Sliding mode based fault detection, reconstruction and fault tolerantcontrol scheme for motor systems

Hemza Mekki a,b,n, Omar Benzineb c,d, Djamel Boukhetala a, Mohamed Tadjine a,Mohamed Benbouzid d

a Ecole Nationale Polytechnique, Automatic Control Department, LCP, B.P 182 Elharrach, Algiers, Algeriab Electrical Engineering Department, University of M'sila, B.P 166 Ichbilia M'sila, Algeriac Electronics Department, University of Blida, B.P 270 Road of Soumaa, Blida, Algeriad University of Brest, EA 4325 LBMS, Rue de Kergoat, CS 93837, 29238 Brest Cedex 03, France

a r t i c l e i n f o

Article history:Received 1 October 2014Received in revised form21 January 2015Accepted 5 February 2015Available online 5 March 2015This paper was recommendedfor publication by Jeff Pieper.

Keywords:Fault-tolerant control (FTC)Sliding mode control (SMC)Sliding mode observer (SMO)Motor systems (MS)Fault detection and reconstruction

a b s t r a c t

The fault-tolerant control problem belongs to the domain of complex control systems in which inter-control-disciplinary information and expertise are required. This paper proposes an improved faultsdetection, reconstruction and fault-tolerant control (FTC) scheme for motor systems (MS) with typicalfaults. For this purpose, a sliding mode controller (SMC) with an integral sliding surface is adopted. Thiscontroller can make the output of system to track the desired position reference signal in finite-time andobtain a better dynamic response and anti-disturbance performance. But this controller cannot dealdirectly with total system failures. However an appropriate combination of the adopted SMC and slidingmode observer (SMO), later it is designed to on-line detect and reconstruct the faults and also to give asensorless control strategy which can achieve tolerance to a wide class of total additive failures. Theclosed-loop stability is proved, using the Lyapunov stability theory. Simulation results in healthy andfaulty conditions confirm the reliability of the suggested framework.

& 2015 ISA. Published by Elsevier Ltd. All rights reserved.

1. Introduction

In the last few decades, abundant research and developmentefforts for motor systems (MS) control technology have been made.The most popular high performance MS control technique is known asvector control (VC), proposed by Hasse and Blaschke. In general, bothconventional PI and PID controllers have the difficulty in making theMS closely follow a reference speed trajectory under rotor timevariation due to temperature and under torque disturbances. In thisregard, an effective and robust speed controller design is needed.

In the recent past years, the sliding mode control (SMC) stra-tegies have received worldwide interest, and many theoreticalstudies and application researches are reported as described in [1]and the theoretical foundations of sliding mode control in electro-mechanical systems was developed by Utkin et al. as presented in

[2]. The most positive feature of SMC consists of the completecompensation of the so-called matched disturbances when thesystem is in the sliding phase and a sliding mode is enforced, thecompensated dynamics become insensitive to matched distur-bances and uncertainties under sliding mode control. The price forthis insensitivity is control chattering and a reaching phase duringwhich the system dynamics is vulnerable to disturbances/uncer-tainties [3].

Despite these disadvantages; the insensitivity and robust-ness of SMC make it suitable for handling system under controlwith satisfactory performance in both normal and faulty operatingconditions [4].

In the last years, a novel SMC with an integral switching surfacehas attracted a lot of attention (see [5–8]). Successively, manyapplication examples of this control strategy have been developedin the literature and different class of systems are studied, Hence,in [5], an electropneumatic servodrive system is considered. Inthat paper, two sliding mode controllers are synthesized with andwithout an integral term in the sliding surface. The experimentalresults show that the second controller provides best resultsespecially for a steady-state error cancellation. Moreover, in [6,7]an electromechanical system is considered. where, comparativestudies between three control strategies are presented. Indeed, the

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ISA Transactions

http://dx.doi.org/10.1016/j.isatra.2015.02.0040019-0578/& 2015 ISA. Published by Elsevier Ltd. All rights reserved.

n Corresponding author at: Ecole Nationale Polytechnique, Automatic ControlDepartment, LCP, B.P 182 Elharrach, Algiers, Algeria. Tel.: þ213 35 54 73 95.

E-mail addresses: hamza.mekki@g.enp.edu.dz (H. Mekki),omar.benzineb@univ-brest.fr (O. Benzineb),djamel.boukhetala@g.enp.edu.dz (D. Boukhetala),mohamed.tadjine@mail.enp.edu.dz (M. Tadjine),Mohamed.Benbouzid@univ-brest.fr (M. Benbouzid).

ISA Transactions 57 (2015) 340–351

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experimental results verify that the SMC with integral surfaceprovides favorable tracking performance, faster and smootherspeed regulation with regard to parameter variations and distur-bances compared with the results obtained from conventionalSMC and classical PID controllers. In addition, the first order SMCwith an integral surface has found extensive applications in motorsystems control domains as presented for induction motor in [8].

On the other hand, in the control design and fault tolerancedomains, there appears to very little new theoretical developmentbased SMC. Especially in [9], where a combination of SMC and on-line control allocation (high level controller) was explored toachieve tolerance to system (ADMIRE benchmark aircraft model)faults/failures throughout the entire system response. Startingfrom those works ([5–9]); in this paper a new given configurationfor induction motor will be presented.

The sliding mode observers (SMO) are used in both linear andnonlinear systems with uncertainties. The sliding mode observercan force the output estimation error to converge to zero in finitetime, while the observer states converge asymptotically to thesystem states. In addition, disturbances within the system can alsobe reconstructed [10]. Moreover, several applications based SMOhas been discussed at several papers recently [11–15], thosepapers are concerned with the use of sliding mode ideas for faultdetection, reconstruction and how this information may be used ina simple way to provide a fault tolerant control scheme.

In the complex systems (nuclear central, aeronautic…) the SMObased faults detection and reconstruction phase will be notsufficient to guarantee the stability and the good performance;thus call FTC unit is needed.

Fault tolerance is no longer limited to high-end systems butalso to spacecraft systems [15–17] and automobile applications[18–20]. It becomes an important means to increase the reliability,availability, and continuous operation of electromechanical sys-tems among the automotive ones [20].

In general, the FTC approaches can be classified into two types: theactive approach as presented in this paper and the passive approach.The survey book [21] reviews the concepts and the state of the art inthe field of FTCs, comparative study between these two approachesand the recent advances have been reported in [22,23].

