_fault diagnosis and fault tolerant control of nonlinear systems
TRANSCRIPT
Fault Diagnosis and Fault Tolerant Control of Nonlinear Systems
Liu Yutian， Li Changgang，Hu Junjie Department of Electronic and Information Engineering
Zhejiang Wanli University Ningbo, Zhejiang Province, China
Abstract - A survey of fault diagnosis and fault tolerant control techniques for nonlinear systems is presented. Firstly, the model of general nonlinear systems is introduced. Some main features of fault diagnosis and fault tolerant control of nonlinear systems are analyzed. Based on these, some main approaches for fault diagnosis and fault tolerant control of nonlinear systems, including sliding mode observer based fault detection approach, unknown input observer based fault diagnosis approach, nonlinear observer based fault tolerant control approach, based robust fault tolerant control, and so on. Finally, the main challenges, difficulties and some future development trends for the field are pointed out.
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Index Terms - nonlinear systems; fault diagnosis; fault tolerant control; robustness;
1 INTRODUCTION
The research on nonlinear systems and fault diagnosis have gain some important achievement, but the inherence complexity in nonlinear systems results in slow research development of fault diagnosis of nonlinear systems. Since the nonlinear systems theory is not yet perfect, most of the research work is focus on a special class of nonlinear systems.
Many methods of fault diagnosis and fault tolerant control of nonlinear systems have been developed in the past decades. As shown in [4-7], sliding mode observer based fault diagnosis method utilized a group of sliding mode observers to generate residuals used to indicate different faults. In [8] and [9], unknown input observers are constructed to detect and isolate faults. In [10] and [11], nonlinear observer based fault tolerant control method are extensively used in a class of nonlinear systems. In [12] and [13], based robust fault tolerant control is discussed. Some other methods can be seen in [14-19].
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Since the safety and reliability of nonlinear systems are paid more and more attention, many approaches for fault diagnosis and fault tolerant control of nonlinear systems have been developed. This paper presents a survey of fault diagnosis and fault tolerant control of nonlinear.
The remainder of the paper is organized as follows. In section 2, we briefly introduce the model and the main features
This work is partially supported by the Ningbo NSF Grant #2009A610106 to Liu Yutian
of general nonlinear systems. In section 3, we discuss main methods of fault diagnosis and fault tolerant control of nonlinear systems, including sliding mode observer based fault detection approach, unknown input observer based fault diagnosis approach, nonlinear observer based fault tolerant control approach, based robust fault tolerant control, and so on. In section 4 and 5, the main challenges, difficulties and some future development trends for the field are point out.
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2 MODEL AND CHARACTERISTICS OF NONLINEAR SYSTEM
2.1 Model of nonlinear system A general nonlinear system can be presented as follows
[20].
⎩⎨⎧
==
),,,(),,,(
s
s
fduxhyfduxfx&
(1)
Here, denotes the states of the system, where n is the dimension of the state vector. denotes the output of the system, is the dimension of the output vector.
denotes the control signals. d denotes disturbance. represents faults. represents nonlinear functions.
nRx∈mRy∈
mrRu∈
sf )(⋅f
The fault diagnosis system of the nonlinear system (1) is
given in Equation (2).
⎩⎨⎧
==
),,(),,(
uyzbruyzaz&
(2)
Here, denotes the assistant states.z r denotes the
residual signal for fault diagnosis. In the ideal condition,
r should meet the following points:
(1) There is no fault, that is , then 0)( =tf s 0)( =tr .
(2) One fault happened, that is , then 0)( ≠tf s 0)( ≠tr .
(3) The ith fault happened, that is 0)( ≠tf si , then
0)( ≠tri .
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2.2 Features of fault diagnosis and fault tolerant control of nonlinear systems
Nonlinear systems have some distinct features, such as nonlinear, complexity, uncertainty and so on. All these determine that fault diagnosis and fault tolerant control of nonlinear systems have the following features: robustness, little prior knowledge, huge fault space and so on.
