Frequency identification of Wiener systems with backlash nonlinearity

This paper addresses the problem of Wiener system identification. The linear subsystem is stable but not necessarily parametric. The nonlinear subsystem is a backlash element with not necessarily symmetric borders. A common difficulty to all Wiener systems is that their models are not uniquely defined: they are unique up to an uncertain multiplicative factor. Then, it makes sense to start the frequency identification process estimating first the system phase as this is identical (modulo π) for all models. To this end, the system frequency response, at a given frequency, is characterized by a family of Lissajous-like curves, each one is characterized by a phase value. It is shown that the only admissible curve (i.e. one that presents lateral straight borders) is the one corresponding to the true phase value (modulo π). Interestingly, the admissible Lissajous-like curves, obtained with different frequencies, are all candidates to represent the system nonlinearity. But, the most convenient one is the less spread.