Hysteretic non-linearity significantly degrades the motion accuracy of piezoelectric actuators (PEAs). Hysteresis modelling and inversion (MI) is a widely-accepted hysteresis compensation approach. Alternately, direct inverse modelling (DIM) approach has also been proposed to directly identify the inverse hysteresis model. DIM is superior to MI as the inversion calculation has been totally eliminated, making DIM applicable in both rate-independent and rate-dependent hysteretic systems. This work proposes a further development of DIM by integrating adaptive projection (AP) algorithm so that parameters of the inverse hysteresis model can be automatically updated without any off-line identification. This work compares the proposed method with other methods via tracking continuous and discontinuous trajectories. Experimental results show that the integration of DIM and AP is effective in attenuating the hysteretic non-linearity and improving the trajectory tracking performance of the PEA.

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