Rate-Dependent Hysteresis Model of Piezoelectric using Singularity Free Prandtl-Ishlinskii Model

Actuators using advance materials like piezoelectric and shape memory alloy are gaining popularity in applications involving high frequency, high precision and also when there's a need in compactness. As time is required for the switching of polarization, the phenomena hysteretic behavior of these materials changes with rate. Most present hysteresis models are based on rate-independent assumption and cannot be applied for non-periodic applications. To make matters worse, the hysteresis actually becomes ill-conditioned when the velocity is high at the turning point. This paper proposes a phenomena rate-dependent model using a modified Prandtl-Ishlinskii (PI) operator without singularity to model the behavior of piezoelectric actuators, even when subjected to varying frequency signals. Past work had shown that the weights of the Prandtl-Ishlinskii operators vary linearly with velocity when the velocity is less than 900μm/s. As the first weight becomes negative when operating at higher frequencies, the threshold value has to be kept large to avoid the singularity problem when computing the inverse Prandtl-Ishlinskii model. Similar ill-conditioned problems also arise when the actuators are subjected to heavy loads. Thus, this paper proposes extensions to the PI operator by mapping the hysteresis data through a linear transformation onto a domain where the singularity problem is removed. The inverse weights are obtained and subsequently used to compute the inverse hysteresis model and implemented as an open-loop feedforward control of a piezoelectric actuator.