Identification and Stability Analysis of Nonlinear Engine Models

Modeling of automotive subsystems, such as the engine, vehicle dynamics etc., is an area that has received much attention for a number of years. It is well recognized that most of these systems are inherently complex and highly non-linear, a number of different approaches have been take to the construction of automotive engine models including (i) first principle or physical understanding based modeling and (ii) input-output system identification. The former method often produces models that quite accurately represent engine behavior but are very detailed and difficult to use either in the design stage for construction of control and monitoring algorithms or in the implementation of algorithms. System identification on the other hand results in simpler models, but due to the relative paucity of nonlinear techniques the identified models often do not adequately model engine behavior. This paper presents the application of a nonlinear system identification technique, called the NARMAX scheme, to the modeling of the dynamics of an internal combustion engine. The models are designed to model engine behavior over a driving schedule, referred to as the IM240 cycle, mandated by the US EPA for emissions testing. The local stability of the constructed models is verified for the operating conditions of the cycle. Further, the conditions for a NARMAX model to be invertible are presented and the IC engine models are analyzed for invertibility. It is also demonstrated that the inverse models can be directly identified from the input-output data.