoelectrically actuated flexible structures

A model-based approach is proposed for the compensation of the piezoelectric hysteresis and creep effects in a feedforward control design for piezoelectric structures. The designed control commands can be favorably used in motion control for applications, e.g. for fast positioning with piezo flexures. They successfully realize fast rest-to-rest motion in the whole voltage operation range of the piezoelectric actuator material, i.e. specifically outside of the linear small-signal regime.The proposed control design combines a flatness-based inversion procedure for the structural dynamics under the assumption of linear piezoelectricity and an inverse piezoelectric operator for compensation of the piezoelectric hysteresis and creep large-signal effects. For that, the overall nonlinear system model is recast in a series connection of an input nonlinearity and the linear dynamics of the mechanical structure, which allows to design the feedforward control in two steps: First, a feedforward control for the linear model part is derived based on an approach exploiting the notion of flatness in combination with modal analysis of the linear dynamics. Thereby, the finite-element method is used to analyze the linear structural dynamics assuming small-signal operation of the piezoelectric material. Secondly, an inverse filter is designed based on the inversion of an operator-based hysteresis and creep model that is capable to compensate these nonlinear effects. By insertion of this filter, very good tracking control performance is achieved in both small and large-signal operation of the piezoelectric actuator.Simulations and experiments for a piezoelectrically actuated plate strip prove that the designed feedforward controls yields excellent tracking performance in large voltage ranges. The achieved time for the rest-to-rest transition is less than half the period of the first structural mode which is a typically limit of comparable methods.