A NEW DRIVE CONCEPT FOR HIGH-SPEED POSITIONING OF PIEZOELECTRIC ACTUATORS

This paper is devoted to the infinite-dimensional control design for a composite piezoelectric trimorph cantilever with complex hysteresis nonlinearities and dynamic creep processes. The control concept being proposed comprises a flatness-based trajectory planning in combination with a passivity-based controller which guarantees the stability of the resulting closed-loop error system. It is well known that at higher electric field strengths the polarization of the piezoelectric material saturates and significant complex hysteretic nonlinearities and dynamic creep effects appear. The mathematical model of the piezoelectric cantilever is approximated in form of a Hammerstein-like model with the hysteretic nonlinearity and the creep dynamic at the input connected in series with a linear infinite-dimensional beam model. The difference principle realized in the trimorph configuration of the piezoelectric bender leads to a special symmetry property of the resulting input nonlinearity and thus admits the application of the Prandtl-Ishlinskii theory for the systematic calculation of an inverse operator for compensating the hysteresis and creep effects. Measurement results on a commercially available serial trimorph bender shows the feasibility of the proposed control strategy, in particular for the case of large displacements.