Rotor Speed Sensor Fault Detection in Induction Motors

Riccardo Marino, Stefano Scalzi, Patrizio Tomei and Cristiano Maria Verrelli

Department of Electronic Engineering, University of Rome “Tor Vergata”, Via del Politecnico 1, 00133 Rome, Italy

Keywords:

Fault Detection, Speed Sensor Faults, Induction Motors.

Abstract:

The problem of detecting a speed sensor fault in induction motor applications with load torque and rotor/stator

resistances uncertainties is addressed. It is shown that in typical operating conditions involving constant

rotor speed and ﬂux modulus and non-zero load torque, a constant non-zero (sufﬁciently large) difference

between the measured speed and the actual speed may be on-line identiﬁed by an adaptive ﬂux observer

which incorporates a convergent rotor resistance identiﬁer and relies on the measured rotor speed and stator

currents/voltages.

1 INTRODUCTION

Three-phase induction motors are widely used for

electric railway and automotive traction (Hill, 1994)

since they offer several advantages such as no com-

mutator, no brushes, no rotor windings in squirrel

cage motors, simple rugged structure, inherent regen-

erative braking capability, ability of tolerating heavy

overloading and of producing high torques with low

weights, small sizes, and low rotating masses. In high

impact automotive applications (see Rehman, 2008)

such as electrical and hybrid electrical vehicles, the

operation continuity is a key feature and high relia-

bility of the drive system should be guaranteed (see

Benbouzid et al., 2007). On the other hand, traction

main drives are often equipped with rotor speed sen-

sors (Guzinski et al., 2009) which are used by clas-

sical induction motor control schemes such as direct

or indirect ﬁeld oriented controls (see Marino et al.,

2010b) for recent adaptive results). In the case of ro-

tor speed sensor fault, a proper and prompt fault de-

tection is required so that an effective action can be

performed and the fault effect is not widely propa-

gated with a resulting hard system failure.

The idea underlying a model-based approach to

fault diagnosis (see for instance (Isermann, 2011) and

(Ding, 2008)) relies on the assumption that certain

process signals carry information about the faults of

interest. The gist of the approach is then to gener-

ate, on the basis of measurements from (and knowl-

edge of) the system, a set of ”residual signals” which

are zero when no fault is present and non-zero when

faults occur (Bennet et al., 1999). However sev-

eral difﬁculties naturally arise for the speciﬁc applica-

tion to induction motors: induction motor dynamics

are nonlinear; ﬂux measurements are not available;

three critical parameters, namely rotor and stator re-

sistances (which vary during operations due to motor

heating) and load torque (which depends on applica-

tions), are typically uncertain and are required to be

on-line estimated.

A ﬁrst intuitive solution (I S ) to speed sensor fault

detection problems relies on designing an adaptive

ﬂux/speed observer which does not use the measured

speed but only stator currents and voltages measure-

ments (see (Guzinski et al., 2010) and (Guzinski et al.,

2009)). The gist of the above design is then to com-

pare the measured speed with the estimated one with

the aim of identifying the possibly occurring speed

sensor fault. Since suitable identiﬁers for the uncer-

tain parameters are to be incorporated in the adaptive

observer in order to avoid false fault detections, the

drawback of the above approach is then constituted

by the well-known identiﬁability and observability is-

sues which arise when only stator currents and volt-

ages are measured. It is in fact well-established

that when the motor operates at constant rotor speed

and ﬂux modulus with non-zero load torque to mini-

mize power losses and maximize power efﬁciency at

steady-state (see Marinoet al., 2010b), the simultane-

ous estimation of rotor speed and rotor resistance can-

not be achieved (see (Ha and Lee, 2000), (Marino et

al., 2008), as well as (Marino et al., 2010a)) and ref-

erences therein) since only a linear combination

L = R

+ γω

of the rotor resistance R

and speed ω (along with

the real γ) can be on-line identiﬁed by stator currents

Marino R., Scalzi S., Tomei P. and Maria Verrelli C..

