research article active fault tolerant control based on ...active fault tolerant control based on...

Research ArticleActive Fault Tolerant Control Based on Bond Graph Approach

Manel Allous1 and Nadia Zanzouri1,2

1 Department of Electrical Engineering, LACS Laboratory, National Engineering School of Tunis,Université de Tunis El Manar, P.O. Box 37, Le Belvedere, 1002 Tunis, Tunisia

2 Preparatory Engineering Institute of Tunis 2, Université de Tunis, Rue Jawaher Lel Nahrou-Monfleury, 1089 Tunis, Tunisia

Correspondence should be addressed to Manel Allous; [email protected]

Received 30 April 2014; Revised 21 September 2014; Accepted 21 September 2014; Published 10 November 2014

Academic Editor: Gorazd Stumberger

Copyright © 2014 M. Allous and N. Zanzouri. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

This paper proposes a structural fault recoverability analysis using the bond graph (BG) approach. Indeed, this tool enablesstructural analysis for diagnosis and fault tolerant control (FTC). For the FTC, we propose an approach based on the inverse controlusing the inverse BG. The fault tolerant control method is also compared with another approach. Finally, simulation results arepresented to show the performance of the proposed approach.

1. Introduction

Due to the growing complexity of the dynamical systems,there is an increasing demand for safe operation, faultdiagnosis (FDI) (fault detection and isolation), and faulttolerant control (FTC) (strategies for control redesign). Dif-ferent approaches have been developed for the designingand the implementation of FDI and FTC procedures [1].These techniques are based on the knowledge of the systemmodel (model-based methods) [2, 3] or its structure (data-based methods) [4, 5]. FTC is categorized into two differenttechniques: passive FTC (PFTC) [6, 7] and active FTC(AFTC) [8, 9]. In PFTC, controllers are fixed and designedto be robust against a class of presumed faults. The AFTCapproach reacts to system component failures actively byreconfiguring control actions and acceptable performance ofthe entire system can be maintained.

This paper is focused on the design of a novel AFTC thatintegrates a reliable and robust fault diagnosis scheme withthe design of a controller reconfiguration system. The FDIand FTC are fully integrated in dynamic systems design inseveral fields of engineering, such as robotic and automotivesystems. Nevertheless, it must have tool that enables couplingthe diagnosis results with fault tolerant control conditions.Therefore, the BG enables integrating both structural diag-nosis results with control analysis. A BG model allows

knowledge of a large amount of structural, functional, andbehavioral information.This information enables computingappropriate control actions that compensate the faults.

The BG has proven to be a powerful tool not only forgenerating the direct model of a system but also for obtainingits inverse model. In [10], the authors have proposed aninverse control strategy based on BG model.

The innovative interest of the present paper is to combinethe inverse control strategy and observer designs to generatethe FDI and FTC algorithms from the BG model. Theproposed approach takes into account the parameter uncer-tainties and considers the fault recoverability with respect tofault compensation, without complex calculations.

In the first part of the paper, we propose a methodologybased on BG model for fault detection and fault tolerantcontrol. In the second part, we have developed a methodwhich compensates the faults in the absence of complexcalculations. Finally, an illustrative example is developedand simulation results show the advantage of the proposedapproach.

2. FDI and FTC Approaches Based onBond Graph

The bond graph approach is proposed by [11] and thendeveloped by [12, 13]. This tool allows the multidomain

Hindawi Publishing CorporationAdvances in Electrical EngineeringVolume 2014, Article ID 216153, 8 pageshttp://dx.doi.org/10.1155/2014/216153

2 Advances in Electrical Engineering

PA < 0 PB < 0

A B

Figure 1: Power and orientation symbol on BG.

Table 1: BG elements.𝑒

⇁

𝑓

𝑅 𝑆𝑒

𝑒

⇁

𝑓

; 𝑆𝑓

𝑒

⇁

𝑓

𝑒=𝑑𝑝/𝑑𝑡

⇁

𝑓

𝐼

𝑒1

⇁

𝑓1

Gy𝑒2

⇁

𝑓2

𝑒

⇁

𝑓=𝑑𝑞/𝑑𝑡

𝐶

𝑒1

⇁

𝑓1

TF𝑒2

⇁

𝑓2

systems (mechanical, electrical, thermal, etc.) to be describedwith the same components. Its causal structure was initiallyexploited to determine structural conditions of controllabil-ity, observability [14], and diagnosability [15, 16].

