126
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 1, JANUARYFEBRUARY 1994
A New Algorithm for Sensorless
Operation of Permanent Magnet Motors
Nesimi Ertugrul and Paul Acamley
-Additional system cost (including sensor and electronic
circuit) which is most meaningful when compared with a
given level of resolution of the sensor [l].
-All shaft sensors present a certain degree of static and
dynamic friction to the input shaft, and the moment of
inertia adds to the motor shaft inertia.
Many of these drawbacks can be eliminated or reduced with
shaft position sensorless operation.
The control of PM motors, stepper motors, and switched
reluctance (SR) motors based on sensorless operation has
been described by many authors (e.g. [3], [4],...[241) in drives
such as stepper motors ([3], [4], [5], [6]) switched reluctance
motors (131, [71, [SI), PMSMs (PI, [lo], [ I l l , [121, [131, [14l,
[151, [161), BDCMs ([171, U81, [191, [201, W I , W I , [231).
I. INTRODUCTION
Two of the methods ([22], [23]) use either an electromagnetic
N RECENT years there has been a significant development position sensing device or a special winding. Most of the
of permanent magnet (PM) motors of various lunds. Im- methods describe indirect position sensing methods by using
provements in the properties of permanent magnet materials and analysing the terminal voltage andor current waveform.
have increased the viability of related types of motor, such However many of the methods work for some, but not all,
as the permanent magnet motor (PMSM) and the brushless dc PM machines.
motor (BDCM). Both motors required alternating stator current
Recently,there has been much interest in techniques for
to produce constant torque, and to control them the rotor flux eliminating the mechanical sensor by analysing the motor’s
position has to be identified. Rotor position information is voltage and current waveforms. A number of scheme for the
used to manage the switching of the supply to the phases of induction motors’ control, which do not use a mechamical
the stator in correct sequence by a control circuit. Since the rotor sensor or an additional sensor in the stator, are also
switching frequency is derived from the rotor, the motor can suggested in the literature. Some of the method use the flux
not lose synchronism.
linkage variation [24] by sensing the terminal voltages of the
The control system requires position information for two induction machine and subtracting the stator voltage drops.
reasons:
The methods proposed by Depenbrock [25], Ohtani et al [26],
1. To indicate to the control circuit which position the and Takahashi [27] analyse the time integral of stator voltages
motor is in and to switch on the correct phase or phases. and the line currents (depending on the magnitude of the stator
2. Although servo applications use a separate velocity iR voltage drop), and calculate torque to generate desired
sensor, a speed signal can also be delivered from the control signals for the induction motors. Baader et a1 [28]
position information.
also applied the method developed by Depenbrock [25] to
Some of the drawbacks of using a mechanical shaft position the speed control of induction motors by calculating the exact
speed without mechanical devices.
sensor may be summarized as below:
The paper describes an alternative method of position detec-Number of connections between the motor and the control
tion
based on the motor terminal voltages and the line currents
system increases.
with
the aim of estimating the winding flux linkages. At each
-Interference increases.
-Limitations in accuracy of the sensor because of environ- time step, using the previous predicted position information
mental factors such as temperature, humidity, vibration. and the flux linkage, the line current of the motor is estimated
in two stages to correct the predicted position and the estimated
Paper MA 4-94, approved by the Industrial Drives Committee of the
flux linkage respectively.
IEEE Industry Applications Society for presentation at the 1992 Industry
The electrical model of the PM motor is discussed and the
Applications Society Annual Meeting, Houston, TX,October 4-9.
The authors are with the Electric Drives and Machines Group, Department
basis of the proposed algorithm described in the Section 2. A
of Electrical Engineering, The University of Newcastle upon Tyne, Newcastle
detailed derivation of the algorithm is presented in Section 3,
upon Tyne, UK.
IEEE Log Number 9213420.
with a short discussion noting the algorithm’s key features. In
Abstract- In this paper, the authors propose and investigate
a new algorithm for shaft position sensorless operation of permanent magnet motors, based on flux linkage and line current
estimation. Measured line current and terminal voltage are used
to estimate the flux linkage of the motor. The algorithm has a
two current-loop structure, with the outer loop used to correct
the position, and the inner loop utilised to correct the estimated
flux linkage. The theoretical basis of the algorithm and individual
definition of the system blocks is explained. Dependencies on
motor parameters and measurementerrors are discussed to show
the effectiveness of the method using real data. As well as giving
a detailed explanation of the new algorithm, the paper presents a
wide range of computed and experimental results, demonstrating
the reliability of the method even during accelerationof the motor
from rest.
