<abstract xmlns="http://www.w3.org/1999/xhtml">The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width <italic>T</italic>. These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [<italic>t −</italic> 2<italic>T, t − T</italic> ] is connected to the left-hand side edge of the right-side window which operates in the interval [<italic>t − T, t</italic>]. The double observer uses different measurements of input/output signals in both the windows, and for each current time <italic>t</italic> simultaneously reconstructs two values of the state—the final value of the state in the left-side window <italic>zT</italic> (<italic>t − T</italic>) and the initial value of the state <italic>z</italic>0(<italic>t − T</italic>) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment <italic>tA</italic> = <italic>t − T</italic> occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.</abstract>

The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T. These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [t − 2T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [t − T, t]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the state—the final value of the state in the left-side window zT (t − T) and the initial value of the state z0(t − T) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment tA = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.

A double window state observer for detection and isolation of abrupt changes in parameters

Department of Applied Computer Science, AGH University of Science and Technology, ul. Mickiewicza 30, 30-059 Kraków,

Department of Automatics and Biomedical Engineering, AGH University of Science and Technology, ul. Mickiewicza 30, 30-059 Kraków,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear...

A double window state observer for detection and isolation of abrupt changes in parameters

Published Online: Sep 29, 2016

Page range: 585 - 602

Received: Jun 18, 2015

Accepted: Apr 26, 2016

DOI: https://doi.org/10.1515/amcs-2016-0041

Keywords
fault detection and isolation, exact state observer, parameter abrupt changes, derivative reconstruction, linear continuous systems

© 2016 Jędrzej Byrski et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A double window state observer for detection and isolation of abrupt changes in parameters

Published Online: Sep 29, 2016

Page range: 585 - 602

Received: Jun 18, 2015

Accepted: Apr 26, 2016

DOI: https://doi.org/10.1515/amcs-2016-0041

Keywordsfault detection and isolation, exact state observer, parameter abrupt changes, derivative reconstruction, linear continuous systems

© 2016 Jędrzej Byrski et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
fault detection and isolation, exact state observer, parameter abrupt changes, derivative reconstruction, linear continuous systems