A Fast Crank Angle Resolved Zero-Dimensional NOx Model Implemented on a Field-Programmable Gate Array

Kenan Muric, Per Tunestål, Ola Stenlåås

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

12 Citations (SciVal)


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.
Original languageEnglish
Title of host publicationSAE international journal of engines
PublisherSociety of Automotive Engineers
Publication statusPublished - 2013
EventSAE World Congress & Exhibition, 2013 - Detroit, Michigan, Detroit, Michigan, United States
Duration: 2013 Apr 162013 Apr 18

Publication series

ISSN (Print)1946-3944
ISSN (Electronic)1946-3936


ConferenceSAE World Congress & Exhibition, 2013
Country/TerritoryUnited States
CityDetroit, Michigan

Subject classification (UKÄ)

  • Other Mechanical Engineering


  • Internal Combustion Engines
  • Diesel Engines
  • FPGA
  • Emission Model


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