Download 2008 - Holtz - Acquisition of position error and magnet polarity for sensorless control of PM synchronous machines(2)

1172
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 44, NO. 4, JULY/AUGUST 2008
Acquisition of Position Error and Magnet Polarity for
Sensorless Control of PM Synchronous Machines
Joachim Holtz, Fellow, IEEE
Abstract—Sensorless control of a permanent-magnet synchronous machine at low and zero speed is based on the injection of an
oscillating high-frequency carrier signal. A particular demodulation technique serves to eliminate the estimation error introduced
by pulsewidth modulation delay and the nonlinear characteristics
of the inverter. Before the drive is started, the initial rotor position and the magnet polarity are detected. The initialization is
performed by injecting an ac carrier and two short current pulses
in a sequence.
Index Terms—Initial rotor position, permanent magnet (PM)
synchronous motor, sensorless control, zero-speed operation.
I. I NTRODUCTION
T
HE ORIGINAL domain of permanent magnet (PM) synchronous machine drives is high-precision positioning
systems for robotic and machine tool applications. The highefficiency and high power density enables a closed construction
of the machine case using natural surface cooling, while slim
rotor dimensions account for a fast dynamic response. Since
the cost of magnet material has drastically reduced in the past
few years, PM machine drives have also become attractive for
less demanding applications. The elimination of a mechanical
position sensor makes these drives even more competitive.
Sensorless control of PM machines can rely on modelbased estimation methods which work well above about 3% of
nominal speed. Operation in the lower speed range, and at zero
speed, requires signal injection techniques for rotor position
estimation. These techniques exploit the anisotropic properties
of PM machines, caused either by the saliency of an interior
magnet rotor, and/or by the saturation of the stator iron. The
latter effect is dominant in surface mount magnet machines.
The injected signal is generally formed by a voltage, being
added to the input of the pulsewidth modulator. Such signal is
referred to as a carrier if it is periodic in time. Its frequency
differs from the fundamental machine frequency. An injected
carrier voltage signal creates a carrier current and a pertaining
flux density component in the machine. These quantities are
influenced by the anisotropic magnetic structures. Easier to
Paper IPCSD-07-102, presented at the 2006 Industry Applications Society
Annual Meeting, Tampa, FL, October 8–12, and approved for publication in the
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Drives
Committee of the IEEE Industry Applications Society. Manuscript submitted
for review October 15, 2006 and released for publication October 17, 2007.
Published July 23, 2008 (projected).
The author is with the Electrical Machines and Drives Laboratory, University
of Wuppertal, 42097 Wuppertal, Germany (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIA.2008.921418
acquire is the carrier current. It needs to be separated from the
fundamental current for further processing. It is the differences
in amplitude and phase angle between the carrier voltage and
the carrier current that carry the information on the orientation
in space of the machine anisotropy.
Standard techniques therefore analyze the carrier current in
its relationship to the injected carrier voltage. As an adverse
effect, not only the anisotropic properties of the machine determine the signal content of the carrier current, but also the delays
and the nonlinear distortion introduced by the pulsewidth modulated inverter that feeds the machine. Its semiconductor power
devices are nonideal switches having storage time delays and a
nonlinear relation between forward voltage and device current.
The distortions of the carrier current by the nonlinear inverter
are difficult to separate from the signals of interest that relate to
the anisotropy of the machine.
Two different types of carrier signals have been used for
rotor position estimation. A revolving carrier is generated by
injecting a rotating voltage vector of higher frequency than the
fundamental. The carrier signal scans the whole circumferential
profile of the magnetic anisotropy of the machine. The magnetization axis is identified by evaluating the negative sequence
component of the carrier current. An observer that models the
mechanical subsystem of the machine serves for extracting the
desired information.
An alternative class of methods relies on injecting not a
rotating, but an alternating carrier that oscillates in a specific,
although time-variable spatial direction. The direction can be
selected in an educated guess to achieve the maximum sensitivity in locating the targeted anisotropy. Use can be made of
already existing knowledge, which is then updated by acquiring
an incremental error per sampling period.
A particular problem is the detection of the rotor position
and of the polarity of the magnetic field at standstill, before
the drive is put in operation. This information is required to
enable a smooth start of the drive. It is important that the initial
rotor position and polarity are detected without generating
electromagnetic torque. Only then will the machine conserve
its original position before it is started by the drive control
system.
The method of injecting a revolving carrier was adapted
in [1] to detect the magnet polarity at standstill [2]. The carrier
current must be high enough to change the saturation level
noticeably whenever the rotating flux wave aligns with the rotor
magnetization axis. This creates a second harmonic component
in the carrier current, which is exploited for magnetization
polarity detection. Major drawbacks are the low sensitivity [2]
and the disturbances caused by the dead-time effect [3].
