Bias compensation based recursive least squares identification algorithm for multivariable Hammerstein nonlinear systems

Abstract The multivariable Hammerstein nonlinear system contains the sum of bilinear parameters, which is not a regression form. By using the special properties of binary signals, we can transform the sum of bilinear parameter matrices into two different models, achieving the parameter separation for parallel nonlinear subsystems and a linear subsystem. In order to improve the accuracy of parameter identification, this paper uses a biased correction technique to compensate a biased recursive least squares estimates. Then, a bias compensation based recursive least squares algorithm is proposed to separately identify the parameters of a linear subsystem and parallel nonlinear systems. The numerical simulation indicate that the proposed algorithm has a higher accuracy than recursive least squares and over-parametrization based identification algorithms. The multivariate Hammerstein nonlinear system is implemented on a case study from the process industry namely the continuous stirred tank reactor. The accuracy of the prediction is improved by a biased correction term.