An Observer-Based Mechanical Sensor FailureFault Tolerant Controller Structure in PMSM drive

Ahmad Akrad, Mickaël Hilairet, Demba DialloLGEP/SPEE Labs; CNRS UMR8507; SUPELEC; Univ Paris Sud-P11;

Univ Pierre et Marie Curie-P6; F-91192 Gif-sur-Yvette(ahmad.akrad,mickael.hilairet,demba.diallo)@lgep.supelec.fr

Abstract—This paper presents a specific controller architecturedevoted to obtain a Permanent Magnet Synchronous Motor driverobust to mechanical sensor failure. In order to increase thereliability which is a key issue in industrial and transportationapplications (Electric or Hybrid ground vehicle or aerospaceactuators) two virtual sensors (a two stage Extended KalmanFilter and a back-emf adaptive observer) and a voting algorithmare combined with the actual sensor to build a fault tolerantcontroller. The observers are evaluated off line with experimentaldata and the robustness against parameter variation is testedthrough simulation results. The Fault Tolerant Controller feasi-bility is proved through simulation of the PMSM drive.

Index Terms—Permanent Magnet Synchronous Motors, po-sition and speed estimation, sensorless drive, position sensorfailure, fault tolerant controller.

I. INTRODUCTION

Several failures afflict electrical motor drives and so far,redundant or conservative design has been used in everyapplication where continuity of operations is a key feature.This is the case of home and civil appliances, such as, forexample, air conditioning/heat pumps, engine cooling fans,and electric vehicles, where reliability is a key issue. Fault-tolerance has become an increasingly interesting topic in thelast decade where the automation has become more com-plex. The objective is to give solutions that provide faultaccomodation to the most frequent faults and thereby reducethe costs of handling the faults. In submerged pumps orhostile environments where accessibility to the drive and tothe sensors is tedious and nevertheless continuity of operationis mandatory even in case of fault occurrence, a sensorlessalgorithm is indispensable to maintain the availability andtherefore increase the reliability.

Due to its capability of field-weakening control, high ef-ficiency, and high power density Permanent Magnet Syn-chronous Motors (PMSMs) are becoming competitive in manyapplications such as railway electric propulsion power train,EV or HEV [1], [2].

There are numerous study results about fault detection andfault-tolerant control [3]- [7], but most of them focused onthe faults of power semiconductors of an inverter and statorwindings of the motor. In [4], a fault tolerant controller forautomotive applications with an induction machine has beenpresented. The proposed system adaptively changes of controltechnique in the event of sensor failure or recovery. In [5], amethod to detect sensor faults and an algorithm to reconfigure

the control system for interior permanent magnet motor drivehave been described. The study focused on the detection ofcurrent sensor faults, the analysis of a current observer, andthe resilient control of the drive system while retaining thesame basic control strategy.

In this paper an active position sensor fault tolerant con-troller (FTC) is presented. It is based on the combination ofthe actual sensor and two virtual ones (a two stage ExtendedKalman Filter and a back-emf adaptive observer). A votingalgorithm (maximum likelihood) parameterized with reliabilitycoefficients dedicated to each sensor on the whole speedrange selects the appropriate input (speed and position) forthe control loops [8].

The paper is composed of two sections. The first section isdedicated to the description of the sensorless algorithms andtheir experimental validation. The sensitivity analysis againstparameter variation of the position and speed estimators isstudied through intensive simulations. In the second section,the FTC architecture is introduced; the sensor and its faultsare presented. The FTC is evaluated through simulation of thePMSM drive.

II. POSITION AND SPEED OBSERVERS

PMSM drive research has been concentrated on the elim-ination of the mechanical sensors at the motor shaft withoutdeteriorating the dynamic performance of the drive-controlsystem [9]- [12]. The advantages of sensorless AC drives arethe lower cost, reduced size of the motor set, cable elimination,and increased reliability [13].

