Parameter estimation of non-linear systems with Hammerstein models using neuro-fuzzy and polynomial approximation approaches

This paper presents two different approaches for parameter estimation of non-linear systems with Hammerstein models. The Hammerstein model consists in the cascade connection of two blocks: a non-linear static part and a linear dynamic part. For modelling the non-linear static function part two different techniques were used: neuro-fuzzy and polynomial approximation approaches. The neuro-fuzzy Hammerstein model (NFHM) approach uses a zero-order Takagi-Sugeno fuzzy model to approximate the non-linear static part and is tuned using gradient decent algorithm. The polynomial approximation Hammerstein model (PAHM) approach uses a polynomial of order n to approximate the non-linear static part and is tuned using a least squares algorithm. For the linear dynamic part both algorithms use the least squares parameter estimation. The methods were implemented off-line, in two steps: first, estimation of the non-linear static parameters and second estimation of the linear dynamic parameters. Finally, a gas water heater non-linear system was modelled as an illustrative example of these two approaches.