Vibration Reduction Method by Instantaneous Current Control in
120-degree Conduction Mode of Compressor Motor
Yusuke Omi, Takumi Yasuda, Takahiro Kumagai, Hiroki Watanabe and Jun-ichi Itoh
NAGAOKA UNIVERSITY OF TECHNOLOGY
1603-1, Kamitomioka-machi, Nagaoka, Niigata, Japan
Tel.: +81 / (258) – 47.9533.
E-Mail: s203129@stn.nagaokaut.ac.jp, t_yasuda@stn.nagaokaut.ac.jp,
kumagai_t1125@stn.nagaokaut.ac.jp, hwatanabe@vos.nagaokaut.ac.jp,
itoh@vos.nagaokaut.ac.jp
URL: http://itohserver01.nagaokaut.ac.jp/itohlab/jp/index.html

Keywords«PMSM», «Compressor», «Three-phasemotor drive», «Vibration suppression», «Sensorless control».

Abstract
This paper proposes the vibration suppression
method for compressors driven in 120-degree
conduction mode. The load torque characteristicof the compressor fluctuates in one period of themechanical angle. Thus, the speed ripple occurs
in the motor, and the compressor vibrates.
Therefore, this paper proposes a vibration
reduction method with an instantaneous current
control with a disturbance observer for thecompressor driven by the 120-degree conduction
mode. The feature of this paper is that motor
speed is estimated by the back electromotive
force (EMF) of the open phase due to the 120degree conduction mode drive. The proposed
method is verified experimentally under a limited
loaded condition of the compressor as afundamental study. As a result, the proposed
control method reduces the fundamental
frequency component of the vibration by 66.4%
at a low speed of 0.19 p.u.

Introduction
Home appliance applications, such as air
conditioners and refrigerators, are required to be
not only compact and highly efficient but also
have low acoustic noise and low vibration. These
home appliances use compressors in order toobtain a high-pressure refrigerant. The
compressor repeats the cycle of (1) suction, (2)compression, and (3) discharge for heat exchange.
This repetitive operation causes a load torquefluctuation and speed ripple in the motor. Besides,

the motor is sealed inside the compressor case. In
addition, speed sensors and position sensors
cannot be attached to the motor because the insideof the compressor case is high temperature andhigh pressure.
Interior Permanent Magnetic Synchronous
Motors (IPMSMs) are often used for thecompressor drive in home appliances thanks totheir distinct advantages of high power density
and high efficiency [1]-[4]. A vibration reduction
method based on the position sensorless control
for the IPMSM using the Fourier transform andrepetitive control has been introduced [5]. The
estimated load torque variation is compensatedusing a simplified Fourier transform and inverse
transform [6]. However, these methods control
the current in the rotating reference frame andrequire complex calculations for the sensorless
vector control (Field orient control), including thecoordinatetransformations.
Thus,amicrocontroller with high processing power isrequired. Then it may increase product costs.
In order to solve these problems, this paper
proposes a vibration reduction method with an
instantaneous current control and feedforward
current command for the compressor driven by
the 120-degree conduction mode. In 120-degree
conduction mode, the rotor position and motor
speed are estimated by detecting the back EMF ofthe open phase [7]. Thus, complex calculations
and motor parameters are not required in 120degree conduction mode. The feature of thispaper is the minimization of the speed ripple
caused by the load torque fluctuation withfeedforward current commands obtained by the
disturbance observer. The proposed method isverified experimentally under a limited-loaded
condition of the compressor as a fundamental
study. The feedforward current command in theexperiment was generated according to themechanical angle by a look-up table. The
mechanical angle estimation is also proposedfrom the electric and offset angles in this paper.
First, this paper clarifies the cause of vibration
when the compressor is driven in 120-degree
conduction mode. Next, this paper shows that the
proposed controller based on the disturbanceobserver suppresses the vibration when the motor
speed is estimated completely in simulation.
Finally, the proposed method demonstrates anexperiment with a compressor. The experimental
results show that the proposed control reduces thefundamental frequency component of thevibration by 66.4% at a low speed of 0.19 p.u.

