1. Position Sensorless Vector Control of
Permanent Magnet Synchronous Motors
for Electrical Household Appliances
Kiyoshi Sakamoto*, Yoshitaka Iwaj i*, Tsunehiro Endo* *,
Tsukasa Taniguchi*, Toru Niki***, Mitsuhisa Kawamata***, and Atsuo Kawamura****
* Hitachi Research Laboratory, Hitachi Ltd., Ibaraki, JAPAN
** Power and Industrial Systems Division, Hitachi Ltd., Ibaraki, JAPAN
* ** Hitachi Appliances, Inc., Ibaraki, JAPAN
* ** * Yokohama National University, Yokohama, JAPAN
Abstract-A position sensorless vector control for a have focused on this control [1-3]. However the position
Permanent Magnet Synchronous Motor (PMSM) suitable estimation methods proposed by the papers, such as the
for electrical household appliance motor drives is described Kalman filter, the state observer, and the disturbance
in this paper. As a position sensorless control, a simple
position estimate equation is presented. The derivation of observer, are relatively complicated and their calculation
the equation is described. A simplified vector control requirements are large. Furthermore, vector control,
method for position sensorless PMSMs is proposed. The which includes a speed-control loop and current-control
proposed method does not employ any automatic speed loop, requires a short control interval. Therefore, a high
regulator or automatic current regulator. However, since performance Micro-Controller Unit (MCU) or Digital
the motor supply voltage Vd and Vq are calculated on the Signal Processor (DSP) is needed for the implementation
control rotation axis, the drive performance of our method
is almost the same as that of a conventional vector control
of the control. Adoption of such an expensive
under a steady-state condition, i.e. constant load and controller/processor is unrealistic for electrical household
constant speed. Simulation and experimental results are appliance motor drives.
shown. Finally, the authors applied the proposed method to In this paper, a simplified vector-control method
a battery-driven cordless vacuum cleaner. By experiment, a suitable for implementation with a low-cost typical MCU
stable drive of 50,000 min'1 was confirmed. is proposed. The position estimation algorithm proposed
by the authors is described. The configuration of the
Index Terms-position sensorless control; vector control; proposed controller and the gain design methodology are
permanent magnet synchronous motor; cordless vacuum presented. Simulation results are given to verify the
cleaner.
effectiveness of the proposed drive system. Finally, the
I. INTRODUCTION
authors applied the proposed control to a battery-driven
cordless vacuum cleaner (maximum motor speed is
In the field of electrical household appliances, 50,000 min-'), demonstrating the high-speed motor drive
especially air-conditioners and refrigerators, Permanent capability of the proposed method.
Magnet Synchronous Motors (PMSM) have become the
standard ac motors for variable speed drives, because of II. POSITION ESTIMATION ALGORITHM
their several advantages, such as superior power density In this section, the derivation process of the proposed
and high efficiency, compared with induction motors. position estimation algorithm of PMSM [6] is described.
The first air-conditioner product, which uses an inverter
driven PMSM, was developed in 1982 in Japan. Since A. Voltage Equation of Salient Pole PMSM
1998, the ratio of inverter-driven household air- The well-known voltage equation of the salient pole
conditioners sold in Japan has risen to over 90 percent. PMSM in the synchronous reference frame d-q axis is as
This trend might spread over the world given recent follows:
global energy and environmental problems.
As a drive method for PMSM for electrical household
[V ] R]+P[Ld i +wr[ L 'i
i [Es] (1)
appliances, a position-sensorless trapezoidal current drive,
i.e. 120-degree commutation drive, is widely used where cor is the rotor angular velocity; Ld, Lq are the d and
because of its simplicity and low-cost implementation. q axes inductances; Vd, vq are the d and q axes voltages; id,
However, the distorted current waveform generates iq are the d and q axes currents; R is the stator winding
pulsating motor torque and motor loss. Presently, the use resistance; p is the differential operator with respect to
of sinusoidal current drive, i.e. 180-degree commutation time; and Eo is the voltage of the back electromotive
drive, is increasing. force (EMF).
