Robust Fault Diagnosis of a Satellite System Using a Learning Strategy and Second Order Sliding Mode...

112 IEEE SYSTEMS JOURNAL, VOL. 4, NO. 1, MARCH 2010

Robust Fault Diagnosis of a Satellite SystemUsing a Learning Strategy and Second

Order Sliding Mode ObserverQing Wu and Mehrdad Saif, Senior Member, IEEE

Abstract—This paper proposes a second-order sliding mode ob-server for fault diagnosis (FD) of a class of uncertain dynamicalsystems. In the proposed FD scheme, a modified super-twistingsecond-order sliding mode algorithm is firstly established to ob-serve the system state in the presence of uncertainties and distur-bances, and then the observer input is designed by using a PID-typeiterative learning algorithm to detect, isolate, and estimate faults.The convergence of the sliding mode algorithm and the parameterupdate law for the iterative learning estimator are both theoreti-cally and rigorously studied. Finally, the proposed fault diagnosisscheme is applied to the dynamics of a satellite with flexible ap-pendages, and the simulation results demonstrate its effectiveness.

Index Terms—Fault diagnosis, satellite systems, sliding mode.

I. INTRODUCTION

I N the last three decades, mathematical model-based faultdiagnosis (FD) schemes have been the subject of many in-

vestigations due to the increasing complexity of modern engi-neering systems and the consideration of safety and economicalissues. Many contributions have been made and are surveyedin the literature (e.g., [1]–[6]). However, when dealing with theproblem of robust model-based fault detection, isolation, and es-timation in nonlinear systems, there remains many challengingopen problems.

Robust fault diagnosis schemes in a class of nonlinear dy-namical systems using learning approaches have been exploredby several researchers in the last decade. In this class of FDschemes, various online adaptive or learning techniques are usedto estimate the deviation of system dynamics caused by faults.Some of the learning methodologies used include adaptive ob-servers (e.g., [7], [8]), neural networks (e.g., [9]–[14]), neuraladaptive observers (e.g., [15], [16]), and iterative learning ob-servers (e.g., [17], [18]), etc. One important feature of this classof FD schemes is that they are not only able to detect and locatethe occurrence of a fault, but also to estimate the magnitude ofthe fault, which is helpful for the fault accommodation.

Manuscript received August 27, 2009; revised January 11, 2010; acceptedJanuary 11, 2010. Date of current version April 07, 2010. This work was sup-ported in part by Natural Sciences and Engineering Research Council (NSERC)of Canada through its Strategic Research Grant Program.

Q. Wu was with the School of Engineering Science, Simon Fraser University,Vancouver, BC V5A 1S6 Canada He is now with Critical Environment Tech-nologies Canada Inc., Delta, BC V4G 1M3 Canada.

M. Saif is with the School of Engineering Science, Simon Fraser University,Vancouver, BC V5A 1S6 Canada (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSYST.2010.2043786

At least two methods are available to achieve robust fault di-agnosis using learning methodologies. The first one uses robustlearning algorithms, where dead-zone operators are adopted tomake the learning algorithms insensitive to small estimation er-rors which are caused by system uncertainties. The other ap-proach is to directly estimate the magnitude of the system uncer-tainties so that the generated residuals only contain the informa-tion about the faults. However, both of these two methods needfurther investigation. The first one reduces the accuracy of thefault estimation, and a threshold has to be carefully selected tobalance the robustness and sensitivity of the FD scheme. More-over, projection operators that can restrict the parameter esti-mation vectors to a predefined compact and convex region areused to prevent parameter drifting in the presence of modelinguncertainties and approximation errors. The second method re-quires information about the uncertainties, which confines thisapproach to be only suitable for a particular class of nonlinearsystems. In addition, from a practical application point of view,the proposed robust FD scheme should be easily implementableto satisfy the real-time computational requirement.

