Transient lean burn air-fuel ratio linear parameter-varying control using input shaping

Feng Zhang, Karolos M. Grigoriadis, Matthew A. Franchek, Imad H. Makki

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Transient air-fuel ratio control for lean burn engines is essential to achieve improved fuel economy and strict federal emission regulations. Unlike conventional Spark Ignition (SI) engines, lean burn engines are no longer operating in a narrow band around stoichiometric resulting in a very challenging air-fuel ratio tracking problem. An approach to combine an input shaping method together with Linear Parameter Varying (LPV) feedback control is proposed in this paper to solve the transient air-fuel ratio tracking problem. LPV air-fuel ratio control has been shown to regulate the air-fuel ratio at steady state engine operating conditions, reduce the variability of the closed-loop system, reject disturbance and guarantee robustness and stability in the presence of variable time delays. In this paper, an input shaping method is used to reduce the cost of feedback, and thereby enhance the air-fuel ratio tracking performance during engine transient operations. The prefilter is designed based on the closed-loop dynamics resulting from the LPV design. A systematic input shaping prefilter design process is developed. The designed prefilter successfully extends the closed-loop air-fuel ratio tracking bandwidth. Simulation results using Federal Test Procedure (FTP) drive cycle data are used to demonstrate the effectiveness of the input shaping prefilter. Moreover, the designed prefilter is structurally simple and computationally efficient.

Original languageEnglish (US)
Pages (from-to)318-326
Number of pages9
JournalInternational Journal of Modelling, Identification and Control
Issue number3
StatePublished - 2008


  • Air-fuel ratio control
  • Input shaping
  • Lean burn
  • Linear parameter varying control

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics
  • Modeling and Simulation


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