Resumen de On the consistency of hysteresis models

Mohammad Fuad Mohammad Naser

• Hysteresis is a nonlinear behavior encountered in a wide variety of processes including biology, optics, electronics, ferroelectricity, magnetism, mechanics, structures, among other areas. One of the main features of hysteresis processes is the property of consistency formalized in [52]. The class of operators that are considered in [52] consists of the causal ones, with the additional condition that a constant input leads to a constant output. For this class of systems, consistency has been defined formally. This property is useful in system modeling and identification as it limits the search for the system's parameters to those regions where consistency holds. The thesis applies the concepts introduced in [52] to some hysteresis models, namely LuGre model and Duhem model. The aim of the thesis is to derive necessary conditions and sufficient one for consistency (or/and strong consistency) to hold. For the LuGre model, the consistency and the strong consistency are studied under minimal conditions in Chapter 2. As a by-product of this study, explicit expressions are derived for the hysteresis. Such expression may be useful for identification purposes as shown in [53]. A classification of the possible Duhem models in terms of their consistency is carried out in Chapter 3. This study shows that a parameter’s should be one for the Duhem model to be compatible with a hysteresis behavior.