Drive system for compressor drive
motorsA. Characteristics of compressor
Fig. 1 shows a schematic diagram of areciprocating compressor considered in this paper.
The reciprocating compressor periodicallyswitches three processes (1) the suction, (2) thecompression, and (3) the ejection by the rotationof the rotor. Fig. 1(a) shows a piston at the top
dead center, which is defined as a state that thepiston is closest to the cylinder wall. Fig. 1(b)shows the piston at the bottom dead center, where
the piston is farthest from the cylinder wall. In
this paper, the mechanical angle θmech at the top
dead center is defined as 0 degrees.
Fig. 2 shows a cross-sectional view of thecompressor drive motor at the top dead center(Fig. 1(a)). This paper uses a six-pole motor withthree couples of the magnet. Fig. 2(b) is anenlarged view of the area around the magnetic
pole N1 in Fig. 2(a). The mechanical andelectrical angle difference θb is defined as a phasedifference between the reference of themechanical angle(TDC position) and the stator
magnetic pole N1, as shown in Fig. 2(b).
Fig. 3 shows the load torque characteristic of
the compressor with respect to the mechanicaland electrical angle difference θb and theelectrical angle. The load torque characteristic of
the compressor fluctuates in one period of themechanical angle. In addition, the load torquecharacteristic is determined by the dischargepressure Pd and suction pressure Ps of therefrigerant in the compressor [8]. 0 degree of theelectrical angle at the stator magnetic pole N1
becomes the mechanical angle of θb.
B. Sensorless 120-degree conduction drive
Fig. 4 shows a conceptual diagram of the 120degree conduction mode. The voltage is applied

Counter weightCon-rod
PistonCrank pin

Discharge

Crankshaft
CylinderA

Suction

A
Shell
Motor

(a) Top dead center (θmech = 0 degrees).
Counter weight
Crank pinCon-rod
PistonDischarge

Crankshaft
CylinderSuction

Shell
Motor

(b) Bottom dead center (θmech = 180 degrees).
Fig. 1. Scheme drawings of compressor.
to the two phases corresponding to the estimatedelectrical angle, and the phases are switchedevery 60 degrees. The current is controlled byadjusting the output voltage by PWM. The
electrical angle is estimated by detecting the zerocrossing point of the back EMF. The zerocrossing point of the back EMF is detected during
the open interval of each phase. The motor speed
is estimated from the time interval between thedetected zero-crossing points of the back EMF.
Fig. 5 shows the relationship between the
conduction mode and the definition of the current
in the 120-degree conduction mode. In the 120degree conduction mode, the control current iad isdefined as the average of the currents of the two
conduction phases.
C. Control strategy of motor drive system
Fig. 6 shows a general control block diagram
for the compressor drive motor using the 120degree conduction mode. Fig. 7 shows the circuit
diagram of the three-phase inverter. The control
block diagram mainly comprises a current control(ACR) and speed control (ASR). The rotation
speed calculation estimates the speed from thezero-crossing detection signals (ZD_U, ZD_V, and
ZD_W) of the back EMF in each phase. The zerocrossing detection signals are obtained by the starconnection resistance connected to the inverter

PWM

(b)
Upper
side

W

N1
S3

S1
N2

Lower
side

N3

U
V
W

S2

Conduction
Mode

Rotor

Stator(a) Overview.
d-axisU
Vqmech = 

1
0

2
60

3

4

5

120 180 240
Electrical angle [deg]

6
300

360

Fig. 4. Conceptual diagram of 120-degree
conduction mode.
Conduction mode

1

Positive voltage
application phase

3

U

Negative voltage
application phase
Control current
iad

2

V

4

5

V
W

6
W

U

V

(Iu ｰ Iv) (Iu ｰ Iw) (Iv ｰ Iw) (Iv ｰ Iu) (Iw ｰ Iu) (Iw ｰ Iv)
2
2
2
2
2
2

Electrical angle 0°

60°

120°

180°

240°

300°

0°

Fig. 5. Relationship between conduction
mode and control current.
N1

qb

S1

detection of the back EMF [9]. Then, the control
method is switched to the sensorless control.

S3(b) Enlarged view of Fig. 2(a).
Fig. 2. Cross section of compressor motor at
top dead center (Cross section of A-A in Fig.
1(a))
3.