Rotor Speed Sensor Fault Detection in Induction Motors.

DOI: 10.5220/0004026500590066

In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2012), pages 59-66

ISBN: 978-989-8565-21-1

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

and voltages measurements. This structural difﬁculty

may be used to our advantage by noting that when the

(constant) measured speed ω

is used by a suitable

adaptive ﬂux observer AF O, the identiﬁable linear

combination becomes

= R

+ γ(ω −ω

If the rotor speed is measured and no speed sensor

fault fault occurs, i.e. ω ≡ ω

, estimating L

coin-

cides with estimating R

; on the other hand, in the

presence of speed sensor failures, estimating L

coin-

cides with estimating a quantity which, depending on

(ω −ω

), may be larger or smaller than any admissi-

ble R

∈ [R

] for the speciﬁc motor in consider-

ation, that is

+ γ(ω −ω

) < R

+ γ(ω −ω

) > R

In this case a speed sensor fault may be on-line

identiﬁed by designing a speed measurement-based

adaptive observer and by monitoring the estimate of

on the basis of the boundary values R

and R

The aim of this paper is to show that an adaptive

ﬂux observer A F O which incorporates a convergent

rotor resistance identiﬁer and relies on the measured

rotor speed and stator currents/voltages may be ef-

fectively used to on-line identify a constant non-zero

(sufﬁciently large) difference ω − ω

in typical oper-

ating conditions involving non-zero load torque and

constant rotor speed and ﬂux modulus. In particular,

denoting by α ∈ [α

,α

] (α

= L

, α

= L

)

the ratio between the rotor resistance R

and the ro-

tor inductance L

and by

α its estimate (provided by

the AF O), we will show that a residual signal for

the speed sensor fault detection may be chosen as

the steady-state distance of

α(t) from the compact set

[α

,α

], i.e.

lim

t→+∞

dist(

α(t); [α

,α

]).

A similar idea (though not analytically motivated)

has been also recently presented in Najafabadi et al.

(2011) even though it relies on an observer which is

adaptive with respect to the rotor resistance only. In

contrast to Najafabadi et al. (2011), we propose a

candidate adaptive ﬂux observer belonging to the set

of all adaptive ﬂux observers which provide conver-

gent estimates of the rotor resistance despite uncer-

tainties in critical parameters such as load torque and

stator resistance. This is to avoid false fault detections

which may be related to uncertainties in those criti-

cal parameters. With this respect, among the adap-

tive observers which have been proposed in the lit-

erature since 1978 (see for instance (Castaldi et al.,

2005), (Hasan and Husain, 2009), (Jeon et al., 2002),

(Kenn

e et al., 2010), (Marino et al., 2000), (Marino

et al., 2011), (Najafabadi et al., 2011), (T¸ iclea and

Besanc¸on, 2006) and references therein), we con-

sider in this paper the one presented in Marino et al.

(2011) which is simultaneously characterized by: i)

an overall structural simplicity with no use of sign

functions, high gains or output time derivatives which

lead to well-known implementation difﬁculties and

high noise sensitivity; ii) persistency of excitation

conditions which are naturally related to motor ob-

servability and parameter identiﬁability and are guar-

anteed to be satisﬁed in the typical case of constant

motor speed and ﬂux modulus and non-zero electro-

magnetic torque; iii) exponential convergence prop-

erties guaranteeing a certain degree of robustness. It

is constituted by an adaptive ﬂux observer which is

able to estimate the motor ﬂuxes and to identify the

rotor resistance and by a stator resistance identiﬁer

whose design is performed on a different time scale

in order to isolate its estimation from the estimation

of motor ﬂuxes and rotor resistance (see also (Jadot

et al., 2009), (Marino et al., 2010c)) for a similar ap-

proach to parameter estimation in induction motors).