Due to the inherent robustness to system uncertainties, tra-ditional and higher order sliding mode have been studied forsystem observation for many years (e.g., [19]–[22], [24]–[27]).Moreover, sliding mode techniques have also been used in therobust fault diagnosis schemes (e.g., [28]–[31]). One FD methodbased on sliding mode is based on a strategy where the observermaintains a sliding motion even in the presence of a fault, andthe fault is reconstructed by manipulating the equivalent outputinjection signal. A different approach is to design an observerin such a way that the sliding motion is destroyed when a faultoccurs. In this case, other online estimators are needed to ap-proximate the fault.

Modern orbital spacecrafts with flexible antennas or solarpanels play important roles in a variety of space applicationssuch as communication, remote sensing, etc. The dynamicmodels of these second-generation spacecrafts are highly non-linear and include interaction between rigid and flexible mode.Due to the characteristics of this class of spacecrafts, severalresearchers have studied their dynamics and designed variouscontrollers for them (e.g., [32], [34]). However, few researchtargets the fault diagnosis for the flexible spacecraft, and thismotivates our work.

In this paper, a new nonlinear observer is developed for faultdiagnosis in a class of nonlinear systems, which is described inSection II. This observer takes advantage of the second-ordersliding mode technique and PID-type iterative learning strategy

1932-8184/$26.00 © 2010 IEEE

WU AND SAIF: ROBUST FAULT DIAGNOSIS OF A SATELLITE SYSTEM 113

in the following aspects. i) The super-twisting second-ordersliding mode algorithm is utilized to observe the system statesin presence of modeling uncertainties. This can avoid param-eter drifting during the fault estimation caused by uncertaintiesand disturbances. ii) The structure of the iterative learningestimator is determined, and only the proportional, integral,and derivative information of the output estimation error isused. This simplifies the procedure of choosing a suitable ar-chitecture for the estimator. iii) The parameters of the estimatorare updated in the iteration domain rather than in the timedomain. This strategy not only guarantees the convergence ofthe update process when the tracking trajectory is time-varyingbut iteration-invariant, but also eliminates the settling time andthe overshoot in the time domain.

The remainder of this paper is organized as follows: The Sec-tion II presents the problem of interest, and certain assumptionsrequired for the developments in the future sections. In the pro-posed robust FD scheme, fault isolation and estimation are re-alized by using an adaptive law to update the parameters of theobserver inputs. Theoretically, the convergence of this updatelaw is proved in Section III. Next, in Section IV, the theoret-ical analysis is followed by an application of the proposed FDscheme to the nonlinear dynamics of a satellite with flexible ap-pendages. Simulation results show that this second-order slidingmode observer-based robust fault diagnosis scheme is effectivefor a certain class of nonlinear systems. Finally, conclusions aregiven in Section V.

II. PROBLEM STATEMENT

The class of nonlinear dynamic systems considered in thisstudy is described in the state space form as

(1)

where is the state vector. The nominalsystem dynamics are represented by the function ,the internal uncertainties are denoted by the term ,and describes the dynamics of the process faults,which are defined as additive actuator faults and/or componentfaults. The function is a step function:

if ,if

(2)

and is the beginning time of the process faults.The solutions to the system (1) are understood in Filippov’s

sense. We assume that the system dynamics functionand the uncertainty function are Lebesgue-measurablein any compact region of . Another two assumptions are intro-duced for designing and analyzing the observer.

Assumption 1: The nominal system dynamics is Lipschitzwith respect to system output, which means a constant existssuch that

(3)

Assumption 2: The uncertainty function satisfies

(4)

where is a positive bound for uncertainty.The objective of this work is to develop a finite-time con-

vergent observer for fault detection, isolation, and estimation ofthe system (1) where only output is measurable. The rela-tive degree from to is two. For the sake of simplicity, onlythe scalar case , is considered. The vector case can be an-alyzed by constructing a bank of observers in parallel for eachcomponent of in the same way.

Remark 1: In this work, we only consider the types of faultdirectly affecting the state of the system, and thus are modeledin the state equation describing the systems. Such faults can beconsidered to be actuator faults and/or component faults in theplant.

