Speed sensorless control of PMSM motors
implemented in real-time simulator
Eisenhawer de M. Fernandes
Denis R. Huller, Alexandre C. Oliveira
Department of Mechanical Engineering
Federal University of Campina Grande (UFCG)
Campina Grande-PB, Brazil, 58429-900
Email: eisenhawer@dem.ufcg.edu.br
Department of Electrical Engineering
Federal University of Campina Grande (UFCG)
Campina Grande-PB, Brazil, 58429-900
Email: aco@dee.ufcg.edu.br
Abstract— The paper presents a method for determining the
transition region between rotor position estimators applied to
permanent-magnet synchronous motors. A speed sensorless control scheme is implemented by combining the voltage injection
method in low speed region, and back-emf estimation in the
high speed region. The transition region is evaluated from the
rms AC content level of the command current. Besides, based
on this criteria, is established the bandwidths of the observers
in function of the speed. Simulation are shown to verify the
proposed technique. Results of the control system implemented
in a real-time simulator are presented.
I. I NTRODUCTION
Permanent-magnet synchronous motor drives (PMSM) has
become important competitors to Induction motor drives (IM)
in applications wide-speed range due to characteristics such as
higher efficiency and better dynamic performance. Permanentmagnet motor drives require rotor position information which
is provided by a rotor position sensor mounted in motor shaft
(encoders or resolvers). The use of rotor position sensor has
disadvantages such as increasing cost, volume, necessity of
mechanical adaptation and reduction of feasibility of drive
system [1],[2]. In this manner, the scientific investigation
aimed at eliminating the position sensor and estimate rotor
position from electrical quantities of the motor, using the
motor itself as position sensor. These solutions are known in
the literature as self-sensing control or sensorless control.
Self-sensing control methods can be classified in two categories, signal injection methods [3], [1], [4], [5], and backemf tracking methods. Signal injection methods are based on
the tracking of the rotor magnetic saliency or rotor anisotropy
of the motor in the low speed region, exploiting the highfrequency model of the motor when an extra signal is applied. The signal injection methods can present effects of the
coupling of the fundamental current, performance affected by
the non-linearities of the voltage converter [6], [7], and extra
power losses [5]. On the other hand, the second category of
methods estimates the rotor position from the back-emf estimation based on the fundamental model of the machine. The
performance of the estimators is dependent on the back-emf
amplitude [1], as well as present dynamic stiffness constraints
in low speed region [8], [9]. Thus, there exists an operation
region which two methods has acceptable performance and
their responses can be combined.
In literature there are several solutions that
combine signal injection methods (suitable for low
speed) and back-emf methods (suitable for high
speed) for self-sensing control for wide-speed range
[18],[11],[12],[5],[13],[8],[14],[2],[9],[15],[16],[17]. In [18],
[19] has been proposed the integration between models based
on saliency and back-emf estimation in a state filter, the
transition between the models is carried out by a non-linear
function of the estimated speed. Others solutions are based
on hybrid topology that combines rotor flux estimation and
signal injection [13],[2], or stator flux estimator and signal
injection method [15]. In [14], a slide-mode observer is
combined with signal injection technique to operate at low
speed for a switched reluctance motor. In [9] is proposed
an stator flux adaptive observer with MRAS in which a
correction factor, function of the speed, is obtained from the
estimation error presented by signal injection technique.
These papers demonstrate the possibility of integration
between rotor position estimation techniques with a smooth
transition between the responses of the estimators for specific
speeds. Usually, the transition rule is a weighting function of
the responses, function of the speed. However, there is no
discussion about the determination of the transition region
between self-sensing techniques in which the rule can be
applied.
The implementation of the integration of the self-sensing
control in commercial drive systems can present some constraints. The implementation of position estimators based
on signal injection methods can presents some drawbacks
[16],[20],[21]: dependency of the saliency ratio lsd /lsq , the
estimation error is dependent of the A/D converter resolution,
the high-frequency current produced by the voltage injection is
affected by the high-frequency voltage distortions produced by
the voltage converter. Besides, the estimation technique based
on back-emf is affected by harmonic components of the backemf and dead-time effect of the voltage converter [22].