The bond graph is based on the graphical representationof the energy exchange within the system to be modeled.Table 1 represents the BG elements: resistor (𝑅), compliance(𝐶), and inertia (𝐼) are passive elements. Effort source (𝑆

𝑒)

and flow source (𝑆𝑓) are the active elements.

Figure 1 indicates the power direction in the system.There are only two types of junctions: the 1 and the 0

junctions (Figure 2). 1 junction has equality of flows and theefforts sum up to zero. 0 junctions have equality of efforts andthe flows sum up to zero (Figure 2).

2.1. Luenberger Observer Based on BG. Bond graph ap-proaches for observers design were developed in someworks,such as Luenberger observers [17, 18], reduced order Luen-berger observers [19], proportional integral observers [20],and nonlinear observers applied to electrical transformers[21].

The objective of this work is to design a Luenbergerobserver by bond graph for fault detection and isolation.

2.2. BG Modeling Bicausality Concept for System Inversion.The concept of “bicausal” introduced by Gawthrop [22]enlarges the possibilities of computation models that can bederived from a bond graph. The bicausal bond graph modelis seen as half-strokes each associated with an effort and aflow variable that can be imposed independently at each endof the bond. Causal half-strokes indicate the fixed or knownvariables of the bond and so determine the right-hand side ofthe assignments form [23] (Figure 3).

The bicausality is used to get systems’ inversion byimposing the output variable without modifying the energystructure. System inversion is an interesting analysis to knowan input considering a given output. Therefore, in the nextsection, we use the bicausality property of the bond graphs.

Some conditions (structural invertibility) are proposed topresent the bond graph-based procedure for system inversion[20].

Proposition 1. A linear system modeled by bond graph isinvertible if there is at least one causal path between the inputvariable and the output variable of the system.

e1

e3e4

f1f2

f3

f401

e2

e1

e3e4

f1f2

f3

f4e2

Figure 2: BG junctions.

System 2 System 1 System 2

e1 e2

f1 f2

e1 e2

f1 f2

System 1

e1 = e2f1 = f2

e2 = e1f2 = f1

} }Figure 3: Bicausal bond graph concept.

2.3. Control Law Design Directly on Inversion Bond Graph.The control strategy proposed by [24] computes the desiredinputs based on the system objectives. Also, in [10], theauthors have proposed an inverse control strategy from theBG model with parameter uncertainties estimated directlyfrom the inverse BG-LFT (linear fractional transformation).The system inversion concept gives the basis to computeappropriate control actions that compensate the faults.Figure 4 shows the control design based on bond graphdeveloped by [10].

In [10], the BG-LFTwas used to estimate the faulty power.Then, to validate these structural results, a local adaptivecompensation based on the inverse control strategy using theinverse BG-LFT was proposed. This strategy computes thedesired inputs based on the system objectives and on theundesired power caused by the fault.

Limitations of this approach are as follows.

(i) The fault estimation is necessary for the controldesign. The inverted model of bond graph uses theestimate fault to compensate it.

(ii) The fault estimationwith a BG-LFT causes FTC delay.

3. Proposed Approach

The principal of our proposed approach AFTC system ispresented in Figure 5. There are basically two parts.

(i) The first part concerns the diagnosis by Luenbergerobserver using BG approach; in this part, the faultestimation and fault isolability are not necessary forsystem recoverability; just the residual is injected tothe control loop.

(ii) The second part shows the control part determined byinverse BG for nominal system.

The following symbols have been used.

I.BG.N.S: Inverse BG for nominal system.𝑦ref: Desired value.𝑦sys: Measured output of system.𝑦obs: Estimated output of observer.

Advances in Electrical Engineering 3

Cn, In Rn

JunctionsDf, De

Cn, In Rn

Junctions

Online

Inverse BGmodel

System

f̂

BG-LFT

Offline

Se

Sf0, 1, TF, GY

0, 1, TF, GY

Figure 4: Control design on bond graph developed by [10].

I.BG.N.S

Process

Observer

Error

Residual

I.BG.N.S

I.BG.N.S Residualur

−+

++

+

+

−

ũ

yref

yobs

unom

uFTC ys ys

Figure 5: AFTC strategy based on bond graph.