0093-9994/$25.00 © 2008 IEEE
HOLTZ: ACQUISITION OF POSITION ERROR AND MAGNET POLARITY FOR SENSORLESS CONTROL
A different approach uses an oscillating carrier in a rotating spatial orientation. The excitation by the carrier current
changes the saturation level when its direction coincides with
the magnet field. Current harmonics of second order are then
created that serve for polarity identification [4]. Results and
drawbacks as those discussed for revolving carrier injection
again apply [2]. Alternatively, a complete scan of the respective
carrier current amplitudes is recorded with the oscillating field
rotating along the circumference of the air gap [5]. The respective maximum and minimum values occur when the oscillating
carrier aligns with the d-axis, of which a higher amplitude value
indicates the direction of the positive d-axis. The detection
of such maximum value is inherently inaccurate [6]. Fuzzy
logic control has been used to mitigate, but not solve this
problem [7].
Most carrier injection methods suffer from basic drawbacks
such as the poor signal-to-noise ratio and the parameter dependence of the revolving carrier methods. A low sensitivity
requires using interior magnet machines that exhibit strong
anisotropic properties. Even more sophisticated methods for
dead-time compensation fail to eliminate periodic rotor position
errors. Torque oscillations are then produced of six times the
fundamental frequency [8]. Also, the forward voltage drop of
the power devices contributes to this type of error.
One of the earliest publications that rely on injecting an
oscillating carrier in alignment with an estimated anisotropy is
attributed to the work of Blaschke [9]. The approach was subsequently adopted by other authors [4], [10]–[12]. The respective
methods differ as regards the signal demodulation technique.
Employing low-pass filters for signal extraction introduces a
time delay [4]. A better response is achieved by fast Fourier
transform [10], or by direct sampling [11], [12]. These methods
can also serve to detect the magnet axis at initialization. The
magnet polarity is subsequently identified by injecting short
voltage pulses. These either increase or decrease the magnet
flux. Of the resulting current pulses, the one having the higher
amplitude indicates the positive d-axis [10].
This paper starts with reviewing the physical background of
Blaschke’s method, followed by a mathematical analysis of the
behavior of the motor in the presence of an injected signal [11],
[12]. Its contribution is a demodulation technique that is robust
against the nonlinearities of the inverter.
II. P RINCIPLE OF O PERATION
To give an introduction to the approach presented in this
paper, a polyphase winding in the stator of an ac machine is
considered. The two-phase equivalent of such winding in terms
of its α- and β-components is shown in Fig. 1. A dc voltage uα
is applied to the terminals of phase α winding which gives
rise to a current iα . A magnetic flux density distribution is
then established in the air gap with its principal direction being
oriented along the winding axis α, which is the real axis in this
case. The resulting flux linkage with the windings of phase β is
zero. This is owed to the orthogonal arrangement in space of the
two-phase windings. A change of the excitation current iα with
respect to time would therefore have no effect on the current in
phase β.
1173
Fig. 1. Two-phase winding system in stator coordinates.
Fig. 2. Two-phase winding system, magnet rotor aligned with α-axis.
: magnetization vector.
M
A PM rotor is added to this arrangement in a next step. Fig. 2
shows the topology of the resulting system. The PM field is
. It saturates the
characterized by the magnetization vector M
stator iron locally, thus increasing the magnetic resistance of
its flux paths. A magnetic anisotropy is thus created, being
modeled in Fig. 2 by a partially enlarged air gap. The flux
iα is generated by the current iα . Its
density distribution B
intensity is assumed small enough not to change the saturation
iα can be therefore
of the iron. The flux density distribution B
considered an independent field component. As long as the
direction of the magnet flux is in alignment with the α-axis,
iα conserves
as shown in Fig. 2, the flux density distribution B
its symmetry with respect to the α-axis, and the flux linkage
with the windings of phase β remains zero.
The situation changes when the magnet rotor assumes a different angular position. Fig. 3 shows how this affects the spatial
iα . Its flux paths get dedistribution of the flux density field B
flected toward regions of lower magnetic resistance. The symmetry with respect to the axis of the exciting phase winding α
iα with the
is then lost which establishes a flux linkage of B
orthogonal phase winding β. It is interesting to note that the
effect so far described is a pure magnetostatic phenomenon.
The effect can be exploited for detecting the angular position
of the magnet rotor. The current iα in the excitation winding must be time-varying for this purpose. The flux density
distribution is then also varying with time, and so is the flux
linkage with the detection winding phase β. As a consequence,
a current iβ is created in these windings. The effect occurs
1174
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 44, NO. 4, JULY/AUGUST 2008
Fig. 3. Two-phase winding system, magnet rotor displaced.
carrier current is displaced in the opposed angular direction:
It locates closer to this axis. The reason is that the magnetic
flux gets attracted by regions of less magnetic resistance. It is
deflected in a clockwise direction as seen from the injection
axis R . The local inductance is higher in these regions than
around the magnet axis R. The carrier current vector is therefore
deflected in an anticlockwise direction.