III. ROBUST FAULT DIAGNOSIS SCHEME

In this section, a nonlinear observer which combines asecond-order sliding mode algorithm and a PID-type iterativelearning estimator is established for fault detection, isolation,and estimation of the systems represented by (1). The proposedrobust fault detection and diagnosis scheme is developed bytwo procedures: i) A second-order sliding mode observer isfirstly constructed to observe the system states in presence ofmodeling uncertainties, prior to the occurrence of any fault.ii) After a fault occurs, an iterative learning estimator is acti-vated to determine the location of the fault and to estimate itsmagnitude.

A. Second-Order Sliding Mode Observer

Based on the system dynamics (1), a nonlinear observer isproposed as follows,

(5)

where and are the state estimations, and are thecorrection variables, and is an iterative learning estimatorto specify the state fault. This estimator will be discussed indetail in Section III-C. The term is the time at which thefault estimator is activated. In order to investigate the propertiesof the sliding mode and iterative learning algorithm clearly, weassume that , where is the time when thestate is observed.

The correction variables and are of the following forms

(6)

and

ifif (7)


where and are defined as the stateestimation errors, “sign” is the discontinuous signum function.

Remark 2: In the proposed second-order sliding mode ob-server, we use an anti-peaking structure [23], [24], where and

reach the sliding manifold one by one in a sort of a recursiveway, that is, reaches the manifold before .

Considering the system dynamics before reaches thesliding manifold, we have

(8)

where .Based on Assumption 1, we have

(9)

for any possible , , , , , and .The convergence property of a super-twisting second order

sliding mode observer has been provided by Davila et al. [26],where the function is bounded by a con-stant . Here, we are ready to use a similar approach to in-vestigate the convergence of the proposed second-order slidingmode observer (5)–(7), where function only satisfies con-ditions (9).

Theorem 1: The first variable pairs converge toin finite time, if condition (9) holds for system (1) and

the parameters of the observer (6) are selected according to thefollowing criteria:

(10)

(11)

where and are defined later.Proof: From (8) and (9), the state estimation errors, and

, satisfy the following differential inclusion:

(12)

Here and in the following part of this paper, all differential in-clusions are defined in the Filippov sense. Using the identity

, we obtain the derivative of withas

(13)

The inclusion (13) is a mathematical description of theboundedness curve drawn in Fig. 1. Since the initial observerstates are set to , the trajectory enters thehalf-plane with a positive initial value andthe half-plane with a negative value of .

In quadrant , the trajectory is confinedbetween the axis , , and the trajectory of the

Fig. 1. Boundedness curve for the finite time convergence of �� .

equation , where . We defineas the intersection of this curve with the axis , and welet be the intersection of this curve with the axis .Solving the differential equation , we obtain ageneral solution as

(14)

where and are two coefficients to be determined.Setting the time from to be , we have the

following four boundary conditions:

(15)

(16)

(17)

(18)

where is the initial time.From (15) and (17), we obtain

(19)

(20)

and from (16), we have

(21)

Consequently, based on (18), we eliminate , and attain

(22)

Two equivalent inequalities can be obtained from above deduc-tion:

(23)

(24)


Therefore, the trajectory of the boundedness curve in quadrant1 is described by an elliptical equation [see Fig. 1, line (a)].

(25)

with , .From the above analysis, we can easily see that is the

maximal . Therefore, according to (10) and (13), we obtainfor ,

(26)

Hence, the trajectory goes down to the axis and entersinto the fourth quadrant.

Then, consider the boundedness curve in quadrant, where based on (26), continues to decrease until

returns back to zero from a negative value. Therefore, theboundedness curve consists of two parts. The first part dropsdown from to , where implies

reaches the smallest value of [see Fig. 1, line (b)].Let the right-hand side of (13) be zero in the worst case;

we have , where. Since, in quadrant 4, , the trajectory approaches

. Thus, the second part of the boundedness curve in thefourth quadrant is the horizontal trajectory fromto [see Fig. 1, line (c)].