Typical passive approaches as described in [24–26] applyunchangeable controllers throughout the normal (fault-free) caseand failure cases. Generally based on robust control theory, thepassive FTC controller is relatively easy to implement since neitherfault detection and diagnosis block nor controller reconfigurationis required. However, as the number of possible failures and thedegree of system redundancy increase, the predesigned FTCcontroller becomes more conservative and attainable controlperformance may not necessarily be satisfactory [27].

In the active approach, the control system tolerates the faultsby changing the control algorithm (also known as reconfiguration).The principle of active approaches, illustrated by Fig. 1, is verysimple. When a fault occurs in the level of, the system deviatesfrom its nominal operating point defined by its input/outputvariables (u0, y0) to a faulty one (uf, yf). The goal of fault-tolerantcontrol is to determine a new control law that takes the degradedsystem parameters into account and drives the system to a newoperating point (uc, yc) such that the main performance para-meters (stability, accuracy, etc.) are preserved (i,e., are as close aspossible to the initial parameters) [28]. It is, therefore, importantto define precisely the degraded modes that are acceptable withregard to the required performance parameters, since alter theoccurrence of faults, conventional Feedback control design mayresult in unsatisfactory performance such as tracking error,instability, and so on.

The contribution of this paper is that it provides very simple andeffective fault detection, reconstruction and tolerance strategy.

Compared to the existing works in the literature [4,9,11–13,15–17,24–25,29–32], the contributions of this paper are highlighted inthe following aspects:

� Compared with the passive FTC based complex internal modelpresented in [24,29] which requires to know or to estimate thevector of the frequencies characterizing the faults. This designmethod becomes very difficult in case of a large frequenciesvector. In this work the designed active FTC require only asimple SMO for fault detection and reconstruction.

� The FTC scheme proposed in this paper (based SMC augmentedby integral switching surface) has certain advantages comparedto [25,30], which are based backstepping and traditional SMCmethods for induction motors.

� In [30,31] authors propose a very complex FTC structure basedprojection method, where, this later needs a switching block(to switch between two controls strategies). In this work wepropose a very simple FTC structure which does not needswitching block and uses only one control strategy (SMC withan integral switching surface).

� Starting from [4,17]; where authors propose a FTC based slidingmode control for nonlinear longitudinal model of a Boeing 747-100/200 airplane to deal with modeling uncertainties andactuator faults and for spacecraft systems in the presence ofunknown actuator failure and control input saturationrespectively.

� Compared with [11–13], where authors used sliding modeobservers for fault detection and reconstruction. In this paperthe sliding mode observer is used to detect, reconstruct thefaults and also to design a sensorless control strategy.

� In [9] a complex FTC scheme based on appropriate combinationof SMC and control allocation has been proposed. In this workthe proposed FTC approach is based on combination betweensimple SMC and SMO the proposed combined scheme could beinteresting and this approach can achieve tolerance to a wideclass of total system failures.

� Starting from [15,16], in those papers authors propose respec-tively a novel combination between fault reconstruction andfault tolerant attitude control for aircraft benchmark undersensor failure and for over-activated spacecraft with reactionwheels under actuator failure based SMO and optimal controlmethod. Indeed, the proposed algorithm in our case is based onSMO and robust control method for motor systems underactuator failure.

� In [25] a sensor-less fault tolerant control based backsteppingcontrol and second-order sliding mode observer is proposed toavoid the speed and flux sensors, and provides passive faulttolerance for rotor resistance variations (þ100%Rr) and loadtorque disturbances.In this work an effective and simple sensor-less fault tolerantcontrol based robust controller (SMC with an integral sliding

Failure Initial Operating Conditions

Normal Operating Conditions

Faulty Operating Conditions

Performances

),( yu

),( ff yu),( 00 yu ),( cc yu

Accommodation

Fig. 1. Fault tolerant control problem.

H. Mekki et al. / ISA Transactions 57 (2015) 340–351 341

surface) and sliding mode observer are proposed to achievespeed and flux finite time convergence. The SMO is designed todetect and reconstruct the faults which represent a major issuein the field of faults detection, diagnosis and FTC. On the otherhand, the proposed approach not only provides an Active (on-line) fault tolerance for one and two broken rotor bars, but canachieve tolerance to wide class of total system failures.

� As stated in [32] “A Recent approach for dealing with uncer-tainties is based on the use of sliding mode method to enhancethe robustness of FTCs. However, the problem of FTC designon SMC schemes is still in its early stage of development,and a few results have been reported in the literature”. In thiscontest and considering the existing results, the systemicdesign of the FTC scheme in this paper focuses on very simplestructure, more sensitive detection and a quicker compensationprocedure.

The paper is organized as follows. The next section introducesthe problem under consideration and gives some preliminaries.Section 3 describes the induction motor systems (IM) healthymodel. Section 4, is devoted to the design of modified SMCtechnique (conventional sliding-mode controller with an integralswitching surface), which is able to steer the flux and speedvariables to their desired references and to compensate the loadtorque disturbance this section will end with the closed-loopstability analyses. Section 5, describes the induction motor modelin presence of broken rotor bars, end-rings faults. Then, the slidingmode observer based fault detection and reconstruction arepresented. Moreover, the global proposed FTC scheme is analyzedin detail, followed by an additional control laws (compensationunits) illustrated from the SMO which will be designed in order tocompensate the additive (broken rotor bars, end-rings) faultseffect. Then, in order to prove the efficiency of the proposedapproach in healthy and during the faulty condition, some simula-tion results will be presented and discussed in Section 6. Finally,some concluding remarks are made in the last Section.

2. Preliminaries and problem statement

The following results will be used in the later analysis. Considerthe following nonlinear system affected by external disturbances

and parameter variationswAℜr , as described in [30] by:

_x¼ f ðxÞþBuþΓwy¼ Cx

(ð1Þ

where f ðxÞ denotes a known smooth function representing thenonlinear characteristics of the system, xAℜn is the state vector,uAℜmis the input vector, yAℜp is the output vector, w is a vectorof unknown parameters and external disturbances (faults),ΓAℜn�r is the distribution matrix for disturbances and parametervariations, is the state matrix, BAℜn�m is the input matrix andCAℜp�n(pom) is the output matrix.

Our control objectives are to design fault detection, reconstruc-tion and FTC approach to drive the system measured and esti-mated outputs to track given reference signalsŷðtÞ-yðtÞ-yref ðtÞwith good tracking performances, under both nominal and faultyconditions.