Computing the Control (𝑢𝐹𝑇𝐶). Various methods have beenproposed to recover as close as possible the system perfor-mance according to the considered fault representation.

Some extensions of the classical pseudoinverse method(PIM) have been proposed to guarantee both the perfor-mance and the stability of the faulty system. The authors in[25, 26] have synthesized a suitable feedback control𝐾feedback.In [27, 28], the authors have proposed to compute a reconfig-urable forward gain 𝐾forward controller in order to eliminatethe steady-state tracking error in faulty case. Therefore, thecontrol signal applied to the system is represented in

𝑢

FTC= 𝐾forward𝑦ref − 𝐾feedback𝑥. (1)

A novel technique to adjust the command equation (1) isproposed by [29] in

𝑢

FTC= 𝐾forward𝑦ref + �̃�. (2)

�̃� given by

�̃� = 𝐾feedback (𝑥 − 𝑥𝑛

) . (3)

−

Inverse BGfor nominal

systemProcess

Observer

f

ErrorResidual

Residual

−+

+

+

+

+

yref

yobs

ysysuFTC

Figure 6: New control based on bond graph.

According to the control law in (1) and (2), we propose a newcontrol which uses the residual signal provided by the FDIbased observer and error. So, the control law is expressed by

𝑢

FTC= 𝐾forward𝑦ref + 𝐾forward(𝑦ref − 𝑦sys⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

error

)

+ 𝐾forward(𝑦sys − 𝑦obs⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟residual

) .

(4)

Or 𝐾forward is a gain of inverse BG for nominal system.In Figure 5, the compensation term 𝑢

𝑟(residual control)

is useful to compensate the fault. Also �̃� (error control) isadded to the nominal control (𝑢nom); this term (�̃�) improvesthe compensation of the fault effect. So this additive controlresults’ role is to reproduce the control signal (𝑢FTC: con-trolled input resulting from (4) for compensating for theeffect of the fault every moment that the fault is detected).

To simplify the calculus of the control input representedin Figure 5, we propose to replace the three inverse BGmodels by a single inverse BG (Figure 6).


Table 2: Parameter values of the DC motor.

𝑅 = 1Ω Rotor resistance𝐿 = 5mH Rotor inductance𝑏 = 10

−4Nm/rd⋅s−1 Coefficient of viscous𝐽 = 0.001Kgm2 Moment of inertia𝑘𝑛= 0.2Nm/A Coefficient of the torque

𝑢nom = 220V Motor voltage

1 1

3

1

2

4

6

7

5

8kn

I : JI : L

R : bR : R

usys

GyDf : Wsys

Figure 7: Bond graph model of DC motor.

So, the new control law is expressed by

𝑢

FTC= 𝐾forward (𝑦ref + error + residual) . (5)

4. Illustrative Example

An example of a DC motor is used to illustrate our new FTCtechnique. The BG model of the system is given in Figure 7,and the state-space equations are presented in (6);

[

�̇�1

�̇�2

] =

[

[

[

−

𝑏

𝐽

𝑘𝑛

𝐽

−

𝑘𝑛

𝐿

−

𝑅

𝐿

]

]

]

[

𝑥1

𝑥2

] + [

0

1

𝐿

] 𝑢,

𝑦 = [

1 0

0 1

] [

𝑥1

𝑥2

] + [

0.1

0

] 𝑑,

(6)

with 𝑥 = (𝑥1, 𝑥2) = (𝑤, 𝑖) being the state vector, 𝑦 the

measured output variable, 𝑢 the control input variable, and𝑑 the disturbance input variable.

The parameters of the DCmotor are presented in Table 2.

Closed Loop System. Figure 8 shows that the AFTC strategyintegrates the FDI module with an inverse BG for nominalsystem and the bond graphmodel is controllable and observ-able [14].

From the controlled input and output signals, the FDImodule provides the residual which is injected to the controlloop, in order to compensate the effect of fault.

The objective is to synthesize a controller so that thestructure of the closed loop system is as close as possibleto that of the desired reference model under the normaloperation or in the presence of fault.