Based on (10)–(11) and (22), we derive

(27)

If we define as the intersectionpoints of system (5) ’s trajectory starting from with theaxis , inequality (27) ensures the finite-time convergenceof the state to .

Remark 3: The boundedness curve that consists of segments(a), (b), and (c) is the “worst” case of the trajectory. Actually,

moves along the direction of (a), (b), (c) within theboundedness curve.

Remark 4: The choice of and depends on the boundof uncertainty and the initial state estimation error in the worstcase. The theoretical result is consistent with that when only thebound of is known. In applications, a sufficiently largeis preferred in order to satisfy (10) and (11).

Obviously, when reaches the sliding manifold, i.e.,, , the dynamics of become

(28)

The convergence of will be discussed in the Section III-C.Remark 5: Note that the traditional sliding mode techniques

are a special case of the high order sliding mode, and they canbe considered as first order sliding mode.

Remark 6: The sliding mode parameters and can notbe chosen too large because, in this work, the sliding mode isthere only to eliminate the effect of the uncertainties.

B. Robust Fault Detection

In model-based fault diagnosis schemes, a residual or resid-uals are usually generated for diagnosing faults. The proposedfault diagnosis scheme is required to not only detect the occur-rence of a fault, but it also should determine its location andestimate its magnitude. Here, the measurable output estimationerror can be selected as the residual for robust fault detection;i.e., see the equation at the bottom of the page. where is athreshold for robust fault detection. With the help of the slidingmode, can be set very small to increase the sensitivity withoutlosing robustness. Moreover, when additive faults occur, the on-line estimator is used to determine the location and to es-timate the magnitude of the faults.

Remark 7: When the nonlinear system (1) is healthy, i.e.,, ideally, the states of observer in (5) should be iden-

tical to the states of the practical system (1), and is sup-posed to be zero. When a fault occurs, the sliding modemotion is expected to be destroyed, and the estimator istriggered to specify the fault.

C. Fault Isolation and Estimation Using Iterative LearningStrategy

In order to reduce the settling time and overshoot when esti-mating the fault, a PID-type iterative learning estimator, usingthe past and current information of the state estimation error, isestablished as follows. At each time , the estimator isiteratively updated according to the following rule [33].

(29)

where is the gain, and , are three pa-rameters of the observer input, and is the sampling time in-terval in the iteration domain. Three external inputs ofare

(30)

ifif


Fig. 2. Nominal system output and actual system output when an incipient actuator fault occurs at the eighth second.

TABLE INOMINAL PARAMETERS OF THE SATELLITE WITH FLEXIBLE APPENDAGES

When using to estimate a fault, an adaptive algorithmis adopted to update the parameters of this estimator. If we writethe parameters in a vector form as

(31)

and

then .The parameter vector is updated in the iteration domain by

(32)

here is the learning rate and is a small positive numberused to prevent the denominator becoming zero.

In this section, stability of the state estimation error usingPID-type iterative learning estimators is explored. Prior to anyfault, the stability of the output estimation error was investi-gated in Section III-A.

Firstly, after the occurrence of a state fault, the estimationerror deviates from zero because the fault works as a new un-known input to the system. However, due to the compensationprovided by the observer input , the state estimation errorshould return to zero, if exactly estimates the fault. Inpractice, due to the existence of fault estimation error, the stateestimation error remains within a small bound. This property isshown in the following theorem.

Theorem 2: If conditions (10)–(11) and the followingequality are satisfied:

(33)

then the state estimation error is uniformly bounded.Proof: The boundedness of output estimation error is

proved in Theorem 1. Then, here, we focus on the stability ofstate estimation error .

The structure of the PID-type iterative learning estimator isquite similar to that of the radial basis function (RBF) networks.Although only three inputs exist, and the output of the esti-mator is a linear combination of the inputs, the PID-type iter-ative learning estimator only needs to approximate a constant


Fig. 3. Time-behaviors of the actual states and estimated states.

value in the iteration domain at each sampling time. Therefore,due to the approximation ability of RBF networks, as long as theiteration number is big enough, it is reasonable to assume thatthe fault function can be approximated by the PID-typeiterative learning estimator as

(34)

where denotes the network approximation error. The optimalparameter is selected such that the norm distance be-tween and is minimized. Note that the artifi-cial parameter is only used for theoretical analysis and isnot for the estimator design.