This work presents an evaluation method of the transition
region between rotor position estimation techniques based on
signal injection and back-emf tracking. The metric is the rms
value of AC content of the q-axis reference current during the
self-sensing operation. Based on the metric, it is established
the bandwidth of the rotor position estimators in function of
the operation speed. Simulation results are shown for selfsensing operation in wide-speed range. A real-time system
based on FPGA with the configuration hardware in the loop,
is used for implementing and testing the algorithm for rotor
position estimation in wide speed range.
II. S IGNAL INJECTION TECHNIQUE - LOW SPEED
OPERATION
Rotor position estimation methods in the low-speed range
are based on the detection of orientation of the magnetic
saliency of the machine. The estimation of the saliency is
performed by the injection of a high-frequency signal. In this
work, it has been implemented the voltage signal injection in
the stationary reference frame. The technique consists of the
application of high-frequency rotating vector ωh and magnitude Vh (1). The machine saliency modulates the amplitude of
the high-frequency current produced by the injection (2).
s
vsdqh
= Vh ejωh t
(1)
issdqh = Ih1 ejωh t + Ih2 ej(ωh t+2θr )
(2)
III. BACK - EMF ESTIMATION - HIGH SPEED OPERATION
For PMSM motor operation at medium and high speeds is
required the use of estimation methods based on back-emf
tracking. The information of the rotor position is extracted
from back-emf estimation, thus, it is not necessary the application of extra signal. In this work, it has implemented
the method proposed by [11]. The technique employs two
cascaded estimators, one for back-emf estimation and other
for rotor position estimation.
The back-emf estimator is a current state-filter implemented
in the stationary reference frame (Fig. 3). The structure is
based on the extended bcak-emf model proposed by [12].
The estimated back-emf has the position information (θr ),
the estimation error is applied to the input of the rotor
position observer. The rotor position observer is a Luenberger
observer which its output are the estimated mechanical speed
(b
ωrm−f cem ) and rotor position (θbrm−f cem ). The observer is
illustrated in Fig. 4.
Several methods for obtain the rotor position has been
proposed in the literature. In Fig. 1 is shown the demodulation
technique which is composed by band-pass filter (BPF) and
synchronous-frame filtering (SFF). The resulting signals of the
process contain the rotor information (pαβ ). These signals are
applied to the observer’s inputs. The responses of the observer
are the estimated mechanical (b
ωrm−sal ) speed and estimated
mechanical position (θbrm−sal ) (2).
pαβ = Ih2 ej2θr
Fig. 1.
(3)
Fig. 3.
State-filter for stationary current and back-emf estimation.
Demodulation scheme for signal injection method.
Fig. 4. Back-emf tracking observer for estimation of position and speed at
high-speed region.
IV. E VALUATION OF THE TRANSITION REGION BETWEEN
ESTIMATORS
Fig. 2. Saliency-tracking observer for estimation of position and speed at
low-speed region.
The previous research presented a method to evaluate the
limit of signal injection techniques and back-emf tracking.
There is no discussion or little information about a criteria
to changeover between these techniques. Thus, in this paper,
is proposed a procedure to determine the transition region
between the techniques using ¡as a metric
¢ the harmonic content
r∗
of the reference current (ir∗
i
sq
sq CA ).
The transition region can be obtained from a profile of
the rms AC content of the commanded current varying the
bandwidth of the position observer in function of the operation
speed. The procedure to determine the transition region has the
following steps:
1. Study of the profile of the estimated speeds in function of
the operating speed, varying the bandwidth of the estimator;
2. Obtain the harmonic content profile of the reference
current (ir∗
sq CA ) in function of the speed (ωrm ) for different
values of observers bandwidth;
3. Determination of the admissible threshold value for
harmonic content level of ir∗
sq CA for whole speed and identical
for both estimation techniques;
4. The transition region which both estimation techniques
present a reasonable performance can be identified by the
r∗
superposition of the curves ir∗
sq CA and the level isq CA M AX
(Fig.5);
variables is 100µs. The DC-link voltage is 300V. The tuning
of the position estimators has been chosen according to pole
placement satisfying the transition criteria Fig. 8).