I
0093-9994/94$04.00 0 1994 IEEE
-
--7
I27
ERTUGRUL AND ACARNLEY: A NEW ALGORITHM FOR SENSORLESS OPERATION OF PERMANENT MAGNET MOTORS
order to verify the method, detailed experimental results are
also given for both the steady-state condition and the transient
condition in Section 4. The effects of parameter deviations
and measurement sensitivity of the method are presented in
Section 5.
And in the star connected with isolated star point motor:
21
+ 22 + i 3 = 0
(5)
Hence,
11. THE MATHEMATICAL
MODEL
The equivalent circuit for the PM machine is presented in
terms of flux linkage variables. The voltage equations for a
3-phase balanced PM ac machine is expressed in the matrix
form as,
[ii]
R O O
= [OO R
O 0R 1
[ ! EI]:[;+
l:]-[O
(1)
A@
(,
M12(8)
-
Am(O -
M13(6)
9)
F)
(2)
Here, , ,A
the magnet flux linkage, is a function of 8,
electrical angle, L,,
is the self inductance of the winding x,
and Mz,(0) is the mutual inductance between two windings
x and y.
We realize that the inductance matrix in Eq. 2 describes the
self and mutual inductance relations of the stator phases of a
symmetrical PM machine. Differentiating Eq. 2, substituting
it into Eq. 1, and rearranging,
(e)
I!:[
R O O
R 01
O O R
- [O
v3
R O
R OO ]
O O R
I!:[
= [OL OL OO ] $ [ ~ ~ ] - $ L ( @ Am(@)
- ? f ~
O O L
A,(@
-
9)
0
where vl, v2, and v3 are the phase voltages, R is the resistance
of the stator winding, i l ,22, and 23 are the line currents, and
Q1, Q 2 , and Q3 are the flux linkages of the windings.
The general flux linkage variables may be defined in the
following form,
Lll(0)
where L = L1 - M I
Differentiating Eq. 6, substituting into Eq. 1 and rearranging,
As explained in later sections, position estimation based on
the flux linkages is achieved by Eq. 2 or Eq. 6 according
to whether the machine has variable winding inductances or
constant inductances. Direct measurement of line current and
phase voltage can allow estimation of the flux linkage. If the
terminal phase voltages of the motor are sensed and stator
voltage drops are subtracted, the change of the flux linkage
of each phase with time can be generated in terms of the
rotor position, line currents, and other motor parameters which
appear in the right-hand side of Eq. 3 and Eq. 7.
111. THE COMPUTER ALGORITHM
AND
THE DEFINITIONOF THE SYSTEM
Fig. l(a) and Fig. l(b) illustrate the methods of measuring
the motor line currents and phase voltages, and estimating the
rotor position of the PM ac motor.
Firstly, measured line current and terminal voltage are used
to estimate the flux linkages of the motor. This is based on
Eq. 1. The function of flux linkage to be evaluated is in the
following form,
[.]
For the machine which has no variable inductance, Eq. 3 can
be rearranged to give more simple system equations. Linear
3-phase coupled systems are magnetically symmetrical if the
diagonal elements of the inductance matrix are also equal [2].
Assuming further that there is no change in the rotor reluctance
with angle, then,
L11 = L22 = L33 = L1
(4)
In general, the function of(v(.) - RZ(.r))does not have
a closed form integral. Since a numerical technique is to be
used, it is appropriate to evaluate the integral function Q ( t )
at discrete time instants. Although, for cases where extremely
high accuracy is required, different integration methods can
be used, the simplest method is integration by the rectangular
rule;
an(k)= A T [ v n ( k ) R i n ( k ) ]+ Qn(k - 1)
R
IC
= 1,2,3
= 1 , 2 ,. . .
(9)
Here A T is the sampling interval, and n is the number of
phases in the motor.
Since the integration starts at k = 1, Qn(0)plays the role of
the initial condition. In PM machines, the initial value of flux
linkage is defined by the position of the magnet. Therefore,
to evaluate Eq. 9 and to set up the initial condition, the rotor
can be brought to a known position which defines the initial
values (Q,(O))
of the iiitegration.