Pd = 0.4, Ps = 0.05 MPa
Pd = 0.4, Ps = 0.1 MPa
Pd = 0.8, Ps = 0.05 MPa
Pd = 0.8, Ps = 0.1 MPa

Torque : T [Nm]

2.5
2.
1.5

Pd : Pressure of ejection side
Ps : Pressure of suction sideTop dead center,TDC(0 deg)

1.
.5


Electric angle [deg]

-.5
360
270
180
90
0

0°(N3)

9

0°(N2)

0°(N1)

18
qb

27

36

Mechanical angle [deg]Fig.3. Relationship between load torquecharacteristics of compressor and mechanicalangle.
output, as shown in Fig. 7. The ASR regulates theaverage motor speed to the command value. Notethat Fig. 6 omits the sequence from the startup to
the transition to the sensorless control. The motor
is first accelerated to the speed of 0.125 p.u. withthe open-loop operation, which enables theAnalysis of compressor vibration
factors
Fig. 8 shows the harmonic analysis of thecompressor vibration at a speed command of 15
rps (0.19 p.u.). The compressor vibration ismeasured using the acceleration sensor (OnoSokki, NP-3120) and the sensor amplifier (OnoSokki, SR-2210, FLAT mode). The acceleration
sensor is attached to the shell in the reciprocating
direction of the piston in the compressor.
The harmonic analysis results indicate that thevibration occurs at the frequency component of
the integral multiples of the mechanical angularfrequency. On the other hand, the vibration of theinteger multiples of the mechanical angularfrequency is caused by periodic load torquefluctuations. In addition, the decrease in theamplitude of the with increasing harmonic orders
is an effect of the mechanical frequency
characteristics of the compressor. Besides, both
vibration components around the switchingfrequency (16 kHz) and that at the 18th orderfrequency, generated by switching the conduction
phase in the 120-degree conduction mode, aresmall. According to these results, the low-orderfrequency components of the load torque are themain cause of the vibration in the compressor

Controller (software)

r

*

r

+ -

r _ es

ASR

iad *

+ -

ACR

Open phaseselection

PWM

INV

IPMSM

iad

Current
selection

iu , iv , iw

ZD_U,V,W

Conduction mode
selection

Zero Crossing
Detection

vu , vv , vw

Rotation Speed
Calculation

Fig. 6. Motor control configuration for compressor drive.
under the 120-degree conduction mode. Thus, itis necessary to suppress the vibration caused by
the load torque.

Sup

Svp

Swp

VDC

M

Proposed vibration suppression
control

3 
1TM = P  miad sin q + ( Ld - Lq ) iad 2 sin 2q 
2 
2...................................................................(1)where P is the number of pole pairs, Ld is the daxis inductance, Lq is the q-axis inductance, ψm is
the field flux linkage, and θ is the load angle.
Inverse function of (1) is included in the
disturbance observer to estimate idis. In the 120-

Svn

Swn

iu

iv

iw vu vv vw

Fig.7. Circuit Configuration of Three-Phase
Inverter.
Amplitude of vibration [m/s2]

This paper proposes a vibration reduction
method with an instantaneous current control andfeedforward current command obtained by adisturbance observer for the compressor driven
by the 120-degree conduction mode. First, thischapter explains the outline of the disturbanceobserver in the 120-degree conduction mode.
Finally, the generation method of thecompensation current command iDOB with the
disturbance observer is explained.
Fig. 9 shows the control block diagram of the
disturbance observer. The disturbance observer isadopted to compensate for the load torque andsuppress the vibration with iDOB. The following
subsection elaborates on the detail of the
disturbance observer.
In Fig. 9, ΔT is the difference between motor
torque TM and load torque TL. Also, idis is the sumof the current that generates TM and the current
that generates -TL. As shown in Fig. 9, ΔT isobtained by differentiating the motor speed andmultiplying the inertia, which is the inverse
model of the internal model of the motor. Here,the relationship between iad and TM is expressed
as

Sun

0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

1st harmonic (15[Hz])2st harmonic (30[Hz])3st harmonic (45[Hz])18st harmonic (270[Hz])16[kHz] component

2

20

200
Frequency [Hz]

2000

20000

Fig. 8. Harmonic analysis results of vibration.
degree conduction mode, the load angle θcontinuously changes, unlike the vector control
with id=0 control. In this paper, the inverse
function of (1) in the disturbance observer issimplified as (2), assuming the load angle θ =90°.
idis =

2T................................................(2)3P m

The compensation current command iDOB isderived by calculating the difference between idis
calculated from (2) and the current command
iad_LPF**, which is a low-pass filter applied to thecompressor current command iad**.

