Nonlinear system identification with applications to selective catalytic reduction systems

The stringent regulations on the emissions levels of heavy duty vehicles create a demand for new methods of reducing harmful emissions from the engine. In order to be able to follow these increasingly stricter legislations, complex aftertreatment systems are used. Achievement of optimal performance of these systems requires accurate models that can be used for control design. As a result, the interest in modelling and control of aftertreatment systems has increased. This thesis deals with the modelling of the nitrogen oxide (NOx) emissions from heavy duty vehicles using the selective catalyst as an aftertreatment system for its reduction. The process of the selective catalytic reduction (SCR) is nonlinear since the chemical reactions involved are highly depending on the operating point. The momentary operating point is defined by the driving profile of the vehicle which, for example, includes cold and hot engine starts, highway and urban driving. The purpose of this thesis is to investigate different methods for nonlinear system identification of SCR systems with control in mind. The first two papers contain the theoretical work of this thesis. The first paper deals with improvement of an existing recursive prediction error method (RPEM) where a more accurate discretisation algorithm was used to improve the accuracy of the estimated nonlinear model. The second paper deals with analysis of the convergence properties of the algorithm. For this analysis several conditions were formulated that link the global and local convergence properties of the algorithm to stability properties of an associated differential equation. Global convergence to a stationary point was shown. In the third paper, the RPEM is used for identification of the SCR system and finally the fourth paper a Hammerstein-Wiener model for identification of the SCR system is applied. In both these cases the black-box models could predict the NOx behaviour of the SCR system quite well. The nonlinear models were shown to describe the SCR system more accurately than linear models.