Preisach Operator Modeling

Preisach operator modeling is a nonlinear methodology widely applied for hysteresis system modeling, demonstrating exceptional performance in fields such as magnetic hysteresis and piezoelectric materials. The core concept involves decomposing hysteresis characteristics into the superposition of numerous elementary hysteresis units (called Preisach units), constructing the overall model through mathematical integration formalism.

Implementing Preisach operator modeling in MATLAB typically requires the following procedural steps: First, define the Preisach plane - the set of all possible input extremum points used to characterize the "memory effect" of hysteresis. This can be implemented using meshgrid functions to create the alpha-beta coordinate system. Next, determine the density function (also called weight function) based on experimental data or theoretical derivation, which governs the contribution of each Preisach unit. The density function estimation can be achieved through optimization algorithms like fmincon or lsnonlin. Finally, compute the output response through numerical integration or discretization methods to simulate system hysteresis behavior, where MATLAB's integral2 function or cumulative sum operations prove particularly efficient.

The key advantage of this approach lies in its ability to accurately capture multi-valued mapping and path-dependent characteristics, making it suitable for strongly nonlinear systems. In practical implementation, the density function can be calibrated using experimental data, or model simplification can be achieved through symmetry assumptions. MATLAB's matrix operations and numerical integration capabilities provide robust support for such modeling, with built-in functions like trapz and cumsum facilitating efficient discretization implementations.