Smooth parametric hysteresis operator for control

Abstract Hysteresis is a non-linear phenomenon present in many physical systems that is usually undesirable and degrades their performance. Models which accurately reproduce hysteresis are often very complex and hard to implement. For that reason, the hysteresis is generally, when the performance specifications are not too strict, treated as a bounded disturbance or is approximated with piecewise affine structures. Control design requires models which extract the most fundamental behavior of phenomena and, in this article, such a model was constructed for the hysteresis phenomenon. It is shown that the obtained model can be easily shaped, mathematically manipulated and used for general control design of hysteretic systems, e.g. feed-forward compensation.