Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

Abstract

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

Keywords:

• B-spline
• De Boor algorithm
• Hammerstein model
• pole assignment controller
• system identification

Acknowledgements

The authors gratefully acknowledge that part of this work was supported by EPSRC in the UK. They also thank the reviewers for their valuable comments.