Motor
TL

r *

r

+ -

r

ASR

iad *

+
iDOB

iad **++ -1
R + sL

ACR

iad

Eq.(1)

+ -

TM

1
sJ

r

Disturbance observer**

LPF

iad _ LPF +- idisEq.(2)

T

sJ

LPF

iDOB

Fig. 9. Control block diagram of disturbance observer

Validation by simulation
This chapter shows that the proposed
controller with the disturbance observer reduces
the motor speed ripple when the motor speed isestimated completely in simulation. Finally, theeffect of reducing the motor speed ripple isconfirmed in the simulation.
A. Simulation conditions
As shown in Fig. 9, the disturbance observer
feeds back the actual speed instead of the speed
estimated from the back EMF. This reason is
explained below.
Table 1 shows the motor parameters and thesimulation conditions. The motor speed ripple isevaluated at a low speed of 0.19p.u. When the
motor is actually driven in 120-degree conductionmode, sampling of the estimated speed detection
is slow. Therefore, the response frequency of the
ASR is set low. In addition, the response
frequency of the ACR is large in order to improve
the follow-up to the compensation current.
Furthermore, the cutoff frequency of the low-passfilter is set to 20 times the mechanical angularfrequency.
B. Simulation results
Fig. 10 shows simulation results of the motor
speed, the compressor current command iad**, andload torque waveforms with and without the
disturbance observer. Fig. 10(a) shows thesimulation results when iDOB is set to zero, andFig. 10(b) shows the results when the load torqueis compensated by the disturbance observer. As
shown in Fig. 10(a), the current command isalmost constant regardless of the change in theload torque. Therefore, the motor speed decreases
significantly as the load torque increases, which
results in a large speed ripple. On the other hand,
as shown in Fig. 10(b), the current commandchanges according to the load torque due to theTable. 1. Simulation conditions.
Parameter
Rating rotation speed
Rating torque
Number of pole pairs
Winding resistanced-axis inductace
q-axis inductace
Field flux linkage
Inertia moment
DC-link voltage
Switching frequency
Speed command value

Symbol

n
Tn
P
R
Ld
Lq
m
J
Vdc
fsw
r*

Value
80 rps
0.237 N・m
3
6.2 W
76.3 mH
136 mH
0.14 Wb
0.00037 kgm2
280 V
16 kHz15 rpsdisturbance observer. As a result, the motor speed
ripple is suppressed.
Fig. 11 shows the harmonic analysis results ofthe motor speed without and with the disturbanceobserver. The harmonic analysis results show thatthe fundamental frequency component of the
motor speed is reduced by 95.4% thanks to the
disturbance observer. Furthermore, the frequency
component at integer multiples of thefundamental frequency is also reduced.
These results indicate that the speed ripple
caused by the load torque is reduced by applying
the disturbance observer.
In the 120° conduction mode, the motor speed
is estimated from the interval between zerocrossing signals of the back EMFs. Therefore, thedetection performances, such as resolution,
response, and accuracy, depend on the motor
speed in the 120° conduction mode. Especiallythe detection performance will be decreased in
low speed regions. Besides, a large speed error
occurs in the estimated speed due to including theload torque fluctuation of high frequecy.
Therefore, a disturbance is expected to bedifficult to estimate accurately when the
disturbance observer is applied using theestimated speed. Thus, vibration suppression by
the disturbance observer is difficult in the 120degree conduction mode at this time.

17

Load Torque [Nm]Current command [A]Speed [rps]

16
15

14
13
12
2

1.5
1

0.5
0
-0.5
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2

20[ms/div]

20[ms/div](a) Before applying
DOB(b) After applying
DOB

Fig.10. Waveform of the motor speed,
compressor current command iad**, and load
torque with and without the disturbanceobserver.

