Online identification of hysteresis functions with non-local memory

This paper discusses the online identification of non-local static hysteresis functions, which are encountered in mechanical friction, magnetic materials, and piezoelectric actuators. The hysteresis function is modeled using a superposition of elementary extended stop-type hysteresis operators. Each hysteresis operator is defined by one characteristic parameter and one state variable. By choosing the characteristic parameters in advance, the identification leads to a linear least squares estimation of the weighting parameters. This can be implemented recursively for the online estimation of these parameter, to track their slow variations, e.g., due to temperature changes. The developed modelling and identification approach is tested by means of simulations and experiments on a piezoelectric actuator. For the simulations, for both static and dynamic systems, containing a hysteresis function are considered.