The position and speed estimations are computed by anOptimal Two-Stage Extended Kalman Filter (OTSEKF) anda back-emf adaptive observer (AO). The first observer isdesigned in the (dq) rotating frame, while the second one isbased on a model in the (αβ) reference frame.

A. Two-stage Extended Kalman filter

1) Continuous motor model: The salient PMSM is modeledin the standard (dq) reference frame as follows :

ddt

X(t) = Ac(Θ)X(t) + Buc (Θ)U(t) + B

Θc (Θ)Θ(t)

Y (t) = C(Θ)X(t)(1)

978-1-4244-4252-2/09/$25.00 ©2009 IEEE 805

with

X =[

isd isq]t

Θ =[

ω θ]t

U =[

vsα vsβ]t

Y =[

isα isβ]t

Ac(Θ) =

[

−RsLd

ωLqLd

−ωLdLq

−RsLq

]

Buc (Θ) =

[

cos(θ)Ld

sin(θ)Ld

− sin(θ)Lq

cos(θ)Lq

]

BΘc (Θ) =

[

0 0− Φ

Lq0

]

C(Θ) =

[

cos(θ) −sin(θ)sin(θ) cos(θ)

]

In these equations vsα, vsβ , isα, isβ are the voltages andcurrents in the (αβ) reference frame, isd, isq are currents inthe (dq) frame, Ld and Lq are the stator inductances, Rs isthe stator winding resistance, and φ is the flux produced bythe magnets. The angular velocity ω is measured in electricalradians per second (the connection between electrical andmechanical variables is ω = PΩ, where P is the number ofpole pairs) and θ is the electrical position.

2) Discretization of the motor model: For the digital imple-mentation of an estimator, a discrete-time state space model isrequired. Provided that the input vector U is nearly constantduring a sampling period Ts (Ts = 200 µs), the previouscontinuous model (1) leads to the following discrete-time statespace model :

X[k + 1] = A(Θ) X[k] + Bu(Θ) U [k] + BΘ(Θ) Θ[k]Y [k] = C(Θ) X[k]

(2)

Tolerating a small discretization error, a first order seriesexpansion of the matrix exponential is used :

eAc Ts ≈ A = I + Ac Ts

A−1c (eAc Ts − I)Bc ≈ B = Ts Bc

This leads to :

A(Θ) =

[

1 − RsLd

TsωLqLd

Ts

−ωLdLq

Ts 1 −RsLq

Ts

]

Bu(Θ) =

[

cos(θ)Ld

Tssin(θ)

LdTs

− sin(θ)Lq

Tscos(θ)

LqTs

]

BΘ(Θ) =

[

0 0− Φ

LqTs 0

]

This discretised model will be used in the prediction step ofthe EKF which is designed to estimate the unknown vector Θpreviously defined.

3) OTSEKF Algorithm: The main objective of the estima-tor is to determine the position and speed of the PMSM.Therefore, those two variables must be concatenated with theprevious state vector X. This leads to an augmented observerwith a state space vector composed of the currents, the speedand position. Treating X[k] as the full order state and Θ[k] asthe unknown states, the state space model is described by :

Xa[k + 1] = A(Θ[k])Xa[k] + B(Θ[k]) U [k] + W [k]

Y [k] = C(Θ[k])Xa[k] + By(Θ[k]) U [k] + η[k](3)

with

Xa[k] =

[

X[k]Θ[k]

]

A(Θ[k]) =

[

A(Θ[k]) BΘ(Θ[k])0 G(Θ[k])

]

B(Θ[k]) =

[

Bu(Θ[k])0

]

C(Θ[k]) =[

C(Θ[k]) D(Θ[k])]

W [k] =

[

W x[k]WΘ[k]

]

where G(Θ[k]) describes the evolution of the unknown statevariable Θ between two time samples. The process noisesW x[k], WΘ[k] and the measurement noise η[k] have theappropriate properties [14].

