Download Discrete-time AC motor control apparatus

United States Patent [191
[11]
[45]
Ueda et al.
-
[54]
[75]
Oct. 15, 1991
OTHER PUBLICATIONS
Inventors: Yoshihim Ue da_ Takaaki Yamada
Lawrence A. Jones, Jeffery H. Lang “A State Observer
’
for the Permanent-Magnet Synchronous Motor”
'
IECON 1987 Conference, Cambridge, MA, Nov. 2-6,
[73] Assignee: Omron Corporation, Kyoto, Japan
[21] APP]_ NO’: 544,427
1987
Yoshihiro Ueda, Takaaki Yamada “A State Observer
.
for the Permanent Magnet Synchronous‘Motor w1th
[22] Flled‘
J'm' 27’ 1990
[30]
Foreign Application Priority Data
Jul. 14, 1989 [JP]
Inductance Variations and its Characteristics” Proceed
ings of the 33rd Ann. Conf. of the Inst. of Systems,
Japan ................................ .. l-l80407
s
ISCIE’ 1989‘
Primary Examiner—Paul Ip
.
""""""""""""" "
Attorney, Agent, or Firm—Dickstein, Shapiro & Morin
318/561; 318/800; 318/803
[58]
Date of Patent:
AC MOTO R C0 NTR OL
both of Tsukub’a Japan
5,057,759
Patent Number: I
[57]
Field of Search .............................. .. 331188//576709—_6g66
[56]
ABSTRACT
In a discrete_time a1 ternatingcurren t motor control
apparatus having a state estimation observer estimating
, References Cited
a rotor angle and a rotor angular velocity based on a
Us PATENT DOCUMENTS
direct ‘quadrature transformation model of the motor,
the gam of the observer is changed over dependmg on
an estimated angular velocity. As a result, the apparatus
gtischke et a1‘ """"""" " 3
4Issoi51s 7/1987 Kur§k;£;';{;ii"j....
I: 318/561
4,695,780
. . . .. 318/561
9/1987
Kurakake et al. . . . . .
slicker CI
31.
----...-..
is applicable in a wide range of the mom’ Speed
‘Furthermore, the phase difference between the winding
voltages and the winding currents Suppligd to the State
.- - -
11;";
gnso}? """"
4’825’773 5/1989 M2138}: t: Z: :1‘ '
' 313/11);
""" 8/187 X
estimation observer is compensated depending on the
estimated angular velocity, thereby improving the con
....... .. 318/616
"01 accuracy
4,s51,754
7/1989
4,943,759
7/1990 Sakamoto et al
Sakamoto ct al. .
4,958,114
9/1990
Ogawa
I4
. 318/565 X
.. ... . . . .. ..
. . . . . . . ..
318/616
.
/
4 Claims, 8 Drawing Sheets
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Oct.15, 1991 '
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DISCRETE-TIME AC MOTOR CONTROL
APPARATUS
rors.
SUMMARY OF THE INVENTION
BACKGROUND OF THE INVENTION
5
It is therefore an object of the present invention to
provide a discrete-time alternating-current motor con
1. Field of the Invention
trol apparatus capable of controlling the motor in a
The present invention relates to a control apparatus
wide range of the motor speed.
of an alternating-current (AC) motor operating in a
Another object of the present invention is to provide
discrete-time fashion.
a control apparatus of a permanent-magnet altemating
2. Description of the Related Art
current motor, said control apparatus unnecessitating
When achieving a positioning control in a control
apparatus of a permanent-magnet (PM) alternating-cur
sensors to measure information items of the angle, the
rent motor, an angle of a rotor of the motor is required
to be sensed for a feedback of information of the rotor
angular velocity, and the magnetic pole.
angle. For this purpose, the conventional technology
carry out an estimation with a high precision or accu
has employed a sensor such as an encoder or a resolver.
racy even when phase differences exist in association
Still another object of the present invention is to
Furthermore, in the alternating-current motor, it is
with the inputs of the winding voltages and winding
necessary to change a phase of a current flowing
currents.
through each winding of the motor depending on the
In accordance with the present invention, there is
rotation angle of the rotor. In order to sense the mag 20 provided a discrete-time alternating-current motor con
netic pole positions of the rotor, the conventional sys
trol apparatus including a state estimation observer
tem employs a sensor such as a pole sensor.
which receives as inputs thereto voltages and currents
However, these sensors above cannot be used in gen
of windings of the alternating-current motor to estimate
eral at a high temperature and is moreover not satisfac
a rotor speed and an angular velocity of the alternating
torily resistive against vibration and shock. In conse 25 current motor based on a model of the motor. The
quence, the conventional motor control apparatus using
observer is characterized by further comprising ob
such sensors has been attended with a problem that the
server gain switch means for setting an optimal gain in
desired control operation cannot be achieved in such an
the state estimation observer according to the estimated
environment.
angular velocity.
