Method and device for controlling a sensorless field-oriented asynchronous machine

A method and a device for controlling a sensorless, field-oriented asynchronous machine, wherein a manipulated variable space vector and a stator frequency are calculated, by means of a two-component current control system, from which control signals are generated using a space vector modulation process. A PI controller of an EMF control system for the d-component of a calculated EMR space vector of the field-oriented control system is deactivated and its output signal set to zero at a stator frequency, determined as a function of a calculated d-component of a calculated EMF space vector and a calculated stator frequency, that is less than or equal to a first limit frequency. Thus, the method may be used for speed control of a sensorless, field-oriented asynchronous machine down to a full stop.

FIELD OF THE INVENTION 
The present invention relates to a method and a device for controlling a 
sensorless, field-oriented asynchronous machine. 
BACKGROUND INFORMATION 
International Application No. WO 9503649 describes a two-component current 
controller with a space vector modulator for an induction machine supplied 
by a pulse-controlled inverter. This field-oriented control system 
includes an input transformer system, an EMF computer, a pre-control 
network, a current control circuit, an active current controller, and an 
output-side coordinate converter. The input-side transformer is supplied 
with two measured phase currents from which orthogonal field-oriented 
actual current components are generated using a flux angle. These actual 
current components are sent both to the current control circuit and to the 
EMF computer. The EMF computer also receives the setpoint voltage 
components, the parameters of the induction machine (stator resistance 
R.sub.s and leakage inductance L.sub..sigma.), and the stator frequency 
.omega..sub.s. The output of the EMF computer is coupled with the 
actual-value input of the active current controller, so that a 
field-oriented, torque-forming setpoint current component appears at the 
setpoint-value input of this control system. The output signal of this 
active current control system is used as a speed-correction for a 
calculated slip frequency, which is added to a measured actual rpm value 
to form the stator frequency. The current-control circuit contains a 
comparator with a downstream controller for each field-oriented current 
component, so that an output signal of the input-side transformer exists 
at each inverting input, and a field-oriented setpoint current component 
exists at each non-inverting input. The outputs of this current-control 
circuit are connected to the outputs of the pre-control network; the 
setpoint current values, the "stator resistance," "leakage inductance," 
and "magnetizing inductance" parameters are fed to the input of the 
pre-control network. The sum signal, consisting of field-oriented 
pre-control values and controller manipulated variables, also known as 
field-oriented manipulated variables, is fed to the output-side coordinate 
converter, which converts these orthogonal components into polar 
components. These polar manipulated variable components, also called 
voltage components, and the stator frequency are fed to the space vector 
modulator, at whose outputs control signals for the pulse-controlled 
inverter are formed. 
For this field-oriented control system with a sensor, active current 
control is used to correct the slip frequency and to adjust parameters 
(rotor resistance). The slip frequency is calculated from the 
torque-forming setpoint current component and a quotient of the rotor 
resistance and setpoint flux. These two signals are multiplied, and the 
product is equal to the slip frequency. Since the "rotor resistance" 
parameter is temperature-dependent, the slip frequency changes in 
proportion to the "rotor resistance" parameter. Using this active current 
control method, the correct slip frequency may be determined, allowing 
maximum torque to be developed. 
This control structure has also proved effective for a sensorless induction 
machine. In a field-oriented controller system without a sensor, an EMF 
control system is used instead of active current control. The actual input 
value of the EMF system is coupled with a d-component output of an EMF 
computer of the field-oriented control system. The integral portion of the 
PI controller for this EMF control system represents the rotational speed, 
including the slip frequency correction. The absolute value of slip 
frequency correction is practically negligible at lower speeds. In this 
manner, the EMF control system delivers a good estimated value for the 
speed at medium and higher speeds. 
The EMF computer, which computes an EMF actual space vector as a function 
of the actual current component, the setpoint voltage component, and the 
machine parameters uses the so-called "voltage model." Since this voltage 
model is very inaccurate at low frequencies because of the low absolute 
value of the motor voltage, field-oriented operation at speeds approaching 
zero is not easily accomplished. At zero frequency, this process is no 
longer useable. In particular, reversing without undesired changes in 
torque is very difficult. Also, strategies for starting up from rest, and 
for decelerating to rest, must be found. 
There are various conventional methods of implementing sensorless operation 
of asynchronous machines. At medium and higher speeds, sensorless 
operation using the conventional methods of field-oriented control may be 
used satisfactorily. There are various approaches for lower frequencies. 