128
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 1, JANUARYEEBRUARY 1994
'dc
v
-
1
T
PM MOTOR
,
(b)
Fig. 1 .
(a) Schematic inverter system diagram. (b) Position estimator block diagram.
The algorithm shown in the block diagram of Fig. l(b)
has a two current-loop structure. The outer loop is used to
correct the initial rotor position estimate which is obtained by
extrapolation of previous position data.
As seen in Eq. 2, we have a general flux linkage function of
several variables 9 = P(0, i l ,i 2 , i 3 ) . Changes in flux linkage
can be written in terms of changes in the variables:
Where Ai,, Ai2, and Ai3 are the current errors and A0 is the
position error.
For each phase, a current estimate is obtained from Eq.
2 using the initial predicted position 0 = OP and the flux
linkage value obtained from terminal measurements (Eq. 9).
The current estimates are compared with the measured currents
to achieve a set of current errors,
Ai3 = i 3 m - i 3 e
Assuming that the flux linkage estimate is correct and does
not change (AP = 0) within the measurement interval, the
position errors may be reproduced in terms of line current
error estimations,
A0, = ($Ai,
+ -Ai2
ai2
+ -Ai3
ai3
)/%
(12)
yielding a set of three position corrections. A single revised
position estimate is obtained by taking the average of three
corrections,
At certain line current levels and rotor position some of
the phases are better indicators of position error than others. Therefore the position error averaging may incorporate
weighting factors which are current and position dependent.
An updated position is calculated, adding the position error to
the previous predicted position,
As clearly seen in Fig. l(b), the outer current loop is used
to estimate the line current, and predicted position is utilised
with estimated flux linkage for current estimation. A position
prediction is obtained by extrapolation of position data at
previous time intervals. A second-order polynomial is 'fitted'
~
ERTUGRUL AND ACARNLEY: A NEW ALGORITHM FOR SENSORLESS OPERATION OF PERMANENT MAGNET MOTORS
129
TABLE I
THE PM MOTOR PARAMETERS
R = 0.8 R
L = 3.12 mH
kemf = 0.417 V/rad/s
J = 0.008 kg.m2
P = 1915 W
IV. EXPERIMENTAL
RESULTS
Polynomial curve fitting.
Fig. 2.
to previous data, since an exact fit is possible in the cases of
constant speed and constant acceleration (Fig. 2).
In Fig. 2, 8e(k-2),!9e(k-l), and Oe(k) are the values of
position estimated in the previous three sampling instants, A T
is the increment or sampling time, and Op(k+l) is the predicted
value of position at the next sampling instant.
= A ( t ) 2 + B ( t )+ C
=C
B,(k - 1) = A(AT)' + B ( A T )+ C
O,(k)
= 4A(AT)' + 2B(AT) + C
e,(#++ 1) = 9A(AT)' + 3 B ( A T )+ C
Assuming
t(k-2) =0
t ( k - 1) = AT
@e
04k-2)
t ( k ) = 2AT
t(k
+ 1) = 3AT
(15)
The simultaneous solution of these equations gives a unique
equation to predict the rotor position using the previous three
positions,
op(k+l)
= 3oe(1c) - 3oe(k-1)
+ oe(k-2)
(16)
The position estimation algorithm represented schematically in Fig. l(b) is executed continuously, and includes a
flux linkage correction loop. This is necessary because the
continuous estimation of flux linkage, using an integration
process, creates unwanted effects in the flux linkage waveform.
Offset is a common problem faced in the implementation of
integration. Moreover, as will be explained in a later section,
other effects, such as the temperature dependent winding
resistance, and inaccuracies in the measurement of current
and voltage, also corrupt the flux linkage estimation. The inner
current estimation loop corrects and updates the measured flux
linkage using the latest predicted position. The flux linkage
corrections are based on Eq. 10. Assuming the errors in the
flux linkage occur only because of current errors,
Here, the current errors are defined as,
Ail 1 - 21m Ail '
'
- 22m Ai!3 '
- 23m - $;e
2
(18)
where iie, aie,and iie are the second current estimations based
on Eq. 2 and the latest predicted position data. The estimated
flux linkage error is used to update the integration,
9n(k)
= %(k)
+ A%@)
(19)
A three phase inverter was constructed with IGBTs, the
transistor base signals being generated from a hysteresis current controller. The algorithm has been tested with a three
phase axial field PM machine which has parameters shown
in Table. I. The motor is star connected internally, and with
access to the star point. In the investigated system, the line
currents were measured with current transducers, and the phase
voltages via differential input isolation amplifiers which were
a part of a data acquisition system.