On the other hand, a state estimation observer has 30
been proposed by Lawrence A. Jones et al. in “A
STATE OBSERVER FOR THE PERMANENT
MAGNET SYNCHRONOUS MOTOR”, IECON
1987 Conference, Cambridge, Mass., Nov. 2-6, 1987. In
this observer, a direct quadrature (dq) transformation
model of a permanent-magnet alternating-current
motor and a linear observer theory are applied to esti
mate a rotor angle and an angular velocity thereof from
winding current and voltage values of the altemating
In accordance with the present invention, since the
estimation state observer means is assigned with an
optimal gain in association with a rotation angular ve
locity of the motor by means of the observer gain
switch means, a predetermined control performance
can be continuously accomplished in a broad velocity
range.
Preferably, the observer gain switch means employs a
hysteresis with respect to the estimated angular velocity
current motor. Furthermore, advantages associated 40 for a gain switch. As a result, the unstable operation is
prevented from being developed in the gain switch
with the direct quadrature transformation model has
operation.
been described in the article.
The alternating-current (AC) control apparatus in
However, in an actual case where a control apparatus
accordance with the present invention further com
is con?gured with a state estimation observer to control
an alternating-current motor, if the state estimation 45 prises origin angle sense means for sensing an origin
position of a rotor of the AC motor and a controller for
observer has a ?xed gain, there have been problems that
controlling the motor based on the estimation result
an estimation value produced by the observer becomes
attained from the state estimation observer means and
unstable when a speed of the motor is changed in a wide
the origin position sensed by the origin angle sense
range and that the response time to obtain the observer
estimation value becomes to be longer. Namely, the 50
means.
alternating-current motor cannot be controlled in a
stable state at a high speed. For example, in a case
where the observer gain of such a motor control system
is set to a value suitable for a speed substantially equal to
With the provision of the above constitution, when
controlling a permanent-magnet alternating-current
motor, there are unnecessitated an angle sensor such as
and encoder or a resolver, an angular velocity sensor
1,500 rotations per minutes (rpm), if the control appara 55 such as a tachometer generator or a frequency-to-volt
age (F/V) converter, and a rotor pole sensing device
tus attempts to control an alternating-current motor
rotating at 500 rpm, the state estimation observer cannot
obtain a converged estimation value.
such as a pole sensor. Furthermore, signal lines to feed
back signals from the various sensors to the respective
Furthermore, the rotation angle estimated by the
signal processing components associated therewith Can
state estimation observer is an electric angle, which 60 be dispensed with. Since these sensors are removed, the
motor above can be employed under various environ
leads to a problem that assuming the number of rotor
mental conditions such as the high temperature, the
poles to be N (22), a unique mechanical angle cannot
be determined.
vibration, the shock in a wider variations as compared
with the conventional case. Owing to the elimination of
In addition, the state estimation observer receives as
inputs thereto winding voltages and currents of the 65 the signal lines for the sensors, there can be attained
advantages that the resistivity against noises and the
alternating-current motor, which results in a problem
that when a phase difference is found in association with
operation reliability are improved in the control appara
the currents and the voltages, a rotation angle and an
tus and that the cost thereof is lowered. In accordance
3
5,057,759
with the present invention, there is implemented a con
trol apparatus of a permanent-magnet alternating-cur
rent motor, said control apparatus unnecessitating the
sensors of the angle, the angular velocity, and the mag
netic pole positions.
‘4
origin sense switch 22. Some components above, for
example, the observer 11, the gain switch unit 12, and
the controllers 13 and 14 are implemented by use of a
computer loaded with an appropriate program.
Of the parameters (physical quantities) used in the
Moreover, in accordance with the present invention,
there is provided a discrete-time alternating-current
cated by codes marked with" thereover, estimated val
motor control apparatus including a state estimation
ues are designated by codes with ~ thereover, and vec
observer which receives as inputs thereto winding volt
tors are denoted by underlined codes.
ages applied to the motor and currents of the motor
windings measured by current sensors to estimate a
rotor speed and an angular velocity of the alternating
current motor based on a model of the motor. The
system is characterized by further comprising means for
compensating phase differences associated with the
voltages and currents of the windings depending on the
estimated angular velocity.