A method for sensorless field-orientation of rotating-field machines down 
to frequency zero is described in the article "Feldorientierung der 
geberlosen Drehfeldmaschine," (Field-orientation for sensorless 
rotating-field machines) which appeared in the German periodical "etz", 
issue 21, 1995, pages 14-23. In this method, dynamic current signals are 
injected into the flux-forming current component of the stator current. 
This injection has little dynamic influence on the torque produced. In 
stationary operation, the model works perfectly. The effect of this 
excitation is evaluated in the measured machine voltages and currents. The 
position of the rotor flux axis may be estimated using the saturation 
characteristics of the rotor leakage, which assures field-orientation. 
This procedure must be replaced by an appropriate field-oriented control 
system in the upper rotational speed ranges, since it can only be used in 
the saturation range of the rotor leakage, and it also requires a 
sufficient voltage reserve to supply the test signal. The machine used 
must have a distinct rotor current saturation characteristic. The 
implementation of this method is very expensive and computation-intensive 
because of the required vector transformation. 
The article "High-dynamic AC machine control without speed or position 
sensor," ETEP, vol. 6, #1, January-February 1996, pp. 47-51, describes a 
method in which the voltage model of the machine is supported by the 
current model at low frequencies. The dynamics of this model are limited 
by the rotor time constant of the machine. Additionally, the current model 
does not produce the proper flux angle necessary for orientation, but 
rather only the rotor flux amplitude. Because of this, it is suitable, for 
this application, only as an observer of parameter compliance for the 
voltage model. Using this method, it is possible, in principle, to 
approach zero rpm and eliminate the effects of thermally-caused 
fluctuations in the stator resistance. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide a method and a device for 
controlling a sensorless, field-oriented asynchronous machine allowing it 
to decelerate down to zero rotational speed. 
Another object of the present invention is to start the sensorless, 
field-oriented asynchronous machine up from zero rotational speed. 
Additionally, the method in accordance with the present invention may be 
expandable so as to make reversing possible without undesired changes in 
torque. 
Based on a field-oriented control with an EMF control system and a 
pre-control system, the PI controller of an EMF control system is 
deactivated, and its output signal gradually set to zero at a stator 
frequency of less than or equal to a first limit frequency, determined as 
a function of a calculated d-component of a calculated space vector and a 
calculated slip frequency. The value of the first limit frequency is much 
smaller than the nominal slip of the sensorless, field-oriented 
asynchronous machine. At stator frequencies less than or equal to this 
first limit frequency, operation takes place with very small setpoint 
torque values, which corresponds to a breakaway torque of a drive 
configuration where no noticeable loss is detectable as a result of the 
deactivation of the EMF control system with delayed setting to zero of its 
integral component. 
In an advantageous method according to the present invention, the output 
signal of the EMF control system for a calculated stator frequency greater 
than the first limit frequency is limited to zero from one direction as a 
function of a setpoint rotational direction. In this manner, only positive 
estimated values (output signals) of the PI controller of the EMF control 
system are forwarded to calculate the stator frequency for a positive 
setpoint rotational direction. Thus, malfunction of the EMF control system 
is prevented in the range of inaccurate voltage calculation. 
The dynamics of the PI controller of the EMF control system, and therefore 
the estimated speed value, are limited because of the gain that can be 
achieved. When the machine is operating under load, the dynamics are 
completely sufficient. They are determined by the resulting moment of 
inertia at the motor output (moments of inertia of the transmission, 
slope, drive mass, etc.). 
In another advantageous method according to the present invention, in order 
to prevent gross errors in orientation in the event of load shedding due 
to insufficient dynamics of the PI controller of the EMF control system, 
the torque-forming setpoint current component is limited as a function of 
a calculated deviation of an actual acceleration value from a setpoint 
acceleration value. This value may be so selected that the acceleration 
limitation only is effective at other than regular operating points. 
The above-described method allows proper startup and operation over the 
entire speed range. During braking operations in motor vehicles, the 
braking torque is reduced to zero as a function of the rotational speed 
until the vehicle comes to rest in order to assure a smooth stop. In this 
manner, the method in accordance with the present invention may also be 
used for this application. 
During a dynamic direction of rotation reversal (reversing during 
operation), the stator frequency zero crossing must be controlled with a 
given torque. Using the above-described method, this operation cannot be 
performed satisfactorily. 
