Identification of fractional Hammerstein system with application to a heating process

In this paper, fractional Hammerstein system identification is considered, where the linear block is of fractional order. The original discrete Hammerstein system is first converted to a fractional polynomial nonlinear state-space model (PNLSS), which allows a better parameterization of the model. An output-error identification approach is developed based on the robust Levenberg-Marquardt algorithm, whose nevralgic point is the calculation of parametric sensitivity functions. These last are developed as a multivariable fractional PNLSS model which effectively reduces the computational effort. Various simulations are used to test the method's efficiency and its statistical performance is analyzed using Monte Carlo simulation. Finally, the method is evaluated through a heating experimental benchmark. The obtained results show good agreement with the real system outputs.