Recursive Online Compensation of Piezoelectric Nonlinearities via a Modified Prandtl-Ishlinskii Approach

Abstract

Piezoelectric actuators are often employed in micro- and nanopositioning devices due to their extremely fine positioning resolution but exhibit strong nonlinear effects (predominantly hysteresis and creep) which pose a considerable challenge for the control community. For online compensation of these effects, the modified Prandtl-Ishlinskii model is particularly suitable since its inverse can be found analytically by a parameter transformation. However, this model-based approach has not yet made its way to devices that target positioning tasks. Therein, trajectories typically contain segments with varying final times, small ranges of motion, or stationary states such that the hysteresis and creep effects are not optimally excited and frequency-dependence is induced which ultimately leads to a deteriorated compensation performance. This paper proposes an online approach to overcome the problem by taking into account prior hysteresis/creep information in a recursive manner based on databases for better tracking performance and a more robust compensation of the aforementioned nonlinearities. In order to show the efficacy of the proposed approach, experimental results are provided by using trajectories with varying final times, stationary states and alternating small/large ranges of motion on a micro-positioning unit driven by piezoelectric actuators.