Identification of linear parameter-varying engine models

The real-time identification and monitoring of automotive engines has posed many challenging problems. The difficulties are mainly due to the nonlinearity of the engine dynamics due to changes in the engine operating conditions. Various recent studies have demonstrated that many of the powertrain subsystems are well approximated as linear parameter-varying (LPV) systems that are described as time-invariant linear systems with feedback multiplied by operating condition dependent parameters that can be measured or otherwise obtained in real time. The LPV structure has linear dynamics at a fixed operating condition, and has been shown to incorporate much of the known governing laws of physics directly into the structure of the dynamic model. Previously available LPV system identification methods are problematic, being iterative or involving an exponentially growing number of terms that can result in low accuracy models. A recently developed subspace method [Larimore(2013a)] avoids these difficulties giving efficient solutions on larger scale problems using well understood linear time-invariant subspace methods. An added benefit is the rigorous determination of the state order of the process that can be valuable for controller implementation. The identification of engine subsystem models in LPV form has the advantages of greatly improved accuracy, greatly reduced data requirements, and dramatic abilities to extrapolate to conditions not contained in the model fitting data. Use of accurate LPV models in other fields has led to the design of global controllers having guaranteed global stability and margin with improved performance, and monitoring methods to detect changes and faults under operating conditions not previously encountered. Potential issues are significant non-linearities of some engine models that may require the use of recently developed Quasi-LPV subspace methods. Also, to achieve the potential high identification accuracy may require the use of quadruple precision computation for SVD of very large matrices, that is starting to be practical for real-time engine model identification.