The object of reversing without undesired changes in torque may be achieved 
in accordance with the present invention in that, with the previously 
described field-oriented control in reversing the setpoint direction of 
revolution starting from a second limit frequency whose value is greater 
than the value of the first limit frequency, the speed point zero is 
crossed in a controlled manner, so that the model speed is modified as a 
function of the actual acceleration value determined at the second limit 
frequency. 
Due to the fact that the EMF control PI controller output signal of the EMF 
control system is controlled within the rpm range between the positive and 
negative values of the second limit frequency as a function of the actual 
acceleration value determined at the time when this limiting frequency is 
reached, the stator frequency passes through zero rpm controlled with a 
given torque. 
In an advantageous method according to the present invention, changes in 
the setpoint values of the torque selection are converted into equivalent 
actual acceleration values during the controlled zero crossing. In this 
manner, changes in torque may also be made during this operation.

DETAILED DESCRIPTION 
FIG. 1 shows a block circuit diagram of a device for carrying out the 
method according to the present invention for control of a sensorless, 
field-oriented asynchronous machine. This device includes a space vector 
modulator 4 and a field-oriented control system 2 which includes an 
input-side transformer 6, an EMF computer 8, a pre-control network 10, a 
current control circuit 12, an EMF control system 14, and an output-side 
coordinate converter 16. The measured phase currents i.sub.R and i.sub.S 
are transformed into flux- and torque-forming actual current components 
i.sub.d and i.sub.q by means of the input-side transformer 6, which 
contains a coordinate converter 18 and a vector rotator 20, and a 
calculated flux position .gamma..sub.S. These actual current components 
i.sub.d and i.sub.q are each passed to a comparator 22 and 24 in the 
current control circuit 12, at whose non-inverting inputs setpoint current 
components i*.sub.d and i*.sub.q are formed. At the output, comparators 
22, 24 are coupled with current controllers 26, 28, whose outputs are 
connected to adders 30, 32, respectively. These current controllers 26, 28 
are supported by the pre-control network 10 in that the pre-control 
network 10 calculates pre-control values u*.sub.d and u*.sub.q as a 
function of the setpoint current components i*.sub.d and i*.sub.q, and 
parameters of the asynchronous machine (stator resistance R.sub.s, leakage 
inductance L.sub..sigma., a calculated stator frequency .omega..sub.S, and 
a setpoint flux .PSI.*). These pre-control values u*.sub.d and u*.sub.q 
are each sent to the corresponding adders 30 and 32. In this manner, 
current controllers 26 and 28 now deliver voltages .DELTA.u.sub.d and 
.DELTA.u.sub.q, also known as controller manipulated variables which are 
not calculated by pre-control network 10 (such as, e.g., dynamic 
components, faults, etc.). The outputs of the two adders 30 and 32 are 
passed to the output-side coordinate converter 16. Using this coordinate 
converter 16, orthogonal components u.sub.d and u.sub.q of the manipulated 
variable space vector u are converted into polar components 
.vertline.u.vertline. and .epsilon..sub.u. The absolute value component 
.vertline.u.vertline. is normalized using a divider 34 at whose second 
input there is an input value u.sub.dc of the pulse-controlled inverter. 
The output value m.sub.a of divider 34 is the control value of the 
pulse-controlled inverter. Divider 34 may also be a component of space 
vector modulator 4. Orthogonal manipulated variable components u.sub.d and 
u.sub.q and the actual current components i.sub.d and i.sub.q are supplied 
to the EMF computer 8, to which the machine parameters stator resistance 
R.sub.s, leakage inductance L.sub..sigma., and calculated stator frequency 
.omega..sub.S are also supplied. At the output of EMF computer 8 there is 
a d-component e.sub.d of an EMF space vector e. Since only one component 
e.sub.d exists in the q-axis of the d- and q-coordinate system rotating 
with stator frequency .omega..sub.s for a correct field orientation of EMF 
space vector e, the d-component e.sub.d must equal 0. This d-component 
e.sub.d is supplied to the EMF control system 14, at whose second input 
the setpoint d-component e'.sub.d is present, which is equal to 0. This 
EMF control system 14 includes a comparator 36 and a PI controller 38. 