The spatial deviation between the carrier voltage uc and
the carrier current ic can be made an input to a superimposed control system that manipulates the injection angle such
that the phase displacement is minimized. The injection angle
and the rotor position angle then converge. The spatial flux
c and the field of the magnet rotor asdensity distribution B
sume orientations with respect to each other as those shown
in Fig. 2.
III. A NALYSIS
A. Machine Equation
The analysis starts considering a PM synchronous machine
as shown in Fig. 4. An ac carrier voltage uc is injected into
the stator windings at an estimated displacement angle γu
with respect to the true field axis. As seen from the stationary
reference frame, the injection angle ϑ̂ deviates from the true
rotor position angle ϑ by the voltage injection angle γu , hence,
Fig. 4. PM synchronous machine. R: rotor axis. R : estimated rotor axis.
S: estimated stator axis. uc : injected carrier voltage vector. ic : resulting carrier
current vector.
ϑ̂ = ϑ + γu .
(1)
The carrier voltage in stationary coordinates is then
although the two-phase windings are orthogonal with respect
to each other. The amplitude of the current iβ is a function
of the magnet displacement angle ϑ. It is proportional to this
displacement angle for small deviations. The direction of the
current iβ is determined by Lenze’s law: The current must
establish a magnetic flux component that tends to counteract
the change of flux linkage of the phase β windings with the
iα . The resulting polarity of iβ is indicated
field component B
in Fig. 3.
To study the effect with a view to detecting the rotor position
in a PM synchronous machine, the system in Fig. 3 is subjected
to a coordinate transformation. The new reference frame is
made to rotate in synchronism with the magnet rotor. The north
pole axis of the magnet rotor defines the real axis of a rotor
oriented reference frame, marked R in Fig. 4. The windings in
the stator are shown in a customary three-phase arrangement.
The excitation of the winding system is chosen as an
ac voltage. It is injected in the spatial direction R of an
estimated rotor position, thus making use of existing a priori
knowledge. The injected voltage, referred to as the carrier
voltage vector uc in the following, creates a carrier current in
the stator windings, represented by the space vector ic , and a
c , both being dependent on the
spatial flux density distribution B
anisotropic conditions caused by the magnet field. Their spatial
orientations deviate from the direction of the injected voltage.
c shows a displacement
While the flux density distribution B
, the space vector ic of the
away from the magnetization axis M
j ϑ̂
u(S)
= rs ic + l(S)
c = uc cos ωc t · e
s ∗
di(S)
c
dt
(2)
where wc is the carrier frequency. The superscript (S) refers
to stationary coordinates. Since the carrier frequency is
much higher than the fundamental frequency, the resistive
voltage rs ic can be neglected.
The carrier current develops under the influence of the
anisotropic properties of the machine. These are represented
in (2) by the inductance tensor l(S)
s (ϑ). This quantity varies as
a function of the rotor position angle ϑ. To obtain a solution
for the carrier current vector ic , (2) is transformed to rotor
coordinates. This is done by multiplying (2) by exp(−jϑ), from
which the differential equation
= uc cos ωc t · ej(ϑ̂−ϑ) = l(R)
∗
u(R)
c
s
di(R)
c
+ jωl(R)
∗ ic
s
dt
(3)
is obtained. Variables in rotor coordinates are marked by the
superscript (R) . The mechanical angular frequency dϑ/dt = w
is assumed to be small which permits neglecting the last term
in (3). The inductance tensor, after its transformation to rotor
coordinates, converts to a constant
=
l(R)
s
ld
0
0
lq
(4)
HOLTZ: ACQUISITION OF POSITION ERROR AND MAGNET POLARITY FOR SENSORLESS CONTROL
1175
which demonstrates that the anisotropies of the machine are
related to the angular position of the rotor. Anisotropies are
caused by magnetic saturation in a surface mount machine,
and, in addition, by the anisotropic rotor construction of interior
magnet machines. The d-axis coincides with the most saturated
region, hence ld < lq .
Being small in magnitude, the excitation at carrier frequency
does not interfere with the behavior of the machine at fundamental frequency. The resulting carrier frequency current ic is
then only determined by the inductance tensor (4), as indicated
in the right-hand side of (3).
