Identification of Hammerstein systems using key-term separation principle, auxiliary model and improved particle swarm optimisation algorithm

The dynamic behaviour of many systems can be approximated by a static non-linearity in series with a linear dynamic part. Systems with static input or output non-linearities are very common in many engineering applications. Such models are known as block-oriented models in the existing literature. The Hammerstein model is a special kind of block-oriented model, where a non-linear block is followed by a linear system. This study investigates the identification of Hammerstein systems with asymmetric two-segment piecewise-linear non-linearities. The basic idea is to employ a key-term separation technique and a corresponding auxiliary model initially. Then, the identification problem of non-linear system is changed into a non-linear function optimisation problem over parameter space. Further, the estimates of all the parameters of the non-linear block, the linear subsystem and the noise part are obtained based on an improved particle swarm optimisation algorithm. Finally, simulation examples are included to demonstrate the effectiveness and robustness of the proposed identification scheme.