Discrete-time AC motor control apparatus

In a discrete-time alternating-current motor control apparatus having a state estimation observer estimating a rotor angle and a rotor angular velocity based on a direct quadrature transformation model of the motor, the gain of the observer is changed over depending on an estimated angular velocity. As a result, the apparatus is applicable in a wide range of the motor speed. Furthermore, the phase difference between the winding voltages and the winding currents supplied to the state estimation observer is compensated depending on the estimated angular velocity, thereby improving the control accuracy.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a control apparatus of an 
alternating-current (AC) motor operating in a discrete-time fashion. 
2. Description of the Related Art 
When achieving a positioning control in a control apparatus of a 
permanent-magnet (PM) alternating-current motor, an angle of a rotor of 
the motor is required to be sensed for a feedback of information of the 
rotor angle. For this purpose, the conventional technology has employed a 
sensor such as an encoder or a resolver. Furthermore, in the 
alternating-current motor, it is necessary to change a phase of a current 
flowing through each winding of the motor depending on the rotation angle 
of the rotor. In order to sense the magnetic pole positions of the rotor, 
the conventional system employs a sensor such as a pole sensor. 
However, these sensors above cannot be used in general at a high 
temperature and is moreover not satisfactorily resistive against vibration 
and shock. In consequence, the conventional motor control apparatus using 
such sensors has been attended with a problem that the desired control 
operation cannot be achieved in such an environment. 
On the other hand, a state estimation observer has 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 estimate a rotor angle and an angular velocity thereof from 
winding current and voltage values of the alternating-current motor. 
Furthermore, advantages associated with the direct quadrature 
transformation model has been described in the article. 
However, in an actual case where a control apparatus is configured with a 
state estimation observer to control an alternating-current motor, if the 
state estimation observer has a fixed gain, there have been problems that 
an estimation value produced by the observer becomes unstable when a speed 
of the motor is changed in a wide range and that the response time to 
obtain the observer estimation value becomes to be longer. Namely, the 
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 1,500 rotations per minutes (rpm), if the control apparatus attempts to 
control an alternating-current motor rotating at 500 rpm, the state 
estimation observer cannot obtain a converged estimation value. 
Furthermore, the rotation angle estimated by the state estimation observer 
is an electric angle, which leads to a problem that assuming the number of 
rotor poles to be N (.gtoreq.2), a unique mechanical angle cannot be 
determined. 
In addition, the state estimation observer receives as inputs thereto 
winding voltages and currents of the alternating-current motor, which 
results in a problem that when a phase difference is found in association 
with the currents and the voltages, a rotation angle and an angular 
velocity thus estimated include estimation errors. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide a 
discrete-time alternating-current motor control apparatus capable of 
controlling the motor in a wide range of the motor speed. 
Another object of the present invention is to provide a control apparatus 
of a permanent-magnet alternating-current motor, said control apparatus 
unnecessitating sensors to measure information items of the angle, the 
angular velocity, and the magnetic pole. 
Still another object of the present invention is to carry out an estimation 
with a high precision or accuracy even when phase differences exist in 
association with the inputs of the winding voltages and winding currents. 
In accordance with the present invention, there is provided a discrete-time 
alternating-current motor control apparatus including a state estimation 
observer which receives as inputs thereto voltages and currents of 
windings of the alternating-current motor to estimate a rotor speed and an 
angular velocity of the alternating-current motor based on a model of the 
motor. The observer is characterized by further comprising observer gain 
switch means for setting an optimal gain in the state estimation observer 
according to the estimated angular velocity. 
In accordance with the present invention, since the estimation state 
observer means is assigned with an optimal gain in association with a 
rotation angular velocity 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 for a gain switch. As a result, 
the unstable operation is prevented from being developed in the gain 
switch operation. 
The alternating-current (AC) control apparatus in accordance with the 
present invention further comprises origin angle sense means for sensing 
an origin position of a rotor of the AC motor and a controller for 
controlling the motor based on the estimation result attained from the 
state estimation observer means and the origin position sensed by the 
origin angle sense means. 