The application of the EKF [14] to the non-linear state spacemodel (3) is described as follows :

Xa[k|k − 1] = A[k − 1]Xa[k − 1|k − 1]+ B[k − 1]U [k − 1]

P [k|k − 1] = F [k − 1]P [k − 1|k − 1]Ft[k − 1]

+ Q[k − 1]

K[k] = P [k|k − 1]Ht[k]

+ (H[k]P [k|k − 1]Ht[k] + R[k])−1

Xa[k|k] = Xa[k|k − 1] + K[k](Y [k]− H[k]Xa[k|k − 1] − By[k]U [k])

P [k|k] = P [k|k − 1] − K[k]H[k]P [k|k − 1]

with

F [k] =

[

F (Θ[k]) E(Θ[k])0 G(Θ[k])

]

H[k] =[

H1(Θ[k]) H2(Θ[k])]

F (Θ[k]) =∂

∂X

(

A(Θ[k])X[k] + BΘ(Θ[k])Θ[k]

+ Bu(Θ[k])U [k])

= A(Θ[k])

E(Θ[k]) =∂

∂Θ

(

A(Θ[k])X[k] + BΘ(Θ[k])Θ[k]

+ Bu(Θ[k])U [k])

E(Θ[k]) =

[

isqLqLd

TsvsqLd

Ts

− ΦLq

Ts −isdLd

LqTs −

vsdLq

Ts

]

G(Θ[k]) =

[

1 0Ts 1

]

D(Θ[k]) =

[

0 00 0

]

H1(Θ[k]) =∂

∂X

(

C(Θ[k])X[k] + D(Θ[k])Θ[k]

+ By(Θ[k])U [k])

= C(Θ[k])

H2(Θ[k]) =∂

∂Θ

(

C(Θ[k])X[k] + D(Θ[k])Θ[k]

+ By(Θ[k])U [k])

806

H2(Θ[k]) =

[

0 −sin(θ)isd − cos(θ)isq0 cos(θ)isd − sin(θ)isq

]

K[k] =

[

Kx[k]KΘ[k]

]

P [.] =

[

P x[.] P xΘ[.](P xΘ[.])t PΘ[.]

]

Q[k] =

[

Qx[k] QxΘ[k](QxΘ[k])t QΘ[k]

]

where, vsd = cos(θ)vsα + sin(θ)vsβ , vsq = −sin(θ)vsα +cos(θ)vsβ are voltages in the (dq) frame.

The Extended Kalman filter (EKF) has a heavier com-putational cost with a rough implementation. The use of atwo-stage Extended Kalman filter reduces the computationtime by 21% by reducing the number of operations [16],while maintaining the same level of performance. The non-linear OTSEKF is derived from the original EKF algorithm byan appropriate transformation so that the variance-covariancematrices are block-diagonal [15]–[17].

B. Back-emf adaptive observer

1) Back-emf estimation: The equation in the (αβ) coordi-nates can be derived from (1) as follows [18] :

d

dt

»

isαisβ

–

=1

Ld

»

−Rs −ω(Ld − Lq)ω(Ld − Lq) −Rs

– »

isαisβ

–

+1

Ld

»

−1 00 −1

– »

esαesβ

–

+1

Ld

»

vsαvsβ

–

(4)

with

e =

»

esαesβ

–

= ((Ld − Lq)(ωisd − i̇sq) + φω)

»

− sin θcos θ

–

(5)

where e is defined as an Extended Electromotive Force(EEMF).

The following disturbance observer of the electrical model(4) can be used to estimate the back-EEMF components esα,esβ , which can be regarded as constant or slowly variabledisturbance in the electrical equations [21].

d

dt

»

îsαêsα

–

=1

Ld

»

−Rs −10 0

– »

îsαêsα

–

+

»

kα1kα2

–

ĩsα

+1

Ld

»

10

–

(vsα − ω̂(Ld − Lq)isβ) (6)

d

dt

»

îsβêsβ

–

=1

Ld

»

−Rs −10 0

– »

îsβêsβ

–

+

»

kβ1kβ2

–

ĩsβ

+1

Ld

»

