Frequency identification of nonparametric Hammerstein systems with backlash nonlinearity

We are considering the problem of identifying continuous-time Hammerstein systems that contain backlash nonlinearities. Both the linear and nonlinear parts are nonparametric and of unknown structure. In particular, the backlash nonlinearity borders are of arbitrary-shape and so may be nonsmooth and noninvertible. A two-stage frequency identification method is developed to get a set of points of the nonlinearity borders and estimates of the linear subsystem frequency gain at a number of frequencies. The method involves easily generated excitation signals and simple Fourier series decomposition based algorithms. All estimators are shown to be consistent.