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 
such as a tachometer generator or a frequency-to-voltage (F/V) converter, 
and a rotor pole sensing device such as a pole sensor. Furthermore, signal 
lines to feed back signals from the various sensors to the respective 
signal processing components associated therewith Can be dispensed with. 
Since these sensors are removed, the motor above can be employed under 
various environmental conditions such as the high temperature, the 
vibration, the shock in a wider variations as compared with the 
conventional case. Owing to the elimination of the signal lines for the 
sensors, there can be attained advantages that the resistivity against 
noises and the operation reliability are improved in the control apparatus 
and that the cost thereof is lowered. In accordance with the present 
invention, there is implemented a control apparatus of a permanent-magnet 
alternating-current motor, said control apparatus unnecessitating the 
sensors of the angle, the angular velocity, and the magnetic pole 
positions. 
Moreover, in accordance with the present invention, there is provided a 
discrete-time alternating-current motor control apparatus including a 
state estimation observer which receives as inputs thereto winding 
voltages 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 invention, the state 
estimation observer means can estimate with a higher precision the values 
of the rotor speed, the angular velocity, and the winding currents of the 
alternating-current motor.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 shows an embodiment of the alternating-current motor control 
apparatus of the discrete-time type in accordance with the present 
invention. 
The configuration includes a permanent-magnet alternating-current motor 30 
as a control object, which is a three-phase motor associated with phases 
a, b, and c. Currents and voltages of the respective phases are 
represented as i.sub.a, i.sub.b, and i.sub.c and v.sub.a, v.sub.b and 
v.sub.c, respectively. 
A discrete-time AC motor control apparatus 10 includes a state estimation 
observer 11, an observer gain switch unit 12, a current controller 13, a 
speed/position controller 14, current sensors 15 and 16, a low-pass filter 
17, sample-and-hold circuit 18 and 19, a pulse width modulation (PWM) 
circuit 20, an inverter 21, and an 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 motor control apparatus 
10, measured values are indicated by codes marked with thereover, 
estimated values are designated by codes with thereover, and vectors are 
denoted by underlined codes. 
As will be shown later, parameters (for example, currents i.sub.a and 
i.sub.b) of the motor 30 are transformed in accordance with an orthogonal 
coordinate system of a two-phase stator. Transformed parameters are 
represented by use of subscripts .alpha. and .beta. as i.sub..alpha. and 
i.sub..beta., for example. Furthermore, for an estimation processing, the 
parameters are subjected to a direct quadrature (dq) transformation based 
on an estimated rotator angle .theta. (a transformation into a biaxial 
orthogonal coordinate system rotating in synchronism with the rotor). The 
parameters after the direct quadrature transformation are expressed, for 
example, as i.sub.d and i.sub.q with subscripts d and q. 
First, a brief description will be given of an alternating-current motor 
model adopted in the state estimation observer. As described in the 
article above, based on a voltage v applied to a winding and a sensed 
winding current i, the observer estimates a winding current i, a rotor 
angular velocity .omega., and a rotor angle .theta. from expressions (1) 
to (3) as follows. 
##EQU1## 
Where: L: Winding inductance, R: Winding resistance, 
K: Torque constant, B: Viscosity friction 
C: Coulomb friction, H: Inertia, 
.tau.: Torque, N: Number of pole pairs 
##EQU2## 
The coulomb friction, the viscosity friction, and the inertia vary 
depending on the magnitude of load imposed on the motor. In addition, the 
inertia expressed above is associated with the mechanical system including 
the motor and the load. 
In the expressions above, i=(i.sub..alpha., i.sub..beta.).sup.T is obtained 
by transforming a sensed winding current (i.sub.1, i.sub.b) in accordance 
with a coordinate system of a two-phase stator. Assuming the 
transformation to be T (.theta.), the result can be expressed as follows. 
EQU i=(i.sub..alpha., i.sub..beta.).sup.T =T(.theta.) (i.sub.a, i.sub.b).sup.T 
The description above also applies to the expression v=(v.sub..alpha., 
v.sub..beta.).sup.T. 
In a discretized form, the expressions (1) to (3) are respectively 
represented by expressions (4) to (7) as follows. 
