A Performance Improvement of V/f Control
using a Disturbance Observer
Jun-ichi Itoh*, Tetsuma Hoshino*, Takayuki Kaneko***Nagaoka University of Technology, Nagaoka, Japan**Fuji Electric Advanced Technology Co., Ltd,Tokyo Japan

Abstract— This paper proposes a dead-time compensation
method with a disturbance observer and a current controller
for V/f control. Dead-time compensation is very important toimprove motor drive performances in the low speed region.
The proposed compensation method is composed in the d-q
rotational frame. The ripple of the d-axis current caused by
the dead-time is suppressed by an auto current regulator, theripple of the q-axis current according to the dead-time issuppressed by the disturbance observer. The control of thed-axis current is added the auto current regulator to the V/fcontrol. As a result, the magnitude of the motor current cankeep more than the rated exciting current in spite of the low
speed region with the V/f control. The control of the q-axis
current only uses the disturbance observer to suppress thevoltage error of the dead-time. In this paper, theperformance of the proposed controller in the low speed
region is discussed based on the experimental results. The
proposed method can improve the current distortion to lessthan quarter against the conventional method. Although the
disturbance observer requires motor parameters, it is not sosensitive.

I.
INTRODUCTIONSIn order to realize energy saving in recent years,
general-purpose inverters are widely used in industry
applications. Particularly, an induction motor controlled
by the inverter is widely applied to adjustable speed drive.
V/f control method of the induction motor is more suitableto general applications than a speed sensor-less vector
control system because the V/f controller is very simple,
and robust for parameters variation of the motor. In otherwords, the speed sensor-less vector control system needs
the many control parameters agreeing with the motor
parameters to obtain high performance.
A voltage source type inverter has to make dead-time
between upper arm and lower arm to avoid a short circuitof dc voltage. The dead-time occurs output voltage error
because the output voltage during the dead-time perioddepends on the direction of a load current. The voltage
error of the dead-time is constant regardless of themagnitude of the output voltage. As a result, the voltage
error caused by dead-time period affects in low voltage
output area such as low speed. Thus, in case of the V/fcontrol, it is very difficult to smoothly work in low speed
region due to no current controller. Therefore thedead-time compensation techniques are very important torealize a low cost motor drive system.
The voltage error compensation method is feed forward
compensation for the output voltage command according
to the sign of the load current and the magnitude of thevoltage error[1]-[8]. This is very simple and the mostpopular compensation method. However, this method can
not compensate in low speed region because it is difficult
to detect the load current sign. As a result, the dead-timeerror is generated current stagnation around zero-crossing
point. In open loop control such as especially the V/fcontrol, the speed and torque ripple in low-speed region
becomes very large. In addition, if a pulse modulation
method is changed, for example, from a three-phasemodulation method to a two-phase modulation method,then the compensation values has to change depending on
the modulation method.
On the other hands, on-line dead-time compensation
methods are proposed in [9]-[10]. The voltage error isestimated by a disturbance observer using motor
parameters. In those papers, the disturbance observer iscomposed for the sensor-less vector control system of apermanent magnet motor in a rotational frame or athree-phase frame. However, the V/f control of theinduction motor is not considered.
This paper proposes the dead-time compensation
method with the disturbance observer and the current
controller for the V/f control. The proposed method iscomposed in the d-q rotational frame. The ripple of thed-axis current caused by the dead-time is suppressed by anauto current regulator, the ripple of the q-axis current
according to the dead-time is suppressed by the
disturbance observer. The control of the d-axis current is
added the auto current regulator to the V/f control. As aresult, the magnitude of the motor current can keep morethan the rated exciting current in spite of the low-speed
region operation of the V/f control. The control of the
q-axis current only uses the disturbance observer tosuppress the voltage error of the dead-time. Although the
disturbance observer requires the motor parameters, it is
not so sensitive. In this paper, the performance in the low
speed region is discussed based on the experimental results.
The proposed method can improve the current distortion toless than quarter against the conventional method.
II.

PROBLEMS OF DEAD-TIME AND CONVENTIONALCOMPENSATION METHOD
Figure 1 shows behavior of the voltage error during thedead-time. The dead-time is added to gate pulses of up andun in order to avoid the short circuit between an upper arm
and a lower arm. To obtain dead-time period, the turned-on
timing of the gate pulse of up and un are adjusted during Td
as shown in Figure 1(b).
The voltage error during the dead-time depends on
direction of flowing current. When the output current of
the leg is flowing to positive, the current in the leg flows
through the FWD of the lower arm during the switch off.