A major example of a sinusoidal current drive is the In the sensorless control system, rotor angular position
position-sensorless vector control. Many research papers and velocity o,r are not measured; thus voltages and
1-4244-0844-X/07/$20.00 ©2007 IEEE. 1 11 9

2. qc q
dVc = R dc + PLd + 2 coL, i q
1 (6)
dt L i 1
Ox
cosAO]
However, equation (6) includes 0cr, which is an
unobservable value of the controller. Substituting
rdc equation (6) into dAO/dt of equation (7), equation (8) is
obtained:
d
AO(d-=d d)d
d- p (7)
d)
(
dt dt dt 2r
Fig. 1. Relation between two synchronous reference frames. The d dV = R d
+PLd
1
d
+CDLqi c
(8)
axis is the rotor frame and the dc axis is the assumed rotor frame.
currents onthe d-q axis cannot be obtained. Therefor +dAS L -ia+ UsinA00
(L d -L q) [coOx
synchronous reference frame dc-qc axis, which is fi
on the assumed rotor, is introduced.
Equation (8) does not include 0r, and is suitable for
Fig. shows the two rotating axes of the PM' deriving the position error equation.
where the assumed dc-qc axis is shifted from the real Combining the Eo, term, equation (9) is obtained:
axis. The difference between the two axes is defined
position error AO given in (2):
EOx coA = v1Ri-PLd
- i I-d LqL i (9)
AO=Odc Od
where Od is the real angular position of the d-axis relati ive - ~~~~~~~~~dt
( d q) i H
to the stationary a-axis and Odc is the assumed angular
To obtain the position error information, the size of the
position of the dc-axis relative to the stationary a-axis.
Converting from the dc-qc axis value into the d-q a) extended EMF is not necessary but the phase angle of the
value, equation (3) can be used: extended EMF is important. Getting tangent tanzl0, the
size of the extended EMF Eo, is eliminated:
V cossAO -sinAO Vdc
[Vq] si:AO cos AO ][vqc] tanAOVdC -( R+pLd )idC +{(Ld Lq)(pAO)} q (10)
B. Position Error Equation
Vqc- (R +PLd)qc -{|L Lq)(PAO)} ' dc
The voltage equation (1) can be transformed i
another expression as follows:
Equation (10) includes the time derivation ofthe motor
[d R[ d
+PLd[. d] 2 Lq[L q]
current and the position error zAS. We assume that the
time derivative of the motor current is negligible under
±v Q d±P(L 2q
d the condition where motor load and motor speed are
constant. We also assume that the time derivation of the
[KE2 ° r + p Ld) iq ±2 °(Ld Lq) id.J position error zlObecomes zero under the same conditions.
Eliminating the time derivation values, a practical
The fourth term of (4) is the summation of the back E position error equation can be obtained as follows:
and induced voltage caused by motor pole saliency.
term is called the extended EMF [4]. In the folloMN AOc = tan' dc Rid +0) iLq *qc] (1 1)
explanation, Eo, expresses the extended EMF term Vqc -R jiqc -aCILq * dcj
follows:
where /10, is the estimated position error value. Note that
E0 =KE r+ P(Lq Ld) iq + r(Ld Lq) id by substituting L-Lq =L in (l1), an equation for non-
(5) salient PMSMs can be obtained.
The voltage equation of the dc-qc axis is obtained by III. SIMPLIFIED VECTOR CONTROL
solving as follows:
In this section the authors would like to propose a
simplified vector control for position sensorless PMSMs.
The proposed control structure is shown in Fig. 2. A
characteristic of our method is that the control structure
of the proposed control is very simple compared with the
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3. (13)
q 1 + TiqS qc
Ct)r -Y Since the detected motor current iqc changes with
Speed
Reference
motor load variation, the value of the q-axis current
command is adjusted properly.