At present the approach has been validated using off-line
data obtained with a 10 ps sampling time. The results from
the position estimation algorithm,s processing of data acquired
with the drive operating in a number of alternative modes are
shown in Figs. 3-7. Results are presented for a wide range
of operating modes: steady-state and transient speed, with and
without current control.
Fig. 3(a) represents a typical 120' actual current waveform
during steady-state operation of the PM motor without current
control. The current is only limited by the back emfs of
the motor. The effect of the back emf voltages appears
superimposed on phase voltage (Fig. 3(b)) because of the
floating star point voltage. The rising and falling parts of the
phase voltage are the actual back emf waveform which occur
when the phase is unexcited. Upward and downward spikes in
the voltage waveform of Fig. 3(b) occur at the commutation
intervals where all three phases of the motor are conducting.
Fig. 3(c) illustrates the estimated flux linkage for one phase
using the actual current (Fig. 3(a)) and the actual phase voltage
(Fig. 3(b)). Since there is discontinuous current conduction in
this mode of operation, small dips occur in the flux linkage
waveform. Fig. 3(d) shows the estimated rotor position. As
seen in the figure, the estimated position is able to track the
actual current waveform which is in phase with the back emf.
Fig. 4 also gives a set of similar results showing the current
controlled during 120' conduction for constant speed operation. The actual current is limited by a commanded current
level and the line current is regulated within a hysteresis band.
The speed is constant since dc rail voltage and the load are
constant during this time. The phase voltage waveform (Fig.
4(b)) is more complicated than in Fig. 3(b), but the estimated
flux linkage (Fig. 4(c)) has a similar waveform. Fig. 4(d) gives
the estimated position which also matches with the actual
current waveform.
Fig. 5 shows result from sinusoidal operation of the PM
machine at constant speed. The actual sinusoidal current
waveform and the phase voltage are given in Fig. 5(a) and
Fig. 5(b) respectively.
The actual current is also regulated around a sinusoidal
demand current by the hysteresis current controller. The main
130
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 1, JANUARYFEBRUARY 1994
0
I
I
1
26
52
78
ume(ms)
I
104
0
I
I
I
38
76
114
=
z
f
om
f
i
l
-1
-1
3
I52
(b)
(b)
:
i
lime(ms)
om
407
G
4 14
0 14
0
52
26
78
time(ms)
IM
(C)
U
76
38
114
lime (ms)
152
(C)
$
1
zB 4
2 4
2
g 2
A"
2
0
0
52
U,
78
time(ms)
IN
0
76
33
11.8
time(ms)
152
(d)
(d)
Fig. 3. Measured and estimated waveforms, 120° excltation, no current
control a) Actual current waveform. b) Measured phase voltage. c ) Estimated
flux linkage. d) Estimated position.
Fig. 4. Measured and estimated waveforms, 120' current excitation, with
hysteresis current control a) Actual current waveform. b) Measured phase
voltage. c ) Estimated flux linkage. d) Estimated position.
difference from previous results is that the estimated flux
linkage has smooth waveform (Fig. 5(c)). No dips appear
in this waveform because current conduction is continuous.
Again the position estimation (Fig. 5(d)) gives adequately
good result. As explained earlier, the demand current is
in phase (no phase advance or delay) with the back emf
waveform. Therefore agreement between the actual current and
the estimated position demonstrates the algorithm's ability to
estimate position.
The angular position of the PM motor must be continuously
determined with acceptable accuracy even during speed transients. The results in Fig. 6 demonstrate the reliability of the
method during acceleration of the motor from rest for 120'
current conduction and no current control. It should be noted
that the high starting current (Fig. 6(a)) diminishes the dc rail
voltage, and causes a dip in the flux linkage estimation (Fig.