In the constitution according to the present inven
tion, the state estimation observer means can estimate
motor control apparatus 10, measured values are indi
As will be shown later, parameters (for example,
currents id and i[,) of the motor 30 are transformed in
accordance with an orthogonal coordinate system of a
two-phase stator. Transformed parameters are repre
sented by use of subscripts a and B as ia and i;;, for
example. Furthermore, for an estimation processing, the
parameters are subjected to a direct quadrature (dq)
transformation based on an estimated rotator angle 0 (a
transformation into a biaxial orthogonal coordinate
system rotating in synchronism with the rotor). The
with a higher precision the values of the rotor speed, the 20 parameters after the direct quadrature transformation
angular velocity, and the winding currents of the alter
are expressed, for example, as id and Iq with subscripts d
nating-current motor.
and q.
First, a brief description will be given of an alternat
BRIEF DESCRIPTION OF THE DRAWINGS
ing-current motor model adopted in the state estimation
These and other objects and advantages of the pres 25 observer. As described in the article above, based on a
ent invention will become apparent by reference to the
voltage 2 applied to a winding and a sensed windving
following description and accompanying drawings
current'i, the observer estimates a winding current i, a
wherein:
rotor angular velocity (2», and a rotor angle 3 from ex
FIGS. 1 to 3 are diagrams for explaining an embodi
pressions (1) to (3) as follows.
ment according to the present invention;
30
FIG. 1 is a functional block diagram showing a con
ceptual structure of a discrete-time alternating-current
motor control apparatus;
FIG. 2 is a schematic diagram showing a switch table
adopted to switch a gain of an observer;
35
FIG. 3 is a graph showing a hysteresis of the gain of
(1)
the observer;
FIGS. 4 to 6 are diagrams for explaining an alterna
tive embodiment according to the present invention;
FIG. 4 is a functional block diagram showing a con
ceptual structure of a discrete-time alternating-current
motor control apparatus;
FIG. 5 is a graph illustratively showing relationships
of phase differences between winding currents and volt
45
ages in the motor;
FIG. 6 is a diagram schematically showing a table
containing phase correction angles; and
FIGS. 7 and 8 are block diagrams showing further
alternative examples of phase compensate means to
45/71: ‘= (3
(3)
Where:
L: Winding inductance, R: Winding resistance,
K: Torque constant, B: Viscosity friction
C: Coulomb friction, H: Inertia,
1': Torque, N: Number of pole pairs
compensate phase differences of the winding currents
and voltages.
DESCRIPTION OF THE PREFERRED
EMBODIMENTS
FIG. 1 shows an embodiment of the altemating-cur 55
rent motor control apparatus of the discrete-time type
in accordance with the present invention.
The con?guration includes a permanent-magnet al
ternating-current motor 30 as a control object, which is
a three-phase motor associated with phases a, b, and c.
v
V
6
l
v
I
ll
i = (I... 1B)’
1 = (Va, "[91
Currents and voltages of the respective phases are rep
resented as ia, i[,, and ic and V“, VI, and vs, respectively.
A discrete-time AC motor control apparatus 10 in
cludes a state estimation observer 11, an observer gain
switch unit 12, a current controller 13, a speed/position 65
controller 14, current sensors 15 and 16, a low-pass ?lter
17, sample-and-hold circuit 18 and 19, a pulse width
modulation (PWM) circuit 20, an inverter 21, and an
811812
62x2 _ [821822]
The coulomb friction, the viscosity friction, and the
inertia vary depending on the magnitude of load im
5
5,057,759
ék+1 and 6k+1 are delivered to the current controller
13 and the upper-level controller (speed/position con
In the expressions above, i=(ia, i3)T is obtained by
transforming a sensed winding current (i1, i[,) in accor
dance with a coordinate system of a two-phase stator.
Assuming the transformation to be T (0), the result can
be expressed as follows.
i: (in, iB)T= 7(5) (Ia 179T
6
The estimated values i¢k+1 and iq,k+1 are fed to the
current controller 13. Moreover, the estimated values
posed on the motor. In addition, the inertia expressed
above is associated with the mechanical system includ
ing the motor and the load.
troller) 14.
