The control problem of (heavy-duty diesel) engines consists of meeting the driver's torque request,
while minimizing fuel consumption and staying within emission legislation constraints. With the
introduction of cylinder pressure sensors, it becomes possible to control the combustion process using
closed-loop control, which enables advanced combustion concepts, improves transient performance
and is more robust to uncertainties. The cylinder pressure sensors necessary for this approach are
relatively expensive and not yet in mass-production for heavy-duty diesel applications. At TNO, a
virtual cylinder pressure sensor concept has been developed in which only one cylinder pressure sensor is
used and the other cylinder pressures are estimated by using the crankshaft position signal. A dynamic
model of the crankshaft and piston system, that provides the relation between cylinder pressures and
angular velocity, plays a crucial role in this algorithm and is developed within this internship project.
Several dynamic crankshaft models can be found in literature. They are either used for structural
design , combustion phasing estimation  or indication of cylinder health . The work presented
in this report is aimed for application in an on-line estimation of heavy-duty diesel cylinder pressure.
The presented model does use six cylinder pressure signals as input and provides the angular velocity
at the location of the position encoder as output. The crankshaft model consists of nine bodies; six of
them represent the cylinders, including a crank-slider mechanism and static friction model. The rear
of the crankshaft is supplemented with a ywheel body, which also contains an amount of lumped
mass due to components connected to it. The front of the crankshaft is supplemented with a torsional
damper and front pulley body. All bodies are interconnected by springs and dampers, which represent
the stiness and damping of the material.
A parameter identication is performed using the least squares error tting algorithm lsqnonlin
of the MATLAB Optimization Toolbox. High-accuracy measurement data of cylinder pressures and
angular velocity were measured at TNO and used for identication. After identifying appropriate
values for the parameters of the model, the model is analyzed in terms of accuracy, complexity and
sensitivity. For nine operating points throughout the operating region of the engine, the average RMS
velocity output error is about 0.5 rad/s (0.3%) and the model performs well in predicting the velocity
waveform. After evaluating multiple model extensions and their performance, the presented model is
considered as a good compromise between complexity, performance and robustness.
Two candidates for model simplication are proposed. The rst proposal is using a constant mass
matrix in the equations of motions, and is shown to be feasible in terms of model output. The second
proposal is a simplied friction modeling in which the instantaneous friction torque is replaced by
a constant average friction torque. This reduces the amount of parameters to be identied at each
operating point. The proposal might be feasible, but should be evaluated using a dedicated parameter
identication. Reducing the crankshaft model to a single rigid-body, which is commonly the approach
for light-duty engines, is shown to be an invalid approach for heavy-duty engines.
A model describing the dynamic behavior of a heavy-duty diesel engine has become available as a
result of this work. Since this control oriented model was required for the next step in the development
and validation of the virtual cylinder pressure sensor concept, this algorithm might now actually prove
itself on real engine data. The virtual sensor will make implementation of closed-loop combustion
control much more attractive and will contribute to cleaner and more fuel ecient vehicles.