Accuracy Evaluation of Generalized Prandtl-Ishlinskii Model in Characterizing Asymmetric Saturated Hysteresis Nonlinearity Behavior of Shape Memory Alloy Actuators

Prandtl-Ishlinskii (P-I) model is one of the powerful operator-based phenomenological models which is used in modeling complex hysteretic nonlinear behavior in piezoelectric, piezoceramic, magnetostrictive and shape memory alloy actuators. The most appealing and unique aspect of the Prandtl-Ishlinskii model comes back to this fact that this model is analytically invertible and therefore could be easily implemented as a feedforward controller for compensating the hysteretic nonlinearity behavior. However, the first form of this model, called the Classical Prandtl-Ishlinskii model, cannot describe systems with output saturation and also results to considerable error when there is an asymmetric in the input-output hysteresis loops. In order to eliminate these shortcomings, some modifications are applied to the Classical Prandtl-Ishlinskii model and these models are called the modified or generalized Prandtl-Ishlinskii models. There are some weaknesses in previous researches that it is not clear whether the developed generalized Prandtl-Ishlinskii is capable in predicting hysteresis minor loops of SMA actuators and how much its level of accuracy in the prediction task is. Some of these research shortcomings are perhaps due to the fact that the tested actuator was not available in the laboratory and therefore further experimental tests were not performable. In this paper the generalized Prandtl-Ishlinskii model is trained by some experimental measured data obtained from an experimental test set-up consisting of a flexible beam actuated by a shape memory alloy wire. The parameters of the generalized Prandtl-Ishlinskii model are identified in order to adapt the model response to the real hysteretic nonlinearity. Then the accuracy of the obtained generalized Prandtl-Ishlinskii model in predicting nonlinear hysteric behavior of the system is validated with some different experimental data. Although the model has been trained with the data of first order descending reversal curves, it is shown that the generalized Prandtl-Ishlinskii model has good power in behavior prediction of first order ascending curves as well as higher order minor loops.