Anais do XX Congresso Brasileiro de Automática
Belo Horizonte, MG, 20 a 24 de Setembro de 2014
SPEED SENSORLESS PMSM MOTOR DRIVE SYSTEM BASED ON FOUR-SWITCH
INVERTER
Eisenhawer de M. Fernandes∗, Euzeli C. dos Santos Jr.†, Welflen R. N. Santos‡
∗
Department of Mechanical Engineering
Federal University of Campina Grande (UFCG)
Aprı́gio Veloso Ave., 882, ZIP 58429-970
Campina Grande-PB, Brazil
†
Department of Electrical and Computer Engineering
Indiana University - Purdue University Indianapolis (IUPUI)
Indianapolis-IN, U.S.A.
‡
Department of Electrical Engineering
Federal University of Piauı́ (UFPI)
Petronio Portela Ave., ZIP 58109-970
Teresina-PI, Brazil
Emails: eisenhawer@ee.ufcg.edu.br, eudossantos@iupui.edu, welflen@dee.ufpi.edu.br
Abstract— This paper proposes a speed sensorless control for PMSM motor drive system. The sensorless
strategy is based on back-emf estimation of the motor, suited for applications at high speed. The drive system
uses a four-switches three-phase inverter. This topology is attractive specially in fault conditions in one leg of the
conventional three-phase converter. The speed sensorless vector control based on the proposed converter provides
a motor drive system with reduction of cost and volume. Relevant characteristics of the converter is presented,
such as: voltage capability, capacitor currents, PWM modulation. Details of the vector control implemented is
addressed. Simulation results are shown and validates the proposed system. The proposed method has been
implemented in an industrial converter and preliminary experimental results are presented.
Keywords— Sensorless control, vector control, permanent-magnet synchronous motor (PMSM), four-switch
three-phase inverter.
Resumo— Este artigo apresenta um método de controle sensorless de velocidade para motor sı́ncrono a ı́mã
permanente (PMSM). A estratégia de controle sensorless implementada está baseada na estimação da fcem do
motor, destinada a aplicações em alta velocidade. O acionamento do motor utiliza um conversor a quatro chaves.
Esta topologia é interessante para condições de falha em um dos braços do conversor trifásico convencional. A
estratégia de controle vetorial implementada sem sensor mecânico de posição utilizando o conversor a quatro
chaves proporciona um sistema de acionamento com redução de custo e volume. São apresentadas as principais
caracterı́sticas do conversor, tais como: tensão máxima do barramento CC, correntes dos capacitores e modulação
PWM. Resultados de simulação são apresentados para validação da proposta. O sistema sensorless proposto foi
implementado em laboratorio em um conversor industrial e resultados experimentais preliminares da proposta
são apresentados.
Keywords— Controle sensorless, controle vetorial, motor sı́ncrono a ı́mã permanente (PMSM), inversor
trifásico com quatro chaves.
1
Introduction
2001),(Jang et al., 2003),(Andreescu et al., 2008).
In this manner, scientific investigation has 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 literature as sensorless or self-sensing control.
Sensorless control methods can be classified in
two categories: signal injection methods (Corley
and Lorenz, 1998),(Jang et al., 2003),(Caruana
et al., 2006),(Holtz, 2008),(Fernandes et al., 2013),
and back-emf estimation methods. Signal injection methods are based on tracking of rotor magnetic saliency or anisotropy of the motor in the low
speed region, exploiting the high-frequency model
of the motor when an extra signal is applied. Second category estimates rotor position from the
back-emf estimation based on the fundamental
model of the motor. The performance of the es-
Permanent-Magnet Synchronous Motors (PMSM)
are widely used in industrial applications such as
servo positioning systems, robots and printing machines and transportation such as electrical vehicles and hybrid vehicles. This type of machine
provides a unique set of advantages and opportunities compared to induction machines. These
advantages are compactness, higher efficiency, robustness, reliability (Pillay and Krishnan, 1991),
(Consoli et al., 2001), (Bolognani et al., 2000a).
