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Charge-based hysteresis compensation in low impedance piezoelectric actuators by a modified Prandtl–Ishlinskii model

Piezoelectric actuators are one of the most popular actuators in micro- and nano-applications. The main deficiency of these actuators is the hysteretic behavior. Hysteresis not only can destroy the positioning accuracy, but also may lead to instability. In previous researches, hysteresis in the mechanical domain (voltage–position) has been modeled and compensated by several approaches. The limiting condition has been position measurement by a high cost, fine resolution sensor. So, an alternative idea can be compensation in the electrical domain (voltage–charge). In fact, it can be demonstrated that hysteresis compensation in the electrical domain can simultaneously compensate the mechanical one. But, experimental results depict that voltage–charge relation may be time dependent due to low internal impedances. It would lead to “time-dependent hysteresis”. As a result, conventional models cannot be applied for hysteresis identification. In this paper, a modified time-dependent Prandtl–Ishlinskii model is proposed to identify the time-dependent hysteresis in low impedance actuators. Utilizing the proposed model, experimental results validate that the mechanical hysteresis would be appropriately compensated as a result of compensation in the electrical domain.