Non-parametric convex identification of extended generalized Prandtl–Ishlinskii models

The Generalized Prandtl–Ishlinskii model (GPI) of hysteresis has wide applicability, partly because of its capability to model asymmetric hysteresis. It is characterized by three unknown functions. Today, GPI models are typically identified through trial and error by ad hoc methods, presuming parameterized expressions for these functions and then using nonlinear least squares to determine the parameters, with concurrent problems of convergence, a dependence on the initial parameter guess, and local minima. Except for the aggregated hysteresis input–output fit the result gives no information as to whether the functions chosen are appropriate or not. Here we present a method to circumvent these problems for a more general class of hysteresis models. First, we introduce an extended GPI model (XGPI), where an additional memoryless function is placed in parallel to the GPI model. This further widens the applicability, allowing, for example, arbitrary orientation of the hysteresis loop. For such models it is shown how its four separate mappings can be identified by convex optimization. Appropriate single-valued functions can then be fitted individually to the resulting mappings and, if necessary, the function parameters found can be fine-tuned using nonlinear least squares on input–output data. The method is applied to simulated data and experimental data from a magnetoelastic torque sensor, and the results are favorably compared to the results of another commonly used hysteresis model.