Generalized Scalar Preisach Models of Hysteresis

Abstract

The classical Preisach model of hysteresis has been discussed in detail in the previous chapter. It has repeatedly been emphasized that this model has some intrinsic limitations. The most important of them are the following:

• 1. The classical Preisach model describes hysteresis nonlinearities which exhibit congruency of minor loops formed for the same reversal values of input. However, many experiments show that actual hysteresis nonlinearities may substantially deviate from this property.

• 2. The classical Preisach model is static in nature and does not account for dynamic properties of hysteresis nonlinearities. However, for fast input variations these properties may be essential.

• 3. The classical Preisach model describes hysteresis nonlinearities with the wiping-out property. This property is tantamount to the immediate formation of hysteresis loop after only one cycle of back-and-forth variation of input between any two reversal values. However, experiments show that hysteresis loop formation is often preceded by some stabilization process which may require large number of cycles to achieve a stable minor loop. This process is also called in the literature “accommodation” or “reptation” process.

• 4. The classical Preisach model deals only with scalar hysteresis nonlinearities. However, in many applications vector hysteresis is encountered. Properties of this hysteresis are usually quite different from scalar hysteresis properties.