Note that determining the time constant parameter of
the LPF (13) is important. The response of the LPF
output should be designed to be lower than the response
of the PLL controller described in the following.
C. PLL controller
The position error ASO expresses the lead-lag
relationship between the assumed axis and the actual axis.
Using this lead-lag relation, the PLL controller adjusts
Fig. 2. Simplified vector control system for position sensorless PMSM the assumed rotor speed o,, i.e. the inverter output
drive. frequency.
conventional one. This simplified vector control structure Actually, the PLL controller is implemented in the use
was reported on in the 1980s for use in induction of proportional control as follows:
machines [5]. The authors apply the idea to PMSM drives. A1 = -KPsAOC. (14)
As shown in Fig. 2, our method does not use an
automatic speed regulator (ASR) or automatic current If z1O, is positive, the assumed axis is ahead of the
regulator (ACR). Thus, the proposed method has no actual axis, and the PLL controller reduces the assumed
advantage over the conventional vector control especially rotor speed o,. Similarly, if z1O, is negative, the assumed
pertaining to the case of disturbance load torque. axis is lagging the actual one, and the PLL controller
However, since the motor supply voltages Vd and Vq increases co,.
are calculated on the dc-qc axis, the drive performance of The dc-axis phase Odc is obtained by an integration
our method under the steady state condition, i.e. constant calculation as follows,
load and constant speed conditions, is almost the same as
that of the conventional vector control. This is an Odc =frdt. (15)
important difference between the well-known V/F type
control and our method.
Another feature of the proposed control is that number D. Other comments concerning the proposed method
of control parameters is smaller than for the conventional The setting of the d-axis current command id* is
method. Thus, controller adjustment is finished with less important for high efficient drive. The current reference
work. of the d-axis, id*, is set to minimize the amplitude of the
The proposed simplified vector control is characterized motor current in order to decrease losses.
by using a voltage command calculator, a q-axis current Changing the speed reference oi) * at a rapid rate is
command generator, and a PLL controller. We describe limited because the voltage command is calculated from
the detail of each constituent block below. the speed reference directly as shown in (12). To generate
A. Voltage command calculator c)r , the use of a ramp function is recommended.
This part calculates the voltage command Vdc* and vqc*
using the motor electrical parameters, motor frequency IV. GAIN DESIGN
reference, and current reference. The calculating formula
is shown in equation (12), which is obtained by The proposed control has two control parameters, a
neglecting the time derivative term of equation (1). time constant parameter of the LPF (13) and a gain Kp of
the PLL controller. In the following, the gain design
Vd method, based on the resonant characteristics of PMSM
[vc]R[] + L .J+LK l]
: clc ] 0 cI 0
C9 I
0 d [d E 1
(12) is described.
A. Resonant characteristics of PMSM
where o, * is frequency reference of the motor.
Fig. 3 shows a salient pole PMSM motor model in the
B. q-axis current command generator rotational reference frame. The relation between the
In the conventional vector control, the ASR determines voltage and current shown in Fig. 3 is obtained from the
the q-axis current command, iq*, as a motor torque voltage equation (1). To analyze the electrical response of
command. On the other hand, in our method, the q-axis the motor, we assume that the motor speed co, is constant.
current command is generated through the LPF equation For simplicity, we also assume that the position error A1O
(13) from detected motor current as follows: equals zero and the motor speed PoV2 is substituted by
c] -
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4. From Fig. 3, the transfer function from Vd to id is input output
obtained as follows: Vd -
> id
= R + sLq (16)
s2LdLq + s R(Ld + Lq)+ R2 + 012LdLq
G=
Using the motor parameters of Table 1, the transfer
characteristics of Go can be plotted as Fig. 4. Fig. 4
shows that Go has resonant characteristic and the resonant
peak becomes sharp with higher o, values.