PMSM 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 sensors represent drawbacks such as increasing cost, volume,
necessity of mechanical adaptation and reduction of feasibility of drive system (Consoli et al.,
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Anais do XX Congresso Brasileiro de Automática
Belo Horizonte, MG, 20 a 24 de Setembro de 2014
timators is dependent on the back-emf amplitude
(Jang et al., 2003),(Ribeiro et al., 2006) therefore
they are suited for applications at medium and
high speed range.
On the other hand, in most of applications,
the PMSM motor is conventionally driven by the
three-phase voltage source inverter. In literature,
motor control research focused on cost-effective
design has presented the four-switch inverter to
drive AC motors (Jacobina et al., 2005),(Lin
et al., 2008). In (Lin et al., 2008), it has been
proposed the use of the four-switch three-phase
inverter to drive BLDC motor with trapezoidal
back-emf. Besides, this configuration has been
adopted in fault-tolerant solutions when in openswitch fault occurs in the inverter (Bolognani
et al., 2000b),(Wallmark et al., 2007).
The objective of this paper is to propose the
use a four-switch three-phase inverter in a speed
sensorless system for PMSM motors. The configuration have been designed for applications where it
is necessary to control two motors independently
by using a standard three-leg inverter. Besides,
it is possible to implement a sensorless strategy
to drive the PMSM in order to increase the mechanical robustness of the overall system (Corley
and Lorenz, 1998). In this work, it was applied
a sensorless strategy based on the fundamental
component voltage model of the machine (Chen
et al., 2000),(Kim et al., 2002).
The paper presents relevant characteristics of
the converter, such as i) voltage capability, sharedleg and capacitor currents, ii) pulse-width modulation techniques based on scalar approaches; iii)
control strategies for providing current control;
and iv) simulation and experimental results.
2.1
Permanent-Magnet Synchronous Motor PMSM
A three-phase permanent-magnet motor is composed by three windings in the stator and by a
rotor where the magnet is placed. The model written in terms of dq variables in synchronous rotor
reference frame describes the dynamic behavior of
the machine given by (Pillay and Krishnan, 1991),
(Corley and Lorenz, 1998):
d r
φ − ω r φrsq
dt sd
d
rs irsq + φrsq + ω r φrsd
dt
lsd irsd + φpm
lsq irsq
P (irsq φpm + (lsd − lsq )irsd irsq )
r
vsd
= rs irsd +
(1)
r
vsq
=
(2)
φrsd
φrsq
=
=
=
Te
(3)
(4)
(5)
r
r
where vsd
and vsq
are d,q-axis stator voltages, irsd
r
and isq , are the d, q-axis stator currents, φsd and
φsq are the stator flux linkages. rs is the phase
resistance, lsd and lsq are d, q-axis inductances.
Te is the electromagnetic torque; ω r is the angular
frequency of the rotor; φpm is the flux linkage due
to the rotor magnets; and P is the number of pair
of poles.
2.2
Four-switch three-phase inverter
The configuration comprises four switches, a dcbus constituted by a capacitor bank with midpoint connection. The converter is composed by
switches q1 , q 1 , q2 , q 2 . The switch-pairs q1 − q 1 ,
q2 − q 2 and q3 − q 3 are commanded complementary.
2.3
PWM Control
The configuration proposed in this work is shown
in Fig 1. In this topology both machines are connected to the dc-bus mid-point. The PMSM machine voltages (vs1 , vs2 , vs3 ) are given by:
vs1 =
Figura 1: Four-switch three-phase inverter supplying a PMSM motor.
2
1
2
v10 − v20
3
3
(6)
2
1
vs2 = − v10 + v20
3
3
(7)
1
vs3 = − (v10 + v20 )
3
(8)
Besides, the PWM relations obtained are
given by:
Proposed Configuration
The proposed configuration is illustrated in Fig.1.
