A parameter-varying filtered PID strategy for air-fuel ratio control of spark ignition engines

Behrouz Ebrahimi, Reza Tafreshi, Houshang Masudi, Matthew Franchek, Javad Mohammadpour, Karolos Grigoriadis

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


In this paper, a new synthesis method is presented to control air-fuel ratio (AFR) in spark ignition engines to maximize the fuel economy while minimizing exhaust emissions. The major challenge in the control of AFR is the time-varying delay in the control loop which restricts the application of conventional control techniques. In this paper, the time-varying delay in the system dynamics is first approximated by Padé approximation to render the system dynamics into non-minimum phase characteristics with time-varying parameters. Application of parameter-varying dynamic compensators is invoked to retrieve unstable internal dynamics. The associated error dynamics is then utilized to construct a filtered PID controller combined with a parameter-varying dynamic compensator to track the desired AFR command using the feedback from the universal exhaust gas oxygen sensor. The proposed method achieves desired dynamic properties independent of the matched disturbances. It also accommodates the unmatched perturbations due to the dynamic compensator features. The results of applying the proposed method to experimental numerical data demonstrate the closed-loop system stability and performance against time-varying delay, canister purge disturbances and measurement noise for both port fuel injection engines and lean-burn engines.

Original languageEnglish (US)
Pages (from-to)805-815
Number of pages11
JournalControl Engineering Practice
Issue number8
StatePublished - Aug 2012


  • AFR control
  • Dynamic compensator
  • Non-minimum phase system
  • Spark ignition engine
  • Time-varying delay

ASJC Scopus subject areas

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


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