A. Transition region
The PMSM speed control system has evaluated for each
estimation strategy and the results are shown in Fig.7. Based
ont the results, one can verify that when AC content value
ir∗
sq is greater than 4% of the rated current (IN = 2, 0A),
occurs an fast increasing of the AC content. This can lead
to faults of the drive system such as excessive heating or
improper action of the protection system [22]. Thus, it has
established as¯ threshold
value 0, 04IN (4%) for whole speed
¯
¯ ≤ 0, 04IN . Based on this value, one
region, i.e., ¯ir∗
sq CA
can identify the intersection region between the curves ir∗
sq CA
for both techniques. In this manner, for the system in study,
the transition region is the range from 125, 66 rad/s (20 Hz)
e 188, 5 rad/s (30 Hz), vide Fig. 7. The lower and higher
limit of the transition region is ωrm low = 125, 66 rad/s and
ωrm high = 188, 5 rad/s, respectively.
B. Bandwidth of the position estimators
back-emf
Transition region
Fig. 5. Determination of the transition region between the signal injection
technique and back-emf estimation.
5. Find the tuning of the position observers that fulfill the
condition 4 in whole operation range;
6. Determine the combination between the estimations and
the contribution of each response.
In this work, the combination between the estimators’
responses is:
θbrm = αθbrm
sal
+ (1 − α)θbrm
f cem
(4)
where α is a parameter that set the contribution of each
estimator in the transition region. The choice of this parameter
is addressed in the next section.
V. S IMULATION RESULTS
The representation of the self-sensing speed control system
is illustrated in Fig. 6. The speed controller is composed by
a PI regulator with bandwidth set at 10Hz. The torque vector
control has been implemented. The current controller is a PI
regulator in the synchronous reference frame. The d − axis
reference current ir∗
sd is zero. The bandwidth of the current
controllers are identical to 250 Hz. The high-frequency voltage
has specification 60V-1, 0kHz. The sampling period of the
1000
900
Saliency−tracking method
800
700
Observer bandwidth [Hz]
Saliency
Threshold
The tuning of the position/speed
estimators
was defined
¯
¯
¯
according to the criteria that ¯ir∗
sq CA ≤ 0, 04IN . In Fig. 8
is shown the bandwidth curves for the rotor position estimator
based on saliency (red lines) and back-emf tracking estimator
(blue lines) in function of the speed ωrm .
From Fig.8, for the back-emf estimator, one can observe
that with the reducing of the speed ωrm shoud be followed
with the reduction of the estimator’s bandwidth, this has been
verified in [22].
In analogous manner, when the control system operates at
low speed and is demanded the increasing of the speed ωrm ,
the estimator’s bandwidth should be decreased.
600
500
400
300
200
Back−emf tracking method
100
0
60
80
100
120
140
160
180
Transition region between
the methods.
¯
200
220
240
260
ω [rad/s]
rm
¯
¯
Fig. 8. Observers bandwidth vs. ωrm for ¯ir∗
sq CA rms ≤ 4%IN : signal
injection (blue lines), back-emf estimation (red lines).
Diagram of PMSM self-sensing speed control for wide-speed range, integration of signal injection technique and back-emf estimation.
|ir*
| [% of rated current]
sq AC
Fig. 6.
9
Increasing of |ir*
| for back−emf tracking
sq AC
− Blue lines
8
7
Increasing of |ir* |
sq AC
for saliency
tracking − Red lines
6
5
Max. value set at |ir*
| <=4%
sq AC
4
3
2
1
Increasing of the BWO for saliency
tracking − Red lines
Increasing of the BWO for back−emf
tracking − Blue lines
0
50
100
150
200
Transition region for
Fig. 7.
r*
|isq|<=4%
250
ωrm [rad/s]
of rated current
¯
¯
¯
Determination of transition region between the techniques assuming ¯ir∗
sq CA ≤ 4%IN : signal injection (blue lines), back-emf estimation (red lines).
C. Choice of parameter α
The parameter α in (4) means the contribution of each
estimator in the transition region between the techniques.