Robustness: Nonlinear systems suffer from complex uncertainties, including model uncertainty, parameter perturbation, external disturbance. These require, the fault diagnosis and fault tolerant system must be robust to all the uncertainties.
Little prior knowledge: Since most of the research work of nonlinear systems is focus on a special class of nonlinear systems, the research work of fault diagnosis also just aim at the special systems. There is little prior knowledge for fault diagnosis of general nonlinear systems.
Huge fault space: There is coupling relationship between each component of nonlinear systems. Once one component failed, it may cause the fault of other components. In this way, the fault space is huge.
Misdiagnosis and miss diagnosis: At the present time, most of the fault diagnosis methods can not totally identify and isolate all faults. Sometimes, it will treat a fault state as a disturbance, or treat a disturbance as a fault state.
3 MAIN METHODS FOR FAULT DIAGNOSIS AND FAULT TOLERANT CONTROL OF NONLINEAR SYSTEM
3.1 main methods for fault diagnosis
3.1.1 Sliding mode observer based method The progress has been made in the application of sliding
mode in nonlinear systems. In some condition, sliding mode observer has more invariability than robustness in uncertainty of fault and parameter variation. So the sliding mode observer based methods are widely used in fault diagnosis of nonlinear systems. Rajiv Sreedhar [16] took the leading in applying sliding mode observers in fault detecting. Edwards [6] have also done some work in the application of sliding mode observers. The main process of the method can be presented as follows. Firstly, before the faults happened, keep the existence of the sliding mode. Based on this, detect if the residual signals are in the specified region given by sliding mode, and judge if the fault happened. When the systems don’t satisfy the condition, it means the sliding mode is broken, and a fault is happened. The details are presented as follows. The (3) presents a special nonlinear system.
⎩⎨⎧
+=+++=
sGfCxytuxDdButuxfAxx ),,(),,(&
(3)
Here, denotes the uncertain disturbance or
unknown disturbance. denotes faults.
),,( tuxd
sf yyey −= ˆ
denotes the error of output. The sliding mode observer is given as (4).
⎩⎨⎧
=−++++=
xCyyyLDvButuxfxAx
ˆˆ)ˆ(),,ˆ(ˆ&̂
(4)
Here, is given by sliding mode, presented as follows. v
⎪⎪⎩
⎪⎪⎨
⎧
≤
>−=
εε
ρ
ερ
yy
yy
y
eifFe
eifFe
Fe
v (5)
Here, ε denotes the width of boundary layers. ρ is a constant.
The principle sliding method observer based fault diagnosis method is presented as follows. Given the residual signal, sy Gfcetr −=)(
(1) If 0=sf , that is, there is no fault, then, ε≤ye .
(2) If 0≠sf , that is, there is a fault, then ε>ye .
Then, by estimating if the residual signal is in the width of boundary layers, the method presented can detect if the fault happened.
3.1.2 Volterra model based fault diagnosis method Because the Volterra series model can completely
describe the transfer characteristics of the nonlinear systems, it can be utilized in the fault diagnosis of a nonlinear system. During the system working, the faults can be recognized by analyzing the change of the nonlinear factors in the Volterra models, which are respectively built before and after the faults happen.
In [21], Jiao L C presents the application of Volterra series in fault diagnosis in 1988. Han C Z, et al, makes an in-depth research, and achieves some prominent results. In abroad, there is no researcher do the same work.
3.1.3 Other methods for fault diagnosis In [2], Chen M Y develops a new diagnosis method
based on the unknown input observers and the concept of equivalent control. In [8], the likelihood function of particle filter is redefined, and sliding-window particle filter algorithm is proposed to obtain the initial estimation of the fault amplitude. In [15], a new fault detection method of nonlinear systems is proposed based on summed kernel independent component analysis. Some other fault diagnosis methods can be seen in [16-19].
