Periodic Time-Varying Observer-Based Learning Control of A/F Ratio in Multi-cylinder IC Engines

  • Tomohiro Hara
  • Tielong Shen
  • Yasuhiko Mutoh
  • Yinhua Liu
Part of the Studies in Computational Intelligence book series (SCI, volume 657)


This paper presents an air–fuel ratio control scheme via individual fuel injection for multi-cylinder internal combustion engines. The aim of presented control scheme is to improve air–fuel ratio precision by real-time compensation of the unknown offset in the fuel path of individual cylinder, which represents the effect of the cylinder-to-cylinder imbalance caused by the perturbations in each injector gain or disturbances in the dynamics of fuel injection path. First, the fueling-to-exhaust gas mixing system is treated as single-input single-output (SISO) periodic time-varying system where the input is fuel injection command for each cylinder and the output is the air–fuel ratio measured at each exhaust bottom dead center (BDC). Then, a periodic time-varying observer is presented that provides an estimation of the internal state of the system. Based on the presented observer, an iterative learning control strategy is proposed to compensate the unknown offset. The effectiveness of the learning control scheme will be demonstrated with the simulation and experiment results conducted on a commercial car used engine with six cylinders.


Fuel Injection Iterative Learning Control Fuel Mass Fuel Ratio Exhaust Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank Mr. A. Ohata, Mr. J. Kako, Mr. K. Sata of Toyota Motor Corporation, Japan, for the creative discussion on the research and to thank Dr. J. Zhang and Mr. Y. Oguri, Sophia University, for their help in conducting the experiments.


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Tomohiro Hara
    • 1
  • Tielong Shen
    • 1
  • Yasuhiko Mutoh
    • 1
  • Yinhua Liu
    • 1
  1. 1.Department of Engineering and Applied SciencesSophia UniversityTokyoJapan

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