Closed-loop Identification of Hammerstein Systems Using Iterative Instrumental Variables

A feedback connection of a Hammerstein system and a linear controller provides a good approach to modeling systems with actuator nonlinearity or input saturation during closed-loop experiments. This paper discusses closed-loop identification of Hammerstein systems where both input and output signals are correlated with noise, and time domain signals are related via a nonlinear map. The static nonlinearity and the linear dynamic system are parametrized independently by using triangle basis functions and rational functions respectively. The independent parametrization method causes overparametrization of the Hammerstein system, but parameter separation is conducted using a singular value decomposition. An iterative Instrumental Variables (IV) method minimizing an (filtered) output error (OE) is proposed to identify system parameters. The proposed iterative IV identification method is applied to the experimental closed-loop time domain data from the servo actuator in a Quantum LTO-3 tape drive and the estimation result shows the effectiveness of the proposed algorithm.