3.2 Main methods for fault tolerant In general, the fault tolerant methods can be classified as
two ways. One is called passive fault tolerant control methods which use such as adaptive controller or robust controller with feedback control to accommodate faults. Another is called
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active fault tolerant control methods that reconfigure controllers or control laws based on fault detection and isolation and reconfigurable logic or switching logic.
3.2.1 Nonlinear observer based method Nonlinear observer based fault tolerant methods utilize
the nonlinear adaptive observers to estimate the amplitude of fault, then, use the fault information to restructure the control laws. Boskovic [10] develops a fault tolerant scheme based on the adaptive interacting multiple nonlinear observers. The scheme they proposed obtained robustness and excellent performance despite the simultaneous presence of actuator failure, control input saturation, bounded external disturbances, parametric uncertainty, and measurement noise. Kobore [11] presents a set of algorithms for fault diagnosis and fault tolerant control strategy for affine nonlinear systems subjected to an unknown time-varying fault vector.
3.2.2 based robust fault tolerant method ∞H
∞H based robust fault tolerant method not only consider the stability of nonlinear systems, but also the dynamic of the systems.
In [23], the reliable filtering problem against sensor failures for a class of continuous-time systems with simultaneous sector-bounded nonlinearities and varying time delay is concerned. In [24], a reliable robust fuzzy controller is designed for uncertain nonlinear continuous-time systems with Markovian jumping actuator faults. The Takagi and Sugeno fuzzy model is employed to represent an uncertain nonlinear system with Markovian jumping actuator faults.
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Other methods for fault tolerant control can be seen in [25-27].
4 SOME PROBLEM
The challenging problems of fault diagnosis and fault tolerant control of nonlinear systems include robustness, real time diagnosis, integration, and so on. a) Robustness
Nonlinear systems suffer from complex uncertainties, including model uncertainty, parameter perturbation, external disturbance. These require, on the one hand, the fault diagnosis system must be robust to minimize misdiagnosing and miss diagnosing, on the other hand, the fault tolerant control system must be robust, so that the system is still stable while the control law is being reconfigured. b) Real time diagnosis
Considering the coupling relationship between the components of real nonlinear systems, the fault space is huge. If the fault couldn’t be detected and diagnosed in time, it will lead to serious consequences. At present time, most methods of fault diagnosis for nonlinear systems can only deal with the special known fault of a special nonlinear system. How to respond to unknown faults quickly is the problem. c) Integration
On the on hand, the complexity of nonlinear systems determines that no one existing method can deal with all the problem of fault diagnosis. Different fault diagnosis methods should be integrated to improve the diagnosis efficacy. On the other hand, to improve the control performance of fault systems, it’s essential to consider fault diagnosis and fault tolerant control simultaneity, that is, integrate fault diagnosis and fault tolerant control.
5 FUTURE TRENDS AND CONCLUSION
The problems mentioned above in section 4 are essential for the research work of fault diagnosis and fault tolerant for nonlinear systems. The key point is technique integration, this includes but not limits to the following: a) Improving robust fault diagnosis method. This includes
how to distinguish disturbance and faults, how to keep the sensitivity to faults, how to diagnosis the faults quickly, and how to handle misdiagnosis and miss diagnosis.
b) Improving robust fault tolerant control technique. Artificial intelligence based active fault tolerant control method and observer based fault tolerant control method are the mainstream direction. Robust fault tolerant control for nonlinear uncertain time-delay systems has got extensive attention.
c) Integrated fault diagnosis method. Mathematical models, signal processing, and knowledge based fault diagnosis methods can be integrated to develop a new method to improve the performance of fault diagnosis.
d) Integrated fault diagnosis and fault tolerant control method. Fault diagnosis is the base of fault tolerant control. The development of fault tolerant control promotes the development of fault diagnosis. Patton [33]: Without this FDI role, the fault tolerant capability of control systems is limited. It has important significance to integrate fault diagnosis and fault tolerant control.
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