Real-Time Performance of DAE and ODE Based Estimators Evaluated on a Diesel Engine
omputation and sampling time requirements for real-time implementation
of observers is studied. A common procedure for state estimation and
observer design is to have a system model in continuous time that is
converted to sampled time with Euler forward method and then the
observer is designed and implemented in sampled time in the real time
system. When considering state estimation in real time control systems
for production there are often limited computational resources. This
becomes especially apparent when designing observers for stiff systems
since the discretized implementation requires small step lengths to
ensure stability. One way to reduce the computational burden, is to
reduce the model stiffness by approximating the fast dynamics with
instantaneous relations, transforming an ODE model into a DAE
model. Performance and sampling frequency limitations for
EKF’s based on both the original ODE model and the reduced DAE
model is here analyzed and compared for an industrial
system. Furthermore, the effect of using backward Euler instead of
forward Euler when discretizing the continuous time model is also
analyzed. The ideas are evaluated using measurement data from a diesel
engine. The engine is equipped with throttle, EGR, and VGT and the
stiff model dynamics arise as a consequence of the throttle between
two control volumes in the air intake system. The process of
simplifying and modifying the stiff ODE model to a DAE model is also
discussed. The analysis of the computational effort shows that even
though the ODE, for each time-update, is less computationally
demanding than the resulting DAE, an EKF based on the DAE model
achieves better estimation performance than one based on the ODE with
less computational effort. The main gain with the DAE based EKF is
that it allows increased step lengths without degrading the estimation
performance compared to the ODE based EKF.
Erik Höckerdal, Erik Frisk and Lars Eriksson
Science China Information Sciences,
2018
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Last updated: 2021-11-10
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