The solution of (3) is
1
uc
1
(R)
sin ωc t ·
cos(ϑ̂ − ϑ) + j sin(ϑ̂ − ϑ) . (5)
ic =
ωc
ld
lq
B. Trajectories of the Carrier Current
To gain insight in the physical nature of the carrier current,
the harmonic functions in (5) are expressed by equivalent
complex space vectors. A multiplication by exp(jϑ) transforms
this equation to stationary coordinates. Referring to (1), the
result can be written as
+
−
i(S)
c = ic + ic
(6a)
where
i+
c =
−juc (ld + lq )ej(ωc t+ϑ̂) + (ld + lq )ej(−ωc t+ϑ̂−2γu )
4ωc ld lq
+
= i+
p + in
(6b)
describes the elliptic trajectory of a current vector that rotates
in a positive direction, and
i−
c =
juc (ld + lq )ej(−ωc t+ϑ̂) + (ld − lq )ej(ωc t+ϑ̂−2γu )
4ωc ld lq
−
= i−
n + ip
−
Fig. 5. Elliptic trajectories of the current vectors i+
c and ic , created by four
circular rotating space vectors. S: stationary coordinates. R: rotor coordinates.
R : estimated rotor coordinates.
We obtain from the respective arguments in (6b)
ωc t1 + ϑ̂ = −ωc t1 + ϑ̂ − 2γu + π,
π
ωc t1 = −γu + .
2
or
(8)
Inserting wc t1 in (6b) yields the equation of the minor axis of
the ellipse
(t1 ) =
i+(S)
c
uc j(ϑ̂−γu )
e
2ωc lq
(9a)
uc jϑ
e .
2ωc lq
(9b)
or, referring to (1),
i+(S)
(t1 ) =
c
(6c)
represents the elliptic trajectory of a negatively rotating current vector. Fig. 5 shows that both elliptic trajectories are
congruent.
Each of the trajectories (6b) and (6c) is defined by the sum
of two current vectors that themselves rotate on circular trajectories in opposed directions. As indicated by (6b), the elliptic
trajectory i+
c that develops in a positive direction decomposes
into a positive sequence current vector i+
p and a negative
.
A
similar
situation
exists for the
sequence current vector i+
n
,
building
up
in
a
negative
direction
and being
trajectory i−
c
composed, according to (6c), of a positive-sequence current
−
vector i−
p and a negative sequence current vector in .
The orientation in space of the ellipse in Fig. 5 is determined
from one of the equations (6b) or (6c). Referring to (6b), for
example, the particular time instant t1 is determined at which
+
the vectors i+
p and in align in exactly opposed directions
+
arg i+
p (t1 ) = arg in (t1 ) + π.
(7)
The spatial orientation of the vector defined by (9b) coincides
with the true rotor position angle ϑ. This demonstrates that
the ellipse in Fig. 5 invariably aligns its minor axis with the
direct axis given by the true rotor position, a fact that is also
confirmed by interpreting (9b) with reference to the vector
diagram Fig. 5.
IV. R OTOR P OSITION E STIMATION
As the true rotor position angle ϑ may not be exactly known,
the ac carrier voltage is injected at a spatial deviation γu from
the true rotor position axis. According to (1) and (2), the
trajectory of the carrier voltage vector uc then coincides with
the R -axis in Fig. 5.
Owing to the magnetic anisotropies of the machine, the
trajectory of the carrier current vector ic deviates from the
trajectory of the injected voltage vector uc . The vector diagram
Fig. 5 shows that the geometric additions over time of all space
vector components in (6) define the locus of a straight line. It is
1176
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 44, NO. 4, JULY/AUGUST 2008
Fig. 6. Space vector diagram showing the trajectories of the oscillating carrier
signals uc and ic . R = rotor coordinates. R = estimated rotor coordinates.
S = stator coordinates.
displaced by the angle γi with respect to the true rotor position
axis R. The displacement angle
γi = a tan
ld
tan γu
lq
(10)
is obtained with reference to (1) and (5).
The equation shows that the current displacement angle γi
depends on the machine anisotropy on one hand, expressed by
the ratio ld /lq , and on the voltage injection angle γu on the
other. The respective angles are shown in the vector diagram
Fig. 6. The enlarged inset shows that the q-component icq of
the carrier current vector in the estimated reference frame R is
an indicator for the angular displacement
∆γ = γu − γi
Fig. 7. Signal flow graph of a sensorless scheme designed for speed control and initial rotor position and magnet polarity detection; block 2N is a
2N -counter.
to the anisotropic properties of the machine. A periodic error
component, created by the nonlinearities of the inverter, appears therefore superimposed on the estimated rotor position
signal [8].
Such adverse effect is eliminated by not using, as is customary, the injected voltage as a reference signal when extracting
the rotor position information from the carrier current. The
carrier current itself is used instead as the reference signal.
The advantage of such approach is that both the position
information and the reference signal undergo the delays and
nonlinear distortions of the inverter. The resulting effect is that
the position information remains undisturbed.