This section addresses the model of the PMSM
motor and the characteristics of the converter.
1343
∗
∗
∗
v10
= vs1
− vs2
(9)
∗
∗
∗
v20
= vs2
− vs3
(10)
Anais do XX Congresso Brasileiro de Automática
Belo Horizonte, MG, 20 a 24 de Setembro de 2014
∗
∗
and v20
have been
Once the pole voltage v10
determined (9)-(10), the pulse-widths τ 1 to τ 3 are
calculated by using:
Ts ∗
Ts
+ vj0
for j = 1 to 2.
τj =
2
E
can be written in manner that can be obtained
the extended back-emf (Eex ):
(11)
s
vsq
These pulse-widths values are used to generate the gating signals for the switches by a programmable registers by comparing the modulation
∗
∗
reference signal v10
and v20
with a high-frequency
triangular carrier signal.
3
Where:
Eex = ω r [(lsd − lsq )issd + φpm ] − (lsd − lsq )
The voltage limit can be determined by considering that all voltages are purely sinusoidal. In (12),
it is written have the limit conditions associated
with the proposed configuration. In (12), Vs is the
voltage amplitude of the three-phase machine and
E is the DC-link voltage, respectively.
√
3Vs
(12)
This topic will be better addressed in the final
version of the paper.
4
Capacitor Currents
The capacitors average currents ic1 and ic2 , over
the sampling time Ts for the proposed configuration are given by:
ic1
is3
=
2
ic2 = −
is3
2
d s
i (17)
dt sq
From (17) it can be seen that it includes the
effects caused by rotor saliency (lsd − lsq ) and the
contribution of flux linkage of the rotor’s magnets (ω r φpm ). The extended back-emf presents
the rotor position information, thus, the rotor position can be estimated from the estimation of
the back-emf. The back-emf can be estimated
from the currents and voltages terminals measurements according to different methods in literature
such as flux observers (Corley and Lorenz, 1998),
state filters (Kim et al., 2002) and Kalman filters
(Bolognani et al., 1999).
In this work, it has been applied the structure presented in combined with a extended Luenberger observer (Corley and Lorenz, 1998),(Kim
et al., 2002), illustrated in Fig.2. The transfer
function obtained for estimated extended backemf and the extended back-emf from model (1)(5):
Voltage Analysis
E=
d s
)i − ω r (lsd − lsq )issq − Eex sin θr (15)
dt sd
d
= (rs + )issq + ω r (lsd − lsq )issd + Eex cos θr (16)
dt
s
vsd
= (rs +
b ex =
E
(13)
Ro s + Rio
Eex
lsd s2 + (rs + Ro )s + Rio
(18)
(14)
The capacitor average currents (13), (14) indicate the discharging of capacitor bank, i.e., the
level of DC-bus voltage ripple.
5
Back-emf tracking method
For PMSM sensorless operation at medium and
high speeds it 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
been implemented the method proposed by (Kim
et al., 2002). The method employs two cascaded
estimators, one for back-emf estimation and other
for rotor position estimation.
The back-emf estimator is a current statefilter implemented in the stationary reference
frame (Fig. 2). The structure is based on
the extended back-emf model proposed by (Chen
et al., 2000). From the machine model (1)-(5), it
Figura 2: State-filter for stationary current and
back-emf estimation.
The estimated back-emf presents the position
information (θr ), the estimation error is applied to
the input of the rotor position observer. The rotor
position observer is composed by a heterodyning
process, a controller(kio , kpo , kdo ) and the physical
model of the motor. The rotor position observer
is a Luenberger observer providing the estimated
mechanical rotor speed (b
ω rm ) and rotor position
b
(θrm ). The observer is illustrated in Fig. 3.
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Anais do XX Congresso Brasileiro de Automática
Belo Horizonte, MG, 20 a 24 de Setembro de 2014
Figura 3: Rotor position observer based on backemf tracking.
Figura 4: Control block diagram of the proposed
drive system.