In this field-oriented controller 2 without a sensor, the imaginary 
component of PI controller 38 of EMF control system 14 forms an estimated 
value .omega. of the speed of the asynchronous motor. This estimated value 
.omega. is added to a calculated slip frequency setpoint value 
.omega.*.sub.r from an adder 40. This calculated slip frequency setpoint 
value .omega.*.sub.r is present at the output of a multiplier 42, at whose 
inputs a torque-forming setpoint current component i*.sub.q and a quotient 
from rotor resistance R.sub.r and setpoint flux .PSI.* are present. Stator 
frequency .omega..sub.s is obtained from the sum of this calculated slip 
frequency setpoint value .omega.*.sub.r and estimated value .omega. 
inputted to a multiplier 44, at whose second input the number of pairs of 
poles f.sub.p of the motor appears; whereby the conversion of the 
mechanical speed to the electrical stator frequency .omega..sub.s is 
produced. 
This stator frequency .omega..sub.s is also supplied to space vector 
modulator 4. This space vector modulator 4 includes an angular integrator 
46, an adder 48, and an arithmetic unit 50. By means of angular integrator 
46 and stator frequency .omega..sub.s, flux angle .gamma..sub.s is 
obtained in the stator-oriented coordinate system which is added to the 
position .epsilon..sub.u of manipulated variable space vector u in the 
flux-oriented coordinate system. The sum of these two angles .gamma..sub.s 
and .epsilon..sub.u is the position .alpha..sub.u of the manipulated 
variable space vector u in the stator-oriented coordinate system. The 
control signals S.sub.1 . . . S.sub.6 for the pulse-controlled inverter 
are obtained from the signals m.sub.a (control value) and .alpha..sub.u 
(position of the manipulated variable space vector u). 
The above-described field-oriented control system 2 for an induction 
machine is described in the aforementioned International Application No. 
WO 95/03649. The control method performed using the field-oriented control 
system 2 is the two-component current control method. International 
Application No. WO 95/03649 makes a reference to an arithmetic unit 50 and 
a pre-control network 10, which is also known as a decoupling network. 
This two-component current controller is expanded to include a shunt arm 52 
which adds controller manipulated variable .DELTA.u.sub.q of current 
controller 20 to the controller manipulated variable .DELTA.u.sub.d of 
current controller 26 by means of an adder 56 through a delaying mechanism 
54. Multipliers 58, 60 are connected in series to each of the inputs of 
shunt arm 52; coefficients .tau. and k appear at the second input of the 
first multiplier 58, and the frequency value of the first multiplier 58 
appears at the second input of the second multiplier 60; the output of 
second multiplier 60 is connected to delaying mechanism 54. By introducing 
this shunt arm, the output of current controller 28 does not only change 
the effective voltage (as in the case of two-component current control), 
but also causes the voltage vector to rotate by changing the reactance 
voltage (as in the case of effective current control). At the same time, 
shunt arm 52 also causes a situation in which a change in the controller 
manipulated variable .DELTA.u.sub.q does not affect the reactive voltage; 
i.e., the control circuits are decoupled. Thus, the slow compensating 
processes typical of the two-component control system with a detuned 
pre-control network 10 no longer occur. For ideal decoupling, the time 
constant .tau. of the delaying mechanism 54 must be selected to be equal 
to the short-circuit time constant of the motor, and the gain k must be 
changed proportionally to the stator frequency. This shunt arm 52 is 
described in detail in European Patent No. 0 633 653 A1, so that it will 
not be explained in more detail here. 
This field-oriented control system 2 features another comparator 62 whose 
output is coupled with a device 64 which deactivates PI controller 38 of 
EMF control system 14 and reduces the integral component of this PI 
controller 38 to zero with a delay. This device 64 is a component of EMF 
control system 14. The inputs of comparator 62 receive a first limit 
frequency f.sub.1 and calculated stator frequency .omega..sub.s. As soon 
as stator frequency .omega..sub.s becomes less than or equal to the first 
limit frequency f.sub.1, device 64 is activated. This device 64 
deactivates PI controller 38 of EMF control system 14, and sets its 
integral component to zero with a delay. In this manner, the estimated 
value .omega. and thus the stator frequency .omega..sub.s slowly drop to 
zero. A value considerably less than setpoint slip frequency 
.omega.*.sub.rn (f.sub.1 .ltoreq.30% .omega.*.sub.rn) is set as the first 
limit frequency f.sub.1. 
By means of this expansion of the field-oriented control 2 of a sensorless, 
field-oriented asynchronous machine, this asynchronous machine may be 
decelerated gradually to zero rpm. Additionally, this asynchronous machine 
can start up from zero rpm. When starting up from zero up to the first 
limit frequency f.sub.1, EMF control system 14 is blocked, so that the 
stator frequency .omega..sub.s is equal to the calculated slip frequency 
.omega.*.sub.r. When the first limit frequency f.sub.1 is exceeded, device 
64 is again deactivated, so that the PI controller 38 of the EMF control 
system 14 becomes active again. 