Simulation and experimental results illustrate the ef-

fectiveness of the proposed solution and show satis-

factory fault detection performances. Such a speed

sensor fault detector constitutes a ﬁrst step toward the

design of effective fault-tolerant control architectures

which involve output feedback adaptive tracking con-

trols (Marino et al., 2010b) minimizing power losses

in conjunction with sensorless adaptive tracking con-

trols (Marino et al., 2010c) imposing rotor speed ob-

servability and resistance identiﬁability. Those fault-

tolerant architectures may be of special interest for

speed-controlled traction applications in which induc-

tion motor controls are required to tolerate rotor speed

sensor faults (see (Benbouzid et al., 2007), (Guzinski

et al., 2010), (Guzinski et al., 2009)) and to main-

tain at the same time high power efﬁciency at every

speed (see (Bennet et al., 1999), (Diallo et al., 2004),

(Lee and Ryu, 2003), (Romero et al., 2010), (Wang et

al., 2006) for the general problem of designing fault-

tolerant induction motor controls).

2 PHYSICAL MODELING

Assuming linear magnetic circuits, the dynamics of a

balanced non-saturated induction motor with one pole

pair in a ﬁxed reference frame attached to the stator

are given by the well known ﬁfth-order model (see for

instance (Marino et al., 2010a) and references therein)

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

dω

= µ(ψ

− ψ

) −

dψ

= −αψ

− ωψ

+ αMi

dψ

= −αψ

+ ωψ

+ αMi

(1)

= −



+ βαM



+ βαψ

+ βωψ

= −



+ βαM



+ βαψ

− βωψ

in which: ω is the rotor speed, (ψ

,ψ

) are the ro-

tor ﬂuxes, (i

) are the stator currents, (u

)

are the stator voltages in a ﬁxed reference attached

to the stator. The constant model parameters are:

load torque T

; motor moment of inertia J; rotor and

stator windings resistances (R

) and inductances

); mutual inductance M. To simplify nota-

tions we use the reparameterization: α =

, β =

σL

µ =

, σ = L

(1 −

). The rotor ﬂuxes (ψ

,ψ

)

are unmeasured variables since ﬂux sensors are usu-

ally not available while the parameters T

, α and R

are typically uncertain owing to load torque depen-

dence on applications and owing to resistance varia-

tions which depend on motor heating. We will only

assume, in the following, the boundedness of state

and input variables while any restriction concerning

the boundedness of stator currents integrals, which

has been proposed for the design of similar adaptive

ﬂux observers in Jeon et al. (2002), (Marino et al.

(2000), is not required.

3 OBSERVER DESIGN

The ﬁrst idea in Marino et al. (2011) is to introduce

the variables z

= i

+ βψ

, z

= i

+ βψ

so that

the motor electro-magnetic equations in (1) become

˙z

= −

˙z

= −

− α(1 +βM)i

− ωi

+ αz

+ωz

(2)

= −

− α(1 +βM)i

+ ωi

+ αz

−ωz

The advantage of using the (z

) variables,

which are physically related to the stator ﬂuxes, is that

their dynamics depend neither on the unmeasured ro-

tor ﬂuxes nor on the uncertain rotor resistance. On the

basis of model (2), the following observer is designed

is a positive design parameter):

= −

−

α(1 + βM)i

− ω

αˆz

+ωˆz

+ k

−

)

= −

−

α(1 + βM)i

+ ω

αˆz

−ωˆz

+ k

−

) (3)

ˆz

= −

+ v

ˆz

= −

+ v

which is a copy of system (2) with: i) the estimates

(ˆz

, ˆz

α,

) in place of the unmeasured/uncertain

, α, R

); ii) stabilizing terms on the current esti-

mation errors (i

−

), (i

−

); iii) the compensat-

ing terms v

yet to be designed. According to the

stability analysis in Marino et al. (2011), the estima-

tion laws for

α and

and the feedback terms v

are chosen as

α = −k

[(1 + βM)i

− ˆz

]

+ [(1 +βM)i

− ˆz

]

= −k

+ v

)

= −k



−



= k





(4)

in which

= i

−

= i

−

are the stator

current estimation errors, k

and k

are positive design

parameters, k

is a sufﬁciently small positive design

parameter.