Thus, the output voltage is decreased by the dead-time
period. On the other hands, when the output current isflowing to negative, the current in the leg flows throughthe FWD of the upper arm. Thus, the output voltage
increases. The value of the voltage error depends on thedead-time period and dc-link voltage. Finally, the voltage
error is decided by Equation (1).

ΔV = f sVdc Td ⋅ sign (iu )

up
Vdc

(1)

PRINCIPLE OF PROPOSED COMPENSATIONMETHOD
Figure 4 shows an equivalent circuit of the induction
motor on d-q rotating frame. This paper proposes a
dead-time compensation method with a disturbanceobserver. The voltage error of the dead-time is estimatedby the load current and the motor parameter. The relation
between the motor voltage v1 and current i1 is obtained by
Equation (2).

iu<0

un

Where, fs: switching frequency, Vdc: dc-link voltage,
Td: dead-time period, iu: output current of the leg,sign(x):sign function. if x>0 then sign(x)=1, if x<0then sign(x)=−1, if x=0 then sign(x)=0.
It is noted that the magnitude of the voltage error does
not depends on the amplitude of the output voltage andload current. Therefore, when the output voltage is small
such as a low speed operation, the affect of the dead-time isstrongly appeared because the ratio of the voltage error tothe output voltage becomes large.
Figure 2 shows the conventional compensation methodof the dead-time voltage error. The compensated voltage
command vu**, vv**, vw** are obtained by adding the voltage
error calculated by Equation (1) to the basic voltage
command vu*, vv*, vw*. Since this method needs only detectcurrent direction, it is very simple. However, if all legs are
not the same modulation e.g. the two-phase modulation,then the compensation value has to distinguish theswitching leg and the stop leg.
Figure 3 shows the stagnation of the load current in the
low speed operation of the motor in case of theconventional compensation method. The positive load
current is decreased by the dead-time voltage error, and thenegative load current is increased by the dead-time error.
As a result, the stagnation of the load current is generated
around the zero-crossing point of the load current. Since
the direction of the load current is not clearly, it is very
difficult to compensate the dead-time voltage error aroundthe current zero-crossing point.

iu>0(a) Inverter leg

u*

ON

up

OFF

ON

OFF

OFF

ON

Td

Td

un

Voltage error

Vdc/2

iu>0

0
-Vdc/2

Voltage error

Vdc/2

iu<0

0
-Vdc/2(b) Relation between reference pulse and voltage error.
Fig. 1. Output voltage error by dead-time

vu*
vv*

vu **

+
vucomp + +

vv**
+ +

vw*

vw**
+

TdVdc fs

III.

⎡ R1 + pLσ⎡v1d ⎤ ⎢ ω L⎢ ⎥ ⎢ 1 σ⎢v1 q ⎥ = ⎢ − R
2
⎢0⎥ ⎢
⎢ ⎥ ⎢
⎣⎢ 0 ⎦⎥ ⎢0⎢⎣−ω1 Lσp

R1 + pLσ

ω1

0

R2
+p
Lm

− R2

ω1 − ω m

iu

Sign

iv

Sign

iw

Sign

Fig. 2. Conventional compensation method of dead-time voltage error.

−ω1⎤⎥ ⎡ i1d ⎤⎥⎢ ⎥i1q− ω1 + ω m ⎥⎥ ⎢ ⎥⎢φ 2 d ⎥⎥⎢ ⎥R2+ p ⎥ ⎣⎢φ 2 q ⎦⎥
⎥⎦
Lm
p

(2)

where, R1:primary resistance, R2: secondary resistance,p = d / dt , Lm: magnetizing inductance, Lσ: equivalentleakage inductance, ω1: primary angular frequency, ωm:rotator angular frequency.
From Equation (2), when d-axis corresponds to vectorof the secondary flux φ2, the q-axis component φ2q is equaliu

v ucomp
Fig. 3. Current waveform and compensation voltage in case of very low
speed region.

to zero and the q-axis voltage v1q is calculated as
v1q = ( R1 + R 2 + pLσ )i1q − ω1 Lσ i1d + ω m φ 2 d