The transfer function of the rotor position estimation can be written as:
J
b
θr (s)
=
θr (s)
³b
lsd −b
lsq
lsd −lsq
´
s3 + kdo s2 + kpo s + kio
b 3 + kdo s2 + kpo s + kio
Js
7
(19)
The speed sensorless control system has been simulated in Matlab. The system has been evaluated for in sensorless manner using the four-switch
three-phase inverter.
The speed controller bandwidth has been set
to 10 Hz. The current controller’s bandwidths has
been set to 250 Hz. The switching frequency is 10
kHz. The sampling time of the variables is 100µs.
The reference speed is set to 900rpm (60Hz).The
DC-link voltage is 300V. The PMSM motor has
the following rated parameters: rs = 0.67Ω,lsd =
22mH,lsq = 33mH,J = 0.084.10−3 kg.m2 ,Iphase =
2.0A,Vphase−phase = 200V,P = 400W, N = 3.000
rpm.
The back-emf estimator gains (Rio ,Ro ) were
determined from the characteristic polynomial of
the back-emf estimator transfer function, in this
case a 2nd order polynomial. Thus, the estimator gains has been chosen according the bandwidth necessary to estimate the back-emf. On
the other hand, it has been adopted a 3rd order characteristic polynomial to the rotor position
observer transfer function to define the observer
gains (ki ,kp ,kd ).
The speed reference is 900 rpm (60Hz). In
Fig. 5 is shown the results for sensorless operation using rotor position observer based on backemf tracking. In Fig. 5 is shown rotor speed (ω r ),
measured position (θr ), estimated position (b
θr )
and phase currents. In Fig. 6 is shown rotor speed
(ω r ), measured position (θr ), dq-axis stator currents (irsd , irsq ). During this test is applied a load
torque equal to 30% of the rated torque. Based
on the results, one can observe a small estimation
error demonstrating a satisfactory performance of
the rotor position estimator.
The rotor position estimator has the property of
zero lag estimation due to the reference torque
feedforward input (Te∗ ).
6
Simulation results
Sensorless control system
The control block diagram of the proposed system
is shown in Fig. 4. The control strategy of the
system is composed by the speed control in cascade with torque and current control loops. The
speed controller is a PI regulator type. The ’vector
control’ block defines the reference currents of dqaxis. The reference current (irsq ) is obtained from
the reference torque (Te∗ ) of the speed controller
output. The d-axis reference current (irsd ) is set
to be zero, thus, irsq defines the required torque.
The stator currents are controlled by two PIcontrollers in the synchronous reference frame.
r∗ r∗
The reference voltages vsd
, vsq are transformed to
∗
∗
∗
. Based
the reference phase voltages, vs1
, vs2
, vs3
on the phase reference voltages, the reference pole
voltages are calculated according to (9)-(??).
The phase currents are measured and transformed back to the synchronous reference frame.
The current controller gains has been designed
according the pole placement criteria. The controller gains cancels the machine poles. As a
result, the controller gains are determined from
the desired bandwidth of the closed-loop transfer
function. The same procedure is applied to define
the gains of the speed controller.
The measured currents and the reference voltages are used as input of the back-emf estimator.
The rotor position observer provides the rotor position used in the transformations between reference frames. Besides, the estimated rotor speed is
used in the speed control loop replacing the mechanical transducer.
7.1
Experimental results
In order to verify the performance of the proposed
system, it was mounted a test setup in laboratory
(Fig. 7). The experimental setup is composed by
a microcomputer equipped by a DSP program-
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Anais do XX Congresso Brasileiro de Automática
Belo Horizonte, MG, 20 a 24 de Setembro de 2014
5
0
0.36
380
0.365
0.37
0.375
0.38
0.385
0.39
0.365
0.37
0.375
0.38
0.385
0.39
370
360
0.36
1
0
−1
0.3
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
Figura 5: Simulation results for sensorless control using four-switch three-phase inverter(top to
bottom): measured position (θr ) and estimated
position (b
θr ), measured speed (ω r ) and estimated
speed (b
ω r ), phase currents is1 , is2 , is3 .
