Diesel engine indicated and load torque estimation using a non-linear observer

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This paper presents a non-linear observer to estimate the indicated torque and the load torque of a single-cylinder diesel engine from crankshaft and coupling angular velocity measurements. Since these variables can be measured using low-cost sensors, the observer may be useful in the implementation of the control or diagnostics strategies that require cylinder indicated torque and load torque, variables that are not easily measured and need expensive sensors. The observer operates in the crank angle domain and is based on a nonlinear dynamic engine model that includes an instantaneous friction model. The effects of inertia variations of the crankshaft assembly with piston pin offset are also included, which significantly increases the accuracy of the pressure estimation at high speeds. Strong chattering is avoided by modifying the sliding gain as a non-linear function of the crank angle. The stability of the observer is proved, and simulation results of the engine indicated torque and load torque are presented, which indicate good agreement with experimental data.

Original languageBritish English
Pages (from-to)775-785
Number of pages11
JournalProceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering
Issue number6
StatePublished - 2006


  • Diesel engine modelling
  • Dynamic modelling
  • Engine diagnostics
  • Non-linear observers
  • Simulation


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