  A turbocharger plays an essential part in reducing emissions and increasing
the fuel efficiency of road vehicles. The pulsating flow of exhaust gases,
along with high heat exchange from the turbocharger casing, makes developing
control-oriented models difficult. Several researchers have used maps provided
by manufacturers to solve this problem. These maps often fail to incorporate
any heat transfer effects and are unsuitable for wide operating regions. Also,
with the availability of more and better sensor data, there is a need for a
method that can exploit this to obtain a better predictive model. Koopman
approaches rely on the observation that one can lift the nonlinear dynamics of
the turbine into an infinite-dimensional function space over which dynamics are
linear. The objective of this paper is to develop a model to predict the
transient and steady-state behavior of the turbine using the Koopman operator
which can be helpful for control design and analysis. Our approach is as
follows. We use experimental data from a Cummins heavy-duty diesel engine to
develop a turbine model using Extended Dynamic Mode Decomposition, which
approximates the action of the Koopman operator on a finite-dimensional
subspace of the space of observables. The results demonstrate superior
performance compared to a tuned nonlinear autoregressive network with an
exogenous input model widely used in the literature. The performance of these
two models is analyzed based on their ability to predict turbine transient and
steady-state behavior.