Amplitude of Speed [rps]1.5

1st harmonic (15[Hz])1.2

95.4% reduces

0.9

Before applying DOB
After applying DOB

0.6

0.3
0

15

30

45

60

75 90 105 120 135 150
Frequency [Hz]Fig. 11. Harmonic analysis results of Motor
speed.

Validation by experiment
The previous chapter showed that the
disturbance observer reduces the motor speed
ripple when the motor speed is completely
estimated in simulation. However, a disturbancewas expected to be difficult to estimate accurately
at low speed.
Therefore, as a fundamental study to confirm
the effectiveness of the feedforward current
command control, this paper uses feedforward
compensation current commands under constantload torque characteristic conditions throughexperiments.
Here,
the
feedforward
compensation current command icomp is derived

from the known load torque characteristics. In
addition, the value of icomp changes according to
the mechanical angle. In this chapter, first, theoutline of the proposed control method is
explained. Next, the mechanical angle estimation
method is explained. Finally, the results of theexperiment are shown by driving the compressor.
A. Overview of the disturbance compensator
Fig. 12 shows the control block diagram of the
disturbance compensator. The proposed control
adds the feedforward compensation current
command icomp to the current command iad* fromthe ASR to obtain the compressor motor current
command iad**. Furthermore, speed control andvibration suppression are achieved by controllingthe current based on iad**. icomp is calculated by
Equation (2) using the known load torquecharacteristics. Fig. 13 shows icomp calculated byequation (2). As shown in Fig. 13, icomp changes
with the mechanical angle. This is because theload torque of the compressor changes with themechanical angle. In this paper, icomp ismemorized in the look-up table and output
according to the estimated mechanical angle
θmech_es. θmech_es is calculated from the electricalangle obtained in 120-degree conduction modeand the offset angle θb. The next subsection
explains the method for estimating the machine
angle.
B. Mechanical Angle Estimation
The mechanical angle estimation is required
to suppress the speed ripple with icomp obtained in
the last subsection.
Fig. 14 shows the relationship between the
motor speed and the electric angle based on eachpole, assuming that the motor is driven only withspeed control (ASR). The motor torque is almost
constant because the response frequency of the
ASR is low. Then, the current command from the
ASR can be treated as a constant over themechanical period. On the other hand, the load
torque fluctuates with the mechanical period, as
shown in Fig. 3. As a result, the motor speed has
ripples with the fundamental mechanicalfrequency. As shown in Fig. 14, the average speedof the motor over one electrical angle differs
depending on the magnetic poles. As shown in
Fig. 14, the electrical angle based on the magnetic
pole N1 is the shortest in three electrical periods.
The proposed method estimates the magnetic poleby comparing the average speed in the electricalperiod based on each magnetic pole. The
mechanical angle estimation block in Fig. 12
outputs the mechanical angle synchronized to theelectrical angle based on the magnetic pole N1 as

r

qb
Off-line cal.
depending on speed
and temperatureand etc..

++ qmech_es

ASR

iad *

Feed-forward
command value tableqmech_N1

iad **

+ +
icomp

qelec

Mechanical angle estimation(Electric angle reference ofthe magnetic pole N1)

ZD_U,V,W
r _ es

Electric angle
calculation

Disturbance compensator

Fig. 12. Control block diagram of disturbance compensator
2.5

1.5

Currnt [A]Pd = 0.4, Ps = 0.05 MPa
2 Pd : Pressure of ejection side
Ps : Pressure of suction side
1.5
Load Torque1
FF current command icomp
0.5

1.2
0.9
0.6

0.3

0
-0.5

0

0

60

High

Motor Speed [rps]

-0.3
360

120
180
240
300
Mechanical angle [deg]Fig. 13. Derived
command icomp

Electric angle [deg]Torque [Nm]

