Fully parametric identification for continuous time fractional order Hammerstein systems

This paper mainly investigates the issue of parameters identification for continuous time fractional order Hammerstein systems. When the commensurate order of linear part in system is prior information, two estimation algorithms are proposed to identify the parameters. Both methods use filters to obtain the derivative of the continuous time signal: one based on the Poisson filter and the other using the auxiliary model to construct the filter. Afterwards, the commensurate order update law is given, which contains the relationship between parameters and orders. In addition, due to the existence of fractional order terms, an irrational item will be introduced, and this paper gives a detailed mathematical derivation to discuss this issue. The effectiveness of proposed methods is demonstrated by the numerical simulations.