Lowering Orders of Derivatives in Non-linear Residual Generation using Realization Theory
Consistency relations are often used to design residual generators
based on non-linear process models. A main difficulty is that they
generally include time differentiated versions of known signals which
are difficult to estimate in a noisy environment. The main results of
this paper show how to lower the need to estimate derivatives of known
signals in order to compute a residual. Necessary and sufficient
conditions for lowering the order of the derivatives one step are
presented and a main step in the approach is to obtain a state-space
realization of the residual generator. An attractive feature of the
approach is that general differential algebraic system descriptions
can be handled in the same way as for example ordinary differential
equations and also that stability of the residual generator is always
guaranteed.
Erik Frisk and Jan Åslund
Automatica,
2005
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