θmech_N1. Note that θmech_N1 has a phase error fromthe mechanical angle defined in Fig. 3. This isbecause the mechanical angle is an angle that
depends on the arrangement of the crankshaft andpiston. Thus, θb is added to adjust the offset inθmech_N1 and obtain θmech_es. In this paper, θb is
obtained from the back EMF when thecompressor motor is free-running. θb is estimatedusing the motor speed, load torque, and electricangle obtained from the back EMF. As a result of
the free-run test, θb was determined at 170
degrees.
C. Experimental results
The motor parameters and experimental
conditions are the same as the simulation
conditions in Table 1. The compressor vibration
is evaluated at a low speed of 0.19p.u.
Fig. 15 shows the calculation process of themodified estimated mechanical angle θmech_m. As
shown in Fig. 15, θmech_N1 is synchronized to theelectric angle based on the magnetic pole N1 by
the proposed method. Furthermore, θb (= 170
degrees) is added to θmech_N1 to obtain theestimated mechanical angle θmech_es, as shown inthe bottom waveform of Fig. 15. These results
verify that the proposed method can estimate themechanical angle from the electrical angle.
Fig. 16 shows the three-phase current
waveforms with and without the proposed
method. The amplitude of the three-phase current
is almost constant when only the speed control by
the ASR is applied, as shown in Fig. 16(a). On theother hand, in Fig. 16(b), the instantaneous
current control with the FF current commandchanges the current amplitude in one period of themechanical angle.
Fig. 17 compares the acceleration sensor
output waveforms with and without applying the
proposed method. In Fig. 17(a), the fundamental
frequency component (15 Hz) of the vibration islarge because the proposed method is not applied.
However, in Fig. 17(b), the fundamental

feedforwardLowcurrent

MiddleMotor Speed

Average speed

360
270
180
90
0

Short

Long
0°(N2)

Middle0°(N3)

0°(N1)

0°(N1)
Time

Fig.14. Relationship between speed ripple andelectric angle.
frequency component of the vibration issuppressed thanks to the proposed method.
Fig. 18 shows the harmonic analysis results ofthe vibration. The fundamental frequency
component of the vibration is dominant when the
proposed method is disabled. The proposed
method suppressed the fundamental frequency
component of the vibration by 66.4%. In addition,
the vibration components of integer multiples ofthe fundamental frequency were also reduced.

Conclusion
This paper proposed a vibration reduction
method with an instantaneous current control anddisturbance observer for the compressor driven
by the 120-degree conduction mode. The
proposed method is verified experimentally underElectric angle : θelec
Mechanical angle synchronized to the: θmech_N1
electrical angle based on the magnetic pole N1
Estimated mechanical angle : θmech_es
Short Long Middle

360°
0°

0
θelec

360°

0°
360°
0°

One period of themechanical angle

0°(N1)

0°(N2) 0°(N3)Acceleration sensor output 0.5 [m/s2]

θmech_N1

40[ms/div]
θmech_es+qb (17)

(a) Speed control by ASR.
20[ms/div]

Fig. 15. Derivation process of θmech_es

One period of themechanical angle

U phase current 1[A/div]00

V phase current 1[A/div]0
W phase current 1[A/div]

Acceleration sensor output 0.5 [m/s2]040[ms/div]
One period of the mechanical angle

10[ms/div](a) Speed control by ASR.

(b) Proposed method.
Fig. 17. Acceleration sensor
waveforms.

U phase current 2[A/div]

Average speed control by ASR
Proposed method

V phase current 2[A/div]0
W phase current 2[A/div]0
10[ms/div](b) Proposed method.
Fig. 16. Three-phase current waveforms.
a limited-load condition of the compressor as thefundamental study. In the fundamental study, thereference value that suppresses vibration isapplied in feedforward according to the estimatedmechanicalangle.
Thus,
thismethodcompensates for the load torque pulsation. As aresult, the proposed control method reduces thefundamental frequency component of thevibration by 66.4% at a low speed of 0.19p.u.
In this paper, the compressor vibration was
suppressed under constant speed and load torquecharacteristics. However, the load torque of acompressor changes with pressure conditions andmotor speed. In future work, the validity of the
disturbance observer will be verified throughexperiments.

Amplitude of vibration [m/s2]

0

One period of the mechanical angle

output

0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

1st harmonic (15[Hz])66.4% reduces

15

30

45

60 75 90 105 120 135 150
Frequency [Hz]Fig. 18. Harmonic analysis results ofvibration.

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