Based on (34), we have

(35)

where is the weight estimation error.Substituting (34) and (35) into (28), after the occurrence of a

fault, we obtain

(36)

Based on (32), we have

(37)

Hence,

(38)

where .In order to investigate the boundedness of , a Lyapunov

function is defined as

(39)

Based on (36) and (38), the derivative of with respect tois

(40)

(41)

(42)

where is a finite operating time for the system.


Fig. 4. Time-behaviors of the incipient actuator fault � ��, �� , and some other observer inputs.

Based on (7), after the output estimation error reaches thesliding manifold , we have .Correspondingly, (40) can be rewritten as

(43)

When the condition (33) is satisfied, the above inequality (43)becomes

(44)

Since the fourth term on the right hand side of above in-equality is always postive, no matter the sign of is, when

(45)

, which means is uniformly bounded.

Remark 8: Theorem 2 guarantees the uniform boundednessof the state estimation error. If (10)–(11) and (33) are satis-fied, then the estimation error converges to a ball described by

in a finite time. Moreover, the perfor-mance of this fault diagnosis scheme can be improved by prop-erly choosing the switching gains, and carefully designing theonline estimators.

IV. APPLICATION TO FLEXIBLE SATELLITE FAULT DIAGNOSIS

In this section, the dynamics of a satellite with flexible ap-pendages is first presented. Then, the proposed fault diagnosisscheme is tested on this flexible satellite.

The model of a flexible satellite is composed of a rigid cen-tral hub, which represents the satellite body, and two flexible ap-pendages, which are usually solar arrays, antennas, or any otherflexible structures. The satellite is assumed to maneuver in acircular orbit. A series of axes has been defined in [34] whenderiving the motion equation of this satellite:

, , —Axes of right-handed coordinate frame;, , —Axes of an inertial frame;, , —Axes of an orbital frame.

When the satellite is slewed around the axis , which isnormal to the orbital plane, the flexible appendages are de-formed. We assume that the appendages suffer elastic transversebending only in the orbital plane - . In [34], consideringthe configuration of the satellite, assuming that the pitch ma-neuver excites the two flexible appendages anti-symmetricallyis reasonable.


Fig. 5. Time-behaviors of the abrupt actuator fault � ��, �� , and some other observer inputs.

The governing equations of the satellite motion were devel-oped via the Lagrangian procedure. The spatial discretizationmethod was used to derive a group of ordinary differential equa-tions to describe the motion of the satellite, although the vi-bration of the appendages can be described by partial differen-tial equations. As a result, the appendage deflections, which arestrictly confined in the orbital plane, are expressed in terms of aset of admissible or shape functions as

(46)

where are the generalized coordinates associated withthese functions, is the distance from a point on the appendageto the center of the hub, and is the radius of the hub. Here,we assume that modes are sufficient for the computationof elastic deformation. are the shape functions that satisfythe geometric and physical boundary conditions. The shapefunctions are given in [34] as

(47)

where is the length of the appendage.

The formulation of the governing equations of this kind ofspacecraft is discussed in [32] and is expressed as

(48)

where is the pitch angle, is the vector ofthe generalized coordinates of the appendage flexibility , isthe orbital rate, and are the mass moments of inertia of thecentral hub and each appendage, respectively, is the controltorque, and , , and are the following modalintegrals:

(49)


where , and are the damping coeffi-cient and modulus of elasticity of the appendages, and is thesectional area moment of inertia with respect to the appendagebending axis.

When satellite maneuvers are relatively fast, the nonlinearterms associated with the pitch angle will dominate over theterms associated with the flexibility generalized coordinates, .Hence, the quadratic terms, and can beneglected and resulting in simplified motion equations,

(50)

where

.