To achieve the above control objectives under nominal andfaulty conditions, we propose in this work a nominal robustcontroller (SMC) noted VnomðtÞ which generate the control lawunder healthy condition and present a natural capability fordealing with some kind of faults (i.e. a reduction in the effective-ness) in system, but cannot deal directly with total additivefailures. This nominal controller is combined with observer basedapproach (SMO) which is designed to detect and reconstruct thefaults signal noted Γw (for example rotor asymmetries or statorasymmetries in the case of motors systems). This combination canachieve tolerance to a wide class of total additive failures. Whenthe fault occurs in the system; then from the faults signalestimation Γ̂w an additive control law can be generatedVfaultyðtÞfor the faulty condition according to the criterion:

VfaultyðtÞ ¼ 0 if Γ̂w¼ 0VfaultyðtÞa0 if Γ̂wa0

(ð2Þ

At the end the total control law will be given by:

VtotalðtÞ ¼ VnomðtÞþVfaultyðtÞ ð3Þ

Once the faults signal is detected and reconstructed by theSMO an additive control law will be generated by this later(VfaultyðtÞa0) in this case, in order to protect the system fromdamages an alarm indicator is added to the design. The alarmsignal will indicate that maintenance is needed.

nomqV

sqV

Faults

*Ω

nomdV

dˆ

Ω

sdV

faultydV

faultyqV

sθ̂sdisqi

bi

*d

ai

Sliding Mode Observer

sqV

sdV

+ +

+ +

ParkTransform

Voltage Source Inverter

PWM

ParkTransform

Alarm Sliding Mode

Controller

ϕ

ϕ

Fig. 2. Block diagram of the overall control strategy.

H. Mekki et al. / ISA Transactions 57 (2015) 340–351342

The additional control laws VfaultyðtÞ (compensation units)which will be designed in order to compensate the additive faultseffect in system (1) is given by:

Vfaulty ¼ �B�1Γ̂w ð4ÞThe proposed scheme is applied to the most widespread

motors in the industry today, which constitute more than 85% ofall industrial motors. This is due to their simple manufacturing,reliability and robustness [33] (induction motor system) withseveral possible faults (parameter variations, external disturbancesand rotor broken bar) that will be considered to demonstrate theeffectiveness of the proposed approach. As presented in thefollowing sections, each part of this block diagram Fig. 2 will bedeveloped.

3. Induction motor healthy model

In field oriented control, the flux vector is forced to align withthe d-axis (ϕq ¼ _ϕq ¼ 0). The induction motor healthy model in thestator direct and quadrature (d�q) reference frame is given by thefollowing state equations [34]:

disddt ¼ _isd ¼ a1isdþωsisqþa2φdþbu1disqdt ¼ _isq ¼ �ωsisdþa1isqþa5φdΩþbu2dφddt ¼ _φd ¼ a8φdþa10isddΩdt ¼ _Ω¼ a14isqφdþa15ΩþdTL

8>>>>><>>>>>:

ð5Þ

ωs ¼ npΩþa7isqφd

ð6Þ

where

u1 u2� �T ¼ Vsd Vsq� �Tφd ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiφ2rαþφ2rβ

q;ωs ¼ _θs; θsð0Þ ¼ 0

8><>:

The components are expressed according to the IM parametersas follows:

a1 ¼ � 1Tsσþ1�σTrσ� �

; a2 ¼ 1�σTrMσ; d¼ �1j ; a5 ¼ �np1�σMσ ;

a7 ¼ a10 ¼ MTr; a8 ¼ � 1Tr; a14 ¼npMJLr

; a15 ¼ � fJ; b¼ 1σLs

8><>:where npis the pole pairs number of the induction motor;Rs; Rr ; Ls; Lr , are the stator and rotor resistances and self-induc-tances, respectively; M is the mutual inductance, J is the momentof inertia of the rotor, f denote friction coefficient and TL representsthe load torque, which is assumed constant.isdand isqdenote thestator current components. Vsdand Vsqare the stator voltagecomponents.Ω,φd, ωsand θsare respectively the rotor speed, therotor flux, the electrical synchronous speed and the synchronousposition. Tr ¼ Lr=Rr ; Ts ¼ Ls=Rsand σ ¼ 1�M2=Lr Ls.

The field oriented control using PI controllers under nominalcondition is very satisfying, but it has many drawbacks especiallythe rotor time variation due to temperature. To overcome theseproblems, a robust control strategy based sliding mode with anintegral sliding surface is proposed for speed and flux IM control.

4. Sliding mode control with integral sliding surfaces

The Sliding Mode Control (SMC) theory is an effective controlstrategy in modern control theory as for its robustness and simplyrealization. Due to its order reduction, disturbance rejection,strong robustness, and simple implementation by means of powerconverter, is one of the prospective control methodologies for

electromechanical systems ([2,6–7]), aircraft systems [9] and EV/HEV traction applications [18]. Indeed, the applications of SMC toinduction motors have been widespread in recent years and adetailed review of SMC development applied to these later arebriefly described in [35]. For more details about the sliding modearea, you can refer to these very interested books [1,2,10,36].

As stated in [5], the sliding mode controller with an integralsurface gives more useful results at all the operating points(central position and extremity). The static error has beendecreased enough relative to the other controller and thedynamics is satisfactory especially at the extremity.

In this contest, taken into account the works presented in [5–8]where authors design a SMC with an integral surface for severalsystems (electropneumatic servodrive, electromechanical systemand induction motors) using two parts switching surfaces; the firstpart may be designed as the linear combination of the systemstates (similar to the conventional Sliding Mode design) and, thesecond part induces an integral term. Then, a sliding modecontroller with integral sliding term is developed for class ofinduction motors systems.

Remark 1. This section develops a systematic design procedurefor the synthesis of a SM controller. There are two steps to design aSM controller as described in [5–8,29,35], in the first step theswitching surface is designed, in the second step, the control lawto induce and maintain a sliding motion is created.

4.1. Sliding surface design

In this step the design of a sliding surface such that the systempossesses the desired performance when it is restricted to thesurface is given. The problem of interest in the present case isgenerating a first order sliding mode by an adequate choice of thesliding surfaceSðtÞ. For this purpose, sliding surface with integralaction can be introduced as (see [6,7]):

SðtÞ ¼ eðtÞþmiZ t0eðτÞdτ ð7Þ

where: mi and eðtÞ represent respectively a positive constant andthe difference between the controlled variable and its reference.