FIG. 2 shows a block circuit diagram of a second embodiment of the device 
for carrying out the procedure according to the present invention to 
control a sensorless, field-oriented asynchronous machine. This embodiment 
differs from the embodiment in FIG. 1 in that a device 66 to limit the 
output signal .omega. of PI controller 38 of EMF control system 14 is 
connected downstream from EMF control system 14. This device 66 is also 
supplied with a setpoint rotating direction S*.sub.dir. Furthermore, an 
additional input of this device 66 is connected to an output of a 
converter 74, whose input is connected to a d-output of EMF computer 8. At 
the output of this converter 74, an actual acceleration value S.sub.acc 
arises which is determined from the d-component of a calculated EMF space 
vector e. For reasons of clarity, comparator 62 and device 64, which are 
preferably components of the EMF control system 14, are not explicitly 
illustrated. By means of device 66, the estimated value .omega. of EMF 
control system 14 is limited to zero from one direction. The estimated 
value .omega. that is limited depends on the setpoint rotational direction 
S*.sub.dir. For a positive setpoint rotational direction S*.sub.dir, only 
positive values of the estimated value .omega. are forwarded. In this 
manner it is achieved that, after PI controller 38 of EMF control system 
14 is active again, errors in EMF control 14 resulting from the still 
inaccurate voltage calculation are not used to determine stator frequency 
.omega..sub.s. 
The dynamics of PI controller 38 of EMF control system 14, and therefore 
the estimated value .omega., are limited because of the gain that can be 
achieved. When the asynchronous machine is under load, the dynamics of 
this EMF control system 14 is sufficient, and determined by the resulting 
moment of inertia at the motor output (moments of inertia of the 
transmission, grade, vehicle mass, etc.). 
In order to prevent high incorrect orientation of the control system in the 
event of load change near frequency zero as a result of inadequate 
dynamics of PI controller 38, device 66 is provided with an actual 
acceleration value S.sub.acc as shown in FIG. 3. FIG. 3 shows an 
additional advantageous embodiment of the device for carrying out the 
method of the present invention for controlling a sensorless, 
field-oriented asynchronous machine. Additionally, this actual 
acceleration value S.sub.acc is supplied to an acceleration control device 
68 whose output is coupled with an adder 72 through limiting device 70. 
The actual acceleration value S.sub.acc is determined by a converter 74 
from d-component e.sub.d of EMF space vector e. 
Acceleration control device 68 features an absolute value former 76, a 
comparator 78, and a PI controller 80. Absolute value former 76 is 
arranged at the input and receives at its input the calculated actual 
acceleration value S.sub.acc. The output of this absolute value former 76 
is connected to an inverting input of comparator 78. At its output, this 
comparator 78 is connected to the PI controller 80 of acceleration control 
device 68. The non-inverting input of comparator 78 receives an absolute 
value .vertline.S*.sub.acc .vertline. of acceleration limit value 
S*.sub.acc. The output of PI controller 80 is connected to adder 72 
through limiting device 70. A torque-forming setpoint current component 
i*.sub.q is provided at the second input of adder 72. The output of adder 
72 is connected to an input of device 66 and to components 42, 10, and 24 
of the field-oriented control system 2. 
From the calculated actual acceleration value S.sub.acc, absolute value 
.vertline.S.sub.acc .vertline. is formed by absolute value former 76 of 
acceleration control system 68. This absolute value .vertline.S.sub.acc 
.vertline. is compared with the absolute value .vertline.S.sub.acc 
.vertline. of an acceleration limit amount S*.sub.acc by comparator 78. As 
long as the actual acceleration absolute value .vertline.S.sub.acc 
.vertline. is less than the acceleration absolute value limit 
.vertline.S*.sub.acc .vertline., a positive output voltage of PI 
controller 80 is not forwarded to adder 72 because of limiting device 70. 
If the actual acceleration absolute value .vertline.S.sub.acc .vertline. 
is greater than the acceleration absolute value limit .vertline.S*.sub.acc 
.vertline., the torque-forming setpoint current component i*.sub.q will be 
reduced until the actual acceleration absolute value .vertline.S.sub.acc 
.vertline. is equal to the acceleration absolute value limit 
.vertline.S*.sub.acc .vertline.. 
This acceleration controller 68 allows avoidance of gross incorrect 
orientation of this controller 2 which may arise from inadequate dynamics 
of PI controller 38 of EMF control system 14 in the event of load 
shedding. 