6(c)) initially. Fig. 6(c) indicates a typical integration showing
offset effect in the measured values ( u , z ) . The effect of the
flux linkage correction can be seen in Fig. 6(d). To examine the
accuracy of the estimation results, the measured and estimated
rotor positions are shown in Fig. 6(e) and Fig. 6(f). As seen,
there is very close agreement.
A second class of transient operating conditions arises from
load changes. Fig. 7 illustrates the response of the algorithm to
a step load change in the system. Since the decleration of the
machine is defined mainly by the mechanical time constant
of the system, to reduce mechanical time constant of drive,
another axial field brushless PM machine was used as a load.
The terminals of the brushless PM generator were connected
to a power resistor via a three phase diode rectifier. While the
drive was operating, a second power resistor was connected in
parallel to the original resistor to increase the load, giving the
effect of a step load change As seen in the current waveform
(Fig. 7(a)), the operation of the drive deviates following the
step in load at 100 ms. Since there is no speed feedback on
the drive while the line current rises in amplitude, the speed
of the motor reduces until the new steady-state speed defined
dy DC rail voltage is reached. The measured speed variation
during this operation was M 30% (from 553 rpm 384 rpm).
The DC rail voltage was 45.2 V before loading, failing to 39.1
V after loading (at steady-state).
131
ERTUGRUL AND ACARNLEY: A NEW ALGORITHM FOR SENSORLESS OPERATION OF PERMANENT MAGNET MOTORS
-
4
i-
E
5
0-
3
i-
P
--
I
0
88
44
132
ume(ms)
176
(b)
I
0
I
88
44
132
rime(ms)
170
(d)
Fig. 5. Measured and estimated waveforms, sinusoidal demand current, with
hysteresis current control. (a) Actual current waveform. (b) Measured phase
voltage. (c) Estimated flux linkage. (d) Estimated position.
As seen in the waveform of measured flux linkage of
Fig. 7(c), since the current level is small before loading, no
noticeable dips occured at current commutation. However,
after loading, the dips showing the commutation instants on
the flux linkage became apparent. The estimated position
is presented in Fig. 7(d). The verification of the mode of
operation can be seen in the estimated position comparing
with actual line current waveform.
v. EFFECTSOF MEASUREMENT
ERRORSAND PARAMETER DEVIATIONS
Since the proposed algorithm is implemented by calculating
the flux linkage based on the phase voltage and the line current,
the performance of the algorithm also depends on the quality
and accuracy of the estimated flux linkages and measured
currents. In addition to this, parameter deviations due to
variations in temperature and saturation should be considered.
Although the state equations of the PM motor are expressed
in Eq. 1, and the general flux linkage variables are defined in
Eq. 2, disturbances occur in the flux linkage estimations due to
measurement errors and parameter variations. The error terms
la
0
234
1%
time(ms)
312
(e)
,
I
I
I
I
m
0
734
I%
timc(ms)
312
(0
Fig. 6.
Transient result accelerating from rest.
in the flux linkage estimation and flux linkage variables may
be expressed as follows:
9=
9=
JLi
+ Q0 + el
+ e2
(v - Ri)dt
- A,(O)
(20)
132
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30. NO. I , JANUARYRBRUARY 1994
014
I
,
I
0
78
I-"
I
1%
I
234
I
time(ms)
312
(b)
Fig. 8.
75
in
225
rime(ms)
1W)
(4
Fig. 7.
The response of the algorithm to the step loading.
Here, elandez are the errors due to measurement and parameter deviations. The corruption sources on the flux linkage
estimation may be classified under term e l as follows:
1. Measurement errors in the terminal quantities,
a) phase shift in the measured values due to measurement devices,
b) magnitude error due to conversion factors and gain,
c) offset in the measurement system.
d) quantization error in the digital system.
2. Temperature effect on the winding resistance R.
The error term el in Eqns. 20 mainly includes measurement
errors. In both voltage and current measurement, one has to
ensure that the measurement device will not introduce a phase
shift, offset or a magnitude error. Another problem in the measurement system is the noisy computer connection to the IEEE
bus. The sensitive analog front end of the instrument can also
be corrupted by a noisy computer connection. One solution is
to place an isolation amplifier between the input side and the
measurement system. However, the isolation amplifier often
limits the performance of the system particularly for high
frequency measurements.
Errors in current and flux linkage estimations. (a) Current error. (b)
Flux linkage error.