(11)
B. Estimation of the Position Error
between the carrier voltage and the current vectors. The displacement angle ∆γ equals zero for γu = γi ; inserting this
into (10) and observing ld = lq yields γu = γi = 0, hence
R → R for icq → 0. This means that the correct rotor position
angle is obtained by minimizing the voltage injection angle
γu . This is achieved by controlling the q-component icq of the
estimated carrier current vector to a zero value.
V. E LIMINATION OF N ONLINEAR I NVERTER E FFECTS
A. Acquisition of the Error Signal
Rotor position estimation methods generally suffer from the
nonlinear distortions that the inverter imposes on the carrier
current. These are caused by the signal delay of the pulsewidth
modulator, and by the storage time delay and the threshold
voltages of the semiconductor switches. Existing rotor position estimation schemes attribute all deviations of the carrier
current from a reference waveform, such as being produced
by a linear power amplifier feeding a symmetrical machine,
Considering a vector controlled synchronous machine drive,
the measured stator currents are transformed to an estimated
rotor reference frame. Fig. 7 shows the signal flow graph of
such current control scheme and also the elements for sensorless position estimation. The oscillating carrier voltage uc is
injected in estimated rotor coordinates. The response of the
machine is an oscillating carrier current ic superimposed to the
stator current is . The measured stator current is transformed
to rotor coordinates. The carrier frequency components are
separated by a bandpass filter BPF from the fundamental
current and from the switching harmonics of the inverter.
An analytical expression for the carrier current is obtained by
transforming (5) from rotor coordinates to the estimated rotor
reference frame R . Referring to (1), (5) is multiplied by the
transformation term exp(−jγu ) to obtain
)
i(R
=
c
uc lq cos2 γu + ld sin2 γu
ω c ld lq
+ j(ld − lq ) cos γu sin γu ) sin ωc t. (12)
HOLTZ: ACQUISITION OF POSITION ERROR AND MAGNET POLARITY FOR SENSORLESS CONTROL
1177
As the error angle γu of the estimation is mostly small, (12)
can be approximated by
) ∼
i(R
=
c
uc
(ld + j(ld − lq ) sin γu ) sin ωc t = icd + jicq .
ω c ld lq
(13)
This alternating current extends in a spatial direction given by
the angular difference ∆γ = γu − γi . According to Fig. 6, the
angle ∆γ is assessed through the imaginary component icq of
the carrier current, which, as an ac signal, does not directly
reveal the sign of ∆γ. The sign is rather hidden in the phase
)
= ic
relationship between icd and icq . The trajectory of i(R
c
in the enlarged inset of Fig. 6 shows that, for the error being
positive, the instantaneous values of icd and icq have the same
sign; a negative error exists when icd and icd have opposed
signs. Hence, the displacement angle ∆γ
∆γn = kn icqn · sign(icdn ).
(14)
The subscript n indicates time-discrete values. The constant
factor kn is assumed to be unity in a first step; it will be later
defined in (15).
Equation (14) demonstrates that it is the very carrier current,
represented in (14) by its dominating component icdn , that is
used as a reference signal for extracting the deviation ∆γ. No
reference is made to the exciting carrier voltage vector uc for
error decoding, see Section V-A.
For kn = 1, the waveform of the error signal ∆γ has the
shape of a rectified sinewave. Its ripple propagates through the
proportional channel of a PI-controller shown in the lower portion of Fig. 7. It superimposes on the estimated speed signal ŵ
(Fig. 7). A ripple content in the feedback signal requires
compromising in the design of the speed control loop, which
deteriorates its bandwidth.
The problem is solved as follows.
1) The carrier frequency fc is synchronized with the switching frequency fs . This defines the integer frequency ratio
N = fs /fc .
2) A cycle of the carrier voltage uc is synthesized from 2N
constant voltage vectors ucn , n ∈ 1 . . . 2N . The vectors
are uniformly distributed in the complex plane [Fig. 8(a)].
They define the injected voltage in estimated rotor coor(R )
dinates as uc = Re{ucn }.
3) The phase angle arg(uc ) is adjusted such that the zero
crossings of the bandpass-filtered carrier current component icd occur exactly in the center between two neighboring sampling instants [identical time intervals T1 in
Fig. 8(b)]. This maximizes the low-amplitude values in
the sampled waveform icqn and introduces a symmetry
that minimizes the number of its amplitude levels. With
N = 4, there are only two levels in Fig. 8(c).
4) Synchronous rectification is performed according to (14).
The constants
kn =
1
|sin (arg(ucn ) − ϕi )|
(15)
in (14) eliminate the 2 fc -ripple from the error signal. The
constant phase displacement ϕi ∼
= π/4 in (15) accounts
Fig. 8. Demodulation of the position error, exemplified for N = 4.
