Output Voltage Correction of an Induction Motor
Drive Using a Disturbance Observer with Speed
Sensor-less Vector Control Method
Tetsuma Hoshino1 and Jun-ichi Itoh1
1 Nagaoka University of Technology/Department of Electrical Electronics and Information Engineering,

Nagaoka-city Niigata, 940-2188, Japan

Abstract-This paper applies and evaluates a method for error
voltage correction using a disturbance observer for an induction
motor where will be controlled by speed-sensor-less vector method.
The disturbance observer uses a fast-response observer, which
responses ten times as fast as a current controller in sensor-lessvector control. The voltage error is efficiently corrected by using
the proposed method. The proposed method is validated on thebasis of the experimental results. This method can reduce thecurrent distortion to about 1/3 times smaller.

I.

INTRODUCTION

Recently, control method of an induction motor for variable
speed driving has continuously been improved. V/f, vector andsensor-less vector-control method are popular control methods
for induction motor driving. Especially, sensor-less vector
control method is particular used for difficult application, which
V/f control method cannot be applied, e.g. constant torquewithout speed sensor.
All voltage source type inverters require a dead-time toprevent a short circuit for switches and capacitors. However, thedead-time results output voltage errors and significant
distortions on the current waveform, which caused torqueripples. When using the sensor-less vector-control method for
induction motor driving, there are current regulators on the dand q axes to correct an error voltage. In low-speed region, theperformance of the error voltage correction is degraded by thedecreasing of the output command voltage that is as small as theerror voltage. And in the middle-speed and high-speed range,
fast-response current regulator is needed to suppress the
distortion of the waveform of the current because frequency ofthe error voltage is raised with frequency of the output voltage.
Therefore, the error voltage correction is an important issue toreduce torque ripples, especially for conveyers or elevators.
Many dead-time compensation methods using a disturbanceobserver have been previously proposed [1-10]. The mostcommon method detects the direction of motor current anddecides the correction voltage according to direction of thecurrent, then adds the correction voltage to the command
voltage. If delay of the polarity detection or mismatching of thecorrection voltage was occurred in the correction process, thehappen of torque ripple and distortion of the current waveformare because of the remained error voltage. Especially, to detect
the polarity is very difficult in low-speed region because
transition of the polarity is slowed down. Therefore, thecorrection method using polarity detection has a limitation. On
the other hand, error correction method by using disturbanceobserver for estimation of disturbance voltage is proposed forvector-controlled systems[1, 9]. The disturbance-observer based
method is a useful method because the method corrects thesaturation voltage drop of switching devices and also thedead-time error voltage.
Methods of dead-time error voltage correction using
disturbance observers have ever been proposed were using
observers for only estimation of averaged error correction
voltage, then the estimated voltage is added to the command
voltage according to the direction of the current[1]. This method
is still based on the polarity detection and difficult to solve theproblem in low-speed region. On the other hand, direct
estimation method of error voltage using disturbance observer
was proposed in PMSM drive[9]. However, there are no further
discussions about the error voltage correction of disturbanceobserver by using no polarity detection on sensor-less vector
control for induction motor.
This paper applies and evaluates the error voltage correction
method by using disturbance observer without the polarity
detection. The advantage of this method is easy to determine
unique control system by the motor model. And, this method canbe used to decrease the current distortion to 1/3 times lesser. At
the result, advantages of using no polarity detection method
were obtained, and compared to the method depend on polarity
detection.
II.

