Identification of hysteresis models using Real-Coded Genetic Algorithms
Finding an accurate model to present the hysteresis nonlinearities behavior of the smart actuator has attracted the attention of the researchers in recent years, since an accurate model has an essential role in the position control application of these actuators. Different models have been developed to describe the hysteresis nonlinearities, the generalized Prandtl-Ishlinskii (GPI) model is one of the most popular used models. This model uses the play operators represented by the threshold values and weights integrated with the odd envelope functions to characterize the hysteresis nonlinearities of smart actuators. The contribution of this paper proposes three different approaches using the Real-Coded Genetic Algorithm (RCGA) for the parameters identification of the Generalized Prandtl-Ishlinskii (GPI) model. In Approach 1, the thresholds and the values of the weights are calculated based on the proposed formulas with the unknown parameters to be identified using RCGA. In Approach 2, the thresholds values are calculated based on the proposed formula with the unknown parameters to be identified using RCGA and the values of the weights are identified directly using RCGA. In Approach 3, the thresholds and the values of the weights are identified directly using RCGA. Also, RCGA was used to identify the values of the coefficients of the envelope functions for all approaches. All approaches are tested through four different examples. Two examples are simulated examples that have linear and tangent hyperbolic envelope functions. Moreover, the other two examples represent experimental data obtained for a piezoelectric actuator and a shape alloy memory (SMA) actuator. The simulation results are carried through by the statistical and convergence analysis of the proposed approaches. The comparison and analysis show that three different approaches can be employed for modeling hysteresis nonlinearities with minimum differences between them.