Parameters Identification of a Generalized Prandtl-Ishlinskii Model for a Micro-Positioning Stage Using Mutual Shape Memory Alloy Actuators

Implementing smart materials as an actuator in fabricating micro-positioning systems has become pervasive in recent years. However, the application of Shape Memory Alloy (SMA) smart materials is limited due to its complex nonlinear mechanical behavior, such as asymmetric hysteresis and saturation characteristics. One of the most potent experimental-based methods of modeling these nonlinearities is the Generalized Prandtl-Ishlinskii (GPI) model. Unlike similar methods such as the Preisach model, this model is analytically invertible. This study aims to develop a micro-positioning stage and identify an experimental-based model describing the system response. The model structure is composed of two cascade sub-models. In the first sub-model, which models the actuator thermal behavior, the parameters of a linear dynamic model are identified. This sub-model predicts the actuator temperature given the electrical current. The second sub-model estimates the phase transformation and consequently the actuator displacement as a function of temperature. The GPI structure has been used for constructing the Wiener sub-model. The experimental and numerical results showed that the proposed black box model can accurately describe the system behavior, although identifying a comprehensive model to adequately describe the SMA actuator is a great challenge.