(a) Definition of the injected voltage Re{ucn }. (b) Components icd and icq
of the carrier current and sampled waveform i
cq . (c) Signal icq rectified.
(d) Error signal ∆γ.
for the lag between uc and ic . The smooth waveform
Fig. 8(d) results, where a circle represents a sampled
value.
The error signal ∆γ thus obtained is passed to the PI
controller in Fig. 7. The controller adjusts its output such
that ∆γ → 0, thus keeping the estimated rotor coordinates
aligned with the d-axis of the machine. The controller output
is interpreted as the angular mechanical velocity ŵ, the integral
of which is therefore the estimated rotor position angle ϑ̂.
This angle is used both for coordinate transformation and for
position control.
It is an advantage of this injection technique that the dynamic
performance of the speed and torque control system is not
impaired, as the carrier signal does not appear in the torque
building current component iq . Therefore, the q-current in the
current feedback path needs not be low-pass filtered. Such
filter is required when using a rotating carrier. It reduces the
bandwidth for the control of the machine torque. According to
Fig. 7, a low-pass filter is only provided for the component id
in the excitation axis.
C. Robustness Against Nonlinearities
The demodulation method is robust against the delay of the
pulsewidth modulator and the nonlinearities of the inverter.
Even a dead-time compensation is not required.
The robustness was proved by introducing an exaggerated
nonlinear effect. Although the device storage time is only
0.8 µs, the lock-out time of the gate control was set to
10.2 µs. An estimated nonzero position signal was generated
using a sensor for position feedback while injecting the carrier
signal in alignment with the a-axis of the stator. The drive was
1178
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 44, NO. 4, JULY/AUGUST 2008
Fig. 10. Robustness against inverter nonlinearities at no load, control with position sensor, carrier signal aligned with the a-axis. From top: phase current ia ,
bandpass-filtered carrier signal icd , sampled components icdn and icqn , uncorrected and corrected position error: ∆γ/kn and ∆γ.
TABLE I
MACHINE DATA; MACHINE II WAS USED FOR FIGS. 13–15,
MACHINE I FOR THE OTHER OSCILLOGRAMS
Fig. 9. Robustness against inverter nonlinearities at load, control with position
sensor, carrier signal aligned with a-axis. (a) Phase voltage ua and phase
current ia . (b) Enlarged portion of (a): current ia , bandpass-filtered carrier
signal icd , and position error ∆γ.
operated at constant low speed. The estimated position signal
then changes sinusoidally with time.
Fig. 9(a) shows that the stator voltage ua changes its gradient
at every zero crossing of the current. This is because the deadtime effect of the fundamental current is compensated as the
current controller forces sinusoidal waveforms. The carrier
current is not controlled in closed loop. The position signal
remains nevertheless undisturbed as shown in the enlarged
portion Fig. 9(b).
The oscillogram Fig. 10 was recorded under the aforementioned conditions, but at no load. The zero crossings now occur
perpetually at carrier frequency. Although the dead-time effect
should affect the amplitudes of the carrier current, its influence
is hardly discernible. When operating in the sensorless mode,
∆γ acts as the position error and assumes a zero value at steady
state. An amplitude error, if any, would not impair the accuracy.
The shape of the waveforms in Fig. 10 confirms the prediction
in Fig. 8. The setting N = 4 applies, as in all other oscillograms
of this paper.
Figs. 9 and 10 give evidence of the high signal-to-noise
ratio of the acquired signal. This permits operating at low
carrier level. A carrier current amplitude of 20 mA was found
sufficient for rotor position angle estimation using machine I
of Table I.
The waveforms of the true and the estimated rotor position
angles measured at 0.4% rated speed, or 6 rev/min, are shown in
Fig. 11 at no load and in Fig. 12 at rated load. Note the absence
of sixth harmonic components in the position error signals. This
is all the more remarkable since the inverter operates without
Fig. 11. Measured signals from a sensorless speed control scheme, operated
at 0.4% rated speed and without load. From top: estimated position angle,
estimation error, and true position angle.
Fig. 12. Measured signals from a sensorless speed control scheme, operated at
0.4% rated speed and rated load. From top: estimated position angle, estimation
error, and true position angle.
dead-time compensation [8]. A second harmonic component
does appear in the error signal; it would indicate the existence
of other anisotropies than the fundamental.
HOLTZ: ACQUISITION OF POSITION ERROR AND MAGNET POLARITY FOR SENSORLESS CONTROL
Fig. 13. Response to a commanded position cycle of ±180◦ .
Fig. 14. Initial rotor angle and polarity detection as in Fig. 11 with the
estimated position at t > t2 being incorrect.
Fig. 13 shows the response of a superimposed speed and
position control loop to a commanded position cycle of ±180◦ .
