Two-stage refined instrumental variable method for identifying Hammerstein-Wiener continuous-time models in closed loop

The continuous-time model identification problem of closed-loop Hammerstein-Wiener system with unknown controller and different noise situations is studied. A two-stage approach is proposed, based on the refined instrumental variable method. With the assumption of monotonic nonlinear function, the closed-loop non linear model is iteratively estimated as an over-parameterized MISO LTI model. To obtain an accurate model in the closed-loop case, the identification is implemented in two stages: 1) identification between the input and the reference signal, which produces estimate of the noise-free input, 2) identification between the output and estimated noise-free input signal. Monte Carlo simulation analysis is carried out to illustrate the effectiveness of the proposed method, in both output and process noise circumstances.