.

.

When we choose the state vector to beand the output vector to be , the above equationscan be written into a form similar to (1). So, the proposed faultdiagnosis scheme in this section can be applied to the satellitewith flexible appendages.

The simulation for the fault diagnosis in system (50) is pre-sented here. The satellite is assumed to maneuver in a circularorbit at an altitude of 400 km. The nominal parameters of thissatellite are listed in Table I. In the simulation, because thesystem has only one control torque, , we consider the casewhen a single actuator fault occurs at the 8th second. An incip-ient fault and an abrupt fault are tested. The fault functions aredescribed as

(51)

and

(52)

The system dynamics are assumed to be subject to disturbancesand measurement noises. In simulation, the disturbance in thecontrol torque is set to be a random signal with a maximum mag-nitude 0.05, and the measurement noises are set to be randomsignals with maximum magnitude 0.5%.

Moreover, this FD scheme can be easily extended tothe case of multiple state faults. The state is divided intofour parts: ,and only and are measurable. Corre-spondingly, a group of observer inputs are constructed as

.In the simulation design, the gain of the PID-type iterative

learning estimator was arrived at using a trial-and-error methodand was set to . The initial values of the external inputs

are all set to 0.5. Simulation results are shown from Figs. 2–5.Several conclusions can be derived from these figures. Firstly,system performance deteriorates when an actuator fault occurs.Secondly, prior to the onset of any fault, the sliding mode worksto reduce the estimation error close to zero, which illustratesthat the proposed fault diagnosis scheme is robust to system un-certainties of certain magnitudes. Thirdly, whether an incipientfault or an abrupt fault occurs, the corresponding observer inputcan characterize the fault with satisfactory accuracy in the pres-ence of uncertainties and measurement noises. Other fault esti-mators still remain zero or close to zero, which implies this FDscheme is able to locate and estimate the actuator fault effec-tively. However, large magnitude of measurement noises impactthe fault estimation performance and probably fail the fault di-agnosis scheme. Therefore, the parameters of the sliding modeand fault estimators need to be adjusted carefully, and filters arenecessary in some cases.

V. CONCLUSIONS

This work proposed a novel nonlinear observer for the faultdetection, isolation and estimation in a class of nonlinear sys-tems. In this robust FD scheme, a super-twisting second-ordersliding mode algorithm was integrated with a PID-type iterativelearning estimator, where the past and current information of theoutput estimation error were adopted to construct the observerinput in a similar way as a PID controller. Theoretically, the con-vergence of the second-order sliding mode algorithm and theparameter update law for the iterative learning estimator wereboth rigorously investigated. In order to demonstrate the perfor-mance of this FD scheme, it was applied to the dynamics of asatellite with flexible appendages, and simulation results illus-trate its effectiveness.

REFERENCES

[1] P. J. Patton, P. M. Frank, and R. N. Clark, Fault Diagnosis in DynamicSystems: Theory and Applications. Englewood Cliffs, NJ: Prentice-Hall, 1989.

[2] J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems.new York: Marcel Dekker, 1998.

[3] J. Chen and R. J. Patton, Robust Model-Based Fault Diagnosis for Dy-namic Systems. Boston: Kluwer Academic Publishers, 1999.

[4] R. J. Patton, R. Clark, and R. N. Clark, Issues of Fault Diagnosis forDynamic Systems. London, U.K.: Springer-Verlag, 2000.

[5] M. Witczak, Modelling and Estimation Strategies for Fault Diag-nosis of Non-Linear Systems. From Analytical to Soft ComputingApproaches. Berlin, Germany: Springer, 2007.

[6] S. X. Ding, Model-Based Fault Diagnosis Techniques. DesignSchemes, Algorithms, and Tools. Berlin, Germany: Springer, 2008.

[7] A. Xu and Q. Zhang, “Nonlinear system fault diagnosis based on adap-tive estimation,” Automatica, vol. 40, pp. 1181–1193, 2004.