PRINCIPLES OF THE DISTURBANCE OBSERVER FOR A
DEAD-TIME ERROR VOLTAGE CORRECTION

A. Problems of dead-time and conventional compensation
Fig. 1 shows the behavior of the voltage error during thedead-time period. Switch off time, it is so called dead-time, isadded to gate pulses of up and un in order to avoid the shortcircuit between an upper arm and a lower arm. To obtaindead-time period, the turned-on timing of the gate pulse up andun are delayed during Td as shown in Fig. 1(b).
The voltage error during the dead-time depends on thedirection of a flowing current. When the output current
direction of the leg is positive which is defined from the leg toload, the current in the leg flows through the free wheeling diode(FWD) of the lower arm during the dead-time period. Thus, theoutput voltage is decreased by the dead-time period. On theother hands, when the output current direction is negative, thecurrent in the leg flows through the FWD of the upper arm.
Thus, the output voltage increased. The value of the voltage
error depends on the dead-time period and dc-link voltage asshown in Fig. 1. Finally, the voltage error is calculated by (1).
∆V = − f sVdcTd ⋅ sign (iu )(1)where, fs: switching frequency, Vdc: dc-link voltage, Td:
dead-time period, iu: output current of the leg, sign(x):signfunction. If x>0 then sign(x) =1, if x<0 then sign(x) = 1, if x=0
then sign(x) =0.
It should be noted that the magnitude of the voltage error does
not depends on the amplitude of the output voltage and theoutput current. Therefore, when the output voltage is small suchas a low speed operation, the affect of the dead-time is strongly
appeared because the ratio of the voltage error to the output
voltage becomes larger.
Figure 2 is a control block diagram of an error voltage
correction according to the current direction. The error
correction voltage is calculated from KFFiu limited to -1 and 1,
where KFF compensates the gain to keep linearity at
zero-crossing point for hunting prevention.
B. Dead-time correction method using disturbance observers
This paper proposes a dead-time compensation method with adisturbance observer. The voltage error of the dead-time isestimated by the output current and the motor parameters shownin Fig. 3, which is the equivalent circuit of an induction motor on
d-q rotating frame, converted a secondary leakage inductanceinto a primary side. The estimation using the formula of relation
between the motor voltage v1 and current i1 is obtained by (2).

 R1 + pLσv1d     ω1Lσ
v1q  = 0    − R2
 0  0− ω1 Lσp

R1 + pLσ

ω1

0

R2
+p
Lm

− R2

ω1 − ωm i 
  1d p  i1q  φ− ω1 + ωm   2 d  φ2 q 



R2
+p 
Lm

− ω1

where,
R1 is the primary resistance,
R2 is the secondary resistance,p is differential operator p = d / dt ,Lm is the magnetizing inductance,
Lσ is the equivalent leakage inductance,ω1 is the primary angular frequency,ωm is the secondary angular frequency,
i1d is d-axis components of the primary current,

(2)

u*

ON

OFF

ON

up

OFF

Td

OFF

un
Vdc/2
0
−Vdc/2Vdc/2
0iu<0−Vdc/2

Td

ON

Voltage error

iu>0(a) An inverter leg

Voltage error(b) Relationship between reference pulse andvoltage error

Figure 1. Relations between reference pulse and voltage error.

Figure 2. Conventional error voltage correction method
according to the direction of motor current.

Figure 3. Equivalent circuit of induction motor.

i1q is q-axis components of the primary current,
v1d is d-axis components of the primary voltage,v1q is q-axis components of the primary voltage,
φ2d is d-axis components of secondary flux,and φ2q is q-axis components of secondary flux.
Figure 4 shows a block diagram for vector control method
using the proposed error voltage collection method. The
disturbance observers calculate difference between command
voltage and actual output voltage of the inverter and estimate theamount of disturbance voltage. The estimated disturbancevoltage is added to the voltage command as disturbancecorrection voltage Vcomp which is calculated using (3).
vdcomp ={(1
v1*d* − (R1c + R2c + pLσc )iid − ω1Lσci1q
1 + sTf

{

(

)}

1
vqcomp =v1*q* − (R1c + R2c + pLσc )i1q − ω1Lσci1d + ωmφ2d
1 + sTf(3))}

where, the suffix C means controller parameter.
In the equation (3), the 1st trm of the right side is the command
value adjusted by Vcomp. The 2nd term is the back EMF of the RL
based on the inverse system of the motor. The 3rd term is the
cross term between d- and q- axis. The 4th term is the speed
electromotive force. If the command voltage was collected by
2nd term only, the 3rd and 4th term will be estimated asωmφ2d − ω1Lσ i1d

