Fuzzy instrumental variable approach for nonlinear discrete-time systems identification in a noisy environment

Nonlinear discrete time systems identification based on instrumental variable (IV) method and Takagi–Sugeno (TS) fuzzy model is proposed in this paper. The IVs, statistically uncorrelated with noise, are adequately chosen and mapped to fuzzy sets, partitioning the input space of the nonlinear plant in subregions for unbiased estimates of the TS fuzzy model consequent parameters in a noisy environment. The fuzzy instrumental variable (FIV) concept is proposed so that consistency and unbias properties of the FIV algorithm are derived from Lemmas and Theorem. Simulation results show the efficiency of the FIV algorithm for nonlinear system identification in a noisy environment and its application for modeling of an aluminium beam, with free–free configuration, which is commonly used for active vibration control design in aircrafts and aerospace vehicles.