Identification of extended Hammerstein systems with hysteresis-type input nonlinearities described by Preisach model
Résumé
This paper introduces Preisach model to describe hysteretic input nonlinearities of extended Hammerstein systems. Preisach model is proved to be an effective model to cover most of hysteretic input nonlinearities studied in the existing literatures on identification of extended Hammerstein systems. That is, Preisach model encloses the backlash-type nonlinearities and the hysteresis-relay nonlinearities as special cases, but excludes the switch-type nonlinearities. Hence, the usage of Preisach model is able to resolve an issue that types of hysteretic input nonlinearities are often inaccessible in practice, but most of existing identification methods have to know the type of input hysteretic nonlinearity a priori. For identification of extended Hammerstein systems with input nonlinearity described by Presiach model, the persistently exciting (PE) condition of input is established and the consistency of estimated model parameters is proved. In particular, the requirement on inputs to meet with the PE condition covers a wide class of signals, which resolves another issue in the existing studies that specially designed inputs are usually required. Numerical and industrial examples are provided to illustrate the obtained results.