10

–

(vsβ + ω̂(Ld − Lq)isα) (7)

where ĩsα = îsα−isα, ĩsβ = îsβ−isβ . It leads to the followinglinear dynamic for the estimation errors :

ddt

[

ĩsαẽsα

]

=

[

kα1 −RsL

− 1L

kα2 0

] [

ĩsαẽsα

]

ddt

[

ĩsβẽsβ

]

=

[

kβ1 −RsL

− 1L

kβ2 0

] [

ĩsβẽsβ

]

where ẽsα = êsα − esα, ẽsβ = êsβ − esβ . A classi-cal pole-placement technique determine the observer gains(kα1, kα2, kβ1, kβ2) so that the estimation error vanishes (sta-ble system) without increasing the noise sensitivity impact.The poles are selected in order to have the same dynamics asthe Extended EMF when the PMSM operates at the nominalspeed.

For the digital implementation, the PMSM is supposed tobe isotropic (Ld = Lq). The continuous state space modelis linear and stationary, therefore it can be discretized by anexact matrix exponential [19], [20].

2) Adaptive observer: The AO is based on (5) with theassumption that (Ld = Lq). Therefore, the EEMF estimatesare expressed as follows :

ėsα = −ω esβėsβ = ω esα

(8)

From (8), the adaptive observer is designed as

˙̂êsα = −ω̂ ˆ̂esβ − L(ˆ̂esα − êsα)˙̂êsβ = ω̂ ˆ̂esα − L(ˆ̂esβ − êsβ)

(9)

where L is a positive observer gain. The observer (6, 7) is usedin order to estimate the back-EMF (αβ) components. Theseestimations are used as measurement inputs for the adaptiveobserver. The error dynamics are given as :

˙̃esα = −ω̃esβ − Lẽsα˙̃esβ = ω̃esα − Lẽsβ

(10)

where ẽsα = ˆ̂esα− êsα, ẽsβ = ˆ̂esβ− êsβ in this sub-paragraph.To guarantee the stability of the above error system, considerthe function V = 12 (ẽ

2sα + ẽ

2sβ + ω̃

2). The derivative of Vbecomes :

V̇ = −L(ẽ2sα + ẽ2sβ) + ω̃ ˙̃ω + ω̃(−ẽsαêsβ + ẽsβ êsα)

where ω̃ = ω̂ − ω. To make V̇ < 0, we must cancel the lasttwo terms (with the assumption that the speed varies slowlyω̇ = 0 in contrast with electrical variables). The adaptivelaw is chosen as ˙̂ω = ẽsαêsβ − ẽsβ êsα. For the digitalimplementation, the integral term is discretized by an Eulerbackward transformation [20]. Moreover, a proportional termis added in order to increase the tracking capabilities duringtransients. Figure 1 represents the back-emf adaptive observerstructure.

vsα,β

isα,β

êsα

êsβˆ̂esβω̂

ˆ̂esαback-emf

estimationadaptive

observer

Fig. 1. Back-emf adaptive Observer diagram

807

C. Simulation and experimental results

The nominal controller based on the standard vector con-trol and the two observers are implemented under Matlab-Simulink R© and downloaded in a dSpace R© 1104 board. Whenthe estimated variables (computed by the observers) are notused in the controller, this mode is called "open loop" and themechanical sensor feeds the controller. The top curves in Figs.2 and 3 show respectively the performances of the speed andposition tracking capabilities of the two-stage EKF and theadaptive observer compared to the sensor output. The lowercurves represent the speed and position errors compared to themeasured variables. The performances are globally satisfactorybut can be improved.

