Parameter identification of Hammerstein systems with Bouc-Wen hysteresis input nonlinearity*

The problem of Hammerstein system identification is addressed in presence of a differential hysteresis nonlinearity. The identification process is based on sampled output measurements and an upper bound on the allowed sampling period is provided. One key idea in the identification method design is that the hysteresis element assumes a linear parameterization in presence of a specific class of periodic excitations. Then, a linearly parameterized representation, involving a set of lumped parameters, can be associated to the whole Hammerstein system. The consistent estimation of these lumped parameters is shown to be possible using a hybrid adaptive observer. Finally, the recovery of the true system parameters is achieved using several tools including matrix SVD and nonlinear least-squares estimators.