Bouc–Wen Modeling and Feedforward Control of Multivariable Hysteresis in Piezoelectric Systems: Application to a 3-DoF Piezotube Scanner

This paper is concerned with multivariable coupled hysteretic systems. The traditional Bouc-Wen monovariable hysteresis model devoted to 1 degree of freedom (DoF) actuated systems is extended to model the hysteresis in systems with multiple DoF, which typify strong cross-couplings. The proposed approach is able to model and to compensate for known hysteresis nonlinearities that affect smart materials. First, after presenting the new multivariable hysteresis Bouc-Wen model, a procedure of identification of its parameters is proposed. Then, we propose a multivariable compensator for the hysteresis. The compensator is based on the combination of the inverse multiplicative structure with the model, which permits to avoid additional calculation of its parameters. Such advantage is essential when the number of DoF is high. All along this paper, the cases of underactuated, overactuated, and fully actuated hysteretic systems are discussed. Finally, the proposed method is used to model and to compensate for the hysteresis in a 3-DoF piezoelectric tube actuator. The experimental results demonstrate its efficiency to linearize the hysteresis in the direct transfers and to minimize the hysteresis of the cross-couplings.