##EQU3## 
The Subscript k denotes that the associated value is attained at a sampling 
time (point of time) k, whereas the subscript k+1 indicates that the value 
is obtained at a point of time when a sampling period of time .DELTA.t is 
elapsed after the point of time k. 
The motor winding currents i.sub.a and i.sub.b respectively attained from 
the current sensors 15 and 16 are sent via the low-pass filter 17, which 
removes noises from the received Signals, to the sample-and-hold circuit 
18. The circuit 18 achieves a sample-and-hold operation at a sampling time 
k on these signals to be supplied respectively as i.sub.a,k and i.sub.b,k 
to the state estimation observer 11. The observer 11 then conducts a 
direct quadrature transformation on the received current values i.sub.a,k 
and i.sub.b,k based on the rotor angle .theta..sub.k estimated at the time 
k-1 to generate current values i.sub.d,k and i.sub.q,k. The state 
estimation observer 11 is also supplied with voltage values V.sub.d,k and 
v.sub.q,k obtained by the current controller 13 through the direct 
quadrature transformation conducted on the voltages applied to the 
windings, which will be described later. Based on the values 
.omega..sub.k, i.sub.d,k, i.sub.q,k and .theta..sub.k estimated at the 
time k-1 and the transformed values v.sub.d,k, v.sub.q,k, i.sub.d,k and 
i.sub.1,k, the state estimation observer 11 estimates values i.sub.d,k+1, 
i.sub.1,k+1, .omega..sub.k+1, and .theta..sub.k+1 at the tlme k+1 from the 
expressions (4) to (7). In consequence, the rotor angle and the angular 
velocity can be obtained without using the angle and angular velocity 
sensors. 
The estimated values i.sub.d,k+1 and i.sub.q,k+1 are fed to the current 
controller 13. Moreover, the estimated values .omega..sub.k+1 and 
.theta..sub.k+1 are delivered to the current controller 13 and the 
upper-level controller (speed/position controller) 14. 
The current controller 13 can decide, based on the estimated value 
.theta..sub.k+1, phases to be assigned to the winding voltages to supply a 
current in association with magnetic pole positions of the rotor. In 
consequence, the magnetic pole sensor ca be dispensed with. 
Moreover, the current controller 13 compares the current instruction values 
i.sub.d,k+1 and i.sub.q,k+1 fed from the upper-level controller 14 with 
the values i.sub.d,k+1 and i.sub.q,k+1 estimated by the state estimation 
observer 11 to compute based on a predetermined control algorithm the 
direct-quadrature transformation values v.sub.d,k+1 and v.sub.1,k+1 of the 
voltage applied to the motor windings, for example, to minimize the 
deviations associated therewith. In addition, the current controller 13 
computes, in accordance with the value .theta..sub.k+1 described above 
voltages v.sub.a,k+1, v.sub.b,k+1 and v.sub.c,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 modulation (PWM) circuit 20, 
which in turn transforms the 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 current controller 13 is 
the speed/position controller 14 as shown in FIG. 1, since the values 
.omega..sub.k+1 and .omega..sub.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 control of the 
speed and positions. 
In this connection, since the rotor angle forecasted by the state 
estimation observer 11 is an electric angle, the obtained value 
.theta..sub.k+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 state 
estimation observer 11 can be accomplished at a high speed, which is 
satisfactory with respect to a time constant of the motor. In consequence, 
at an initiation of the motor operation, the motor can be started by use 
of the current controller and hence the origin angular position can be 
sensed by the origin sense switch 22. The origin sense signal is fed from 
the origin sense switch 22 to the current controller 13 and the 
speed/position controller 14. Based on the origin sense signal and the 
value .theta..sub.k+1 forecasted by the state estimation observer 11, the 
mechanical angle is computed. As described above, through the calibration 
above at the start point of the motor operation, the position control can 
be accomplished without using an angle sensor. 
Subsequently, a description will be given of the observer gain switch unit 
12. The state estimation observer 11 develops a nonlinear dynamics 
characteristic with respect to an angular velocity .omega..sub.k as 
represented with the expressions (1) to (3) or (4) to (7). The dynamics 
characteristic alters depending on the observer gain values 
G.sub.2.times.2 and G.sub.1.times.2. 
