Estimation of Hammerstein nonlinear systems with noises using filtering and recursive approaches for industrial control

Abstract

This paper discusses a strategy for estimating Hammerstein nonlinear systems in the presence of measurement noises for industrial control by applying filtering and recursive approaches. The proposed Hammerstein nonlinear systems are made up of a neural fuzzy network (NFN) and a linear state`-space model. The estimation of parameters for Hammerstein systems can be achieved by employing hybrid signals, which consist of step signals and random signals. First, based on the characteristic that step signals do not excite static nonlinear systems, that is, the intermediate variable of the Hammerstein system is a step signal with different amplitudes from the input, the unknown intermediate variables can be replaced by inputs, solving the problem of unmeasurable intermediate variable information. In the presence of step signals, the parameters of the state-space model are estimated using the recursive extended least squares (RELS) algorithm. Moreover, to effectively deal with the interference of measurement noises, a data filtering technique is introduced, and the filtering-based RELS is formulated for estimating the NFN by employing random signals. Finally, according to the structure of the Hammerstein system, the control system is designed by eliminating the nonlinear block so that the generated system is approximately equivalent to a linear system, and it can then be easily controlled by applying a linear controller. The effectiveness and feasibility of the developed identification and control strategy are demonstrated using two industrial simulation cases.