The theory and application of double window exact state observer for detection of abrupt changes in parameters of continuous systems

Jędrzej Byrski and Witold Byrski


fault detection and diagnosis, exact state observer, parameter abrupt changes, linear continuous systems, parameter identification


In this paper the special structure of double moving window state observer for detection of rapid changes in parameters in continuous system is presented. As the state observer it was not applied an asymptotic estimator (like Kalman Filter) but integral observer which can reconstruct the exact value of the state vector using input/output measurements on finite time interval window. The quite new concept presented in this paper is that the observer uses double moving window in time domain. It means that it consists of two windows coupled each other with common edge. The right hand side edge of the left window in interval [t-2T, t-T] is connected to the left hand side edge of right window which operates in the interval [t-T, t]. The double observer operates in both windows with different measurements of input/output signals and simultaneously reconstructs the final value of the state in the left window zT(t-T) and the initial value of the state z0(t-T) in the right window. If the system parameters are constant and known the values of the both states are the same zT(t-T)= z0(t-T). If in the system abrupt changes (faults) of parameters at the moment (tA=t-T) occur then step changes in some elements of the state vector will happen and zT(t-T)≠z0(t-T) will be detected. It will enable localization of faulty parameter in cascade structure of the system.

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