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A Fast Crank Angle Resolved Zero-Dimensional NO x Model Implemented on a Field-Programmable Gate Array

Journal Article
ISSN: 1946-3936, e-ISSN: 1946-3944
Published April 08, 2013 by SAE International in United States
A Fast Crank Angle Resolved Zero-Dimensional NO
 Model Implemented on a Field-Programmable Gate Array
Citation: Muric, K., Tunestal, P., and Stenlaas, O., "A Fast Crank Angle Resolved Zero-Dimensional NOx Model Implemented on a Field-Programmable Gate Array," SAE Int. J. Engines 6(1):246-256, 2013,
Language: English


In the automotive industry, the piezo-based in-cylinder pressure sensor is getting commercialized and used in production vehicles. For example, the pressure sensor offers the opportunity to design algorithms for estimation of engine emissions, such as soot and NO
, during a combustion cycle. In this paper a zero-dimensional NO
model for a diesel engine is implemented that will be used in real time. The model is based on the thermal NO
formation and the Zeldovich mechanism using two non-geometrical zones: burned and unburned zone. The influence of EGR on combustion temperature was modeled using a well-known thermodynamic identity where specific heat at constant pressure is included. Specific heat will vary with temperature and the gas composition. The model was implemented in LabVIEW using tools specific for an FPGA (Field-Programmable Gate Array). In order to simplify and implement the model, least-squares-criterion-based polynomial approximations are used that enables the utilization of fast algorithms as well as sub-routines (sub-VIs). The sub-routines can be used to save space on the Field Programmable Gate Array (FPGA) and thus minimizing the risk of potential issues regarding overmapping of the hardware. In this case the interpolating functions are polynomials that only consume addition and multiplication operations. This is suited for the objective in mind due to the fact that the model tailored for an FPGA cannot, in a sufficient manner, handle highly complex calculations nor divisions. The time results obtained during the execution of the model indicates that it is possible to update the NO
, at a given temporal state, well below the time corresponding to a crank angle degree. The FPGA NO
model was tested against measurement data collected from a Scania engine. The time needed to execute an iteration of the model was approximately 3 μs.