In order to find the resonant characteristics, equation
(16) is changed to a 2nd_order system equation as follows: Fig. 3. A model of salient pole PMSM in the rotational reference frame.
R + sLq C 2
= q -
(17)
° R2 + C LLS &si i
C.
ct
Q.)
2
R
(,01 +LL
90 91=0 100 =25% °1=50% p1=75% p1 100% (233Hz)
where (18) ........... ........... .......
L~LqR . (Ld + Lq) 10 .0 ...0.0
. . . . . . . ....... . ... ....
2VLE (R2+ 2LdLq) -90 ,_
10 ioo 100 O
Equation (17) indicates that the resonant frequency CoI Inverter frequency[Hz]
Fig. 4. Transfer characteristics from d-axis voltage to d-axis current
and the damping coefficient 4 vary with changing tl. If
t), is the higher value, ozh, comes close to o, and the value Actual Position Estimated
of 4 is reduced. Thus, the resonant oscillation of PMSM position error position
can hardly be damped at higher rotation speed. Od AO K 0dc
B. Resonant suppression strategy of Simplified Vector +S
Control PLL controller
Generally, in order to suppress the resonance of the Fig. 5. Simplified model of PLL controller.
PMSM mentioned above, a decoupling control is
employed. The decoupling controller calculates the d-q
axis interference value and compensates the voltage R *(Ld + Lq)
COn (20)
command reference. However, complete decoupling is 2*LdLq
impossible, because the computation interval of the
controller output is limited and the motor's electrical Here we call the right value of (20) a critical damping
parameters are different from the actual values. frequency tnO:
Simplified vector control avoids the resonance in
another way. The method is limiting the variation of the R (Ld + Lq) (21)
voltage command reference. If the frequency of the 0)nO
2 LdLq
voltage reference is lower than the resonant frequency ozI,
no resonant oscillation occurs and the PMSM system
becomes stable. C. Gain Design Methodology
In the following, we clarify the critical resonant The PLL gain Kp should be set at the critical damping
condition. The relation between the resonant frequency frequency tnO
(I)n and the damping coefficient X is expressed by
equation (19): Kps = 0) n0
' (22)
R-(Ld+Lq) (19) Selecting the gain Kp as shown in equation (22), the
2- LdLq *
transfer characteristic from AS0 to Odc becomes the LPF
n
response and the cutoff frequency is COJo because the PLL
The case of coefficient 4=1 is known as the critical controller can be simplified as Fig. 5. Therefore, the
damping condition. Thus, we can derive the stable frequency component PLL controller output is less than
condition by solving for ; >1.0 Equation (19) is
.
0nO and the PMSM system becomes stable.
Note that the response speed of the LPF (13) is also
changed to the following inequality: important. It is recommended that the LPF setting be
about 0.1 times slower than the PLL response.
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5. V. SIMULATION AND EXPERIMENT frequency is set to 5kHz. The 3-phase voltage reference is
To confirm the validity of the proposed control, several computed every 1OOVts. The computation interval of (12)
simulations and experiments were made. The
specifications for the test motor used in this simulation
are shown in Table 1. TABLE 1. SPECIFICATIONS OF THE TEST MOTOR.
In this case, the critical damping frequency C0o Rated Power 3.7 kW
becomes 74rad/s. Therefore we set the control parameters Rated Speed 3500 r/min
to K, =80rad/s and Tiq=125ms. The PWM carrier signal Pole Number P 8
Inductance Ld, Lq 2.5, 3.3 niH
200 Resistor R 0.21 Q
---.---.---------.---......................................... Rotor Inertia 0.0034 kg cm2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
20
0
-20
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
150
100 . A .
50 ...........
-50
°0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
20
lo ............ ............
10 .
-20
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
40
20
(a) Phase current and inverter frequency
> 20 _ . .
-40
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
150
100. -
50
50
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6[s]
Fig. 6. Performance of speed response. (Simulation)
240
30 .
