Modeling and compensation of asymmetric hysteresis in a piezo actuated metrological AFM

Multivariable Generalized Bouc-Wen modeling, identification and feedforward control and its application to multi-DoF piezoelectric actuators

“…i.e. y = KU − ż z = AU − Ψdiag(U )|z| (9) where |z| ∈ R n is a state vector and A ∈ R n×n , the hysteresis scale control matrix. Ψ is represented by equation (10) and corresponds to the multivariable hysteresis shape control matrix, extended from equation 4.…”

“…Assuming now that the parameters of the multivariable Bouc-Wen hysteresis model in (9) are identified, we present in this section a (multivariable) compensator for the hysteresis. The compensator is built in a way such that the general feedforward controlled system as depicted in Fig.1a satisfies the following condition:…”

“…However, many hysteresis behaviour encountered in piezoelectric actuators like piezo-stack actuators [14], piezoelectric multimorph cantilevers [17], piezotube scanners, etc, are non-symmetrical. To model this class of hysteresis, additional models have been introduced (Dahl [18]), and some of the existing models have been extended or modified: Extended Coleman-Hodgdon [9], Modified Preisach [7], Modified Prandtl-Ishlinskii [2] and Generalized Bouc-Wen [1].…”

“…[15][16] [18] focused on the modeling of multivariable hysteresis which are symmetrical. In [9], the compensation of hysteresis in a multi-DoF piezoelectric actuator has been considered. However, only the direct transfers have been controlled and the couplings were not considered.…”

Characterization, Modeling and H∞ control of n‐DOF Piezoelectric Actuators: application to A 3‐DOF Precise Positioner

“…In these works, various feedback control techniques, including H ∞ , have been applied but the cross‐couplings between the different axes of the actuator were not explicitely accounted for and were not identified for further consideration during the controller design. In , the cross‐couplings were identified but the controllers were finally synthesized for frequency ranges outside the validity of these cross‐couplings. Finally, an explicit and simultaneous consideration of the hysteresis, the creep, the dynamics and the cross‐couplings in a generalized n ‐DOF (degrees of freedom), has not yet been treated.…”