FIG. 3 also shows that the actual acceleration value S.sub.acc and the 
torque-forming setpoint current component i*.sub.q are also supplied to 
device 66 for limitation of output signal .omega. of PI controller 38 of 
EMF control system 14. Furthermore, a second limit frequency f.sub.2, 
whose value is greater than that of the first limit frequency f.sub.1, is 
supplied to this device 66. 
Since field-oriented controller 2 is based on a microprocessor, components 
62, 64, 66, 68, 70, 72, and 74 are also based on microprocessors. This 
means that the existing software for conventional known field-oriented 
control system 2 is expanded by at least one additional program. Device 66 
includes modules as follows: comparator, device for controlled 
modification of the estimated value .omega., and arithmetic unit to 
accomplish its task of limiting the output signal .omega. of the EMF 
control system 14 as a function of input signals S.sub.acc, f.sub.2, and 
i*.sub.q. The calculated stator frequency .omega..sub.s and the value of 
the second limit frequency f.sub.2 are supplied to the comparator. The 
output signal from the comparator is supplied to the device for controlled 
modification of the estimated value .omega., at whose second input an 
actual acceleration value S.sub.acc is received. The arithmetic unit 
calculates an actual moment of inertia as a function of the calculated 
actual acceleration value S.sub.acc (f.sub.2) at the time of the second 
limit frequency f.sub.2 and the torque-forming setpoint current component 
i*.sub.q. This moment of inertia is supplied to the device for controlled 
modification of the estimated value .omega.. This new actual value for the 
moment of inertia is then used for the modification of the estimated value 
.omega. if setpoint value changes appear in the torque selection during 
the controlled transition through the speed point zero. These changes in 
the torque selection can be recalculated into equivalent acceleration 
values by means of the arithmetic unit. 
In the event of a dynamic rotational direction reversal indicated by a 
change in the sign of the setpoint rotational direction s*.sub.dir as soon 
as the stator frequency .omega..sub.s drops below the second limiting 
frequency f.sub.2, the actual value of the moments of inertia existing at 
that time remains constant. The estimated value .omega. of the EMF control 
system 14 is controlled as a function of the actual acceleration value 
S.sub.acc (f.sub.2) in such a manner that the zero point is crossed. The 
limiting side that is opposite this rotational direction is dynamically 
limited to zero in accordance with the new setpoint rotational direction 
S*.sub.dir. 
For example, when a reversing sequence (dynamic rotational direction 
reversal) occurs at a time when stator frequency .omega..sub.s is greater 
than the positive value of the limit frequency f.sub.2 and the setpoint 
rotational direction S*.sub.dir is positive, then the setpoint rotational 
direction S*.sub.dir and the torque-forming setpoint current component 
i*.sub.q change their signs. In this manner, the stator frequency 
.omega..sub.s is reduced together with the actual moment of inertia value 
and a setpoint torque value. If the stator frequency .omega..sub.s drops 
below the second limit frequency f.sub.2, the instantaneous actual 
acceleration value S.sub.acc remains unchanged. The estimated value 
.omega..sub.s is so controlled as a function of the actual acceleration 
value S.sub.acc (f.sub.2) that the zero point is crossed. Since the sign 
of the setpoint rotational direction S*.sub.dir is negative, the negative 
limit is removed. After the negative value of the limiting frequency 
f.sub.2 has been exceeded, the positive limit is activated. 
Since the actual acceleration value S.sub.acc (f.sub.2) contains both the 
information regarding the attrition inertia and the instantaneous torque, 
and since the inertia is assumed to be constant in the controlled range, 
no undesired changes in torque occur in this controlled range. Based on 
this fact, this torque selection may take place in the event of setpoint 
value changes in the torque selection during the controlled zero point 
crossing. For this purpose, a value of the acceleration may be calculated 
as a function of the constant inertia and the new torque with which the 
estimated value .omega. can then be modified. 
FIGS. 4-7 show various signal curves at startup, reversal, and braking for 
the sensorless operation of a field-oriented asynchronous machine. The 
measurements were conducted on a machine with no load and maximum setpoint 
torque, and therefore show the greatest acceleration that may occur for 
the motor used. 
Using the method according to the present invention and its various 
advantageous embodiments, it is possible to achieve field-oriented control 
of the speed of an asynchronous machine without a sensor, which may be 
gradually slowed down to a standstill and then started up again. 
Additionally, reversing without undesired changes in torque is also 
possible.