220
(0 0.1 0.2 0.3 0.4 0.5 0.6
40
(b) Phase current and estimated axis error AOc
L20
-20 r
40
°H-lIE .;il ltil lb,,i.';:
IL... '
.1
'i Fig. 7. Performance of speed response. (Experimental result)
-.C:) 0 0.1 0.2 0.3 0.4 0.5 0.66
ct
0 -
200
't
100t
a)
LI
0
-4- ;z
0 M.
0 -50
-4- 0 0.1 0.2 0.3 0.4 0.5 0.6
40
20
-2 .........................................................................
-40
0 0.1 0.2 0.3 0.4 0.5 0.6
40
. -20 i
-40
0 0.1 0.2 0.3 0.4 0.5 0.6
200
.iqc
100 --............... .....
0* .-I-._
0 0.1 0.2 0.3 0.4 0.5 0.6 Is]
Fig. 8. Load torque variation response. (Simulation). Fig. 9. Load variation response. (Experimental result)
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6. is set to 900 ts, and the computation interval of (11) and
(14) is set to 500is.
Fig. 6 shows the simulation result of the speed
response. In this simulation, the load torque of the test
motor is set to zero. The frequency reference increases
from 30Hz to 230Hz.
The result of this simulation shows that the motor
torque rise is delayed, and furthermore, that ASO occurs at
the speed variation point. However, zAO becomes zero
during speed up. Within this simulation, the proposed
control method has adequate capability. Fig. 1U. External view o0 the test motor.
Fig. 7 shows the experimental result of applying our
control system to an actual apparatus. The motor phase DC24V
current, inverter frequency, o,, and estimated position
error zIO, are shown. The motor current amplitude is
different from the simulation because of the wind loss of
the actual motor. Except for this point, the experiment
tends to agree well with the simulation results.
Fig. 8 shows the simulation result of the torque step
measurement
response. In this simulation, 100% load torque is added to
Fig. 11. Experimental apparatus.
the motor during the maximum rated rotation speed.
From this increase in the load the motor speed 0cr
decreases, and the inverter frequency, o,, follows cr, TABLE 2. SPECIFICATIONS OF THE TEST SYSTEM.
After applying the load, the motor torque Tm is adjusted Maximum Rated
for about 0.4s to balance with the load. Speed
50,000 r/min
Fig. 9 shows an experimental result of the torque step Pole Number P 2
response. The motor current is quite similar to the
simulation but its amplitude is fluctuating. It seems that Inverter Output 500 W
the mechanical model difference causes the fluctuation. DC voltage 24 V
We chose a simple 1-mass model for the motor
mechanical model of the simulation.
VI. APPLICATION EXAMPLE OF HOUSEHOLD APPLIANCES
The proposed method has been applied to various
household appliances, such as room air conditioners and
refrigerators [7]. In this paper, we will outline its
application to a cordless vacuum cleaner as one case.
A cordless vacuum cleaner has some drawbacks
because all the power is supplied from a battery. For
example, the problem is that the suction power is poor
and available operating time is short. These problems
result from the use of a commutator motor. To improve
the performance, substituting a PMSM for the
commutator motor has been investigated [8]. Fig. 12. Startup waveforms.
In order to boost the suction power, a rotation speed of
about 50,000r/min is necessary for the PMSM. Thus, the
motor driver of cordless vacuum cleaner requires high
rotation-speed drive capability. The authors applied the
simplified vector control to driving such a high-speed
motor.
Fig. 10 shows the external view of the test motor. The
specifications of the test motor are shown in Table 2. The
test motor is designed to operate using a 24V DC battery.
The structure is an interior permanent-magnet
synchronous type. The output power of the drive circuit is
500W. As a micro-controller unit, a 32bit SH7046 RISC
processor made by Renesas Technology is employed. PWM carrier frequency: 8kHz
The experimental apparatus is shown in Fig. 11. Fig. Fig. 13. Motor phase current waveform in high-speed region
(50000minm1).