The current controller 13 can decide, based on the
estimated value 01<+1, phases to be assigned to the wind
ing voltages to supply a current in association with
magnetic pole positions of the rotor. In consequence,
10 the magnetic pole sensor ca be dispensed with.
Moreover, the current controller 13 compares the
The description above also applies to the expression
current instruction values idyk+l and iq,k+1 fed from the
ppper-level controller 14 with the values id,k+1 and
X=( Va’ VB)T~
In a discretized form, the expressions (1) to (3) are
iq,k+1 estimated by the state estimation observer 11 to
compute based on a predetermined control algorithm
respectively represented by expressions (4) to (7) as
follows.
the direct-quadrature transformation values ing/(+1 and
{IL/(+1 of the voltage applied to the motor windings, for
example, to minimize the deviations associated there
with. In addition, the current controller 13 computes, in
accordance with the value 9k+1 described above volt
ages va,k+1, vb,k+1 and vc,k+1 to be applied to the motor
windings. The resultant voltage values are passed via
the sample-and-hold circuit 19 to the pulse-width modu
lation (PWM) circuit 20, which in turn transforms the
25
received values into pulse widths. The obtained signals
are delivered via the inverter (switch circuit) 21 to the
motor windings.
In a case where the upper-level controller of the
30
current controller 13 is the speed/position controller 14
as shown in FIG. 1, since the values (Ii/(+1 and ¢I>k+1
estimated by the state estimation observer 11 are fed to
the speed/position controller 14, the angle and angular
velocity sensors become to be unnecessary for the con
Where:
35 trol of the speed and positions.
In this connection, since the rotor angle forecasted by
the state estimation observer 11 is an electric angle, the
At: Sampling time
obtained value 9k+1 cannot be directly adopted to
achieve the position control. However, a rotor angle
necessary for the current control is an electric angle;
furthermore, the convergence in the operation of the
The Subscript k denotes that the associated value is
state estimation observer 11 can be accomplished at a
attained at a sampling time (point of time) k, whereas
high speed, which is satisfactory with respect to a time
the subscript k+ 1 indicates that the value is obtained at
constant of the motor. In consequence, at an initiation of
a point of time when a sampling period of time At is
45 the motor operation, the motor can be started by use of
elapsed after the point of time k.
the current controller and hence the origin angular
p The motor winding currents in and i1, respectively
position can be sensed by the origin sense switch 22.
attained from the current sensors 15 and 16 are sent via
The origin sense signal is fed from the origin sense
the low-pass ?lter 17, which removes noises from the
switch 22 to the current controller 13 and the speed/po
received Signals, to the sample-and-hold circuit 18. The
sition contrpller 14. Based on the origin sense signal and
circuit 18 achieves a sample-and-hold operation at a
the
value 0k+| forecasted by the state estimation ob
sampling time k on these signals to be supplied respec
server 11, the mechanical angle is computed. As de
tively as imk and ib,k to the state estimation observer 11.
scribed above, through the calibration above at the start
The observer 11 then conducts a direct quadrature
point of the motor operation, the position control can be
transformation on the received current values imk and
accomplished without using an angle sensor.
ilnk based on the rotor angle 0k estimated at the time
Subsequently, a description will be given of the ob
14-1 to generate current values Lu and lq'k. The state
estimation observer 11 is also supplied with voltage
values V“ and vqJc obtained by the current controller
13 through the direct quadrature transformation con
ducted on the voltages applied to the windings,“ which
will be described later. Based on the values 6k, idyk, iq,k
and 0k estimated at the time k-l and the transformed
values Vd'k, v“, i4_;; and ilyk, the state estimation ob
server 11 estimates values id,k+1, i1,k+1, é:k+1, and
server gain switch unit 12. The state estimation ob
server 11 develops a nonlinear dynamics characteristic
with respect to an angular velocity éik as represented
with the expressions (1) to (3) or (4) to (7). The dynam
ics characteristic alters depending on the observer gain
values 62x2 and 61x2.
Consequently, in a general motor control apparatus in
which the control speed range is not limited, in order to
0k+1 at the tlme k+1 from the expressions (4) to (7). In 65 retain the control performance of the apparatus, the
gain of the state estimation observer is required to be
consequence, the rotor angle and the angular velocity
switched
according to the speed. For the observer gain,
can be obtained without using the angle and angular
velocity sensors.
an optimal value can be in advance computed by use of
7
5,057,759
linearized error equation (expression (8) below) associ
ated with the expressions (1) to (3).