[8] F. Caccavale and L. Villani, “An adaptive observer for fault diagnosisin nonlinear discrete-time systems,” in Proc. Amer. Control Conf.,Boston, MA, Jun. 2004, pp. 2463–2468.

[9] T. Marcu and L. Mirea, “Robust detection and isolation of processfaults using neural networks,” IEEE Control Syst. Mag., vol. 17, pp.72–79, 1997.

[10] Y. M. Chen and M. L. Lee, “Neural networks based scheme for systemfailure detection and diagnosis,” Math. Comput. Simul., vol. 58, pp.101–109, 2002.

[11] M. M. Polycarpou, “Stable learning scheme for failure detectionand accommodation,” in Proc. IEEE Int. Symp. Intelligent Control,Columbus, OH, Aug. 1994, pp. 315–320.

[12] M. M. Polycarpou and A. J. Helmicki, “Automated fault detection andaccommodation: A learning systems approach,” IEEE Trans. Syst.,Man, Cybern., vol. 25, pp. 1447–1458, 1995.


[13] A. B. Trunov and M. M. Polycarpou, “Automated fault diagnosis innonlinear multivariable systems using a learning methodology,” IEEETrans. Neural Netw., vol. 11, pp. 91–101, 2000.

[14] M. M. Polycarpou and A. B. Trunov, “Learning approach to nonlinearfault diagnosis: Detectability analysis,” IEEE Trans. Automat. Control,vol. 45, pp. 806–812, 2000.

[15] A. Alessandri, “Fault diagnosis for nonlinear systems using a bank ofneural estimators,” Comput. Industry, vol. 52, pp. 271–289, 2003.

[16] Q. Wu and M. Saif, “Neural adaptive observer based fault detectionand identification for satellite attitude systems,” in Proc. Amer. ControlConf., Portland, OR, Jun. 2005, pp. 1054–1059.

[17] W. Chen and M. Saif, “An iterative learning observer-based approachto fault detection and accommodation in nonlinear systems,” in Proc.40th IEEE Conf. Decision and Control, Orlando, FL, Dec. 2001, pp.4469–4474.

[18] W. Chen and M. Saif, “Fault detection and accommodation in nonlineartime-delay systems,” in Proc. Amer. Control Conf., Denver, CO, Jun.2003, pp. 4255–4260.

[19] C. Edwards and S. K. Spurgeon, “On the development of discontinuousobservers,” Int. J. Control, vol. 59, no. 5, pp. 1211–1229, 1994.

[20] S. Drakunov and V. Utkin, “Sliding mode observers. Tutorial,” in Proc.34th Conf. Decision and Control, New Orleans, LA, USA, Dec. 1995,pp. 3376–3378.

[21] I. Haskara, U. Ozguner, and V. Utkin, “On sliding mode observersvia equivalent control approach,” Int. J. Control, vol. 71, no. 6, pp.1051–1067, 1998.

[22] F. Floret-Ponetet and F. Lamnabhi-Lagarrigue, “Parametric identifica-tion methodology using sliding modes observer,” Int. J. Control, vol.74, no. 18, pp. 1743–1753, 2001.

[23] J. P. Barbot, T. Boukhobza, and M. Djemai, “Sliding mode observerfor triangular input form,” in Proc. 35th Conf. Decision and Control,1996, pp. 1489–1490.

[24] Y. Xiong and M. Saif, “Sliding mode observer for nonlinear uncer-tain systems,” IEEE Trans. Automat. Control, vol. 46, no. 12, pp.2012–2017, 2001.

[25] T. Boukhobza and J. P. Barbot, “High order sliding modes observer,”in Proc. 37th IEEE Conference on Decision and Control, Tampa, FL,Dec. 1998, pp. 1912–1917.

[26] J. Davila, L. Fridman, and A. Levant, “Second-order sliding mode ob-server for mechanical systems,” IEEE Trans. Automat. Control, vol. 50,pp. 1785–1789, 2005.