0 0.5 1 1.5 2 2.5 3 3.5−500

0

500

rotor speed ωmes

(−−) and its estimation ωkal

(−.−)

rpm

0 0.5 1 1.5 2 2.5 3 3.5−150

−100

−50

0

50

100

150

difference of rotor speed estimation ε = ωmes

−ωkal

rpm

time (s)

0 0.5 1 1.5 2 2.5 3 3.5

0

1

2

3

4

5

6

rotor position θmes

(−−) and its estimation θkal

(−.−)

rad

0 0.5 1 1.5 2 2.5 3 3.5−1.5

−1

−0.5

0

0.5

1

1.5

rotor position error ε = θmes

−θkal

rad

time (s)

Fig. 2. Experimental results for the OTSEKF in open loop configuration.

0 0.5 1 1.5 2 2.5 3 3.5−500

0

500

rotor speed ωmes

(−−) and its estimation ωobs

(−.−)

rpm

0 0.5 1 1.5 2 2.5 3 3.5−80

−60

−40

−20

0

20

40

60

rotor speed error ε = ωmes

−ωobs

rpm

time (s)

0 0.5 1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

7

rotor speed ωmes

(−−) and its estimation ωobs

(−.−)

rad

0 0.5 1 1.5 2 2.5 3 3.5−0.2

0

0.2

0.4

0.6

0.8

1

1.2

rotor position error ε = θmes

−θobs

rad

tims (s)

Fig. 3. Experimental results for the AO in open loop configuration.

Intensive simulations are performed to evaluate the robust-ness of both observers to the stator resistance variation on thewhole operating range in the torque-speed frame. From Figs.4 to 6, we can deduce that for a variation of ±50% of thestator resistance, the steady state speed and position errorsare negligible and are symmetrical with the speed. We canconclude that both observers reveal a good robustness.

However, in order to implement the fault tolerant controller,the robustness of the observers needs to be evaluated alsoduring the transients. This analysis is mandatory to extract

for each observer the reliability coefficients required by thevoting algorithm. Fig. 7 shows the evolution of the errorson the speed range for a resistance detuned of +50% fromthe nominal value. From these results, we can conclude theBack-EMF Adaptive Observer exhibits better performancesand robustness at medium and high speed and is also lesssensitive to stator resistance variation. Which means that inthe medium to high-speed range, higher reliability coefficientswill be attributed to the Back-EMF AO compared to the EKF.

0 0.5 1 1.5 2 2.5 3 3.5

−0.2

−0.1

0

0.1

0.2

OTSEKF speed error

rpm

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−8

−6

−4

−2

0

2

4

6

8x 10

−6 AO speed error

rpm

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02OTSEKF position error

rad

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−0.05

0

0.05AO position error

rad

load torque (Nm)

5040075011101500

Fig. 4. Steady state speed and position errors (Rs = Rsnom).

0 0.5 1 1.5 2 2.5 3 3.5

−0.2

−0.1

0

0.1

0.2

OTSEKF speed error

rpm

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−1

−0.5

0

0.5

1x 10

−5 AO speed error

rpm

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02OTSEKF position error

rad

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−0.05

0

0.05AO position error

rad

load torque (Nm)

5040075011101500

Fig. 5. Steady state speed and position errors (Rs = 1.5Rsnom).

III. FAULT-TOLERANT CONTROL

Apart from faults arising in the machine or inverter, the driveis sensitive to fault in different sensors that provide informationused by the control system. For a PMSM drive, these sensorstypically measure phase currents (at least two of the threephase currents are measured), dc-link voltage (since it is proneto variation), and rotor position. The loss of a sensor leads tounsatisfactory or dangerous behaviour if no mitigation actionhas been forecast. In the following section, we focus only onmechanical sensors.

A. Position sensor faults

A 12-bit absolute encoder is used as position sensor in thisapplication and can exhibit the following fault conditions [3] :

808

0 0.5 1 1.5 2 2.5 3 3.5

−0.2

−0.1

0

0.1

0.2

0.3OTSEKF speed error

rpm

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−8

−6

−4

−2

0

2

4

6

8x 10

−6 AO speed error

rpm

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02OTSEKF position error

rad

load torque (Nm)

0 0.5 1 1.5 2 2.5 3 3.5−0.05

0

0.05AO position error

rad

load torque (Nm)

5040075011101500

Fig. 6. Steady state speed and position errors (Rs = 0.5Rsnom).

