Implementation, identification, and adaptation of Preisach like hysteresis models

Licentiatavhandling, 2013

The extended generalized Prandtl-Ishlinskii model (XGPI) of hysteresis has a wide applicability, partly because of its capability of modelling highly asymmetric hystereses. For a given parameterization, it is typically identified using non-linear least squares optimization with concomitant problems of convergence, dependence on initial parameter guess and local minima. The parameterization itself is in general not found analytically, but is based on experience and trial and error. Here, we study the uniqueness properties of the XGPI model, and describe a method for convex identification of the model, which is particularly useful for finding a close to optimal parameterization, including a nominal parameter vector, which can be essential for calibration of hysteretic sensors and actuators in serial production. The method is applied for finding parameterizations of XGPI models for three physical systems and their inverses, and the results are compared to other hysteresis models. In particular, it is shown that the exponential weight function is close to optimal in these models. It is well known that the GPI model is a restriction of the Preisach model of hysteresis. For a better understanding of this connection, an explicit relation is derived, and we also give a general implementation and parametric identification scheme for the two models. This scheme is based on the classical implementation scheme based on Everett integrals, but with a slight modification to handle hysteresis which is not completely saturated on the input interval. The main application is a magnetoelastic torque sensor in a vehicle application, and 4 copies of the sensor are considered here. It is illustrated how small amounts of data can be used for satisfying identification results. A recursive model identification scheme is derived, which is applied to adapt the inverse sensor models based on zero torque indications, to make them more robust against wear and aging. Based on experimential data, it is illustrated that for a particular application, the effects of wear and aging can essentially be eliminated using the method.