In this work, using the reduced nonlinear induction motormodel in (5), it is possible to design speed, flux and currentssliding mode controller. Then, starting from (7) four slidingsurfaces with integral action are used and taken as follows sincea first order model is used (see [8]):

S1 ¼ φd�φndþm1R ðφd�φndÞdt

S2 ¼Ω�Ωnþm2R ðΩ�ΩnÞdt

(ð8Þ

S3 ¼ isq� insqþm3R ðisq� insqÞdt

S4 ¼ isd� insdþm4R ðisd� insdÞdt

(ð9Þ

where: ðinsd; insqÞ, φnd and Ωn represent respectively the currents, fluxand speed references respectively. m1,m2, m3and m4 are positiveconstants.

4.2. Sliding mode control laws

The application of the sliding mode control strategy with anintegral sliding surface to induction motor in this case is dividedinto two steps:

4.2.1. Step 1: Flux and speed regulatorsThe condition necessary for the system states follow the

trajectory defined by the sliding surfaces is Si ¼ 0 which bringsback us to define the rotor flux module and speed equivalent

H. Mekki et al. / ISA Transactions 57 (2015) 340–351 343

control in the following way:

S1 ¼ 0S2 ¼ 0

()

_S1 ¼ _φd� _φndþm1ðφd�φndÞ ¼ 0_S2 ¼ _Ω� _Ωn þm2ðΩ�ΩnÞ ¼ 0

(ð10Þ

In this case the equivalent currents references are given by:

insdeq ¼ 1a10ð _φn

d�a8φd�m1ðφd�φndÞÞinsqeq ¼ 1a14φdð _Ω

n �a15Ωn�d1TL�m2ðΩ�ΩnÞÞ

(ð11Þ

The control law which ensures the attractivity is:

insdn ¼ �k1signðS1Þinsqn ¼ �k2signðS2Þ

(ð12Þ

Finely the total reference currents illustrated from (11) and (12)are:

insd ¼ insdeqþ insdninsq ¼ insqeqþ insqn

8<: ð13Þ

4.2.2. Step 2: Currents regulatorsAccording to the derivative of the currents surfaces, the tension

on the (d–q) axis can generated as follow:

_S3 ¼ _isq�_in

sqþm3ðisq� insqÞ ¼ 0_S4 ¼ _isd�_i

n

sdþm4ð_isd�_in

sdÞ ¼ 0

8<: ð14Þ

To give a simple an adequate form let take:

eq ¼ ðisq� insqÞed ¼ ðisd� insdÞ

(and

eφ ¼ ðφd�φndÞeΩ ¼ ðΩ�ΩnÞ

(

In this case the control law is taken as:

u2eq ¼ 1b ðdin

sq=dtÞ� f 2ðxÞ�a14φdeΩ�m3eq� �

u1eq ¼ 1b ðdin

sd=dtÞ� f 1ðxÞ�a10eφ�m4ed� �

8<: ð15Þwhere

f 1ðxÞ ¼ a1isdþωsisqþa2φdf 2ðxÞ ¼ �ωsisdþa1isqþa5φdΩ

(

The attractive control law is ensured by:

u2n ¼ �k3signðS3Þu1n ¼ �k4signðS4Þ

(ð16Þ

Finely the healthy control law illustrated from (15) and (16) is:

u2nom ¼ Vsq ¼ u2eqþu2nu1nom ¼ Vsd ¼ u1eqþu1n

(ð17Þ

4.3. Closed loop stability analysis:

The closed-loop system stability analysis consists here of theanalysis for (d–q) axis subsystem which adopts sliding modecontroller. The objective is to steer the currents (isd) and (isq), theflux and the speed to their desired references ðisdÞref andðisqÞref , φndand Ωnrespectively.

Leted,eq,eφandeΩbe the tracking errors of the currents, the fluxand the speed then the dynamic of the tracking errors are givenby:

_ed ¼ a1isdþωsisqþa2φdþbVsd�ðdinsd=dtÞ_eq ¼ �ωsisdþa1isqþa5ϕdΩþbVsq�ðdinsq=dtÞ_eϕ ¼ a8φdþa10ed� _φndþa10insd_eΩ ¼ a14φdeqþa15ΩþdTL� _Ω

n þa14φdinsq

8>>>><>>>>:

ð18Þ

By taking k1 ¼ ðkφ=a10Þandk2 ¼ ðkΩ=a14x3Þin (12) then (13) will be:

insd ¼1a10

ð _φnd�a8φd�m1eφ�kφsignðS1ÞÞ ð19Þ

insq ¼1

a14φdð _Ωn�a15Ω�dTL�m2eΩ�kΩsign ðS2ÞÞ ð20Þ

From (19) and _eϕand from (20) and _eΩwe get respectively:

_eφ ¼ a10ed�m1eφ�kφsign ðS1Þ_eΩ ¼ a14φdeq�m2eΩ�kΩsign ðS2Þ

(ð21Þ

By taking k3 ¼ ðkq=bÞ andk4 ¼ ðkd=bÞ in (16) then (17) will be:

Vsq ¼1bðωsisd�a1isq�a5φdΩ�a14x3eΩ�m3eq

þðdinsq=dtÞ�kqsignðS3ÞÞ ð22Þ

Vsd ¼1bð�a1isd�ωsisq�a2φd�a10eφ�m4ed

þðdðinsd=dtÞ�kdsignðS4ÞÞ ð23ÞFrom (22) and _eqand from (23) and _edwe get respectively:

_eq ¼ �m3eq�a14φdeΩ�kqsign ðS3Þ_ed ¼ �m4ed�a10eφ�kdsign ðS4Þ

(ð24Þ

Consider the following Lyapunov function:

V ¼ 12

e2dþe2qþe2φþe2Ω� �

The derivative of V with respect to time is:

_V ¼ edð�m4ed�a10eφ�kdsign ðS4ÞÞþeqð�m3eq�a14φdeΩ�kqsign ðS3ÞÞþeφða10ed�m1eφ�kφsign ðS1ÞÞþeΩða14φdeq�m2eΩ�kΩsign ðS2ÞÞ ð25ÞTo assure the stability mi (i¼ 1;…;4) must be chosen as

follows:

m444 kdsign ðS4Þ�� ��

max

m344 kqsign ðS3Þ�� �� max

(and

m144 kϕsign ðS1Þ�� ��

max

m244 kΩsign ðS2Þ�� ��

max

(

Then the derivative of the Lyapunov function (25) becomes:

_Vo�m4e2d�m3e2q�m1e2φ�m2 e2Ω ð26ÞFinally from (26) it is shown that ( _Vr0) the derivative of the

complete Lyapunov function be negative definite, this implies thatthe error variables ed; eq; eϕ and eΩ are globally uniformly bounded.

