Implementation of Two Distinct Hysteresis Models

The system under consideration exhibits two types of hysteresis loops, namely backlash and Preisach. Backlash hysteresis, typically caused by internal friction and mechanical clearance in the system, can be implemented in code using dead-zone models with memory of previous input extremes. Preisach hysteresis, attributed to magnetic domain wall movements in ferromagnetic materials, requires a more complex implementation involving the superposition of elementary hysteresis operators (hysterons) that track switching thresholds. The Preisach model can be programmed using weight function matrices that store historical state transitions. It's worth noting that Preisach hysteresis is mathematically described by a hysteron model, which accounts for the system's history-dependent behavior through integration over past input values. Therefore, understanding the distinct characteristics and implementation approaches for each hysteresis type is crucial for accurate system modeling and control design. Code implementations typically require state variables to memorize previous input extrema for backlash, while Preisach needs extensive memory storage for historical state transitions.