Multivariable classical Prandtl-Ishlinskii hysteresis modeling and compensation and sensorless control of a nonlinear 2-dof piezoactuator

A multivariable approach of modeling and feedforward control of rate-independent hysteresis in multi-dof piezoelectric actuators is proposed in this paper. For that, the classical Prandtl-Ishlinskii (CPI) hysteresis model is extended into multivariable. Then, based on the inverse multiplicative structure and on the multivariable CPI model, a compensator is suggested. The proposed compensator does not require an extra-calculation: As soon as the model is identified, the compensator is obtained by structure. Furthermore, inversion of the model is avoided. Additionally to the hysteresis suppression, the multivariable compensator permits to reduce the cross-couplings between the axes which is not possible with standard techniques. The modeling and the inversion-free compensator are afterward applied to a two-degrees-of-freedom (2-dof) piezoactuator. The extensive investigated experimental tests demonstrate that the strong cross-couplings and the strong hysteresis in the two axes can be substantially reduced and linearized, respectively.