H2-optimal digital control of piezoelectric actuators

Piezoelectric actuators have nonlinearities such as hysteresis and creep, which make the control of such actuators difficult. One promising method is to find the inverse of the model describing the nonlinearities and cascade it to the nonlinear plant to compensate for the nonlinearities, thus leaving only the linear behaviors, and then a linear controller can be designed. Following this idea, in this study, the hysteretic behavior of a piezoelectric actuator is modeled by the classical Preisach hysteresis model (CPM). The inversion of CPM is formulated and then cascaded to the nonlinear piezoelectric actuator model to compensate for the hysteresis part. Then an H₂-optimal digital controller is designed according to the linear part of the model. The effectiveness of the controller design is demonstrated by some preliminary simulations and experiments.