The two-time-scale arguments in Marino et al.

(2011), under certain identiﬁability assumptions at

steady-state, allow for isolating the estimation of the

stator resistance from the estimation of motor ﬂuxes

(achieved through the estimation of (z

)) and rotor

resistance so that the following persistency of excita-

tion condition:

: there exist two positive reals t

and k

such that

the persistency of excitation condition (I

is the

3 × 3 identity matrix)

t+t

(τ)Γ(τ)dτ ≥ k

, ∀ t ≥ 0 (5)

holds with

Γ =



α ω β(ψ

− Mi

)

−ω α β (ψ

− Mi

)



is obtained. Inequality (5) is naturally related to mo-

tor observability and parameter identiﬁability: when

the rotor speed and the rotor ﬂux modulus are con-

stant and the load torque is zero so that ψ

= Mi

RotorSpeedSensorFaultDetectioninInductionMotors

and ψ

= Mi

, it cannot be satisﬁed; when a positive

load torque is applied and when the rotor speed and

the rotor ﬂux modulus are constant with ψ

+ ψ

> 0, it is satisﬁed.

The gist of the estimation design in Marino et al.

(2011) and the required assumptions can be simply

explained in the following terms: if the adaptive ob-

server (3)-(4) (with no stator resistance identiﬁer) is

used with a constant value of the stator resistance that

is slightly different from its actual value, then a non-

zero steady-state solution appears that causes a suit-

able measured output function s

= v

to be,

in ﬁrst approximation, monotone with respect to the

-estimation error

= R

−

; thus, by adjusting

the R

-estimate

on the basis of this output func-

tion (slowly, in order not to deviate too much from

the steady-state solution) one can obtain the correct

estimation of R

and the consequent exponential con-

vergence to zero of all the estimation errors

− ˆz

, z

− ˆz

, α −

α,

. Exponential rotor ﬂux re-

covering can be ﬁnally obtained by





= −



− ˆz



where the ﬁltered estimates (

) are preferred to

the measured (i

) for practical implementation is-

sues. The following second-order load torque identi-

ﬁer (k

and k

are positive design parameters):

ω = µ(

−

) −

+ k

(ω −

ω)

= −k

(ω −

ω)

is ﬁnally proposed in Marino et al. (2011). It can be

used in conjunction with the adaptive observer (3)-(4)

to provide an exponentially convergent estimate of the

load torque once convergent estimates of rotor ﬂuxes

have been obtained. The proof, which is reported in

Marino et al. (2010a), is based on the quadratic func-

tion

+ ε

in which

ω = ω −

ω,

= T

−

and ε > 0 is a suf-

ﬁciently small positive real.

4 SENSOR FAULT DETECTION

The aim of this section is to prove that a constant non-

zero (sufﬁciently large) difference between the mea-

sured speed and the actual speed may be on-line iden-

tiﬁed by the adaptive ﬂux observer (3)-(4) (in which

the measured speed ω

replaces the actual speed ω) in

typical operating conditions involving non-zero load

torque and constant rotor speed and ﬂux modulus. To

this purpose, we preliminarly note that in those con-

ditions we have

z }| {

+ ψ

≡ 0

ω ≡ 0,

from which we obtain

= ψ

− cψ

= ψ

+ cψ

(6)

with (ω

is the slip speed [see (Marino et al., 2010a)])

c =

Jµc

= ω

/α.

