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

  • Gregor Dolanc
  • Stanko Strmčnik
Part of the Advances in Industrial Control book series (AIC)


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.


Transfer Function Controller Parameter Linear Parameter Excitation Signal Programmable Logic Controller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The financial support of the Slovenian Research Agency through Programme P2-0001 is gratefully acknowledged.

This chapter is based on: Dolanc G, Strmčnik S (2005) Identification of non-linear systems using a piecewise-linear Hammerstein model. Systems & Control Letters, 54:145–158, ©Elsevier and Dolanc G, Strmčnik S (2008) Design of a nonlinear controller based on a piecewise-linear Hammerstein model. Systems & Control Letters, 57:332–339, ©Elsevier.


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Gregor Dolanc
    • 1
  • Stanko Strmčnik
    • 1
  1. 1.Department of Systems and ControlJožef Stefan InstituteLjubljanaSlovenia

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