Output Error Identification of Closed-loop Hammerstein Systems

A feedback connection of a Hammerstein system and a linear controller provides a good approach to modeling systems with static actuator nonlinearity or input saturation during closed-loop experiments. This paper discusses the Output Error (OE) identification of such closed-loop Hammerstein systems that requires a nonlinear optimization due to the non-convexity of the output error. An iterative IV (Instrumental Variables) identification algorithm is proposed for the nonlinear optimization. The basic idea is to express the nonlinear parameter estimation as an iterative IV estimation using gradient based updates. The proposed iterative IV identification method is applied to the simulation data from a Hammerstein system with input static nonlinearity. The simulation study shows the effectiveness of the proposed identification algorithms.