(i) Computing the Residual (r) in Normal Operating. By causalpath, we deduce the structural equations from the BG ofFigure 8. We compute the residual 𝑟

1with the following

equations:

(a) structural equations for system model:

𝑓1𝑠

= 𝑓2𝑠

= 𝑓3𝑠

= 𝑓4𝑠

,

𝑒1𝑠

= 𝑒2𝑠

+ 𝑒3𝑠

+ 𝑒4𝑠

;

𝑒4𝑠

= 𝑘𝑛𝑓

5𝑠

,

𝑒5𝑠

= 𝑘𝑛𝑓

4𝑠

;

𝑓5𝑠

= 𝑓6𝑠

= 𝑓7𝑠

= 𝑓8𝑠

,

𝑒5𝑠

= 𝑒6𝑠

+ 𝑒7𝑠

+ 𝑒8𝑠

;

𝑓5𝑠

=

𝑒4𝑠

𝑘𝑛

,

𝑓5𝑠

=

𝑒1𝑠

− 𝑒2𝑠

− 𝑒3𝑠

𝑘𝑛

;

(7)

(b) structural equations for Luenberger observer:

𝑓1ob= 𝑓2ob= 𝑓3ob= 𝑓4ob,

𝑒1ob= 𝑒2ob+ 𝑒3ob+ 𝑒4ob;

𝑒4ob= 𝑘𝑛𝑓

5ob,

𝑒5ob= 𝑘𝑛𝑓

4ob;

𝑓5ob= 𝑓6ob= 𝑓7ob= 𝑓8ob,

𝑒5ob= 𝑒6ob+ 𝑒7ob+ 𝑒8ob;

𝑓5ob=

𝑒4ob

𝑘𝑛

,

𝑓5ob=

𝑒1ob− 𝑒2ob− 𝑒3ob

𝑘𝑛

.

(8)

From junctions equations (7) and (8), we generate theresidual 𝑟

1:

𝑟1= 𝑓8𝑠

− 𝑓8ob= 𝑓6𝑠

− 𝑓6ob= 𝑓5𝑠

− 𝑓5ob=

𝑒4𝑠

𝑘𝑛

+

𝑒4ob

𝑘𝑛

,

𝑓5𝑠

=

1

𝑘𝑛

[𝑈𝑠− 𝐿

𝑑𝑓2𝑠

𝑑𝑡

− 𝑅𝑓2𝑠

] ,

𝑓5ob=

1

𝑘𝑛

[𝑈ob − 𝐿𝑑𝑓2obs

𝑑𝑡

− 𝑅𝑓2ob− 𝑟1𝐾11] ,

𝑟1=

1

𝑘𝑛

[𝑈𝑠− 𝐿

𝑑𝑓2𝑠

𝑑𝑡

− 𝑅𝑓2𝑠

− 𝑈ob + 𝐿𝑑𝑓2ob

𝑑𝑡

+ 𝑅𝑓2ob] .

(9)


MSeMSe MSe MSe

1 1 1 1

1 1

09

10

MSf

MSf

MSf

Process

Observer

Inverse BG fornominal system

+ −

f̃8

1c3c

2c

4c

R : b R : R

5c

6c

7c8c

I : J I : L

kn

1s

3s

2s

4s 5s

6s

7s

8s

ys

r1r2+

−

R : bR : R

9c

I : JI : L

R : R R : b

I : L I : J+

kn

−

kn 8s

yref

Wobs

Gy uFTC Gy

Gy

9ob 10ob 11ob 12ob

3ob 7ob

1ob 2ob 4ob 5ob 6ob

8ob

K22 K21 K12 K11

Figure 8: FTC based on BG model.

Or

𝑈𝑠= 𝑈obs,

𝑓2𝑠

=

𝑒5𝑠

𝑘𝑛

=

1

𝑘𝑛

[𝐽

𝑑𝑓6𝑠

𝑑𝑡

+ 𝑏𝑓6𝑠

] ,

𝑓2ob=

𝑒5ob

𝑘𝑛

=

1

𝑘𝑛

[𝐽

𝑑𝑓6ob

𝑑𝑡

+ 𝑏𝑓6𝑠

− 𝐾11𝑟1] ,

𝑟1=

1

𝑘𝑛

[

[

𝑈𝑠− 𝐿

𝑑 (1/𝑘𝑛) [𝐽(𝑑𝑓

6𝑠

/𝑑𝑡) + 𝑏𝑓6𝑠

]

2

𝑑𝑡

− 𝑅

1

𝑘𝑛

[𝐽

𝑑𝑓6𝑠

𝑑𝑡

+ 𝑏𝑓6𝑠

]−𝑈ob

+ 𝐿

𝑑 (1/𝑘𝑛) [𝐽 (𝑑𝑓

6ob/𝑑𝑡) + 𝑏𝑓

6𝑠

− 𝐾11𝑟1]

𝑑𝑡

𝑅

×

1

𝑘𝑛

[𝐽

𝑑𝑓6ob

𝑑𝑡

+ 𝑏𝑓6𝑠

− 𝐾11𝑟1] − 𝑟1𝐾12

]

]

.