Remark 2. It is important to notice that any first order sliding modecontroller (with or without integral sliding surface) introduces thechattering in the system. In order to overcome this problem, severalsolutions are presented in [1,2] and in these new interested books[10,36] to chattering avoidance (Attenuation and Elimination). More-over, it is suggested checking these books ([1,2,10,36]) in order toimprove more knowledge about the theory of sliding modes.

In the next section the induction motor model under brokenrotor bars and end-ring faults will be presented. In order toestimate the faults (FDI unit) and the flux (sensorless controlstrategy), a sliding mode observer (SMO) is introduced. Then, theglobal FTC strategy will be designed thanks to SMC and SMO.

5. Fault detection, reconstruction and FTC

5.1. IM faulty model

Induction Motors (IM) are subjected to various faults, around 5–10% of total induction motor failures are rotor failures and, more

H. Mekki et al. / ISA Transactions 57 (2015) 340–351344

specifically, broken rotor bars and end-ring faults [33]. Indeed, manystudies [37,38] showed that broken rotor bars faults revealed harmo-nics at specific frequencies in the induction machine stator currents.

In this section we briefly review how the IM model will bemodified in presence of faults which can be both of mechanicaland electrical nature. Following the recent work in [24,25] andwith reference to [39], the faults dealt with in this paper can besummarized in the class of rotor asymmetries, mainly due to brokenbars. Several research efforts have focused in the last years on thestudy of the effect of broken bars faults in the IM, see ([33,37–42]).

When broken cage bars, end-ring faults, or abnormal levels ofeccentricity occur in the IM, asymmetry in the rotor air-gap appear andspurious harmonics at well defined characteristic frequencies coming outin the stator current spectrum as presented in [40–42]. In the two-phasemodel, it is possible tomodel this effect thinking of a sinusoidal componentwhich corrupts the stator currents, (for more detail see [24,43]).

The sinusoidal components generated by the presence of therotor broken bars faults can be modeled by the following exosys-tem [24,29]:

_w¼ δ ϖð ÞUw wAℜ4nf þ2 ð27Þ

with

ϖ ¼ ðω1 ω�1 … ωnf ω�nf Þ

where ϖ: The pulsations vector., nf : The broken bars faults numbers.

δ ϖð Þ ¼ diag ðδr;1;…δr;nf Þ

δr;k ¼ diag0 ωk

�ωk 0

!;

0 ω�k�ω�k 0

! !

where ω7 k,k¼ 1;…;nf are the pulsations of the harmonics gener-ated by the rotor faults.

Faults caused by rotor asymmetry due to broken bars yieldsharmonics component at the frequency as described in [39,41,42]:

f r;k ¼ ð172kswÞf ð28Þ

where sw: The slip (sw ¼ωs�ω), f : The supply frequency, k:Positive integer (k¼ 1;…;nf )

The amplitudes and the phases of the harmonics are unknown;they depend on the initial state wð0Þ of the exosystem. Then, theadditive sinusoidal terms can be as a suitable combination of theexosystem state, i.e:

isd-isdþQdwisq -isq þQqw

(ð29Þ

with

Qd ¼ 1 0 1 0 … 1 0� �

Qq ¼ 0 1 0 1 … 0 1� �(

Recalling the current dynamics in the un-faulty operativecondition reported in the previous section, a simple computationshows that, once the perturbing terms Qdw and Qqw are added, byderiving (29) the id� iq

� �dynamics modify as:

disddt ¼ a1isd þ ωsisq þ a2φd þ bu1

þ a1Qdwþ Qdδw−ωsQqwdisqdt ¼ _x2 ¼ −ωsisd þ a1isq þ a5φdΩþ bu2

þ a4Qqwþ Qqδwþ ωsQdw

8>>>>><>>>>>:

ð30Þ

Bearing in mind the dynamics of the rotor currents in thenormal (i.e., in the absence of faults) operative conditions, it is alsosimple to get the IM dynamics after the occurrence of a fault. As amatter of fact, taking (30) it is readily seen that the IM model in

presence of faults is given by (5) with an exogenous input.

_isd ¼ a1isd þ ωsisq þ a2φd þ bu1 þ Γdw_isq ¼ −ωsisd þ a1isq þ a5ϕdΩþ bu2 þ Γqw_φd ¼ a8φd þ a10isd_Ω ¼ a14isqφd þ a15Ωþ dTL

8>>>><>>>>:

ð31Þ

with

Γdw ¼ ða1Qd þ Qdδ−ωsQqÞwΓqw ¼ ða4Qq þ Qqδþ ωsQdÞw

(

In this work the pulsations ω7k,k¼ 1;…;nf are assumed to beunknown. In order to reconstruct the fault effectsΓdw and Γqw, asliding mode observer is used.

5.2. SMO based fault detection and reconstruction

Sliding mode observers can be used for fault estimation inuncertain linear and nonlinear systems subject to additive (actuator,system and sensor) faults. They permit to reconstruct explicitly thefaults by analyzing the dynamic of the estimation error when thesliding mode occurs. In [11,12–14] the sliding mode observers areused for FDI and fault reconstruction designs. In ([44,45]) a sensorlessIMs control strategies based sliding mode observers are designed.

In this paper, in order to estimate the fault effects Γdw, Γqw(fault detection and reconstruction unit) and the flux (sensorlesscontrol strategy), a sliding mode observer (SMO) is introduced aspresented in [11–14,44,45], where the currents isd, isq and the speedare assumed to be measured. In this section from the inductionmotor faulty model (31) the SMO will be introduced as follows:

_̂isd ¼ a1ˆisd þ ˆωsisq þ a2ˆφd þ bu1−udsign εd_̂isq ¼ −ˆωsisd þ a1ˆisq þ a5ˆφdΩþ bu2−uqsign εq_ˆφd ¼ a8ˆφd þ a10isdωs ¼ npΩþ a7ðisq=ˆφdÞÞ

8>>>><>>>>:

ð32Þ

where: îsd ,̂isq are the observed stator currents and φ̂dis the esti-mated flux, ud40 and uq40 are design parameters whereεd ¼ îsd� isd and εq ¼ îsq� isq are the observer sliding surfaces.