The transient response of the load current for the output
voltage is constrained by time constant Te=Lσ/(R1+R2).
Figure 5 shows the configuration of the disturbanceobserver based on Equation (3). It is very simple idea to
use the inverse system to calculate the terminal voltage ofthe motor as shown in Figure 5(a). However, the inverse
system includes the pure differential calculation. It isdifficult to calculate the pure differential calculation
without the error due to the noise in an actual system. Thus,
the terminal voltage of the motor in the proposed method is
calculated as Figure 5(b). In case of the low speed
operation, ω1 and ωm becomes the small to other terms.
Thus, those terms can be neglected. Finally, The voltage
error is estimated by Equation (4).
k
(R1 C + R2C + sLσC )I1q
1 + sTΔVˆ =i1

Vq (s )ΔV (s )

Fig. 4. Equivalent circuit of induction motor.

Δvvq * +G2 (s ) =V (s )

ωn
Lσ Ts 2 + (Lσ + RT )s + R
2
2
R+k (RC − R )s + 2ζω n s + ω n

1
R1 + R2 + sLσ

vq
+

+
+

iq

ωmφ2 d − ω1 Lσ i1d-+k
1 + sT

R1C + R2C + sLσC-

ω mC φ 2 d C − ω1C LσC i1dC(a) With inverse system

R+k (RC − R )Lσ T

1 Lσ +k (LσC − Lσ )+RT
ζ =2 Lσ T {R+k (RC − R )}(6)

G2 (s → 0 ) =R
R+k (RC − R )R

R+k (RC − R )

vq +

Motor

-

+

+

1
R1 + R2 + sLσ

vq

+

iq

+
ω mφ 2 d − ω1 Lσ i1d ≈ 0+
1
1 + sT-

R1C + R2C + sLσC
1 + sT(7)
k(8)

From Equation (5) and (6), the steady state value of
output voltage Vq for the step input of the voltage error ΔV
or the output voltage command Vq* becomes Equation (9)and (10).
G1 (s → 0 ) = (1 − k )

Δv

vq**

*

where R=R1+R2, RC=R1C+R2C, the damping factor ζ andthe natural angular frequency ωn of Equations (5) and (6)are obtained as Equation (7) and (8).
ωn =

+

2

2

=

Motor

-

+

Lσ Ts + {(1 − k )Lσ +RT }s + (1 − k )Rωn
(5)2
R+k (RC − R )s 2 + 2ζω n s + ω n

Vq (s )
*
q

vq**

(4)

2

=

R2/slipLm

v1

where, suffix C: controller parameter, T: time constantof the observer, k: observer gain, s: Laplace parameter.
The transfer functions to the output voltage Vq from thevoltage error ΔV or from the command voltage Vq* areobtained as
G1 (s ) =

Lσ

R1

(3).

(9)

(10)

From Equation (7) and (8), except controller gain k=0,
the mismatch of controller parameters affects the damping
factor and the natural angular frequency.
The proposed method is robust to change of motor
parameters RC and LσC as shown in Equation (9). The
voltage error rejection needs only set to observer gain k =1.
On the other hands, Equation (10) represents that theoutput voltage is equal to the command voltage under
RC=R. It also shows that k=1 cannot cancel the affect frommismatch of motor parameter RC to controller DC gain.

(b) Without pure differential calculation
Fig. 5. Configuration of disturbance observer.

Figure 6 shows a bode diagrams of Equation (5) and (6).
A solid line shows under ideal condition that k=1, RC=R
and LσC=Lσ. And dashed lines show under various
conditions that either RC or LσC equals to R or Lσ multipliedor divided by 10. The other parameters in use to calculate
bode diagrams are shown in Table. 1.
From Figure 6, parameter mismatch of LσC does notaffect the gain of the controller in high- or low-frequency
region. However, the parameter mismatch of R affects thegain of the controller as inversely proportional to RC / R at
low-frequency region. Therefore RC must be decided withconsideration for error of R.
If parameters have an ideal condition, i.e. k=1, RC=R andLσC=Lσ, then the transfer function of Equation (11) is
obtained by Equation (5).
Vq
ΔV

=

sT
sT + 1

(11)

(12)

