LiU startsida
Abstract |
Observer Design and Model Augmentation for Bias Compensation with Engine Applications
Control and diagnosis of complex systems demand accurate knowledge of
certain quantities to be able to control the system efficiently and
also to detect small errors. Physical sensors are expensive and some
quantities are hard or even impossible to measure with physical
sensors. This has made model-based estimation an attractive
alternative. Model-based estimators are sensitive to errors in the model and since
the model complexity needs to be kept low, the accuracy of the models
becomes limited. Further, modeling is hard and time consuming and it
is desirable to design robust estimators based on existing models.
An experimental investigation shows that the model deficiencies in
engine applications often are stationary errors while the dynamics of
the engine is well described by the model equations. This together
with fairly frequent appearance of sensor offsets have led to a demand
for systematic ways of handling stationary errors, also called bias,
in both models and sensors. In the thesis systematic design methods for reducing bias in
estimators are developed. The methods utilize a default model and
measurement data. In the first method, a low order description of the
model deficiencies is estimated from the default model and measurement
data, resulting in an automatic model augmentation. The idea is then
to use the augmented model for estimator design, yielding reduced
stationary estimation errors compared to an estimator based on the
default model. Three main results are: a characterization of possible
model augmentations from observability perspectives, an analysis of
what augmentations that are possible to estimate from measurement data,
and a robustness analysis with respect to noise and model uncertainty. An important step is how the bias is modeled, and two ways of
describing the bias are introduced. The first is a random walk and the
second is a parameterization of the bias. The latter can be viewed as
an extension of the first and utilizes a parameterized function that
describes the bias as a function of the operating point of the
system. The parameters, rather than the bias, are now modeled as
random walks, which eliminates the trade-off between noise suppression
in the parameter convergence and rapid change of the offset in
transients. This is achieved by storing information about the bias in
different operating points. A direct application for the parameterized
bias is the adaptation algorithms that are commonly used in engine
control systems. The methods are applied to measurement data from a heavy duty diesel
engine. A first order model augmentation is found for a third order
model and by modeling the bias as a random walk, an estimation error
reduction of 50\,\% is achieved for a European transient cycle. By
instead letting a parameterized function describe the bias, simulation
results indicate similar, or better, improvements and increased
robustness.
Erik Höckerdal
2008
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Last updated: 2021-11-10
