Method and apparatus for starting an electric motor

A method and apparatus for controlling an AC motor are described wherein a frequency generator is configured to generate a signal representative of the stator electrical frequency and to estimate the rotor electrical frequency of the motor during operation. The generator operates on torque and flux current reference signals and on d-axis voltage reference and feedback signals to determine the electrical frequencies. The generator ramps up gain values applied to the torque current reference signals and to a voltage error signals representative of the difference between the d-axis voltage reference and feedback signals during a startup phase of operation to enhance performance and stability of the drive during this phase. The generator includes feedforward and feedback portions that contribute components of the final stator frequency signal. The components are filtered differently during startup and running phases of operation to provide the desired frequency signals.

BACKGROUND OF THE INVENTION 
The present invention relates generally to the startup and control of AC 
electric motors. More particularly, the invention relates to a method and 
apparatus for starting an electric motor and for subsequent variable 
frequency field oriented control of an electric motor utilizing a 
frequency generating technique. 
Vector, or field oriented control techniques are generally known for 
variable speed control of industrial AC motors. In general, such 
techniques attempt to determine and apply the proper driving signals to 
the motor to maintain the orientation of "q-axis" rotor flux to zero. In 
one known technique, termed "indirect field oriented control" rotor flux 
is identified by analysis of feedback signals representative of rotor 
shaft position and by estimating slip in the motor. Assuming the slip 
estimate is correct, this analysis permits resolution of the stator 
current into a torque producing or "q-axis" component and a flux 
producing, or "d-axis" component. By knowing and using these components of 
stator current, the motor drive can properly control the amount of current 
applied to the motor so as to respond to changing load requirements, while 
maintaining proper vector orientation (i.e. q-axis rotor flux of zero). 
These techniques generally provide excellent dynamic torque response and 
accurate steady state torque as compared to other approaches, such as slip 
controlled drives. 
A difficulty in known field oriented motor controllers arises from thermal 
variation of motor parameters. When not properly accounted for, such 
variations can substantially degrade the performance of the controller, 
resulting in a slip controlled drive. Various solutions have been proposed 
to account for thermal variations to achieve field oriented control. In 
one known technique, motor voltage is sensed and used as a basis for 
adapting for thermal variation of rotor resistance, and the d-axis 
component of motor voltage is used to identify the slip gain necessary to 
orient the q-axis rotor flux to zero. This value of slip gain is then 
multiplied by the torque current command to provide the desired slip 
frequency. The stator electrical frequency is determined using the 
resultant slip frequency value. A rotor shaft encoder provides feedback of 
rotor position and speed, and the rotor electrical frequency can be 
calculated based upon this speed and the rated motor frequency and number 
of pole pairs. Finally, the stator electrical frequency can be determined 
from the rotor electrical frequency and the slip frequency. The resulting 
stator electrical frequency is then used to control stator current so as 
to maintain the desired orientation of the q-axis component of rotor flux 
and achieve field oriented control. An example of a field oriented motor 
controller of this type is described in U.S. Pat. No. 5,032,771 issued on 
Jul. 16, 1991 to Kerkman et at., and hereby incorporated herein by 
reference. 
While such controllers do achieve superior field oriented control, they are 
not without drawbacks. For example, because sensed values of rotor 
position and speed are used to determine rotor electrical frequency, 
feedback signals must be generated by encoders or similar feedback devices 
and continuously analyzed. While attempts have been made to provide 
sensorless field oriented control, many have resulted in drives having 
poor dynamic performance. Moreover, certain known control implementations 
comprise inaccurate or low bandwidth current controllers, and inadequately 
compensate for second order effects such as power switching device 
characteristics, and thus do not achieve field oriented control. 
Another difficulty in such control devices is the proper adjustment of 
control parameters, including system gains, bandwidths and the like during 
the various phases of operation. For example, depending upon the technique 
employed to control the motor, certain system gains must be adjusted with 
respect to one another in order to achieve proper torque during starting, 
while maintaining system stability and proper field orientation. These 
difficulties become particularly troublesome for drives designed to 
operate without speed feedback signals from the driven motor. 
There is a need, therefore, for an improved controller for driving AC 
motors that is capable of providing smooth and stable starting in addition 
to sensorless field oriented control. In particular, there is a need for a 
motor controller that is capable of properly adjusting key system gains 
and bandwidths in order to achieve the desired level of control both 
during startup and subsequent running of the motor. 
SUMMARY OF THE INVENTION 
The invention features a novel technique for controlling an AC electric 
motor designed to respond to these needs. The technique generates stator 
frequency directly from a feedback voltage and a reference voltage in the 
synchronous reference frame without recourse to sensed speed feedback 
signals. The frequency generator includes a feedforward portion and a 
feedback portion, each generating frequency-related signals that are 
combined to determine the stator frequency. The generator is configured to 
properly adjust or adapt system gains and bandwidths with respect to one 
another during startup of the motor and for subsequent steady state 
operation. The resulting field oriented control offers excellent low speed 
adjustability as well as stable performance during startup. 