Figure 7 shows the control block diagrams in the
proposed V/f controller. The d-axis current is controlled byauto current regulator e.g. PI controller. The d-axis current
command can be decided since the rated exciting current is
known from the motor parameters. The current control
boosts the output voltage at a low speed, and keeps theexciting current for the induction motor.
The proposed controller in Figure 7 is very simple
controller compared with sensor-less vector control system.
It is noted that the proposed dead-time compensation
method can be used together with the conventional method
as shown in Figure 2. Since the disturbance observer also
cancels electromotive force in the middle and high-speed
region, the proposed method gradually adjusts thedisturbance observer gain k to small according to theincrease of the motor speed.
IV.
EXPERIMENTAL RESULTS
Figure 8 shows the experimental results of theconventional compensation method as shown in Figure 2.
The tested motor and inverter as shown in Table 1 are usedin the experiment. The time division is 200ms/div., thecurrent division of iu is 2A/div. and id or iq is 0.2pu/div.
The output frequency is 1Hz (2% to rated frequency), at noload. Then, T.H.D. is 14.4%, and the current magnitude is
0.51A in the conventional compensation method. Though
the voltage command is compensated the voltage error ofthe dead-time by following Equation (1) makes theexciting current greatly reduced. Particularly, the q-axis
current is decreasing. There are two reasons in these results.
First, the actual dead-time is not only Td due to including
the delay of a switching device and a gate drive circuit.
Second, it is difficult to detect the direction of the load
current at the low speed region.
Figure 9 shows the experimental results of the proposedcompensation method. The time division is 200ms/div.,
the current division of iu is 2A/div. and id or iq is 0.2pu/div.
The experimental condition is the same as Figure 8. Then,
T.H.D. of 1.7% and the fundamental current magnitude of
2.87A are obtained by the proposed method, respectively.
The d-axis current is kept the constant at the rated exciting
current by the PI controller. The ripple of the q-axis current
is suppressed by the proposed disturbance observer. T.H.D.
is improved less than a quarter, and the rated exciting
current is almost obtained.
Figure 10 shows the comparisons under variations ofcontroller parameters; k, RC, LσC, and T, in order to discuss
influence of parameter mismatches through theexperimental result.
References:
Conventional method: Figure 10 (a)Proposed method: Figure 10 (b)These waveforms are same to Figure 8(a) and Figure

LC = L / 10
k=1
RC = R / 100-20

RC = 10R
LC = 10L

-40
-60
-80

-100 -1
10

100

101

102

103

104

Frequency (Hz)105(a)The transfer function from the voltage error Δv to the output voltage Vq
20

RC = R / 10

15

k=1

LC = L / 10

10
5
0
-5

-10
-15

LC = 10L

RC = 10R-20 -1
10

100

101

102

103

104

Frequency (Hz)105(b) The transfer functions from the command voltage Vq* to the
output voltage Vq
Fig. 6. Bode diagrams of proposed controller.

id*

Kp

id

1 + sTisTivu*dq to UVW

1
18 f

Magnitude (dB)T<

20

Magnitude (dB)Thus, the time constant of the observer is set out
according to frequency of the voltage error due to dead-time.
Since the voltage error on q-axis has 6 times frequency ofthe output frequency. And the voltage error has been
neglected after 3 times time constant, the time constant of
the disturbance observer is obtained by Equation (12).

f-e conversion

f-e conversion

ω*

vq* +

vq**

+

k

vv*
vw*

1
1 + sT+-

R1C + R2C + sLσC
1 + sT

1
s

i1q

θ

Fig. 7. Control block diagrams of the V/f control with the proposed
dead-time compensation method.

Table 1 Calculation and experimental conditions
Items(motor)
Values
Items(motor)
ValuesRated power
750W
Poles
4
Rated Voltage
200V
Rated Frequency 50Hz
Rated Current
3.6A
Rated speed
1420 r/min
Rated exciting
2.0A
Primary
2.78Ω
current
resistance
Leakage
11.0mH
Secondary
2.44Ω
inductanceresistanceItems(controller)
Dc voltage

