Identification and Control of Nonlinear Systems Using a Piecewise-Linear Hammerstein Model

This chapter introduces a new method for the identification and control of nonlinear systems, which is based on the derivation of a piecewise-linear Hammerstein model. The approach is motivated by several drawbacks accompanying identification and control via the classical type of Hammerstein models. The most notable drawbacks are the need for specific identification signals; the limited ability to approximate strongly nonlinear and discontinuous processes; high computational load during the operation of certain control algorithms, etc. These problems can be overcome by replacing the polynomial in the original model with a piecewise linear function. As a consequence, the resulting model opens up many new possibilities. In the chapter, first the new form, i.e., the piecewise-linear form of the Hammerstein model, is introduced. Based on this model, two new algorithms are derived and connected into a uniform design approach: first, a recursive identification algorithm, based on the well-known least-squares method, and second, a control algorithm that is a modification of the pole-placement method. Both algorithms are tested in an extensive simulation study and demonstrated on a case study involving control of a ferromagnetic material sintering process. Finally, some problems and limitations regarding the practical application of the proposed method are discussed.