Actuator fault detection and interval
reconstruction based on interval observers
⋆
Shenghui Guo
1,2
Fanglai Zhu
1
1. College of Electronics and Information Engineering, Tongji
University, Shanghai 201804 China. (e-mail:
zhufanglai@tongji.edu.cn)
2. College of Electronics and Information Engineering, Suzhou
University of Science and Technology, Suzhou 215009 China. (e-mail:
12gsh@tongji.edu.cn).
Abstract: This paper presents an actuator fault detection and interval reconstruction scheme
based on interval observers for systems with both actuator faults and disturbances. To begin
with, two full-order interval observers which are sensitive to actuator faults are designed to
achieve the goal of actuator fault detection. Then, two reduced-order interval observers are
constructed, and they are robust to the actuator faults in that the interval observer constructions
are fulfilled without using the boundary information of the actuator faults. An interval actuator
fault reconstruction method is developed based on the reduced-order interval observers. Finally,
the validities of the prop osed methods are verified by a numerical simulation example.
Keywords: estimation theory; discrete-time system; fault detection and isolation; interval fault
reconstruction
1. INTRODUCTION
Fault detection and isolation (FDI), which is very imp or-
tant in improving the performances (stability, reliability,
etc.) of control systems when they are subjected to various
faults, has been received increasing attention in the past
decades. And many significant model-based FDI methods
including observer-based FDI, filter-based FDI, parameter
estimation, and parity space etc. have been developed.
Among these model-based FDI methods, observer-based
FDI has become one of the most effective ones and many
results have been reported in the literature (Chen and
Patton (2012); Edwards et al. (2000); Frank (1990); Jiang
et al. (2004); Kulcsar and Verhaegen (2012); Gao et al.
(2015); Wang et al. (2014); Zhang et al. (2012); Zhang and
Jaimoukha (2014); Zhu and Yang (2013), and references
therein). For the fault detection (FD) purpose, an observer
which is robust to model uncertainties and/or external
disturbances but sensitive to faults should be constructed
as fault detector. And then a residual is designed based
on the measured outputs of the original system and the
observer. One can tell whether a fault occurs or not by
observing the residual. Although the residual-based FD
techniques can alarm us the occurrence of the actuator
faults, it cannot tell us some more information about fault-
s, such as how many actuators being with faults and which
one being with faults. For this reason, fault isolation (FI)
technique is needed. Since fault reconstruction method can
not only tell us the location but also the exact value or even
the dynamic behavior of a fault, it has been one of the
most powerful FI techniques, and of course, has attracted
⋆
This work was supported by the National Natural Sci-
ence Foundation of China (61573256). Corresponding author: F.
Zhu(zhufanglai@tongji.edu.cn)
much more attention than residual-based FD technique
(Edwards et al. (2000); Zhang and Jaimoukha (2014); Zhu
and Yang (2013), and references therein). Although many
significant methods of FDI based on traditional observer
have been developed and they show many advantages, they
also have some disadvantages which need to be addressed.
Some methods are proposed under some very restrictive
assumptions, for example, the so-called observer matching
condition.
Recently, a special kind of observer named interval ob-
server has become a p opular observer design method for
the systems with unknown inputs (mode uncertainties,
external disturbances and actuator faults) (Gouz´e et al.
(2000); Bernard and Gouz´e (2004)). Different from the
classical observer, the interval observer is constructed only
to produce both upper and lower boundaries (denoted
as x
+
(t) and x
−
(t), respectively) of the system states
x(t) rather than asymptotical estimations. That is, for
∀t ≥ 0 , the state estimations of an interval observer
are x
+
(t) and x
−
(t) which satisfy x
−
(t) ≤ x(t) ≤ x
+
(t).
Compared with the traditional observer design, construct-
ing an interval observer becomes much more convenient,
for much information about the unknown inputs or/and
the nonlinear terms, such as the condition of Lipschitz
(Wang et al. (2014); Zhu and Yang (2013)), which is cru-
cial in traditional observer design, can be ignored (Wang
et al. (2015)). Now, interval observer design has become
a hot research topic recently, and many methods have
been proposed (Efimov et al. (2012, 2013b,a); Mazenc
and Bernard (2011); Mazenc et al. (2014); Moisan et al.
(2009); Moisan and Bernard (2010); Ra¨ıssi et al. (2012);
Zheng et al. (2016b,a)) . Unlike FDI based on tradition-
al observer, to the best of our knowledge, only a few
researchers have investigated interval-observer-based-FD
Preprints of the 20th World Congress
The International Federation of Automatic Control
Toulouse, France, July 9-14, 2017
Copyright by the
International Federation of Automatic Control (IFAC)
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