Values280V

Dead-time

3.0μs

Switchingfrequency

20kHz

Items(controller)
Observer
Gain
Time constant ofLPF
d-axis ACR

Values1
1ms
used

9(a). The following discussion is based on waveforms
Figure 10(a) and (b).
iuChanging Time constant T:
T multiplied by 10: Figure 10 (c)From Equation (11), cut-off frequency is pulled to low
frequency by time constant. Thus, a high frequency
component such as the ripple of q-axis current is increased.
No A.C.R. on d-axis: Figure 10 (d):The disturbance observer on q-axis obtains q-axis
current. However, d-axis current includes the ripple
because of d-axis current controller lost.
Changing observer gain k:
k is set to 0.5: Figure 10 (e)k is set to 1.5: Figure 10 (f)From Equation (9), the DC gain of the dead-time error
correction has been changed, Figure 10(e) is reduced or
Figure 10(f) is exceeded. Thus, the voltage error due to thedead-time affects to output voltage.
Changing controller parameter RC:
RC is set to 2/3R: Figure 10 (g)RC is set to 1.5R: Figure 10 (h)k=1 rejects the voltage error of the dead-time. But, from
Equation (10), parameter mismatch of motor resistancechanges DC gain of controller. Then, the DC component of
q-axis output current is increased in Figure 10(g) or
decreased in Figure 10(h).

iqid(a) Current waveforms
6

Iβ [A]

4
2
0
-2
-4
-6
-6

-4

-2

0

2

4

6

Iα [A](b) Current vector locus
Fig.8 Conventional compensation method.
(Output frequency 1Hz, no load, 750W induction motor)

iu

Changing controller parameter LσC:
LσC is set to 1/2Lσ: Figure 10 (i)LσC is set to 2Lσ: Figure 10 (j)From Equation (9) and (10), DC gains are robust to achange of the inductance of the motor. Thus, Figure 10(i)and Figure 10(j) are similar result to Figure 10(b).

iqid(a) Current waveforms

As a result, too small parameter RC causes increasing ofcurrent amplitude. So, be careful to set RC. And observertime constant T gives a good result in shorter value. The
other parameter LσC is not critical to disturbance rejection
characteristics. These experimental results are according toanalytical results. It says a validity of the analysis.

6

V.
CONCLUSIONSIn this paper, several new approaches to improve theperformance based on V/f control have been proposed andtested, with the disturbance observer, d-axis current
regulator. Summary of the outcomes indicated in this paper
is as follows:-The conventional dead-time compensation is noteffective in the low speed region.
-The disturbance observer can cancel the voltage errorof the inverter dead-time.
-The d-axis current regulator is very effective based on
the V/f control.
-T.H.D. is improved less than a quarter against theconventional compensation method, and the rated
exciting current is almost obtained by the proposed
dead-time compensation.
The V/f control is very important in the general-purpose
inverter. It is noted that the dead-time compensation is also

-2

Iβ [A]

4
2
0

-4
-6
-6

-4

-2

0

2

4

6

Iα [A](b) Current vector locus
Fig.9 Proposed compensation method.
(Output frequency 1Hz, no load, 750W induction motor)

important in the sensor-less vector control due to use thevoltage command for the speed estimation. The
disturbance observer is not complicated, and does not
require the high accuracy for the motor parameter. The
proposed system is suitable for the general-purpose
inverter.

iu

iu

iq
id

I1=0.51A
T.H.D.:14.4%

iqid(a)Conventional compensation method.*

I1=2.87A
T.H.D.:1.69%(b)Basic conditions : T=1ms, RC=R, LσC=Lσ, k=1

iu

iu

iq

I1=2.87A
T.H.D.:7.11%

id

iq
id

I1=1.57A
T.H.D.:11.1%(d)No d-axis ACR*(c)Longer time-constant : T=10ms*

iqiu
I1=2.12A
T.H.D.:8.29%

id
iq

I1=5.23A
T.H.D.:7.76%

idiu(f)Higher gain : k=1.5*(e)Lower gain : k=0.5*

iqiu
I1=5.93A
T.H.D.:3.81%

idiu

I1=2.22A
T.H.D.:1.69%

idiq(h)Bigger resistance : RC=1.5R*(g)Smaller resistance : RC=0.66R*

iu

iu
iq

I1=2.87A
T.H.D.:1.67%

id

iq
id

I1=2.87A
T.H.D.:1.63%(j)Bigger inductance : LσC=2Lσ*(i)Smaller inductance : LσC=0.5Lσ**
Where (a) and (c) to (j), no parameter information means that parameters are same to (a).
All waveforms have a same time division 200ms/div., iu has a current division 2A/div and id, iq has a current division 0.2pu/div.

Fig. 10. Comparison variations of parameter mismatch from the ideal condition.

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