By adding and subtracting in (2) suitable terms

proportional to ω

= ω − ω

and by using (6), equa-

tions (2) can be equivalently rewritten as

˙z

= −

˙z

= −

− ω

+ ω

+α[z

− (1 +βM)i

] + ω

− i

)

= −

+ ω

− ω

+α[z

− (1 +βM)i

] − ω

− i

)

with the last two equations reading

= −

− ω

+ ω



α +



− (1 +βM)i

)

= −

+ ω

− ω



α +



− (1 +βM)i

In other terms, in typical operating conditions in-

volving non-zero load torque and constant rotor ﬂux

modulus and (measured and actual) speeds, an equiv-

alent constant α

= α + ω

/c appears in the motor

model (with ω

in place of ω): it incorporates any

possibly non-zero difference between the measured

speed and the actual speed.

By virtue of the same analysis presented in Marino

et al. (2011) and discussed in Section 3 (with ω

place of ω), the adaptive observer (3)-(4) is able to

guarantee exponential convergence to zero of all the

estimation errors

, z

− ˆz

, z

− ˆz

, α

−

α,

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

(provided that initial errors belong to the region of at-

traction of the origin for the error system dynamics).

Exponential estimation of motor ﬂuxes, equivalent α

and stator resistance are therefore achieved. In par-

ticular, lim

t→+∞

dist(

α(t);[α

,α

]) may be used as a

residual signal for speed sensor fault detection since

when rotor speed ω and ﬂux modulus

+ ψ

are

constant along with the measured speed ω

, the α-

estimate

α(t) is guaranteed to exponentially converge

to α

. It is clear that only the speed sensor faults that

lead to a value of α

outside the compact set [α

,α

]

can be in this way identiﬁed. An estimate of ω

(and

therefore of the sensor failure magnitude) can be ﬁ-

nally obtained according to

(α

− α) = ω

once the load torque (through the load torque identi-

ﬁer) and the rotor ﬂuxes have been estimated.

5 SIMULATION RESULTS

The aim of this section is to illustrate the previ-

ously presented results even in the presence of time-

varying perturbations of the motor resistances and

step-wise variations of the load torque. To this pur-

pose, the nonlinear adaptive observer (3)-(4) and the

load torque identiﬁer are simulated for the three-phase

single pole pair 0.6-kW induction motor OE-MER

7-80/C in Marino et al. (2010a) whose parameters

are: J = 0.0075 kgm

, R

= 5.3 Ohm, R

= 3.3 Ohm,

= 0.365 H, L

= 0.375 H, M = 0.34 H. The motor

(with initial conditions ψ

(0) = ψ

(0) = 0.1 Wb) is

illustratively controlled by the input-output feedback

linearizing control reported in Section 2.4 of Marino

et al. (2010a) (which relies on exact rotor speed

and stator current measurements and on the perfect

knowledge of all motor parameters). The rotor speed

and the ﬂux modulus are reported in Figure 1. The de-

sign parameters are chosen as (all the values are in SI

units): k

= 120, k

= 3, k

= 450, k

= 0.1, k

= 200,

= 100

J. All the observer initial conditions are set

to zero excepting for

α(0) = 9 s

−1

and

(0) = 5.4

Ohm. For t < 1.8 s the measured speed is equal to the

actual one (ω ≡ ω

) while for t ≥ 1.8 s a speed sensor

fault occurs leading to ω − ω

= 0.4ω. The equiva-

lent rotor resistance R

= L

is thus equal to R

for

t < 1.8 s and equal to R

+ω

for t ≥ 1.8 s. The

rotor ﬂuxes, the load torque, the equivalent rotor resis-

tance, the stator resistance along with the correspond-

ing converging estimates are reported in Figures 2-5.

Fast estimation is obtained: the speed sensor fault can

be promptly identiﬁed by monitoring the estimated

Figure 1: Rotor speed ω and ﬂux modulus

+ ψ

Figure 2: Rotor ﬂuxes ψ

,ψ

(dash) and their estimates

(solid); rotor ﬂuxes ψ

,ψ

estimation errors.

Figure 3: Load torque T

(dash) and its estimate

(solid).