VI. I NITIAL R OTOR A NGLE AND P OLARITY D ETECTION
It is important that the position angle and the magnetization
polarity of the rotor be identified before the drive is initially
started. No electromagnetic torque must be produced during
the identification process. The current reference signal i∗s of the
control system in Fig. 7 is therefore set to zero, while a lowamplitude carrier signal uc is injected. It creates an alternating
carrier current in an arbitrary direction. A nonzero displacement
angle ∆γ between the injected voltage uc and the carrier
current ic is therefore detected. It activates the closed-loop
position estimation scheme Fig. 7, thus making the estimated
rotor position align with one of the rotor axes. The rotor angle
thus estimated is ϑ̂. It either indicates the correct direction of
the magnet flux, or it is in error by a displacement of π rad.
The magnet polarity of the rotor is determined next. Referring to the estimated rotor position angle ϑ̂, two short voltage
pulses having the opposed spatial directions ± exp(j ϑ̂) are
injected into the stator winding. Each voltage pulse is synthesized by a sequence in time of the two switching state vectors,
encountered in close neighborhood to the respective injection
angle ϑ̂. The ratio of their respective on-durations controls the
injection angle, while the total volt-seconds of both pulses are
identical. They are chosen such that the resulting current pulses
equal, or exceed, the nominal current amplitude of the machine.
1179
Fig. 15. Initial rotor angle and polarity detection. The rotor orientation is
determined within time interval t1 < t < t2 . The difference of amplitudes of
the two short current pulses defines the magnet polarity. The original alignment
was correct in this example.
Being aligned with the direct axis, the current pulses do not
produce torque.
One of the pulses aligns with the direction of the magnet
flux, thus increasing the magnetization of the stator iron and
driving the direct axis inductance ld into deeper saturation. As
a current builds up in the direction of applied voltage pulse, the
inductance value reduces. The other current pulse opposes the
direction of the magnet flux. This tends to desaturate the stator
iron and lets the inductance value of ld increase.
The volt-second values of the injected voltage pulses being
identical, the amplitudes of the current pulses differ as the
respective inductance values differ. That current pulse having
the higher amplitude indicates the positive direction of the
rotor axis.
The oscillograms Figs. 14 and 15 illustrate the initialization
process of the position control scheme. The machine remains at
standstill throughout this process. The rotor position estimation
scheme Fig. 7 first changes the orientation of the oscillating
carrier to coincide with the estimated d-axis of the machine.
A certain value of ϑ̂ is thus obtained at t = t2 . The carrier
injection is subsequently discontinued to determine the magnet
polarity. The example of Fig. 14 shows that the first current
pulse exhibits a higher amplitude, meaning that the estimated
rotor position value is correct.
The case of an initial error of the rotor position search is
shown in Fig. 15. It is the second current pulse here that
exhibits the higher amplitude. The original estimate of ϑ̂ is
therefore replaced by ϑ̂ + π/2. In both cases the injection of the
carrier is resumed at t > t3 , and the position control scheme is
subsequently started.
VII. S UMMARY
An alternating carrier is used for estimating the rotor position
of a PM synchronous machine. The signal is injected in the
spatial direction of the estimated rotor position axis. A particular demodulation technique makes the estimation immune
against the delay of the pulsewidth modulator and the nonlinear
distortions of the inverter. The position estimation scheme
works accurately even without dead-time compensation. This
is achieved by using a reference signal for decoding that has
1180
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 44, NO. 4, JULY/AUGUST 2008
passed through the inverter and, thus, has undergone the same
distortions as the position error signal.
Before the drive is started, the initial rotor position and the
magnet polarity are detected. The spatial orientation of the
magnet axis is identified using the carrier injection scheme.
The polarity of the magnet is determined by injecting two short
current pulses in alignment with the estimated magnet axis, but
in opposed directions. The difference of the pulse amplitudes is
used to identify the north pole axis.
The proposed method exhibits high-sensitivity and good
signal-to-noise ratio. It requires only 20 mA carrier amplitude
in a machine of 15.2 A maximum peak current. It operates
well with surface mount PM machines having weak anisotropic
properties. Not identifying the rotor position but rather the
position error ensures high positioning accuracy. The injected
signals do not produce torque, neither at initial rotor angle and
polarity detection, nor during regular operation. Therefore, the
q-current must not be low-pass filtered which permits higher
dynamic performance at closed-loop torque control.
[6] S. Nakashima, Y. Imagaki, and I. Miki, “Sensorless initial rotor position estimation of surface permanent-magnet synchronous motor,” IEEE
Trans. Ind. Appl., vol. 36, no. 6, pp. 1598–1603, Nov./Dec. 2000.