0 500 1000 15000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Ω (rpm)

rad

ΘMES

−ΘAO

ΘMES

−ΘOTSEKF

ΘAO

−ΘOTSEKF

Fig. 7. Estimation error during transient with (Rs = 1.5Rsnom).

• Intermittent sensor connection (F1),• Complete sensor outage (F2),• DC Bias in sensor measurement (F3),• Sensor gain drop (F4),

The most severe faults are F1 and F2 [3], since they imply amomentary or complete lack of information. Potential closed-loop instability could appear if no proper action is undertaken.To increase the reliability of the drive, the controller mustaccommodate the fault and be able to operate without themechanical sensor.

B. Absolute encoder faults simulation

One type of absolute encoder failure is presented in thispaper : complete sensor outage in the event of a power failure.

The top and bottom curves of Fig. 8-a show respectively thereal position, the encoder output and the quantification error.Fig. 8-b represents the same data in case of a complete sensoroutage at 0.02s. We can notice the important errors due to thefaults. The speed derivation from the position will worsen theimpact on the drive if a fault tolerant controller forecasts nomitigation action.

C. Fault-tolerant controller

The structure of the FTC is shown in Fig. 9. The votingalgorithm in the control decision block computes the mostaccurate information (speed and position) from the inputs

a) b)

0 0.002 0.004 0.006 0.008 0.010

0.005

0.01

0.015

0.02

real position θ (−.−) and encoder position θmes

(−−)

rad

0 0.002 0.004 0.006 0.008 0.01−8

−6

−4

−2

0

2

4

6

8x 10

−4 position error ε = θ−θmes

rad

time (s)

0 0.005 0.01 0.015 0.02 0.025 0.030

0.01

0.02

0.03

0.04

0.05

0.06

real position θ (−.−) and encoder position θmes

(−−)

rad

0 0.005 0.01 0.015 0.02 0.025 0.03−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

position error ε = θ−θmes

rad

time (s)

Fig. 8. Position got from encoder and real position in the normal case andin the event of a power failure.

of the sensor and the observers. The control decision blockrelies on a voting algorithm type in which the emergingoutput has the highest approval. Several voting techniques havebeen described in the literature of which the inexact majority[23], and weighted average voters [24] are widely used incontrol and safety-critical applications. Inexact majority votersproduce an output from redundant inputs if there is agreementbetween a majority number of voter inputs. Weighted averagevoters always produce an output regardless of the agreement,or otherwise, between redundant inputs by amalgamating theinputs. A major difficulty with inexact majority voters is theneed to choose an appropriate threshold value, which has adirect impact on the voter performance. The weighted averagevoters suffers from a lack of accuracy in normal conditions,i.e. without a fault, because the measured position and speedare mixed with those of the observers producing less accuratevalues. The other method which is used here is the MaximumLikelihood voting algorithm [25] in which a probability χj foreach input j is computed based on reliability coefficients. Thecomputation of the probability coefficients that the output jis correct is slightly modified to introduce a threshold and innormal operating conditions to choose the position sensor asthe emerging output :

χj =

N∏

i=1

∆j(i)

/ N∑

k=1

N∏

i=1

∆k(i)

-ω∗ mΣ−

+

6

- Controller -- Controller

Current-

-P−1

-vs1

-vs2

-vs3

-isd-isqP

-is1-is2

PMSM

Sensor

6perturbation

�VotingAlgorithm

�two-stage EKF θ̂, ω̂

�adaptiveobserver

θ̂, ω̂

θθmes, ωmes

Fig. 9. Fault tolerant controller structure.

809

with

∆k(i) =

{

fk if |xi − xk| ≤ Dmaxik1−fkN−1 else

After extensive simulations, the threshold Dmaxik is set to0.1 rad at zero speed and to 0.15 at the nominal speed. Thereliability coefficients determined over the whole speed rangefor each observer are set as follows :

• 0.96 at zero speed to 0.92 at the nominal speed for theOTSKE,

• 0.92 at zero speed to 0.96 at the nominal speed for theBack-emf AO,

• A constant reliability coefficient (0.99) for the speedsensor.

