Mathematical Representation
A mathematical framework represents hysteretic behavior by summing the outputs of many independent, bistable switching elements called hysterons. This formulation, known as the Preisach model, simulates the complex multi-valued relationships found in magnetic, piezoelectric, and ferroelectric materials. It allows engineers to predict sensor output based on the history of the applied input signal.
It is widely used in precision actuator control and sensor design.
Functional Mechanism
Individual hysterons are defined by two distinct threshold values representing the transition states between high and low levels. As the input signal rises or falls, each hysteron switches state independently, creating a combined output that retains a memory of the input extrema. The Preisach model maps these transitions using a density function on a triangular domain called the Preisach plane.
By integrating this function over the active region, the total hysteretic output is calculated for any arbitrary input trajectory. This approach is highly effective for simulating the non-linear response of smart material transducers. Without this model, precise control of such devices is difficult because of the memory-dependent positioning errors.
Parameter Identification
Experimental measurements from first-order reversal curves are used to calibrate the density function. This calibration process requires a sequence of rising and falling input cycles to identify the Preisach model parameters.
Software Implementation
Digital signal processors run discretized versions of the algorithm in real time. This allows for live correction of hysteretic errors using the Preisach model.