Figura 7: Experimental setup: two three-phase
servodrives, two three-phase PMSM motors and a
SPIM machine.
380
375
370
365
360
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
1
0.5
0
0.3
Figura 8: Experimental results for sensorless control using standard three-phase inverter(top to
bottom): measured position (θr ) and estimated
position (b
θr ), estimation error (θr − b
θr ), is1 .
Figura 6: Simulation results for sensorless control
using four-switch three-phase inverter:(top to bottom): measured speed (ω r ) and estimated speed
(b
ω r ), dq-axis currents irsd , irsq .
results will be addressed in the final version of the
paper.
ming board and two commercial PMSM servodrives. The servodrives consist of PWM VSI with
8kHz switching frequency and power modules with
a dead-time of 1µs. The three-phase PMSM motor is driven by Converter 1 which is programmed
with the desired control algorithm. On the other
hand, Converter 2 and PMSM2 are used to emulate different load conditions to PMSM1. The control algorithm is programmed to the internal DSP
of Converter 1 (Renesas SH7047). It performs
closed loop speed and current control and generates the PWM relations (9)-(10). Bandwidths of
the speed controller and current controllers are set
to be 15 Hz and 120 Hz, respectively. The command signals are generated with a sampling time
of 140µs.
In Figs. 8-9 presents the experimental results for the speed control system based on sensorless control using conventional three-phase inverter. In Fig. 8 is shown the measured rotor position (θr ) and estimated rotor position (b
θr ) and
phase current (is1 ). In Fig. 9 is shown the measured and estimated speed for the same condition.
The experimental results for the sensorless strategy based on the four-switch three-phase inverter
are still ongoing. A complete set of experimental
8
Conclusions
The paper presents a speed sensorless control system based on four-switch three-phase inverter.
This topology is interesting specially in fault conditions in one-leg of the conventional three-phase
converter. The speed sensorless vector control
based on the proposed converter provides a motor
drive system with reduction of cost, volume and
increase the reliability of the overall drive system.
The speed sensorless control is based on the
back-emf tracking of the PMSM motor. The backemf is estimated from a current state-filter and
applied to a Luenberger-style rotor position observer. The estimated rotor position and speed
are used replacing the information provided by
motion transducers. Then, the rotor position is
extracted by using the motor itself. Details of
structure and characteristics have been shown.
The performance of sensorless control has
been validated by simulations. Preliminary results
of the control system in a test setup are shown.
Experimental results for the proposed system are
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Anais do XX Congresso Brasileiro de Automática
Belo Horizonte, MG, 20 a 24 de Setembro de 2014
Corley, M. J. and Lorenz, R. (1998). Rotor position and velocity estimation for a salient-pole
permanent magnet synchronous machine at
standstill and high speeds, IEEE Trans. on
Industry Applications 34: 784–789.
Fernandes, E. M., Oliveira, A. C., Lima, A. M. N.,
Jacobina, C. B. and Santos, W. R. N. (2013).
A comparative evaluation of signal injection
methods for pmsm self-sensing control, Proc.
of COBEP 2013 pp. 821–827.
Holtz, J. (2008). Acquisition of position error and
magnet polarity for sensorless control of pm
synchronous motors, IEEE Trans. on Industry Applications 44(4): 1172–1180.
Figura 9: Experimental results for sensorless control using standard three-phase inverter(top to
bottom): measured speed (ω r ) and estimated
speed (b
ω r ), is1 .
Jacobina, C. B., dos Santos Jr., E. C., Correa, M.
B. R. and da Silva, E. R. C. (2005). Ac motor
drives with a standard number of switches
and boost inductors, Proc. of IEEE Applied
Power Electronics, APEC 2005 pp. 733–739.
still ongoing.
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