Vehicle Engine Torque Estimation via Unknown Input Observer and Adaptive Parameter Estimation

Jing Na, Anthony Chen, Guido Herrmann, Richard Burke, Christian Brace

Research output: Contribution to journalArticlepeer-review

113 Citations (SciVal)
350 Downloads (Pure)


This paper presents two torque estimation methods for vehicle engines: unknown input observer (UIO) and adaptive parameter estimation.We first propose a novel yet simple unknown input observer based on the crankshaft rotation dynamics only. For this purpose, an invariant manifold is derived by defining auxiliary variables in terms of first-order low-pass filters, where only one constant (filter coefficient) needs to be tuned. These filtered variables are used to calculate the estimated torque. Robustness of this UIO against sensor noise is studied and compared to two other estimators. On the other hand, since the engine torque dynamics can be formulated as a parameterized form with unknown time-varying parameters, we further present several adaptive laws for time-varying parameter estimation. The parameter estimation errors are derived to drive these adaptive laws and time-varying adaptive gains are introduced. The two proposed estimators only use the measured air mass flow rate and engine speed, and thus allow for improved computational efficiency. Both estimators are verified via a dynamic engine simulator built in a commercial software GT-Power, and also practically tested via experimental data collected in a dynamometer test-rig. Both simulations and practical tests show very encouraging results with small estimation errors even in the presence of sensor noise.

Original languageEnglish
Article number8010342
Pages (from-to)409-422
Number of pages14
JournalIEEE Transactions on Vehicular Technology
Issue number1
Early online date14 Aug 2017
Publication statusPublished - 1 Jan 2018


  • Engine torque estimation
  • Mean value engine model
  • Time-varying parameter estimation
  • Unknown input observer

ASJC Scopus subject areas

  • Automotive Engineering
  • Aerospace Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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