8
circuit 20 and the inverter 21. Due to delays associated
with these circuits, precisely, the values 0d,], and v91‘ are
(8)
A"?ee,
N)
Furthermore, éd stands _for a differentiated value of ad.
This also applies to a, em, and eg.
According to results from experiments, it has been
con?rmed that the observer gain need not be switched
different from the voltages applied to the motor wind
ings at the point of time k. Namely, the values v,“ and
a”, are applied to the motor windings at a point of time
or changed over between the respective values for each 20 t; succeeding the point of time k as shown in FIG. 5.
speed, namely, the switch operation of the observer
On the other hand, the state estimation observer 11 is
gain is t be conducted between predetermined appropri
supplied with the currents ink and ibyk, which are motor
ate speed ranges. 'In consequence, there is prepared a
winding currents undergone the sampling at the point of
table, as shown in FIG. 2, containing values of the ob
time k. However, these currents are sent through the
server gain associated with the angular velocity 60 be 25 current sensors 15 and 16 and the low-pass ?lter 17 to
forehand computed from the expression (8). The table is
loaded in a memory of the observer gain switch unit 12.
the sample-and-hold circuit 18. Owing to the phase lags
associated with these circuits, exactly, the currents iLk
In this table, for the respective estimated angular veloc
and ibyk are different from the motor winding currents of
ity ranges wito mi+1(i=1~n), gain values gm, gm, g2“,
the motor 30 at the point of time k. In actual operation,
822i, g'1 “and g'lzi are stored in association therewith. In 30 there are supplied the currents ?owing in the motor
operation, a value (bk estimated by the state estimation
windings at a point of time t1 following the point of time
observer 11 at a point of time k is delivered to the ob
k as shown in FIG. 5.
I
server gain switch unit 12, which acquires from the
As above, the winding voltages in), and v” and the
table an optimal gain associated with the value (bk to
winding currents id'k and ihk are different from the re
supply the obtained value as a gain (Gk+1)at a point of 35 spective actual values developed at the point of time k
time"+1 to the state estimation observer 11. Based on
and hence a phase difference AT exists between the
the optimal gain given by the observer gain switch unit
winding voltages and currents, which leads to the fol
_12, the observer 11 computes the estimation values
lowing problem. Since the state estimation observer 11
id,k+1iq,k+1, G>k+1 and §k+1 at the point of time k+1,
thereby developing a predetermined control perfor
treats the winding currents and voltages as ones sensed
at the same point of time, due to the phase difference AT
mance in the overall control speed range.
therebetween, the estimated rotor angle, the angular
velocity, and the winding currents include estimation
At boundaries (m2, m3, etc.) of the speed for switching
the observer gain, when the angular velocity rises and
falls, the‘ observer gain is frequently changed over. This
errors.
In order to remove the problem above, a phase com
causes the state estimation observer 11 to carry out an 45 pensating unit 23 is disposed in a discrete-time alternat
unstable operation and hence exerts a disadvantageous
in?uence on the motor control characteristic. To cope
ing-current motor control apparatus 10A of FIG. 4. The
phase compensator unit 23 may also be implemented by
with the problems above, the observer gain is supplied
use of a computer provided with an appropriate pro
gram. In the constitution of FIG. 4, the same constitu
shown in FIG. 3, thereby removing the problems 50 ent components as those of FIG. 1 are assigned with the
above. In this situation, the observer gain switch unit 12
same reference numerals and a redundant description
need only conduct a decision processing to determine
thereof will be avoided.
whether or not the received angular velocity rink is
The phase compensating unit 23 is supplied with
with a hysteresis with respect to the angular velocity as
within the hysteresis width. When the angular velocity
winding current imk and ib,k from the sample-and-hold
is within the range, it need only be achieved to produce 55 circuit 18 and with the estimation values 0k and {bk
a gain with a value identical to the value of the previous
estimated by the state estimation observer 11. The phase
output.
.
compensator unit 23 advances the phases of the re
Referring next to FIGS. 4 to 6, a description will be
ceived winding currents ink and iq,k by the phase differ
given of the discrete-time alternating-current motor
control apparatus including a phase compensating unit.
