Relay based identification of Hammerstein model

In this article, a Hammerstein system with a more generalized linear subsystem is identified using a hysteretic relay in feedback. The system delay is measured from the plot of derivatives of the output. Linear subsystem parameters are first estimated with simple state space calculations using the plots of input and output data. The intermediate signal is then estimated as the input to the linear subsystem. Then the non-linearity is approximated as a polynomial curve fitting between the input to the system and the intermediate signal. For each test, the relay heights are chosen as Chebyshev nodes to mitigate the effect of Runge’s phenomenon of over-fitting. The procedure is tested in simulation with an example. Smoothing spline based curve fitting technique is used to recover the output signal from measurement noise. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.