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7. 12 shows the motor current and motor frequency signal
waveforn recorded while the motor was accelerating. In
this case, the acceleration to 50,000r/min (top speed) was REFERENCES
completed in just 5s. [1] T. Takeshita, M. Ichikawa, J-S Lee, and N. Matsui, "Back
Here, it is necessary to explain the start sequence in EMF Estimation-Based Sensorless Salient-Pole Brushless
detail. At the beginning of rotation, an open-loop start-up DC Motor Drives", T IEE Japan, Vol. 11 7-D, No. ] pp. 98-
method, i.e. the synchronous drive method, is used in this 104 (1997-1) (in Japanese)
[2] L. A. Jones and J. H. Lang, "A state observer for
experiment. The start-up method flows more current than permanent magnet synchronous motor," IEEE Trans.
the vector control. You can find the start-up period by the Industrial Electronics, Vol. 36, No. 3, 1989, pp. 374-382.
difference of motor current amplitude shown in Fig. 12. [3] S. Bolognani, R. Oboe, and M. Zigliotto, "Sensorless full-
After the start-up, the proposed simplified vector digital PMSM drive with EKF estimation of speed and
control is activated. During acceleration to the top speed, rotor position," IEEE Trans. Industrial Electronics, Vol. 46,
significant fluctuation of the motor current was not No. 1, Feb. 1999, pp. 184-191.
observed. Fig. 13 shows a close-up of the motor current [4] S. Ichikawa, Z. Chen, M. Tomita, S. Doki, and S. Okuma,
"Sensorless Controls of Salient-Pole Permanent Magnet
waveforn at the top speed. The motor current involves a Synchronous Motors Using Extended Electromotive Force
high frequency component. These components are caused Models", T. IEE Japan, Vol.122-D, No.12 pp.1088-1096,
by the back electromotive force with harmonic distortion Dec. 2002. (in Japanese).
and use of the pulse width modulation (PWM) control. In [5] T. Okuyama, N. Fujimoto, and H. Fujii, "Simplified
this experiment, the PWM carrier frequency was set to Vector Control System without Speed and Voltage
8kHz. Sensors", T. IEE Japan, Vol.1 10-D, No.5 pp.477-486, May
1990. (in Japanese).
We conclude from the experiment described above [6] K. Sakamoto, Y. Iwaji, T. Endo, and Y. Takakura,
that the proposed simplified vector control can be applied "Position and Speed Sensorless Control for PMSM Drive
to a high speed PMSM drive. The proposed control might Using Direct Position Error Estimation," Proc. of
be applied not only to vacuum cleaners but also high- Industrial Electronics Society, 2001. IECON '01. The 27th
speed fan motor drives and spindle motor drives. Annual Conference ofthe IEEE, vol.3, pp.1680-1685, 2001
[7] D. Li, T. Suzuki, K. Sakamoto, Y. Notohara, T. Endo, C.
Tanaka, T. Ando, "Sensorless Control and PMSM Drive
VII. CONCLUSIONS System for Compressor Applications." Proc. of Power
A simplified vector control for position sensorless Electronics and Motion Control Conference, 2006. IPEMC
PMSMs is proposed. Configuration of the proposed '06. CESIIEEE 5th International, vol.2, pp. 1-5, Aug. 2006
method and the position estimation method are shown. [8] T. Taniguchi, H. Mikami, K. Sakamoto, K. Ide, H. Harada,
The methodology of the control gain setting is introduced. F. Jyoraku, "Basic Study of High-Speed Brushless DC
motor with Battery System," Proc. of The 2005
The effectiveness of the proposed control is verified by International Power Electronics Conference, IPEC 2005,
simulation and experiments. pp. 1033-1037, April. 2005
Using the results of this paper, the cordless vacuum
cleaner, type CV-XG20, shown in Fig. 14 has been made
available in stores since October 2003.
Fig. 14. Cordless vacuum cleaner. CV-XG20
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