Identification hysteresis behavior of hydraulic proportional relief valve by the generalized prandtl - ishlinskii model

The Prandtl-Ishlinskii (P-I) model is one of the powerful models which is used in modeling complex hysteretic nonlinear behavior in systems. The initial form of this model، called the Classical Prandtl-Ishlinskii model، cannot describe systems with output saturation and also results have considerable error when there is an asymmetric in hysteresis loops. In order to eliminate these defects، some modifications are applied to the Classical Prandtl-Ishlinskii model and these models are called the generalized or modified Prandtl-Ishlinskii models. This model is usually utilized in modeling complex hysteresis nonlinear behavior in piezoceramic، piezoelectric، magnetostrictive and shape memory alloy actuators، but in this work، the model is used for identification hysteresis behavior of hydraulic proportional relief valve consist of asymmetric hysteresis loops. This model is trained by the experimental data which are obtained of hydraulic proportional relief valve and then the parameters of the model are identified in order to adapt the model response to the real hysteretic behavior. The data consist of the descending reversal curves of major loop. Then the accuracy of the obtained model in predicting nonlinear hysteresis behavior of the valve is validated with some different experimental data. The results show this model has well accurate and good ability in behavior prediction of proportional relief valve.