To evaluate the fault tolerant controller, a position sensorfailure (event of a power failure) and recovery is introducedbetween 1.5 → 2.5s, 3.8 → 4.5s, 5.5 → 6, 5s, 7.5 → 8.5sand 9.8 → 10.5s. Fig. 10 shows the response of the faulttolerant controller. At low and medium speed, the OTSEKFoutput is selected in the case of failure. At high speed, itis the AO output which is engaged to maintain the levelof performance. The position and speed estimation error isevaluated as the difference between the real position and speed(non erroneous measured speed) and the emerging outputs ofthe voting algorithm.

0 2 4 6 8 10

0

2

4

6

rad

measured position

0 2 4 6 8 100

1

2

3

selected speed (1 : EKF, 2 : AO, 3 : measured speed)

0 2 4 6 8 10

0

2

4

6

rad

output voting algorithm−position

0 2 4 6 8 100

200

400

600

800

1000

rpm

output voting algorithm−speed

0 2 4 6 8 10

−0.01

0

0.01

0.02

0.03

rad

position estimation error

time (s)0 2 4 6 8 10

−40

−20

0

20

40

rpm

speed estimation error

time (s)

Fig. 10. Simulation results in the event of a power failure.

IV. CONCLUSIONThis paper has described a fault-tolerant control system for a

high-performance PMSM drive. The FTC is an observer-basedstructure with a voting algorithm, which selects the appropriatespeed and position in case of mechanical sensor failure fromtwo observers. An EKF and a Back-emf AO have beendesigned and evaluated off line with experimental data. Theyalso exhibit good robustness against stator resistance variation.The transient behaviour of both observers are analysed toextract the reliability coefficients required by the MaximumLikelihood voting algorithm. Finally the FTC feasibility hasbeen proven in case of an absolute encoder failures (completeoutage and bit errors) and recovery on the whole speed range.

REFERENCES

[1] Z. Q. Zhu, D. Howe, “Electrical machines and drives for electric, hybrid,and fuel cell vehicles,” Proceedings of the IEEE, Vol. 95, N◦4, April2007, pp. 746-765.

[2] B. K. Bose, “Modern power electronics and AC drives,” Prentice Hall,New Jersey, 2002.

[3] D. U. Campos-Delgado, E. Palacios, D. R. Espinoza-Trejo, “Fault-tolerant control in variable speed drives : a survey” IET Electric PowerApplications, Vol. 2, Issue2, Mars 2008, pp. 121-134.

[4] D. Diallo, M. E. H. Benbouzid, A. Makouf, “A fault-tolerant controlarchitecture for induction motor drives in automotive applications,” IEEETransactions on Vehicular technology, Vol. 53, N◦6, 2004, pp. 1847-1855.

[5] Y. S. Jeong, S. K. Sul, S. E. Schulz. N. R. Patel, “Fault detection andfault-tolerant control of interior permanent-magnet motor drive systemfor electric vehicle, ”IEEE Transactions on Industry Applications, Vol.41, N◦1, January-February 2005, pp. 46-51.

[6] G. Bisheimer, C. De Angelo, J. Solsona, G. Garcia, “Sensorless PMSMdrive with tolerance to current sensor faults,” IEEE International Confer-ence on Industrial Electronics IECON, Orlando, USA 2008.

[7] O. Wallmark, L. Harnefors, O. Carlson, “Control algorithms for a fault-tolerant PMSM drive,” IEEE Transactions on Industrial Electronics, Vol.54, N◦4, 2007, pp. 1973-1980.

[8] M. Hilairet, M. E. H. Benbouzid, D. Diallo, “A Self-Reconfigurable andFault-Tolerant Induction Motor Control Architecture for Hybrid Elec-tric Vehicles,” IEEE, International Conference on Electrical Machines,ICEM06, Chania, Greece, 2006.