Consequently, in a general motor control apparatus in which the control 
speed range is not limited, in order to retain the control performance of 
the apparatus, the gain of the state estimation observer is required to be 
switched according to the speed. For the observer gain, an optimal value 
can be in advance computed by use of linearized error equation (expression 
(8) below) associated with the expressions (1) to (3). 
##EQU4## 
Furthermore, e.sub.d stands for a differentiated value of e.sub.d. This 
also applies to e.sub.q, e.sub..omega., and e.sub..theta.. 
According to results from experiments, it has been confirmed that the 
observer gain need not be switched or changed over between the respective 
values for each speed, namely, the switch operation of the observer gain 
is t be conducted between predetermined appropriate speed ranges. In 
consequence, there is prepared a table, as shown in FIG. 2, containing 
values of the observer gain associated with the angular velocity .omega. 
beforehand computed from the expression (8). The table is loaded in a 
memory of the observer gain switch unit 12. In this table, for the 
respective estimated angular velocity ranges .omega..sub.i to 
.omega..sub.i+1 (i=1.about.n), gain values g.sub.11i, g.sub.12i, 
g.sub.21i, g.sub.22i, g'.sub.11i and g'.sub.12i are stored in association 
therewith. In operation, a value .omega..sub.k estimated by the state 
estimation observer 11 at a point of time k is delivered to the observer 
gain switch unit 12, which acquires from the table an optimal gain 
associated with the value .omega..sub.k to supply the obtained value as a 
gain (G.sub.k+1)at a point of time.sup.k+1 to the state estimation 
observer 11. Based on the optimal gain given by the observer gain switch 
unit 12, the observer 11 computes the estimation values i.sub.d,k+1 
i.sub.q,k+1, .omega..sub.k+1 and .theta..sub.k+1 at the point of time k+1, 
thereby developing a predetermined control performance in the overall 
control speed range. 
At boundaries (.omega..sub.2, .omega..sub.3, etc.) of the speed for 
switching the observer gain, when the angular velocity rises and falls, 
the observer gain is frequently changed over. This causes the state 
estimation observer 11 to carry out an unstable operation and hence exerts 
a disadvantageous influence on the motor control characteristic. To cope 
with the problems above, the observer gain is supplied with a hysteresis 
with respect to the angular velocity as shown in FIG. 3, thereby removing 
the problems above. In this situation, the observer gain switch unit 12 
need only conduct a decision processing to determine whether or not the 
received angular velocity .omega..sub.k is within the hysteresis width. 
When the angular velocity is within the range, it need only be achieved to 
produce a gain with a value identical to the value of the previous output. 
Referring next to FIGS. 4 to 6, a description will be 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 v.sub.d,k and 
v.sub.q,k supplied to the state estimation observe 11 are resultant values 
of the direct quadrature transformation produced at the point of time k 
from the current controller 13 which outputs the value via the 
sample-and-hold circuit 19. Actually, the motor windings of the 
alternating-current motor 30 ar supplied with these voltages through the 
pulse width modulation circuit 20 and the inverter 21. Due to delays 
associated with these circuits, precisely, the values v.sub.d,k and 
v.sub.q,k are different from the voltages applied to the motor windings at 
the point of time k. Namely, the values v.sub.d,k and v.sub.q,k are 
applied to the motor windings at a point of time t.sub.2 succeeding the 
point of time k as shown in FIG. 5. 
On the other hand, the state estimation observer 11 is supplied with the 
currents i.sub.a,k and i.sub.b,k, which are motor winding currents 
undergone the sampling at the point of time k. However, these currents are 
sent through the current sensors 15 and 16 and the low-pass filter 17 to 
the sample-and-hold circuit 18. Owing to the phase lags associated with 
these circuits, exactly, the currents i.sub.1,k and i.sub.b,k are 
different from the motor winding currents of the motor 30 at the point of 
time k. In actual operation, there are supplied the currents flowing in 
the motor windings at a point of time t.sub.1 following the point of time 
k as shown in FIG. 5. 
