### Optimal Control of Heat Transfer Rates in Turbochargers

The turbocharger is an important component of competitive environmentally
friendly vehicles. Mathematical models are needed for controlling turbochargers
in modern vehicles. The models are parameterized using data, gathered from
turbocharger testing in gas stands (a flow bench for turbocharger, where the engine
is replaced with a combustion chamber, so that the exhaust gases going to
the turbocharger can be controlled with high accuracy). Collecting the necessary
time averaged data is a time consuming process. It can take more than 24 hours
per turbocharger. To achieve a sufficient level of accuracy in the measurements,
it is required to let the turbocharger system reach steady state after a change of
operating point. The turbocharger material temperatures are especially slow to
reach steady state.
A hypothesis is that modern methods in control theory, such as numeric optimal
control, can drastically reduce the wait time when changing operating point.
The purpose of this thesis is to provide a method of time optimal testing of turbochargers.
Models for the turbine, bearing house and compressor are parameterized.
Well known models for heat transfer is used to describe the heat flows to and
from exhaust gas and charge air, and turbocharger material, as well as internal
energy flows between the turbocharger components. The models, mechanical
and thermodynamic, are joined to form a complete turbocharger model, which is
validated against measured step responses.
Numeric optimal control is used to calculate optimal trajectories for the turbocharger
input signals, so that steady state is reached as quickly as possible, for
a given operating point. Direct collocation is a method where the optimal control
problem is discretized, and a non-linear program solver is used. The results show
that the wait time between operating points can be reduced by a factor of 23.
When optimal trajectories between operating points can be found, the possibility
of further gains, if finding an optimal sequence of trajectories, are investigated.
The problem is equivalent to the open traveling salesman, a well studied
problem, where no optimal solution can be guaranteed. A near optimal solution
is found using a genetic algorithm.
The developed method requires a turbocharger model to calculate input trajectories.
The testing is done to acquire data, so that a model can be created,
which is a catch-22 situation. It can be avoided by using system identification
techniques. When the gas stand is warming up, the necessary model parameters
are estimated, using no prior knowledge of the turbocharger.

*Max Johansson*

**2018**

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Last updated: 2021-11-10