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View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by VBN Aalborg Universitet Active Fault Diagnosis by Controller Modification Stoustrup, Jakob; Niemann, Henrik Published in: International Journal of Systems Science DOI (link to publication from Publisher): 10.1080/00207720903470197 Publication date: 2010 Document Version Early version, also known as pre-print Link to publication from Aalborg University Citation for published version (APA): Stoustrup, J., & Niemann, H. (2010). Active Fault Diagnosis by Controller Modification. International Journal of Systems Science, 41(8), 925-936. https://doi.org/10.1080/00207720903470197 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research. ? You may not further distribute the material or use it for any profit-making activity or commercial gain ? You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us at [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from vbn.aau.dk on: November 29, 2020 International Journal of Systems Science 2010, 1–12, iFirst Special Issue on Fault Diagnosis and Fault Tolerant Control Active fault diagnosis by controller modification Jakob Stoustrupa* and Henrik Niemannb aDepartment of Electronic Systems, Automation & Control, Aalborg University, Fr. Bajers Vej 7C, DK-9220, Aalborg, Denmark; bDepartment of Electrical Engineering, Automation and Control, Technical University of Denmark, Elektrovej, Building 326, 2800 Kgs. Lyngby, Denmark (Received 4 December 2008; final version received 8 October 2009) Two active fault diagnosis methods for additive or parametric faults are proposed. Both methods are based on controller reconfiguration rather than on requiring an exogenous excitation signal, as it is otherwise common in active fault diagnosis. For the first method, it is assumed that the system considered is controlled by an observer-based controller. The method is then based on a number of alternate observers, each designed to be sensitive to one or more additive faults. Periodically, the observer part of the controller is changed into the sequence of fault sensitive observers. This is done in a way that guarantees the continuity of transition and global stability using a recent result on observer parameterization. An illustrative example inspired by a field study of a drag racing vehicle is given. For the second method, an active fault diagnosis method for parametric faults is proposed. The method periodically adds a term to the controller that for a short period of time renders the system unstable if a fault has occurred, which facilitates rapid fault detection. An illustrative example is given. Keywords: active fault detection; parametric faults; observer parameterisation 1. Introduction temporarily change the observer into one, which has The task of designing a fault diagnosis system shares a been tuned to be maximally sensitive to one or more number of challenges with that of performing a system specific faults. This procedure is then repeated identification, where the notion of persistent excitation cyclically for all faults that should be detected. is crucial to obtain a high quality model. Similarly, if a The assumption of an observer-based controller is detection approach is based on a ‘passive’ approach, without loss of generality, as any linear controller can i.e. only by logging the unmodified inputs and outputs, be (re-) written as an observer-based controller, pos- faults can easily remain undetected, particularly if they sibly extended by a Youla-Kucera parameter. are parametric and reside in a part of the system, which The proposed method can be used as an on-line is never excited. Stoustrup and Niemann (1999) algorithm, provided that emphasising the faults is presents an approach to fault diagnosis for systems acceptable. Otherwise, the method can be used off-line, Downloaded By: [Aalborg University] At: 08:18 8 March 2010 with parametric faults. meaning that the system is in a test mode (see below). To that end, recently there has been significant Along the same lines we will also propose a more attention to the so-called active fault diagnosis methods, radical approach in this article. Rather than just (see e.g. Nikoukhah (1998); Nikoukhah, Campbell, and detuning the controller a bit to make it more sensitive Delebecque (2000); Campbell, Nikoukhah, and Horton to faults, in this more aggressive approach an additional (2002); Campbell and Nikoukhah (2004); Niemann and term is added to the controller, intended to destabilise Poulsen (2005); Niemann (2006) and references the system temporarily in the presence of a parametric therein). In the active fault diagnosis methods, it is fault. The rationale for this is that if the system becomes assumed to be admissible to superimpose the control unstable, this will be apparent very quickly, no matter input with a dedicated fault diagnosis signal, which is how much noise is present. Once the instability, and designed to excite the faults in such a way that they hence the fault has been detected, of course the become better discernible at the output. destabilising controller part will be removed at once. In this article, two other approaches are suggested Destabilising the system is inadmissible for many to make indiscernible faults temporarily visible without systems. Examples of systems where the method could having to add an external excitation signal. be applied is to discover short-circuits in electrical The first approach proposed embarks from an motors, where it might be admissible to let the observer-based controller. The main idea is then to magnetising currents increase shortly; a blocked air *Corresponding author. Email: [email protected] ISSN 0020–7721 print/ISSN 1464–5319 online ß 2010 Taylor & Francis DOI: 10.1080/00207720903470197 http://www.informaworld.com 2 J. Stoustrup and H. Niemann passage in a supermarket refrigeration system, where it where u 2Rnu is the control input signal vector, x 2Rnx could be admissible to let the air temperature drop is the state vector of the system, and y 2Rny is the or increase for a few minutes; or a clogging in a measurement vector, d 2Rnd is a vector of external fermentation process, where a mass-flow can be disturbances and f 2Rnf is the vector of potential allowed to change for some while. additive fault signals. The auxiliary signal pair w 2Rnw Another approach for the latter method is to apply and z 2Rnz is introduced in order to model parametric the method as an off-line fault diagnosis approach. It faults or faults of parasitic dynamics, which can in will be possible in many cases to do a fault diagnosis on either case be done by closing a loop by an artificial the system when it is out of work. This example can be feedback of the form in connection with the service of the system. It will then be possible to do the fault diagnosis in a controlled w ¼ Dz, ð2Þ environment. In some cases, it will be possible to place where D represents the parametric faults in the system, the system in a test bench. It is clear that this off-line or parasitic dynamics. approach can only be applied on systems with slowly The feedback interconnection model of the system varying parametric faults. presented in (1) and (2) is based on the so-called The rest of this article is organised as follows. standard model which is extensively used in robust A problem formulation is given in Section 2. Section 3 control (see e.g. Zhou, Doyle, and Glover (1995)). It is includes some preliminary results. The main results are well-known that a model structure of this type can be given in Section 4 and two illustrative examples are employed to represent parametric faults that can be given in Section 5. This article is closed with a modelled as parametric variations of the individual conclusion in Section 6. parameters in a state space model, where the param- eters depend functionally on the faults as rational functions (of several variables). For non-rational 2. Problem formulation functional dependency (e.g. log, sin, ...,), it can be exploited that all differentiable functions can be As mentioned above, in this article we shall propose approximated arbitrarily well by rational functions. two methods for active fault diagnosis based on Based on this general model, we shall address the controller reconfiguration. In the first problem formu- following two design issues. lation, we shall seek to design the controller reconfi- guration in order to sensitise the controller to a number of fault signals. In the second and more radical approach, we shall design the controller 2.1. Controller reconfiguration for fault sensitization reconfiguration in order to destabilise the system temporarily in the presence of a fault. We assume that the system (1) is controlled by a In the sequel, we will consider a fault to be a full-order observer-based controller given by Downloaded By: [Aalborg University] At: 08:18 8 March 2010 phenomenon which causes a system to exhibit an _ x^ ¼ Ax^ þ Bu þ L0ð y À Cx^Þ, abnormal and/or undesired behaviour. A fault signal is a signal that models the effect of a fault as a signal u ¼ Fx^, introduced in a differential equation or difference where x^ 2Rn is the estimate of the state vector, equation model of the nominal system. An additive pÂn L0 2R is an observer gain for which A þ L0C is fault is defined as a fault which can be modelled as Hurwitz and F 2RmÂn is a feedback gain for which introducing an additional additive term in the differ- A þ BF is Hurwitz.

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