(10)

The residual 𝑟1of the system is realized as

𝑟1=

−𝐽𝐿

𝑘

2

𝑛

𝑑

2

𝑟1

𝑑𝑡

−

𝑑𝑟1

𝑑𝑡

[

𝑅𝐽 + 𝐿𝑏 + 𝐾11𝐿

𝑘

2

𝑛

]

− 𝑟1[

𝑅𝑏 + 𝐾11𝑅

𝑘

2

𝑛

+

𝐾12

𝑘𝑛

] ,

[1 +

𝑅𝑏 + 𝐾11𝑅

𝑘

2

𝑛

+

𝐾12

𝑘𝑛

] 𝑟1+ [

𝑅𝐽 + 𝐿𝑏 + 𝐾11𝐿

𝑘

2

𝑛

]

𝑑𝑟1

𝑑𝑡

+

𝐽𝐿

𝑘

2

𝑛

𝑑

2

𝑟1

𝑑𝑡

= 0.

(11)

The 𝑟2is deduced with similar method.

The inverse system enables computing appropriate con-trol actions that compensate the faults.

(ii) Computing the Control (𝑢𝐹𝑇𝐶). The control law can bedesigned directly from the BG model:

structural equations for inverse BG model:

𝑓1𝑐

= 𝑓2𝑐

= 𝑓3𝑐

= 𝑓4𝑐

,

𝑒1𝑐

= 𝑒2𝑐

+ 𝑒3𝑠

+ 𝑒4𝑠

;

𝑒4𝑐

= 𝑘𝑛𝑓

5𝑐

,

𝑒5𝑐

= 𝑘𝑛𝑓

4𝑐

;

𝑓5𝑐

= 𝑓6𝑐

= 𝑓7𝑐

= 𝑓8𝑐

,

𝑒5𝑐

= 𝑒6𝑐

+ 𝑒7𝑐

+ 𝑒8𝑐

.

(12)


0 5 10 15 20 25 30

Time (s)

0

5

10

15

Velocity (approach of [10])Velocity (our approach)

Desired velocity

13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6

Time (s)

8

8.5

9

9.5

10

Zoom

Velocity (approach of [10])Velocity (our approach)

Desired velocity

Figure 9: Simulation results when the fault is compensated.

The control law 𝑢FTC of the system is shown as

𝑢

FTC= 𝑒8𝑐

= 𝑒5𝑐

+ 𝑒6𝑐

+ 𝑒7𝑐

,

𝑒5𝑐

= 𝑘𝑛𝑓

1𝑐

,

𝑓1𝑐

= 𝑓10+

̃

𝑓8+ 𝑓9,

𝑓10= 𝑤des = 𝑦ref,

̃

𝑓8= 𝑓8𝑠

− 𝑓8ob= 𝑟1,

𝑓9= 𝑤des − 𝑓8

𝑠

= 𝜀,

𝑒6𝑐

=

𝐿𝑑𝑓6𝑐

𝑑𝑡

, 𝑒7𝑐

= 𝑅𝑓

7𝑐

= 𝑅𝑓

6𝑐

.

(13)

Or 𝑟1= residual and 𝜀 = error.

So, the control law 𝑢FTC is

𝑢

FTC= 𝑅𝑓

6𝑐

+

𝐿𝑑𝑓6𝑐

𝑑𝑡

+ 𝑘𝑛(residual + 𝑦ref + error) . (14)

5. Simulation Results

Simulation results are carried out in the bond graph simula-tion software 20-sim [30] with parameter values described inTable 2.

Figure 9 shows the system output (velocity) evolutionwith a single fault (parameters 𝑅: 𝑏, 𝑅fault = 𝑅 + 𝛿, and𝛿 = 0.01) introduced at the time 13 s.

