Discrete Preisach hysteresis algorithm

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Discrete Preisach hysteresis algorithm

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The Discrete Preisach hysteresis algorithm is a computational approach for modeling hysteresis behavior in various physical systems, such as ferromagnetic materials, piezoelectric actuators, and smart materials. The Preisach model, originally developed for magnetism, has become a widely adopted framework for capturing hysteresis due to its ability to account for memory effects and nonlinear responses.

### Core Concept The Preisach model represents hysteresis as a superposition of elementary hysteresis operators, often called "hysterons." Each hysteron has a simple binary behavior—switching between two states (e.g., +1 and -1) based on past input extrema. In the discrete version, the continuous Preisach plane is approximated using a finite grid, making it computationally feasible.

### Algorithmic Implementation Discretization of the Preisach Plane: The continuous Preisach plane (defined by thresholds α and β) is divided into a finite grid, where each cell represents a hysteron.

Memory Effect Tracking: The algorithm keeps track of past input extrema, as hysteresis depends on the history of input variations rather than just the instantaneous value.

Output Calculation: For a given input, the active hysterons are determined, and their contributions are summed to produce the total output. The weight of each hysteron can be calibrated based on experimental data.

### Applications The Discrete Preisach algorithm is useful in control systems where hysteresis introduces nonlinearity, such as in precision positioning systems using piezoelectric actuators. It also finds applications in material science for characterizing ferromagnetic or ferroelectric behaviors.

### Strengths and Limitations Strengths: Captures memory-dependent nonlinearity effectively. Adaptable to different hysteresis shapes via weight adjustments. Limitations: Requires identification of hysteron weights, which can be data-intensive. Computational cost increases with finer discretization.

This algorithm provides a structured way to model systems where hysteresis plays a crucial role, enabling better control and prediction in engineering applications.