A low-complexity circuit model of hysteresis

A circuit architecture modelling rate-independent hysteretic phenomena is presented and discussed. The core of the circuit is a ladder structure with longitudinal nonlinear resistors and transverse linear capacitors. In a separate loop, a linear combination of input and capacitor voltages provides the driving voltage for a resistor with monotonic, piecewise-linear driving-point characteristic. The resistor current represents the output variable. The circuit parameters can be found from experimental data through a standard quadratic programming optimization procedure. The model fitting features are tested by using two experimental data sets. One is the B(H) function of a magnetic material; the other is the deformation of a piezoelectric actuator as a function of the applied voltage. In this last case, an accurate comparison with the predictions of the well-known Preisach model evidences that the circuit model achieves the same accuracy with a much smaller number of parameters. All the circuit simulations are performed by using PSPICE.