MATLAB Implementation of Duhem Hysteresis Model

The Duhem hysteresis model is a classical mathematical framework for describing nonlinear system hysteresis characteristics, widely applied in piezoelectric materials, magnetostrictive materials, and related fields. Here is an analytical approach to implementing this model in MATLAB:

Mathematical Model Formulation The Duhem model is typically described by differential equations where the output response depends on the rate of change of the input signal. The model expression may incorporate piecewise-linear or nonlinear functions requiring parameter adjustments based on material properties. Key implementation involves defining the derivative function for ode solvers.

Numerical Solution Methodology Utilize numerical methods like Euler's method or Runge-Kutta schemes (e.g., ode45) to solve the differential equations. After discretizing time steps, implement iterative calculations for output values at each time point using while/for loops, ensuring solution stability through appropriate step size selection.

Critical Parameter Design Define hysteresis slope parameters, saturation thresholds, and asymmetric coefficients. Parameter selection directly influences model characteristics (hysteresis loop width/height), typically determined through experimental data fitting using optimization functions like fminsearch or lsqcurvefit.

Input-Output Processing Generate periodic input signals (sine waves, triangular waves) using linspace and sin/tripuls functions to excite system hysteresis. Implement real-time output updates through array indexing and store results in matrices for hysteresis loop plotting.

Visualization Validation Plot input-output curves using plot/scatter functions to observe typical hysteresis loops. Validate model capabilities for capturing symmetry and saturation characteristics through parameter tuning with interactive sliders (uicontrol) or GUI components.

This implementation supports research in smart material control and sensor modeling scenarios. Future extensions may include parameter identification systems or inverse model compensation applications using system identification toolbox functions.