∆vq
∆ vd
i1d

*

ACR

v1d *
+

+
-

i1d

+

**
v1d

+

-

− ω1Lσ i1q
+

+

v1d

Inverteri1d

1
R1+R2+sLσ

+

-

ACR

v1q
+

+
-

*

v1*q*

+

-

+

+

v1q

Inverter

+

1
1+sTf

+

-

1
1+sTf

R1c+R2c+sLσ c
1+sTf

+
+

R1c+R2c+sLσ c
1+sTf

+
+

i1q

1
R1+R2+sLσ

Motorvqcompi1q

Motor

vdcomp
1
1+sTf

i1q*

ωmφ2d

1
1+sTf

− ω1Lσ i1q+-

ω1Lσ i1d(a) d-axis(b) q-axis

Figure 4. An error voltage correction method using a disturbance observer.

disturbances. So the system is instable because correction
voltage is exceeded in actual disturbance voltage ∆v shown infigure 4. These terms should be calculated, measured or
estimated.
Additionally, it is desirable that the disturbance observers
responses faster than the current regulator. If the disturbancevoltage was corrected by the disturbance observer, output of thecurrent regulator is considered to be an actual output voltage of
inverter. Then the output-voltage- and speed-sensor-less vector
control will be achieved. So, this method is able to use in V/f or
vector control method. In latter section, results and notes ofthese control method are shown.
C. Using disturbance observers for V/f control method
This subsection describes the way to use the correction
method to V/f control method. It is difficult to separate primary
current into field and torque components because V/f control
method does not estimate secondary-side flux. Instead of flux
estimation, a current controller was used to determine the flux
component of the motor current. On the other hand, V/f control
and the correction method were used in orthogonal axis. It
should be noted that the axis using current controller anddisturbance observer is called d- and q- axis, respectively.
Fig. 5 shows a block diagram for the proposed compensation
method using V/f control. The feedback filter using the Tf (fastresponse disturbance observer) estimates the back EMF in
addition to the disturbance voltage. To estimate only the voltage
error from dead-time in the middle- or high-speed range, thefeedback filter of the Ts (slow response disturbance observer) isused to cancel the back EMF. On the other hand, the ACR on
the d-axis corrects the dead-time voltage error on d-axis andmaintains the rated excitation current of the motor.
III.

EXPERIMENTAL RESULT

A. Error voltage correction for sensor-less vector control
Fig. 6(a) shows a block diagram of an experimental system.
The experimental system is composed of a general induction
motor and an inverter. The motor is controlled using

Motor

InverterV
V1q**

V1q* +

+

m 2d+

+V1q

−

+

∆Vˆ

+

1
RC+sL C

I1q

Fast disturbance observer
1
1+sTf

+ −

RC+sL C
1+sTf

+ −

1
1+sTs

+ −
1*

1L I1dRC+sL C
1+sTs
Slow disturbanceVˆEMF
observer10

disableenableFigure 5. Block diagram of error voltage correction system
for V/f control.

speed-sensor-less vector control to keep at constant speed. The
sensor-less vector control shown in figure 6(a) is based onreference (10). This method obtains zero-volt for d-axis induced
voltage.
Fig. 7 shows the waveforms of motor speed, d-axis, q-axis andu-phase current under conditions where the motor speed is
300r/min with the rated load torque (1.0pu). It should be notedthat result shown in figure 7(a) is not using error voltage
corrections and 7(b) is using the disturbance observer based on
the error voltage correction method, respectively. In Fig. 7(a),the current distortion occurs on the zero crossing point of theu-phase current because the error voltage is changing
significantly at this point. In contrast, the distortion is almost
corrected in Fig. 7(b) by the fast response disturbance observer.
And the total harmonic distortion (THD) of the current shown in
Fig.7(b) is 1.20%, with a 1/3 reduction from the result as shownin Fig. 7(a).

