Identification of series-parallel systems composed of linear and nonlinear blocks

Most works on system identification of block-oriented nonlinear systems were devoted to Wiener and Hammerstein systems. This article is focused on a more general, and so more complex, nonlinear model structure. Specifically, the system under study is a series connection of two subsystems each one being constituted of linear dynamic block and a nonlinear static block coupled in parallel. Clearly, this system structure generalizes those of Wiener and Hammerstein systems. Interestingly, the linear blocks can be parametric or not and are allowed to be of unknown structure. We develop a two-stage frequency-type identification method that provides accurate estimates of the all system parts. The proposed identification method enjoys the simplicity and the consistency of developed estimators. Furthermore, the parameters of linear dynamic blocks can be easily decoupled without any further experiments. The performances of the proposed identification method are highlighted by several simulation results. As perspectives, one or the two nonlinearities can be considered non-static, for example, of backlash type.