[7] M. Tursini, R. Petrella, and F. Parasiliti, “Initial rotor position estimation method for PM motors,” IEEE Trans. Ind. Appl., vol. 39, no. 6,
pp. 1630–1640, Nov./Dec. 2003.
[8] C. Silva, G. M. Asher, and M. Sumner, “Influence of dead-time compensation on rotor position estimation in surface mounted PM machines using
HF voltage injection,” in Proc. IEE-J/IAS PCC, Osaka, Japan, Apr. 2002,
pp. 1279–1284.
[9] F. Blaschke, “Sensorless field orientation at zero flux frequency,” in
Conf. Rec. IEEE IAS Annu. Meeting, San Diego, CA, Oct. 7–10, 1996,
pp. 189–196.
[10] T. Aihara, A. Toba, T. Yanase, A. Mashimo, and K. Endo, “Sensorless
torque control of salient-pole synchronous motor at zero-speed operation,” IEEE Trans. Power Electron., vol. 14, no. 1, pp. 202–208, Jan. 1999.
[11] M. Linke, “Injection of alternating carrier signals for sensorless control of
AC machines,” Ph.D. dissertation, Wuppertal Univ., Wuppertal, Germany,
May 2003. (in German).
[12] M. Linke, R. Kennel, and J. Holtz, “Sensorless speed and position control
of synchronous machines using alternating carrier injection,” in Proc.
IEEE IEMDC, Madison, WI, Jun. 1–4, 2003, pp. 1211–1217.
ACKNOWLEDGMENT
The author would like to thank O. C. Ferreira for the
fruitful discussions and for his cooperation in preparing the
experiments.
R EFERENCES
[1] M. J. Corley and R. D. Lorenz, “Rotor position and velocity estimation
for a salient-pole permanent magnet synchronous machine at standstill
and high speeds,” IEEE Trans. Ind. Appl., vol. 34, no. 4, pp. 784–789,
Jul./Aug. 1998.
[2] Y.-S. Jeong, R. D. Lorenz, T. M. Jahns, and S.-K. Sul, “Initial rotor
position estimation of an interior permanent magnet synchronous machine using carrier-frequency injection methods,” IEEE Trans. Ind. Appl.,
vol. 41, no. 1, pp. 38–45, Jan./Feb. 2005.
[3] N. Teske, G. M. Asher, M. Summer, and K. J. Bradley, “Analysis and suppression of high-frequency inverter clamping saliency in sensorless position controlled induction motor drives,” IEEE Trans. Ind. Appl., vol. 39,
no. 1, pp. 10–18, Nov./Dec. 2003.
[4] J.-I. Ha and S.-K. Sul, “Sensorless field-oriented control of an induction
machine by high-frequency signal injection,” IEEE Trans. Ind. Appl.,
vol. 35, no. 1, pp. 45–51, Jan./Feb. 1999.
[5] M. E. Haque, L. Zhong, and M. F. Rahman, “A sensorless initial rotor position estimation scheme for a direct torque controlled interior permanent
magnet synchronous motor drive,” IEEE Trans. Power Electron., vol. 18,
no. 6, pp. 1376–1383, Nov. 2003.
Joachim Holtz (M’87–SM’88–F’93) received the
Dipl.-Ing. and Ph.D. degrees from the Technical
University Braunschweig, Braunschweig, Germany,
in 1967 and 1969, respectively.
He was an Associate Professor in 1969 and a
Full Professor and Head of the Control Engineering
Laboratory in 1971, Indian Institute of Technology,
Madras, India. In 1972, he was with the Siemens
Research Laboratories, Erlangen, Germany. From
1976 to 1998, he was a Professor and Head of the
Electrical Machines and Drives Laboratory, University of Wuppertal, Wuppertal, Germany. He is currently a Professor Emeritus
and a Consultant. He has extensively published, among others, two invited
papers in the PROCEEDINGS OF THE IEEE, and 12 invited papers in other
journals. He is a coauthor of four books and is the holder of 31 patents.
Dr. Holtz is a past Editor-in-Chief of the IEEE TRANSACTIONS ON
INDUSTRIAL ELECTRONICS, Distinguished Lecturer of the IEEE Industry
Applications Society (IAS) and the IEEE Industrial Electronics Society, Senior
AdCom Member of the IEEE Industrial Electronics Society, member of the
Static Power Converter Committee of the IAS, and Chair, William E. Newell
Award Committee. He has earned 13 Prize Paper Awards. He was the recipient
of the IEEE Industrial Electronics Society Dr. Eugene Mittelmann Achievement
Award, the IEEE Industry Applications Society Outstanding Achievement
Award, the IEEE Power Electronics Society William E. Newell Award, the
IEEE Third Millenium Medal, the Anthony J. Hornfeck Service Award, and
the IEEE Lamme Gold Medal.