The currents and flux estimation errors are defined by theobserver sliding surfacesεd,εqandεϕ ¼ φ̂d�φd, then the errorsdynamics are given by:

_εd ¼ a1εdþðω̂s�ωsÞisqþa2εφ�Γdw�udsign εd_εq ¼ �ðω̂s�ωsÞisdþa1εqþa5Ωεφ�Γqw�uqsign εq_εφ ¼ a8εφ

8><>: ð33ÞConsider the SMO Lyapunov function given by:

V ¼ 12ε2dþ

12ε2q ð34Þ

The derivative of (34) with respect to time is given by:

_V ¼ εdða1εdþðω̂s�ωsÞisqþa2εφ�Γdw�udsign εdÞþεqð�ðω̂s�ωsÞisdþa1εqþa5Ωεφ�Γqw�uqsign εqÞ ð35Þ

By choosing:

ud4 a1εdþðω̂s�ωsÞisqþa2εφ�Γdw�� ��

max

uq4 �ðω̂s�ωsÞisdþa1εqþa5Ωεφ�Γqw�� ��

max ð36Þ

the sliding mode occurs, i.e.:εd ¼ _εd ¼ 0andεq ¼ _εq ¼ 0.Therefore the Eq. (33) become:

ðˆωs−ωsÞisq þ a2εφ−Γdw−udsigneqεd ¼ 0−ðˆωs−ωsÞisd þ a5Ωεφ−Γqw−uqsigneqεq ¼ 0_εφ ¼ a8εφ

8><>: ð37Þ

H. Mekki et al. / ISA Transactions 57 (2015) 340–351 345

Eq. (37) shows that εφ converges to zero as t-1 , then ω-ω̂ and thefaults can be estimated where the estimates of the faults are given by

Γ̂dw¼ �udsigneq εdΓ̂qw¼ �uqsigneq εq

ð38Þ

Remark 3. The function signeq represents the average value of thesignfunction; it can be obtained by the use of a low pass filter or bya continuous approximation of the sign function. Here thesignfunction is approximated by a saturation (sat) function.

5.3. Global control reconfiguration

As presented in Section 2. The structure of the proposed faulttolerant controller is given by:

Vsd ¼ u1nomþVdfaultyVsq ¼ u2nomþVqf aulty

(ð39Þ

where: u1nom, u2nom are the sliding mode control laws (22) and (23)designed in un-faulty mode (wðtÞ ¼ 0) to steer the tracking errorsof speed and flux to zero and to compensate the disturbance andthe load torque effect.

Vdfaulty,Vqf aulty are additional control laws (compensation units)that will be designed in order to compensate the additive faults effect.

If the additional control laws is taken as:

Vdfaulty ¼ �1bΓ̂dwVqf aulty ¼ �1bΓ̂qw

(ð40Þ

where the estimates Γ̂dw and Γ̂qw are given by Eq.(38). Then, thefaults are compensated.

Proof: The dynamics of the tracking errors are given by:

By substituting (39) in (41):

_ed ¼ −kdeval ed−a10eφ þ Γdw−ˆΓdw_eq ¼ −kqeval eq−a14φdeΩ þ Γqw−ˆΓqw_eφ ¼ −kφeval eφ þ a10ed_eΩ ¼ −kΩeval eΩ þ a14φdeq

8>>>><>>>>:

ð42Þ

Remark 4. This Section presents the faults detection and reconstruc-tion using a sliding mode observer also show that Γdw-Γ̂dw andΓqw-Γ̂qw then the faults are compensated and the resulting closedloop system is stable. Its stability is proved in Section 4 by theLyapunov function.

Remark 5. When the faults signal is detected and reconstructedby the SMO an additive control law will be generated by this later(VfaultyðtÞa0) in this case, in order to protect the system fromdamages an alarm indicator is added to the design (see Fig. 2). Thealarm signal will indicate that maintenance is needed.

6. Numerical simulation

To validate the performances of the proposed approach describedin the previous section, a series of computer simulation conductedfor a cage rotor induction motor are provided, whose rated valuesand nominal electrical and mechanical parameters are shown inTable 1. The simulation was made with MATLAB/Simulink. The speed

and flux references are fixed at Ω¼ 100 rad=s and φd ¼ 0:9 Wb;respectively, also a nominal load disturbance TL¼5 Nm is applied.The sliding mode gains adopted for simulation activities are chosenas follows:kφ ¼ 68, kΩ ¼ 50, kd ¼ 220, kq ¼ 250,m1 ¼ 300, m2 ¼ 270,m3 ¼ 600, m4 ¼ 680, ud ¼ 3400 and uq ¼ 3400.

To highlight the performance of the proposed approach, threesituations are presented and discussed. The first scenario analyzesthe performance due to different speed profiles (sudden step) andto the torque changes. The second one investigates the perfor-mance of IM in closed loop when only one rotor fault occurs attime t¼0.4 s. The last scenario illustrates the case of two rotorfaults occurs at time t¼0.4 s.

6.1. Case 1- IM under different speed and torque profiles

In this case the IM is subjected to various tests with differentspeed and load torque profiles, where two situations are consid-ered. In the first one the IM subjected to trajectory tracking testwith nominal load disturbance TL¼5 N m. Hence, a sudden stepincreases in speed from 100 rad=sto 150 rad=sis applied at time

)(and)( titi sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

4

8

12

Isd

Isq

)(and)( tVtV sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-200

0

200

400

VsdVsq

sec

Fig. 3. Simulation results. Currents (isdðtÞandisqðtÞ) upper plot; and voltages (VsdðtÞ andVsqðtÞ) lower plot in case of speed sudden step, with the IM controlled via SM Controller.

Table 1Nominal parameters of the IM adopted for simulation.

Rated values Power 1.08 kWVoltage 220/380 VFrequency 50 Hznp 2Speed 1480 Rpm

Rated parameters Rs 10 ΩRr 6.3 ΩLs 0.4642 HLr 0.4612 HM 0.4212 HJ 0.02 Kg m2

f 0.0005 ISTL 5 N m

_ed ¼ a1isd þ ωsisq þ a2φd þ bVsd þ Γdw− 1a10ð−a8ða8φd þ a10isdÞ þ ̈φ

⁎d−kφeval _eφÞ

_eq ¼ −ωsisd þ a1isq þ a5φdΩþ bVsq þ Γqwþ ða8φdþa10 isdÞ

a14φ2dð̇Ω ⁎

þ dTL−kΩeval _eΩÞ −1

a14φdð ̈Ω ⁎−kΩeval _eΩÞ_eφ ¼ a10ed−kφeval eφ _eΩ ¼ a14φdeq−kΩeval eΩ

8>>>>><>>>>>:

ð41Þ

H. Mekki et al. / ISA Transactions 57 (2015) 340–351346

t¼0.4 s. The simulation results obtained are presented in Figs. 3 and4. In the second situations the IM subjected to load torque changestest with fixed speed Ω¼ 100 rad=s. The simulation starts withnominal load torque TL¼5 N m, and at time t¼0.4 s, the load torqueTL steps from 5 to 10 N m; as described in Figs. 5 and 6.