Figure 4: Equivalent rotor resistance R

(dash) and its esti-

mate

(solid).

rotor resistance on the basis of the available bound-

ing values R

= L

= 2.8 Ohm, R

= L

= 6.9

Ohm. In order to illustrate the possibility of detecting

false faults by using adaptive observers with no stator

resistance identiﬁer (as in (Najafabadiet al., 2011)),

the same simulation is carried out in the presence of

no speed sensor fault for the adaptive observer (3)-

RotorSpeedSensorFaultDetectioninInductionMotors

Figure 5: Stator resistance R

(dash) and its estimate

(solid).

Figure 6: Observer with no R

-adaptation: rotor resistance

(dash) and its estimate

(solid).

Figure 7: First experimental test (ω

= 70 rad/s, ω = 88

rad/s).

(4) with the stator resistance value 5.4 Ohm in place

. As illustrated by Figure 6, a non-zero resid-

ual results even in the case of no speed sensor fault:

this is only due to stator resistance uncertainties and

motivates the use of adaptive observers which provide

convergent rotor resistance estimates despite stator re-

sistance uncertainties.

6 EXPERIMENTAL RESULTS

In this section we present the results of three exper-

imental tests which have been carried out with ref-

erence to a 0.25 kW C4T34FB5B Leeson induction

motor driven by a 20 kHz PWM-based open loop

voltage/frequency control (61 V, 16.7 Hz). The ap-

plied load torque, which is proportional to the induc-

tion motor speed, is provided by the WSM-3-32-1

Sangalli Servomotori DC permanent magnet motor

directly connected to the shaft of the induction mo-

tor. The nonlinear adaptive observer (3)-(4) and the

load torque identiﬁer are executed (at 12.5 kHz) when

the motor has reached its steady-state. The nomi-

nal values of the parameters (provided by the man-

ufacturer) L

= 0.268 H, L

= 0.298 H, M = 0.258

H, J = 0.005 kgm

are used, the control gains (all

the values are in SI units) k

= 600, k

= 3, k

= 10,

= 0.65, k

= 100, k

= 5 are chosen while zero ini-

tial conditions, excepting for

α(0) and

(0) (equal

to 12.75 s

−1

and 10.45 Ohm) are set. The ﬁrst test,

whose steady-state results are reported in Figure 7,

involves a partial speed sensor fault (ω

= 70 rad/s,

ω = 88 rad/s) occurring at t = 3.84 s. The second

test, whose steady-state results are reported in Figure

8, involves a larger partial speed sensor fault (ω

= 44

rad/s, ω = 88 rad/s) occurring at t = 2.02 s. The third

test, whose steady-state results are reported in Figure

9, ﬁnally involves a full speed sensor fault (ω

= 0

rad/s, ω = 88 rad/s) occurring at t = 1.66 s. All the

three tests conﬁrm the theoretical results presented in

the paper: as expected, the speed sensor fault can be

promptly identiﬁed (R

= 6 Ohm) by monitoring the

estimated rotor resistance which converges to α

Figure 8: Second experimental test (ω

= 44 rad/s, ω = 88

rad/s).

7 CONCLUSIONS

A constant non-zero (sufﬁciently large) difference be-

tween the measured speed and the actual speed may

be on-line identiﬁed, even in the presence of uncer-

tainties in load torque and rotor/stator resistances, in

ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics

Figure 9: Third experimental test (ω

= 0 rad/s, ω = 88

rad/s).

typical operating conditions involving non-zero load

torque, constant rotor speed and ﬂux modulus. An

adaptive ﬂux observer which incorporates a conver-

gent rotor resistance identiﬁer and relies on the mea-

sured rotor speed and stator currents/voltages is used

to this purpose. A relevant consequence of the pre-

sented analysis is that rotor ﬂuxes (and therefore mo-

tor torque), load torque and stator resistance can be

actually estimated even in the presence of speed sen-

sor faults.

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ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics