Model-based design of dynamic firing patterns for supervisory control of diesel engine vibration

Dheeraj B. Gosala, Harikrishnan Raghukumar, Cody M. Allen, Gregory M. Shaver, James E. McCarthy, Timothy P. Lutz

Research output: Contribution to journalArticlepeer-review


Diesel engine cylinder deactivation (CDA) has been demonstrated to provide significant efficiency and aftertreatment thermal management benefits, enabling fuel-efficient emissions reduction from modern diesel engines at low load engine operation. Dynamic cylinder activation (DCA), a variant of CDA where the set of deactivated cylinders varies on a cycle-by-cycle basis, has been demonstrated to enable greater control over driveline torsional vibration while maintaining the fuel efficiency and thermal management benefits shown by fixed CDA via appropriate design of firing patterns. A model-based algorithmic approach to designing firing patterns during DCA – to control driveline torsional vibration in a user-defined frequency range, given firing density, engine speed, and maximum length of firing pattern – is described in this article. The described algorithm is generalizable to any engine configuration including different piston–cylinder layouts and number of cylinders. The algorithm is extended to design firing patterns for constrained DCA operation when CDA hardware is installed on a subset of cylinders of the engine. The resulting optimal firing patterns using the algorithm, for various combinations of inputs, are presented through an experimentally-validated simulation framework and discussed. It is demonstrated that the weighted phase-angle approach can accurately predict the frequencies and relative amplitudes of the vibration content, and, if theoretically possible, the proposed algorithm determines firing patterns that meet the specified requirements. The presented algorithm can be easily extended in future work for simultaneous selection of firing density and firing pattern during online, real-time implementation during both steady-state and transient operating conditions.

Original languageEnglish (US)
Article number104681
JournalControl Engineering Practice
StatePublished - Feb 2021
Externally publishedYes


  • Cylinder deactivation (CDA)
  • Drivetrain resonance
  • Dynamic cylinder activation (DCA)
  • Firing frequency
  • Firing pattern design
  • Noise vibration and harshness (NVH)
  • Phase angle diagrams
  • Torsional vibrations
  • Vibration control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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