In the motor control apparatus 10 of FIG. 1, the
values {1d,}: and ‘7%,, supplied to the state estimation ob
ence AT and conducts a direct quadrature transforma
tion on the obtained signals to resultantly'supply the
state estimation observer 11 with values id'k and iqyk
having a phase identical to the phase of the winding
serve 11 are resultant values of the direct quadrature
voltages a“ and m. That is, since the state estimation
transformation produced at the point of time k from the
observer 11 conducts the operation based on a direct
current controller 13 which outputs the value via the 65 quadrature transformation model, by use of a value
sample-and-hold circuit 19. Actually, the motor wind
ings of the alternating-current motor 30 ar supplied
with these voltages through the pulse width modulation
obtained by adding a correction angle A0 associated
with the phase difference A T to the rotor angle 0k
estimated by the state estimation observer 11, the coor
9
5,057,759
-
dinate transformation is accomplished according to the
following expression (9) to equivalently equalize the
phase between 'the voltage values m and m and the
While particular embodiments of the invention have
been shown and described, it will be obvious to those
skilled in the art that various changes and modi?cations
may be made without departing from the present inven
tion in its broader aspects.
What is claimed is:
1. A discrete-time alternating-current motor control
current values idyk and iq,k, respectively.
[5112,1.,]:
(9)
Where, T(ék+Aék) is a matrix employed to transform
apparatus comprising:
the winding currents ink and ilLk in accordance with an
orthogonal coordinate system of a two-phase stator.
Thekcorrection angle Aék to be added to the rotor
state estimation observer means for receiving as in
puts thereto winding voltages and winding cur
angle 0k varies depending on the rotor angular velocity
(Bk and can be determined in advance. In consequence, 15
it is favorable to store the correction values associated
with the values of the rotor angular velocity (Bk in a
form of a table as shown in FIG. 6. Namely, from this
table, the phase compensating unit 23 obtains a correc
tion angle 130k associated with the rotor angular veloc
thereby conducting the com utation based on the ex
pression (9). Fixed values A k may be naturally deter
mined for the respective appropriate ranges of the rotor
the alternating-current motor; and
observer gain switch means for setting an optimal
gain to said state estimation observer means ac—
cording to the estimated angular velocity.
ity for a gain switch operation.
25
FIGS. 7 and 8 are schematic diagrams showing alter
native embodiments according to the present invention.
In the constitution of FIG. 7, in order for the state
estimation observer 11 to acquire the winding currents
imk and ibyk at a point of time when the voltages v“ and
3. A motor control apparatus in accordance with
claim 1 further comprising:
origin angle sense means for sensing an origin posi
tion of a rotor of the alternating-current motor; and
a controller for controlling the alternating-current
motor based on an estimation result from said state
estimation observer means and an origin position
v,” are actually applied to the windings, a delay circuit
24 is disposed to delay the current lqyk and ilhk. The delay
time of the delay circuit 24 is controlled depending on
the angular velocity (bk estimated by the state estimation
observer 11.
rents of an alternating-current motor and for esti
mating based on a model of the alternating-current
motor a rotor angle and a rotor angular velocity of
2. A motor control apparatus in accordance with
claim 1 wherein said observer gain switch means assigns
a hysteresis with respect to an estimated angular veloc
ity (Bk supplied from the state estimation observer 11,
angular velocity (bk.
10
server 11 The sensed voltages vabyk vbak are transformed
into vdyk and vq,k in the state estimation observer 11.
sensed by said origin angle sense means.
4. A discrete-time alternating-current motor control
apparatus comprising:
35
state estimation observer means for receiving as in
puts thereto winding voltages applied to an alter
nating-current motor and winding currents sensed
The con?guration of FIG. 8 includes voltage sensors
26 and 27 respectively measuring voltages vab and vbc
actually applied to the windings of an altemating-cur
by a current sensor and for estimating based on a
model of the alternating-current motor a rotor
rent motor 30. Current values in and i1, respectively
sensed by the current sensors 15 and 16 and voltages
val, and vbc respectively obtained by the voltage sensors
26 and 27 are supplied to the sample-and-hold circuit 25
to be sampled at an identical point of time. The sampled
values are delivered as sensed values ia,k, ibJc, vabJ‘ and
angle and a rotor angular velocity of the alternat
ing-current motor; and
means for compensating based on the estimated angu
lar velocity a phase difference between the wind
ing voltages and the winding currents.
vbgk at the point of time k to the state estimation ob 45
50
55
65
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it
t
It
‘I
‘I