Simulations results in healthy condition illustrate that theproposed SM Controller (SMC with an integral sliding surface)force the speed and flux to tracking their desired references withgood dynamics. Therefore, robustness with sliding mode control-ler is demonstrated through simulation in case of different speedprofiles (sudden step) as presented in Figs. 3 and 4 and in case ofload torque changes (see Figs. 5 and 6). The regulator performancewith sensorless control scheme based sliding mode observerworks very well with the present flux estimation algorithm.

6.2. Case 2- IM under one rotor fault

In this case the IM has been damaged by introducing one rotorbroken bar failure at time t¼0.4 s with the IM controlled via thedesigned SM Controller (upper plots) and using the proposed

faults detection, reconstruction and fault tolerant controller (lowerplots) as described in Figs. 7–10. Fig. 11 presents the real additivefaults Γdw ðtÞ and Γqw ðtÞcaused by rotor broken bar and the SMObased faults estimation response Γ̂dw ðtÞ and Γ̂qw ðtÞwhich repre-sent the additional controls inputs (will be spent for fault com-pensation) (upper plots).

These simulations results prove the importance of the proposedSMC (nominal control) where the speed and the flux trajectoriesconverge to their desired references with good dynamics. Moreover,the load torque is very well rejected, but the SMC proves to beinsufficient in the event of rotor fault.

In this respect a SMO is designed in order to detect and reconstructthe faults signal then an additional control laws (compensation units)that will be designed in order to compensate this additive faults. Aspresented in Fig. 11, the faults tracking errors converge to zero.

Remark 6. The finite-time convergence of the speed and the fluxtracking errors to zero is achieved even in presence of load torquedisturbance (before combination between SMC and SMO) and onebroken bar faults (after combination). Furthermore, the used SMO

)(ˆand)( tt dd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.85

0.9

0.95

realest

sec

)(tΩ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

100

120

140

160

realref

ϕ ϕ

Fig. 4. Simulation results. From upper to lower plots: speedΩ ðtÞ and Flux (realφdðtÞ and estimated φ̂dðtÞ) trajectory tracking performance under speed sudden stepapplied at time t¼0.4 s, with the IM controlled via SM Controller.

)(and)( titi sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

4

8

12Isd

Isq

)(and)( tVtV sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-200

0

200

400

Vsd

Vsq

sec

Fig. 5. Simulation results. Currents (isdðtÞandisqðtÞ) upper plot; and voltages (VsdðtÞand VsqðtÞ) lower plot in case of load torque variations of þ100% LT at time t¼0.4 s,with the IM controlled via SM Controller.

)(ˆand)( tt dd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.85

0.9

0.95

realest

sec

)(tΩ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.899

99.5

100

100.5

101

ϕ ϕ

Fig. 6. Simulation results. Speed Ω ðtÞ (upper plot), real φdðtÞand estimated φ̂dðtÞFlux (lower plot) trajectory tracking performance under load torque variations ofþ100% LT, with the IM controlled via SM Controller.

sec

)(and)( titi sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

4

8

12

IsdIsq

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

4

8

12

Isd

Isq

Fig. 7. Simulation results. From upper to lower plots: currents isdðtÞandisqðtÞ whenone rotor fault occurs at time t¼0.4 s, with the IM controlled via the designed SMController and using the proposed faults detection, reconstruction and faulttolerant controller.

H. Mekki et al. / ISA Transactions 57 (2015) 340–351 347

converges in a finite time and permits to give good flux estimation andvery well faults reconstruction as shown in Figs. 4, 6 and 9–11. Thephase portrait, which is given in these figures, demonstrates that theconvergence of the sliding mode variables in finite time is assured.

6.3. Case 3- IM under two rotor faults

In this second case the IM has been damaged by introducing twobroken bar faults at time t¼0.4 s with the IM controlled via the adoptedSM Controller (upper plots) and using the proposed faults detection,reconstruction and fault tolerant controller (lower plots) as shown inFigs. 12–15. Fig. 16 presents the real additive faults Γdw ðtÞ and Γqw ðtÞcaused by two broken rotor bar and the SMO based faults estimationresponse Γ̂dw ðtÞ and Γ̂qw ðtÞwhich represent the additional controlsinputs (will be spent for fault compensation) (upper plots).

From these numerical simulations we can noticed that theproposed SMC (nominal control) force the speed and the fluxtrajectories converge to their desired references with gooddynamics and present robustness compared to the load torquedisturbance, but cannot deal directly with two broken bar additive

)(and)( tVtV sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-200

0

200

400

VsdVsq

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-200

0

200

400

VsdVsq

sec

Fig. 8. Simulation results. From upper to lower plots: voltages (control laws)VsdðtÞandVsqðtÞ when one rotor fault occurs at time t¼0.4 s, with the IM controlledvia SM Controller and using the proposed faults detection, reconstruction and faulttolerant controller.

)(tΩ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.899

99.5

100

100.5

101

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.899

99.5

100

100.5

101

sec

Fig. 9. Simulation results. Speed tracking Ω ðtÞin case of one rotor failure occurs attime t¼0.4 s, with the IM controlled via SMC (upper plot) and using the proposedfaults detection, reconstruction and Fault Tolerant Controller (lower plot).

)(ˆand)( tt dd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.85

0.9

0.95

realest

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.85

0.9

0.95

realest

sec

ϕ ϕ

Fig. 10. Simulation results. Real and estimated Flux tracking φdðtÞ and φ̂dðtÞ in caseof one rotor failure occurs at time t¼0.4 s, with the IM controlled via SM Controller(upper plot) and using the proposed faults detection, reconstruction and FTC(lower plot).