Moreover, in star connected systems, if the current regulation in the third phase is reconstructed from the regulation
of the other two phases, errors in the third line current might
be increased. The error in flux linkage estimation is mainly
due to measurement errors, but it may not be separated from
deviation of the winding resistance R.
The error term e2 also includes current measurement error.
However, it is mainly affected by magnet flux linkage and
winding inductance. For PM motors which have large air gap,
saturation effects caused by current level may be ignored.
Deviations in the magnet flux linkages and changing back emf
constant with temperature may be taken into account.
The effects of parameter variations have been studied with
reference to initially measured motor parameters. In order to
check the ability of the method to perform in the presence of
parameter variations, a test has been carried out changing the
value of the winding resistance, the back emf constant, and
the winding inductance within a &lo% range.
Changing the resistance value causes small phase shift
and noticeable dc offset in the estimated flux linkage waveform which can be overcome by the flux linkage correction.
Referring to the initially estimated position, measurements
have shown that changing the resistance value *lo% for the
operating condition in Fig. 6 changes the first electrical period
by about 2 ms. When the motor reaches the steady state, the
difference becomes smaller. During constant speed operation,
the zero crossing points in the position waveform shifted 2.5"
electrical which corresponds to +0.7% position error.
Changing the back emf constant causes a magnitude
difference between estimated and corrected flux linkage.
The deviation can be recovered by flux linkage correction.
Changing the back emf constant +lo% affects the position
estimation about 3" electrical during constant speed operation
for the case in Fig. 6.
Both changing the value of the inductance and offset effect
does not introduce noticeable position error, However, small
errors can be eliminated by flux linkage correction. Two typical
waveforms of outer current loop error and error in linkage
ERTUGRUL A N D ACAKNLEY A N t W ALGOKITHM t O R F t h S O R L E S S OPERATION OF P L R M A N E N T M A G N E T M O T O R S
-
estimation for acceleration from rest are given in Fig. 8. The
high initial
error in ~ i 8(a)
~ is. related to an error in the
initial position of the motor. Static friction in the mechanical
system and incorrect initial value of the integration may cause
this error in real system applications.
I
VI. CONCLUSION
The experimental results demonstrate that stator voltages
and current signals from a PM motor can be used to obtain
position information. The proposed algorithm for shaft position
sensorless operation has been tested with a commercially
available PMSM operating with both 120” electrical degrees
conduction and sinusoidal excitation. The method can also be
applied to motors which have position dependent inductance,
and allows detection of rotor position over a wide speed range
including acceleration from rest. The method is based on flux
linkage estimation, so the algorithm can be applied to any other
machine, such as the trapezoidal permanent magnet machine
and reluctance-type machines. A more versatile approach may
be implemented using machine specific look-up tables for rotor
flux linkage variations. The next step in this work is to test the
method using a digital signal processor for on-line real-time
processing of the voltage and current data.
ACKNOWLEDGMENT
The authors
like to
the financial
provided for this work by Esprit Project No. 2656: IDRIS,
and Mr. Ertugrul would like to thank the Istanbul Technical
University for funding his phD research at the university
of
Newcastle upon Tyne.
I33
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Nesimi Ertugrul was born in Turkey in 1960. He
received the B.Sc. and M.Sc. degrees in electrical
engineering and in electronic and communication
engineering from the Istanbul Technical University,
Istanbul, in 1985 and 1989, respectively.
After the BSc., he worked three years as a
research and teaching assitant at Istanbul Technical
University. Mr. Ertugrul recently received the Ph.D.
degree from the University of Newcastle upon Tyne,
UK.
His research interests include simulation, analysis, real-time control and design of PM motor drive systems, solar energy
battery charging systems, and switched reluctance drives.
Paul Acarnley received the B.Sc. and Ph.D. degrees
in electrical engineering from Leeds University, UK,
in 1974 and 1977, respectively.
After seven years in the Department of Engineering at Cambridge University, he joined the Electric
Drives and Machines Group at the University of
Newcastle upon Tyne, UK, in 1986. As Reader in
Electrical Engineering, his principal research interest is in the control of electric drives, including
m
work on state and parameter estimation. He has also
made contributions in the areas of stepping motors,
permanent-magnet generators and brushless dc drives.
Mr. Acarnley is a Fellow of the Institution of Electrical Engineers.