One important feature is how to set this parameter related to
the speed. Different relations has been proposed in literature,
linear [13], [23] or non-linear functions [18]. In this work, it
has been established
the¯ profile of α with the evolution of the
¯
¯
AC content of ¯ir∗
that α has the
sq CA . It has been
¯
¯ r∗assumed
¯
¯
behavior inverse to the profile of isq CA when the system
operates in self-sensing control based on the signal injection
estimator. Thus, the parameter α is a linear function of ωrm ,
such that: ωr < ωr low , α = 1; se ωr > ωr high , α = 0.
D. Speed ramp command
The simulation results for self-sensing speed control for a
speed ramp command is shown in Fig.9. For this situation,
the frequency of the reference is varied from 0 to 60 Hz in
the time interval of 10 s. After t = 10s, the speed reference
is constant and decreased to zero at t = 25s. The tuning of
the rotor position estimators (signal injection and back-emf
tracking) is function of the reference speed in order to has the
bandwidth shown in Fig.8.
Fig. 10. Representation of real-time system used for implementation of the
algorithms.
Fig. 9. Self-sensing speed control for ramp speed command (0 − 60Hz):
(a) speed (ωr ), (b) estimated speed (ω
br ), (c)¯ rotor positions
(θr ) e estimated
¯
¯ r∗ ¯
position (θbr ), current ir∗
sq , (e) rms value of isq CA
¯
¯
¯
The rms value of ¯ir∗
sq CA is performed FFT of the waveform from a window with 1024 samples [24]. The transition
region between the techniques is represented by the symbols
ωr high and ωr low . From the curves of the Fig. 9, one can
verify that the performance is good with the AC content of
ir∗
sq under the specified limit (4%IN ). The signal injection
method is applied until the motor speed be greater than ωr high
s
s
during the ramp, after this, vsdqh
is zero. The voltage vsdqh
is
applied again when ωr > 1, 05ωr high . The saliency tracking
estimator is set with last values of ω
br ,θbr presented by backemf estimator. In this simulation the load torque is 25% of the
rated torque.
VI. R ESULTS OF THE REAL - TIME SYSTEM
A real-time system based on FPGA has been used for implementing the PMSM self-sensing speed control. The model of
the PM motor was implemented in a Altera development board
(FPGA cyclone II). The system has a configuration emulated
Hardware-in-the-loop.
The modules has different time steps. The module ’PMSM’
(DE-2) has time step of 1µs while the module ’Control’ (DE-0)
has time step of 100µs. Unfortunately, constraints associated
to space memory of FPGA boards, it has been tested only
the operation of rotor position estimator based on back-emf
tracking for constant speed. Besides, it is shown the results
for same operation obtained with the software PSIM.
In Fig. 11 is shown the simulation results with the software
PSIM for speed reference 377 rad/s (60 Hz). In Fig. 12 is
shown the real-time simualation with the FPGA system. The
bandwidth of the speed controller is 10 Hz. The bandwidth of
the current controllers has bandwidth of 120 Hz. The results
of the back-emf estimator presented a good performance
with small estimation error. Besides, the results of the realtime system are compatible with the ones obtained with the
software PSIM.
VII. C ONCLUSION
The work presented a procedure for determining the transition region between rotor position estimator techniques used
for self-sensing control of permanent-magnet synchronous motors. The procedure allows for the integration of the responses
of the rotor position estimators in order to estimate rotor
position for wide speed range.
The rotor position estimators has been implemented in
software (C++/PSIM) and simulation results are addressed in
the paper. On other hand, the algorithms has been implemented
in a real-time simulator system based on FPGA. During the
period of the implementation has been detected some problems
related to the memory space of the FPGA modules used in the
test-bench. Thus, the rotor position estimator based on signal
injection method has not tested and consequently it was not
Fig. 11.
Performance of the back-emf tracking observer (PSIM):
r
r∗ r
∗ ,ω
speeds (ωrm
rm ), currents (isq , isq ), current (isd ), rotor positions (θr ,
b
θrm−f cem ).
Fig. 12.
Performance of the back-emf tracking observer (FPGA):
r
r∗ r
∗ ,ω
speeds (ωrm
rm ), currents (isq , isq ), current (isd ), rotor positions (θr ,
b
θrm−f cem ).
possible to evaluate the proposed transition technique between
the methods studied.
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ACKNOWLEDGMENT
The authors would like to thank to the Conselho Nacional
de Pesquisa (CNPq).
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