[27] Y. B. Shtessel and A. S. Poznyak, “Parameter identification of affinetime varying systems using traditional and high order slding modes,”in Proc. 2005 Amer. Control Conf., Portland, OR, USA, Jun. 2005, pp.2433–2438.

[28] C. Edwards, S. K. Spurgeon, and R. J. Patton, “Sliding mode obseversfor fault detection and isolation,” Automatica, vol. 36, pp. 541–553,2000.

[29] C. P. Tan and C. Edwards, “Sliding mode observers for detection andreconstruction of sensor faults,” Automatica, vol. 38, pp. 1815–1821,2002.

[30] W. Chen and M. Saif, “Robust fault detction and isolation in con-strained nonlinear systems via a second order sliding mode observer,”in Proc. 15th Triennial World Cong. IFAC, Barcelona, Spain, Jul. 2002.

[31] T. Floquet, J. P. Barbot, W. Perruquetti, and M. Djemai, “On the robustfault detection via a sliding mode disturbance observer,” Int. J. Control,vol. 77, no. 7, pp. 622–629, 2004.

[32] K. Karray, A. Grewal, M. Glaum, and V. Modi, “Stiffening control of aclass of nonlinear affine systems,” IEEE Trans. Aerosp. Electron. Syst.,vol. 33, no. 2, pp. 473–484, 1997.

[33] Z. X. Li, R. T. Zhao, Y. H. Li, and D. H. Sun, “Real-time predictablecontrol based on single-neuron psd controller,” in Proc. Second Int.Conf. Machine Learning and Cybernetics, 2003, pp. 720–725.

[34] S. N. Singh and R. Zhang, “Adaptive output feedback control of space-craft with flexible appendages by modeling error compensation,” ActaAstronautica, vol. 54, pp. 229–243, 2004.

Qing Wu received the B.S. and M.S. degrees incontrol theory and engineering from HuazhongUniversity of Science and Technology, Wuhan,China in 1999 and 2002, respectively, and the Ph.D.degree in engineering science from Simon FraserUniversity, Vancouver, BC, Canada, in 2008.

He is currently an Engineer at the Critical Environ-ment Technologies Canada Inc., Delta, BC. He was aReaching and Research Assistant at Huazhong Uni-versity of Science and Technology for 2002–2003.His research interests include fault diagnosis, com-

putational intelligence, control systems, etc.

Mehrdad Saif (SM’06) received the B.S. degreein 1982, the M.S. degree in 1984, and the Ph.D.degree in 1987, all in electrical engineering. Duringhis graduate studies he worked on research projectssponsored by NASA Lewis (now Glenn) ResearchCenter, as well as Cleveland Advanced Manufac-turing Program (CAMP).

In 1987, he joined the School of EngineeringScience at Simon Fraser University, Vancouver, BC,Canada, as an Assistant Professor. He is currentlya Full Professor and Director of the same School.

From 1993 to 1994, he was a Visiting Scholar at General Motors NorthAmerican Operation (NAO) R & D Center, Warren, MI. At GM he was amember of the Powertrain Control Group in the Electrical and ElectronicsResearch Department where he worked on engine control and on-board enginediagnostic problems. His research interests are in estimation and observertheory, model based fault diagnostics, and application of these to automotive,power, and other complex engineering systems. He has published over 160refereed journal and conference papers plus an edited book in these areas. hehas been a consultant to a number of industries and agencies such as GM,NASA, B.C. Hydro, Ontario Council of Graduate Studies, etc.

Dr. Saif served two terms (1995, 1997) as the Chairman of the VancouverSection of the IEEE Control Systems Society, and is currently a member of theeditorial board of the IEEE Systems Journal, International Journal of Controland Computers, IEEE CDC, and ACC. He is a Registered Professional Engineerin British Columbia.

Robust Fault Diagnosis of a Satellite System Using a Learning Strategy and Second Order Sliding Mode...

Documents

Transcript of Robust Fault Diagnosis of a Satellite System Using a Learning Strategy and Second Order Sliding Mode...