Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents linear dynamic component placed between the first two Some common model structures include rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive extra input (ARX), moving average exogenous inputs (ARMAX), and output-error (O-E) structure. This paper presents new structure, improvement is proposed, consisted basic models an improved function Müntz-Legendre type. We extension generalised Malmquist polynomials that represent Müntz polynomials. Also, detailed mathematical background for performing almost polynomials, in combination models, proposed. proposed approach used to identify strongly hydraulic system via function. To compare results obtained, well-known Legendre, Chebyshev, Laguerre types exploited.