(a) sensor-less vector control type(b) vector control type

∆v̂

1
s

(c) V/f control typeFigure 6. Evaluation systems of correction performance.

r*,

r

r : 0.05pu/div

r*

iq
id

iq, id : 0.4pu/div

iu

iu : 2A/div

THD=3.91% (50ms/div.)(a)No correction method(b)Correction method based on disturbance observer

Figure 7. A Comparison of Correction performance for a disturbance observer on sensor-less vector control method.

iq

iq

iq:0.2pu/div

iq:0.2pu/div

id

id

id:0.2pu/div

0 (id)

0 (id)

0 (iq)
0 (iu)

0 (iq)
0 (iu)

iu:5A /div
THD:1.11%

iu

id:0.2pu/div

iu

iu:5A /div
THD:0.35%
5ms/div

5ms/div(a)No correction method(b)Correction method based on disturbance observer

Figure 8. A Comparison of Correction performance for a disturbance observer on vector control method.

THD:8.91%(a)No correction method

THD:0.98%(b)Correction method based on disturbance observer

Figure 9. A Comparison of Correction performance for a disturbance observer on V/f control method.

Table 1. summary of current THD on each control method
Control method

A: No correction

B: Correction method based on disturbance observer

B compared with A

Sensor-less vector

3.91%

1.20%

≤1/3

Vector

1.11%

0.35%

≤1/3

V/f

8.91%

0.98%

≤1/9

B. Error voltage correction for vector control
Fig. 6(b) shows a block diagram of an experimental system.
The 2.2kW motor is controlled using the vector control to keep
at constant speed.
Fig. 8 shows the waveforms of d-axis, q-axis and u-phasecurrent under conditions where the motor speed is 750r/min
with rated load torque (1.0pu). The current distortion on thezero-crossing point of the u-phase current is also suppressed
when using the error voltage correction method based on the
disturbance observer. And the total harmonic distortion (THD)of the current shown in Fig.8(b) is 0.35%, with a 1/3 reduction
from the result as shown in Fig. 8(a).
C. Error voltage correction for v/f control
Fig. 6(c) shows a block diagram of an experimental system.
The 750W motor is controlled using V/f control to keep atconstant primary frequency. In Fig. 6(c), the boost voltage iscalculated as ω* 
vboost = R1i1q 1 − 1  ................................................... (4).
 ωn 
Fig. 9 shows the waveforms of d-axis, q-axis and u-phasecurrent under conditions where the primary side angularfrequency is 1Hz with no load torque. The current distortion on
the zero-crossing point of the u-phase current is also suppressed
when using the error voltage correction method based on the
disturbance observer. And the total harmonic distortion (THD)of the current shown in Fig. 9(b) is 0.98%, with a 1/9 reduction
from the result as shown in Fig. 9(a).
D. Comparisons of each result
In former sections, the correction method using disturbanceobserver was applied into sensor-less vector, vector and V/fcontrol method. The stability of the correction method is
discussed in the following sentences.
First, the combination of such system and disturbanceobserver will be a stable system. The vector control method
calculates accurately d- and q- axis of motor from current andspeed of a motor, then the stability of the correction method will
be obtained.
Second, we discuss about the sensor-less vector control
method. When a sensor-less control is worked properly, the axisof motor and controller will be same. Then the correction
method will also work properly. It should be noted that thevoltage sensor using the sensor-less control only has minimum
speed of response to estimate the motor speed, which means
insufficient to correct error voltage.
Last, a V/f control will not equate the axis of motor andcontroller. So the current regulator on d-axis retains excitation
current to obtain the stability of correction. And it is difficult to
calculate important terms to prevent over correction, which are
the speed-EMF and cross term. Instead of calculation, theimportant terms are estimated by the disturbance observers
which have the fast and slow response.
Table 1 shows a summary of current THD on each control
method. The correction method using disturbance observer

reduces the distortion of current on any control methods.
Especially, THD reduction on V/f control was marked because
original V/f control method has no current controllers. So, theTHD on original V/f control is higher than others. As the result,
THD reduction is achieved evenly on vector and sensor-lessvector control. Therefore the voltage error correction method iseffective on any control method.
IV.

CONCLUSIONS

A disturbance observer, used for dead-time error voltage
correction, was applied to sensor-less vector controlled in an
induction motor. Then the THD of the motor current wasevaluated. At the result, this method is able to decrease thecurrent distortion to 1/3 times smaller than the original method.

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