[9] M. J. Corley, R. D. Lorenz, “Rotor Position and Velocity Estimation fora Salient-Pole Permanent Magnet Synchronous Machine at Standstill andHigh Speeds,” IEEE Transactions on Industry Applications, Vol. 34, N◦4,1998, pp. 784-789.

[10] A. Consoli, G. Scarcella, A. Testa, “Industry Application of Zero-Speed Sensorless Control Techniques for PM Synchronous Motors,” IEEETransactions on Industry Applications, Vol. 37, N◦2, 2001, pp. 513-521.

[11] Y. H. Kim, Y. S. Kook, “High Performance IPMSM Drives without Ro-tational Position Sensors Using Reduced-Order EKF,” IEEE Transactionson Energy Conversion, Vol. 14, N◦4, 1999, pp. 868-873.

[12] G. Zhu, A. Kaddouri, L.A. Dessaint, O. Akhrif, “A Nonlinear State Ob-server for the Sensorless Control of a Permanent-Magnet AC Machine,”IEEE Transactions on Industry Electronics, Vol. 48, N◦6, 2001, pp. 1098-1108.

[13] P. P. Vas, “Sensorless vector and direct torque control,” Oxford Univer-sity Press, 1998.

[14] M. S. Grewal, A. P. Andrews, “Kalman filtering, theory and practice,”Prentice Hall, Englewood Cliffs, New Jersey, 1993.

[15] C. S. Hsieh, F. C. Chen, “Optimal solution of the two-stage Kalmanestimator,” IEEE Transactions on automatic control, Vol. 44, N◦1, 1999,pp. 194-199.

[16] A. Akrad, M. Hilairet, D. Diallo, “A sensorless PMSM drive using atwo stage extended Kalman estimator, ” IEEE International Conferenceon Industrial Electronics IECON, Orlando, USA 2008.

[17] M. Hilairet, E. Berthelot, F. Auger, “Speed and rotor flux estimationof induction machines using a two-stage extended Kalman filter, ”Automatica, accepted for publication as regular paper, 2009.

[18] Z. Chen, M. Tomita, S. Doki, S. Okuma, “An Extended ElectromotiveForce Model for Sensorless Control of Interior Permanent Magnet Syn-chronous Motors,” IEEE Transactions on Industry Electronics, Vol. 50,N◦2, 2003, pp. 288-295.

[19] Z. Boulbair, M. Hilairet, F. Auger, L. Loron, “Sensorless Control ofa PMSM Using an Efficient Extended Kalman Filter,” InternationalConference of Electrical Machines ICEM04 ,Cracovie, Pologne, 2004.

[20] W. Levine, “The control handbook,” CRC Press.[21] B. Nahid-Mobarakeh, F. Meibody-Tabar, F. Sargos, “Mechanical sensor-

less control of PMSM with online estimation of stator resistance, ”IEEETransactions on Industry Applications,Vol. 40, N◦2, March/April 2004,pp. 457-471.

[22] C. W. De Silva, “Mechatronics: An Integrated Approach,”CRC Press,2005.

[23] J.M. Bass, P.R. Croll, P.J. Fleming, L.J.C. Woolliscroft, “Three DomainVoting In Real-time Distributed Control Systems,” 2nd Euromicro Work-shop on Parallel and Distributed Processing, 1994, pp. 317-324.

[24] G. Latif-Shabgahi, J.M. Bass, S. Bennett, “History-based weightedaverage voter: a novel software votingalgorithm for fault-tolerant com-puter systems,” Proceedings. Ninth Euromicro Workshop on Parallel andDistributed Processing, 2001, pp. 402-409.

[25] Y. Leung, “Maximum likelihood voting for fault-tolerant software withfinite output-space ,” IEEE Transactions on Reliability, Vol. 14, N◦3,1995, pp. 419-427.

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