)(~

twqΓ

)(ˆand)( twtw qq ΓΓ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1

0

1

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-80

0

80

estreal

sec

)(~

twdΓ

)(ˆand)( twtw dd ΓΓ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-80

0

80

estreal

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1

0

1

2

sec

Fig. 11. Simulation results in case of IM controlled via the proposed faults detection, reconstruction and FT Controller, when one rotor fault occurs at time t¼0.4 s. Left plots:the real and estimated output of the fault Γdw ðtÞ and Γ̂dw ðtÞ (upper plot) and the fault tracking error ~Γdw ðtÞ (lower plot). Right plots: the real and estimated output of thefault Γqw ðtÞ and Γ̂qw ðtÞ(upper plot) and the fault tracking error ~Γ qw ðtÞ (lower plot).

H. Mekki et al. / ISA Transactions 57 (2015) 340–351348

failures. This is checked by simulations represented above whenthe SMO does not exist. In this respect the SMC is combined withSMO which it designed to on-line detect and reconstruct theadditive faults signals also this observer shown high performancefor flux estimation and for the design of a faults tolerant controller.

Remark 7. The proposed SMC strategy cannot provide finite-timeconvergence of the sliding variable to zero in the presence ofbroken bar faults. This problem is solved by an adequate combina-tion between SMC and SMO as shown in Figs. 9–11 and Figs. 14–16.The phase portrait, which is given in these figures, demonstratesthat the convergence of the sliding mode variables in finite time isassured (the state trajectory is moving towards the origin alongthe sliding surface).

Remark 8. As presented in Remark 3, both the sign function doesnot perform accurately in a discrete-time system, resulting inoscillations and undesired chattering. A linear function with aproper gain (sat) provides much better results in reducing oscilla-tions (Chattering) while still maintaining the properties of slidingmode (see [2]). In this paper the sign function is approximated by asaturation (sat) function.

Remark 9. Compared to the existing works already reported inthe literature [4,9,24,29,30,35,43] which are based on IFOC, back-stepping control and traditional sliding mode control methods.The scheme proposed in this paper base robust SMC with anintegral sliding surface has certain advantages. In [29,43] theproposed FTC approach require a very complex internal modelassumption. However, in this work it requires only a simple SMO.This observer presents a remarkable dynamics for on-line additivefault detection, reconstruction and FTC also for the design ofsensorless control strategy. Moreover, the proposed controller isvalidated by both three cases numerical simulations.

Remark 10. Several fault detection schemes deal with broken rotorbar in induction motors are presented in [37,38,42], using multiplesignature processing, Wavelet packet decomposition and Globalfault index respectively. However, the main proposed scheme basedSMO which is designed not only to online detect the fault but alsoto reconstruct this later. Moreover, the proposed approach providesan active fault tolerance for rotor broken bar faults, also can achievetolerance to wide class of total system failures.

)(and)( titi sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

4

8

12Isd

Isq

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

4

8

12Isd

Isq

sec

Fig. 12. Simulation results. From upper to lower plots: currents isdðtÞ and isqðtÞwhen two rotor faults occur at time t¼0.4 s, with the IM controlled via a standardISM Controller and using the proposed faults detection, reconstruction and FTC.

)(and)( tVtV sqsd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-200

0

200

400

VsdVsq

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-200

0

200

400

VsdVsq

sec

Fig. 13. Simulation results. From upper to lower plots: voltages (control laws) VsdðtÞand VsqðtÞ when two rotor faults occurs at time t¼0.4 s, with the IM controlled viaSM Controller and using the proposed faults detection, reconstruction and FTController.

)(tΩ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.899

99.5

100

100.5

101

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.898

99

100

101

102

sec

Fig. 14. Simulation results. Speed tracking Ω ðtÞin case of two rotor failure occurs attime t¼0.4 s, with the IM controlled via SMC (upper plot) and using the proposedfaults detection, reconstruction and Fault Tolerant Controller (lower plot).

)(ˆand)( tt dd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.85

0.9

0.95

realest

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.85

0.9

0.95

realest

sec

ϕ ϕ

Fig. 15. Simulation results. Real and estimated Flux tracking φdðtÞ and φ̂dðtÞin caseof one rotor failure occurs at t¼0.4 s, with the IM controlled via SM Controller(upper plot) and using the proposed faults detection, reconstruction and FTC(lower plot).

H. Mekki et al. / ISA Transactions 57 (2015) 340–351 349

7. Conclusion

This paper presents a new improved sliding mode based faultsdetection, reconstruction and fault-tolerant control scheme for motorsystems with typical actuator faults. It is shown that the controlscheme based on sliding mode method with an integral slidingsurface not only ensure the stability of closed loop system, but alsomake the convergence rate and the disturbance reject performancemuch better, but cannot deal directly with total additive failures. Toovercome this problem a combination between the proposed nom-inal controller (SMC) and the standard sliding mode observer ispresented. Where, this observer is used to detect and reconstruct theunknown faults presented in the motor model, also to estimate somevector states components. Therefore, this combination can achievetolerance to a wide class of total additive failures. An induction motorsystems case study is presented in order to introduce the conceptand to prove the efficiency of the proposed approach. Moreover,computer numerical simulation based on deferent faults (brokenrotor bars, end-rings) scenarios in induction motor show the effec-tiveness of the proposed approach.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-150

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-150

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150

estreal

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-1

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Fig. 16. Simulation results in case of IM controlled via the proposed faults detection, reconstruction and FT Controller, when two rotor faults occurs at time t¼0.4 s. Leftplots: the real and estimated output of the fault Γdw ðtÞ and Γ̂dw ðtÞ (upper plot) and the fault tracking error ~Γ dw ðtÞ (lower plot). Right plots: the real and estimated output ofthe fault Γqw ðtÞ and Γ̂qw ðtÞ(upper plot) and the fault tracking error ~Γ qw ðtÞ (lower plot).

H. Mekki et al. / ISA Transactions 57 (2015) 340–351350

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Sliding mode based fault detection, reconstruction and fault tolerant control scheme for motor systemsIntroductionPreliminaries and problem statementInduction motor healthy modelSliding mode control with integral sliding surfacesSliding surface designSliding mode control lawsStep 1: Flux and speed regulatorsStep 2: Currents regulators

Closed loop stability analysis:

Fault detection, reconstruction and FTCIM faulty modelSMO based fault detection and reconstructionGlobal control reconfiguration

Numerical simulationCase 1- IM under different speed and torque profilesCase 2- IM under one rotor faultCase 3- IM under two rotor faults

ConclusionReferences