As above, the winding voltages v.sub.d,k and v.sub.q,k and the winding 
currents i.sub.a,k and i.sub.b,k are different from the respective actual 
values developed at the point of time k and hence a phase difference 
.DELTA.T exists between the winding voltages and currents, which leads to 
the following problem. Since the state estimation observer 11 treats the 
winding currents and voltages as ones sensed at the same point of time, 
due to the phase difference .DELTA.T therebetween, the estimated rotor 
angle, the angular velocity, and the winding currents include estimation 
errors. 
In order to remove the problem above, a phase compensating unit 23 is 
disposed in a discrete-time alternating-current motor control apparatus 
10A of FIG. 4. The phase compensator unit 23 may also be implemented by 
use of a computer provided with an appropriate program. In the 
constitution of FIG. 4, the same constituent components as those of FIG. 1 
are assigned with the same reference numerals and a redundant description 
thereof will be avoided. 
The phase compensating unit 23 is supplied with winding current i.sub.a,k 
and i.sub.b,k from the sample-and-hold circuit 18 and with the estimation 
values .theta..sub.k and .omega..sub.k estimated by the state estimation 
observer 11. The phase compensator unit 23 advances the phases of the 
received winding currents i.sub.a,k and i.sub.q,k by the phase difference 
.DELTA.T and conducts a direct quadrature transformation on the obtained 
signals to resultantly supply the state estimation observer 11 with values 
i.sub.d,k and i.sub.q,k having a phase identical to the phase of the 
winding voltages v.sub.d,k and v.sub.q,k. That is, since the state 
estimation observer 11 conducts the operation based on a direct-quadrature 
transformation model, by use of a value obtained by adding a correction 
angle .DELTA..theta. associated with the phase difference .DELTA. T to the 
rotor angle .theta..sub.k estimated by the state estimation observer 11, 
the coordinate transformation is accomplished according to the following 
expression (9) to equivalently equalize the phase between the voltage 
values v.sub.d,k and v.sub.q,k and the current values i.sub.d,k and 
i.sub.q,k, respectively. 
##EQU5## 
Where, T(.theta..sub.k +.DELTA..theta..sub.k) is a matrix employed to 
transform the winding currents i.sub.a,k and i.sub.b,k in accordance with 
an orthogonal coordinate system of a two-phase stator. 
The correction angle .DELTA..theta..sub.k to be added to the rotor angle 
.theta..sub.k varies depending on the rotor angular velocity .omega..sub.k 
and can be determined in advance. In consequence, it is favorable to store 
the correction values associated with the values of the rotor angular 
velocity .omega..sub.k in a form of a table as shown in FIG. 6. Namely, 
from this table, the phase compensating unit 23 obtains a correction angle 
.DELTA..theta..sub.k associated with the rotor angular velocity 
.omega..sub.k supplied from the state estimation observer 11, thereby 
conducting the computation based on the expression (9). Fixed values 
.DELTA..theta..sub.k may be naturally determined for the respective 
appropriate ranges of the rotor angular velocity .omega..sub.k. 
FIGS. 7 and 8 are schematic diagrams showing alternative 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 i.sub.a,k and i.sub.b,k at a point of 
time when the voltages v.sub.d,k and v.sub.q,k are actually applied to the 
windings, a delay circuit 24 is disposed to delay the current i.sub.a,k 
and i.sub.b,k. The delay time of the delay circuit 24 is controlled 
depending on the angular velocity .omega..sub.k estimated by the state 
estimation observer 11. 
The configuration of FIG. 8 includes voltage sensors 26 and 27 respectively 
measuring voltages v.sub.ab and v.sub.bc actually applied to the windings 
of an alternating-current motor 30. Current values i.sub.a and i.sub.b 
respectively sensed by the current sensors 15 and 16 and voltages v.sub.ab 
and v.sub.bc 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 
i.sub.a,k, i.sub.b,k, v.sub.ab,k and v.sub.bc,k at the point of time k to 
the state estimation observer 11 The sensed voltages v.sub.ab,k v.sub.bc,k 
are transformed into v.sub.d,k and v.sub.q,k in the state estimation 
observer 11. 
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 modifications may be made without departing from the present 
invention in its broader aspects.