We remark that the output decreases less than in the caseof control considered in [10], and then it reaches the nominalvalues quicker at instant 𝑡 = 13.05 s. So, the control law (FTC)is able to stabilize the system on the desired output and tocompensate the fault in the system with a very short timedelay.

0 5 10 15 20 25 300

1

2

3

4

13.2 13.4 13.6 13.8 14 14.22

2.1

2.2

2.3

2.4

2.5

Zoom

Time (s)

U FTC (approach of [10])U FTC (our approach)

U FTC (approach of [10])U FTC (our approach)

13

Time (s)

Figure 10: Control input.

Time (s)0 5 10 15 20 25 30

0

5

10

Error of velocity (approach of [10])Error of velocity (our approach)

13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6

0

0.5

1

1.5

2

Zoom

−5

Time (s)

Error of velocity (approach of [10])Error of velocity (our approach)

Figure 11: Velocity error.

From a control point of view, the reconfigurable controlmechanism requires more energy to reach the target and toguarantee system performance, as shown in Figure 10.

These results can be confirmed by the control input 𝑈FTCof Figure 10. In [10], the control input increases slowly tryingto compensate for the fault affecting the system. In ourapproach, the control input increases quickly and enablesrapid fault compensation on the controlled systemoutput andallows compensating the convergence delay.

In Figure 11, the velocity error quickly converges to zerowith the new approach.


6. Conclusion

In this paper, we propose an active FTC design based onBG approach.The novel strategy combines an observer basedmodel and inverse BG model.

The proposed approach enables computing appropri-ate control actions for compensating the faults. The faultsare detected by Luenberger observer technique based onBG modeling. Fault isolation and fault estimation are notnecessary to the FTC. The comparison between the twoapproaches shows the efficiency of the proposedmethod.Theapplication of a FTC approach to induction DC motor andsimulation results illustrate the performance of the proposedFDI-FTC structure. Our future works concern the onlineimplementation of the proposed techniques on a real process.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

References

[1] D. Chilin, J. Liu, X. Chen, and P. D. Christofides, “Faultdetection and isolation and fault tolerant control of a catalyticalkylation of benzene process,” Chemical Engineering Science,vol. 78, pp. 155–166, 2012.

[2] P. M. Frank, “Fault diagnosis in dynamic systems using analyti-cal and knowledge-based redundancy. A survey and some newresults,” Automatica, vol. 26, no. 3, pp. 459–474, 1990.

[3] J. Gertler, “Fault detection and isolation using parity relations,”Control Engineering Practice, vol. 5, no. 5, pp. 653–661, 1997.

[4] S. Srinivas, “A probabilistic approach to hierarchical model-based diagnosis,” in Proceedings of the 10th Conference onUncertainty in Artificial Intelligence (UAI ’94), pp. 538–545,1994.

[5] Y. Qian, L. Xu, X. Li, L. Lin, and A. Kraslawski, “LUBRES:an expert system development and implementation for real-time fault diagnosis of a lubricating oil refining process,” ExpertSystems with Applications, vol. 35, no. 3, pp. 1252–1266, 2008.

[6] F. Liao, J. L. Wang, and G.-H. Yang, “Reliable robust flighttracking control: an LMI approach,” IEEE Transactions onControl Systems Technology, vol. 10, no. 1, pp. 76–89, 2002.

[7] H. Niemann and J. Stoustrup, “Passive fault tolerant control of adouble inverted pendulum—a case study,” Control EngineeringPractice, vol. 13, no. 8, pp. 1047–1059, 2005.

[8] P. Mhaskar, “Robust model predictive control design for fault-tolerant control of process systems,” Industrial and EngineeringChemistry Research, vol. 45, no. 25, pp. 8565–8574, 2006.

[9] Z. Zhang and W. Chen, “Adaptive output feedback control ofnonlinear systems with actuator failures,” Information Sciences,vol. 179, no. 24, pp. 4249–4260, 2009.

[10] R. Loureiro, R. Merzouki, and B. O. Bouamama, “Bond graphmodel based on structural diagnosability and recoverabilityanalysis: Application to intelligent autonomous vehicles,” IEEETransactions onVehicular Technology, vol. 61, no. 3, pp. 986–997,2012.

[11] H. M. Paynter, Analysis and Design of Engineering Systems, TheMIT Press, 1961.

