  Hysteresis-controlled devices are widely used in industrial applications. For
example, cooling devices usually contain a two-point controller, resulting in a
nonlinear hybrid system with two discrete states. Dynamic models of systems are
essential for optimizing such industrial supply technology. However,
conventional system identification approaches can hardly handle
hysteresis-controlled devices. Thus, the new identification method Sparse
Identification of Nonlinear Dynamics (SINDy) is extended to consider hybrid
systems. SINDy composes models from basis functions out of a customized library
in a data-driven manner. For modeling systems that behave dependent on their
own past as in the case of natural hysteresis, Ferenc Preisach introduced the
relay hysteron as an elementary mathematical description. In this new method
(SINDyHybrid), tailored basis functions in form of relay hysterons are added to
the library which is used by SINDy. Experiments with a hysteresis controlled
water basin show that this approach correctly identifies state transitions of
hybrid systems and also succeeds in modeling the dynamics of the discrete
system states. A novel proximity hysteron achieves the robustness of this
method. The impacts of the sampling rate and the signal noise ratio of the
measurement data are examined accordingly.