[12] D. Karnopp, D. Margolis, and R. Rosenberg, Systems Dynamics:A Unified Approach, John Wiley and Sons, 1975.

[13] R. Rosenberg and D. C. Karnopp, Introduction to PhysicalSystem Dynamics, McGraw-Hill, 1983.

[14] C. Sueur and G. Dauphin-Tanguy, “Bond-graph approach forstructural analysis of MIMO linear systems,” Journal of theFranklin Institute, vol. 328, no. 1, pp. 55–70, 1991.

[15] B. Ould-Bouamama, A. K. Samantaray, M. Staroswiecki, and G.Dauphin-Tanguy, “Derivation of constraint relations from bondgraph models for fault detection and isolation,” in Proceedingsof the International Conference on Bond Graph Modeling andSimulation (ICBGM ’03), pp. 104–109, Orlando, Fla, USA,January 2003.

[16] Y. Touati, R. Merzouki, and B. Ould Bouamama, “Robustdiagnosis to measurement uncertainties using bond graphapproach: application to intelligent autonomous vehicle,”Mechatronics, vol. 22, no. 8, pp. 1148–1160, 2012.

[17] D. Karnopp, “Bond graphs in control: physical state variablesand observers,” Journal of the Franklin Institute, vol. 308, no. 3,pp. 219–234, 1979.

[18] P. J. Gawthrop and L. P. S. Smith,Meta Modelling: Bond Graphsand Dynamic Systems, Prentice Hall, 1995.

[19] C. Pichardo-Almarza, A. Rahmani, G. Dauphin-Tanguy, andM. Delgado, “Bond graph approach to build reduced orderobservers in linear time invariant systems,” in Proceedings of the4th International Symposium on Mathematical Modelling, 2003.

[20] C. Pichardo-Almarza, A. Rahmani, G. Dauphin-Tanguy, andM.Delgado, “Proportional-integral observer for systems modelledby bond graphs,” Simulation Modelling Practice andTheory, vol.13, no. 3, pp. 179–211, 2005.

[21] G. Gonzalez-A and I. Nuñez, “A nonlinear observer of anelectrical transformer: a bond graph approach,”World Academyof Science, Engineering and Technology, vol. 58, pp. 814–820,2009.

[22] P. J. Gawthrop, “Bicausal bond graphs,” in Proceedings ofthe International Conference on Bond Graph Modelling andSimulation (ICBGM ’95), pp. 83–88, 1995.

[23] R. F. Ngwompo, S. Scavarda, and D. Thomasset, “Inversion oflinear time-invariant SISO systems modelled by bond graph,”Journal of the Franklin Institute B: Engineering and AppliedMathematics, vol. 333, no. 2, pp. 157–174, 1996.

[24] N. Yadaiah and N. Venkata Ramana, “Linearisation of multi-machine power system: modeling and control—a survey,” Inter-national Journal of Electrical Power and Energy Systems, vol. 29,no. 4, pp. 297–311, 2007.

[25] Z. Gao and P. J. Antsaklis, “Stability of the pseudo-inversemethod for reconfigurable control systems,” International Jour-nal of Control, vol. 53, no. 3, pp. 717–729, 1991.

[26] M. Staroswiecki, “Fault tolerant control: the pseudo-inversemethod revisited,” in Proceedings of the 16th Triennial WorldCongress of International Federation of Automatic Control (IFAC’05), pp. 418–423, July 2005.

[27] Y. M. Zhang and J. Jiang, “Active fault-tolerant control systemagainst partial actuator failures,” IEE Proceedings on ControlTheory and Applications, vol. 149, no. 1, pp. 95–104, 2002.

[28] F. Guenab, D. Theilliol, P. Weber, J. C. Ponsart, and D. Sauter,“Fault tolerant control method based on cost and reliabilityanalysis,” in Proceedings of the 16th Triennial World Congressof International Federation of Automatic Control (IFAC ’05), pp.490–495, Prague, Czech Republic, July 2005.


[29] Y. Zhang and J. Jiang, “Fault tolerant control system designwith explicit consideration of performance degradation,” IEEETransactions on Aerospace and Electronic Systems, vol. 39, no. 3,pp. 838–848, 2003.

[30] 20 Sim Controllab Products B.V., http://www.20sim.com/.

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


research article active fault tolerant control based on ...active fault tolerant control based on...

Documents