Thus, in accordance with a first aspect of the invention, a method is 
provided for starting an alternating current electric motor having a 
stator and a rotor. The method comprises the steps of generating a first 
component of an electrical frequency signal from a voltage reference 
signal, a voltage feedback signal, and a current reference signal, and 
generating a second component of the electrical frequency signal from the 
first component and from the current reference signal. The first and 
second components of the frequency signal are filtered in a first manner 
during a startup phase of operation of the motor, and a filtered in a 
second manner following the startup phase of operation. The components are 
then combined to generate the electrical frequency signal as a basis for 
generating control signals for driving the motor. 
In accordance with another aspect of the invention, a method is provided 
for control of an alternating current electric motor having a rotor and a 
stator. The method includes the steps of generating a torque current 
command signal representative of a desired current and multiplying the 
current command signal by a first gain value. A d-axis voltage command 
signal representative of a desired voltage and a d-axis voltage feedback 
signal representative of actual voltage applied to the motor are also 
generated and are combined to generate a voltage error signal. The voltage 
error signal is multiplied by at least a second gain value and the signals 
produced by applying the first and second gain values to their respective 
signals are combined to generate a frequency signal as a basis for 
regulating control signals for driving the motor. The first and second 
gain values are then increased as the motor increases speed during a stamp 
phase of operation. 
The invention also provides an apparatus for controlling an electric motor 
including a power circuit, regulating circuitry, feedback circuitry and 
control circuitry. The power circuit includes an inverting circuit for 
converting direct current power to controlled alternating current power 
for driving the motor in response to control signals. The regulating 
circuitry is configured to generate current reference signals 
representative of desired current levels. The feedback circuitry is 
configured to generate voltage feedback signals representative of voltage 
applied to the motor. The control circuitry is coupled to the power 
circuit, the regulating circuit and the feedback circuit. The control 
circuit is configured to receive the current reference signals and the 
voltage reference signals and to generate the control signals for 
converting the direct current power to controlled alternating current 
power. The control circuitry includes a frequency generator configured to 
generate the stator electrical frequency signal in a first manner during a 
startup phase of operation of the motor and in a second manner following 
the startup phase of operation.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Turning now to the drawings and referring to FIG. 1, a controller 10 for 
driving a motor 12 is illustrated diagrammatically. Controller 10 includes 
a power converter circuit 14 designed to be coupled to a source of 3-phase 
AC power 16 and configured to rectify the AC power from the source and to 
convert the AC power to constant magnitude DC power that is output from 
converter circuit 14 over a DC bus 18. Controller 10 also includes an 
inverter circuit 20 coupled to converter circuit 14 via the DC bus 18 for 
generating DC power transmitted over bus 16 to voltage, frequency and 
current controlled AC power for driving motor 12. Inverter circuit 20 
typically includes an array of solid state switching devices, such as 
IGBT's, that are switched between conducting and non-conducting states in 
response to control signals to generate the controlled AC power in the 
form of pulse-width-modulated (PWM) signals of fixed magnitude and varying 
pulse width approximating sinusoidal AC power waveforms, in a manner 
generally known in the art. These controlled AC power waveforms are then 
transmitted to motor 12 via a, b and c phase conductors 22, 24 and 26 to 
drive motor 12 at desired speeds and in response to varying loads. Power 
converter circuit 14 and inverter circuit 20 may conveniently be formed on 
a power substrate board (not shown) and electrically coupled via 
conductive traces forming DC bus 18. 
Signals for switching elements of inverter circuit 20 are applied to 
circuit 20 by a PWM command circuit 28 in response to functional circuits 
configured to convert command and feedback signals to control signals as 
described below. Certain of the functional circuits, preferably configured 
in an appropriately programmed microprocessor, are illustrated 
diagrammatically in FIGS. 1, 2 and 3. These include a flux regulating 
circuit 30, a speed regulating circuit 32, a synchronous-to-stationary 
transformation circuit 34, a current regulating circuit 36, a two-to-three 
phase transformation circuit 38, phase signal generating circuit 40, 
three-to-two phase transformation circuits 44 and 46, 
stationary-to-synchronous transformation circuit 48, and motor model and 
frequency generator circuit 50. The operation of these functional circuits 
will be described in greater detail below. 
In the following description of motor controller 10, the following 
nomenclature will be used to refer to the various signals and values 
generated by the functional circuitry of controller 10 for controlling the 
speed and torque of motor 12: 
______________________________________ 
q-axis quadrature axis component of various parameters (for the 
present purposes, where field orientation is maintained, the 
q-axis component of stator current corresponds to a torque 
producing current component; the use of q-axis nomenclature 
with respect to voltage signals is defined below with reference 
to equation (13)); 
d-axis direct axis component of various parameters (90 degrees 
lagging the q-axis; for the present purposes, where field 
orientation is maintained, the d-axis component of stator 
current corresponds to a flux producing current component; 
the use of d-axis nomenclature with respect to voltage signals 
is defined below with reference to equation (11)); 
fe stator electrical frequency; 
fr rotor electrical frequency; 
f' intermediate frequency signal; 
fe.sub.-- ave 
filtered stator frequency; 
fr.sub.-- ave 
filtered rotor frequency estimate; 
fe.sub.-- base 
rated frequency; 
Gn non-linear gain; 
ias.sub.-- fbk 
stationary reference frame current of a phase; 
ibs.sub.-- fbk 
stationary reference frame current of b phase; 
ics.sub.-- fbk 
stationary reference frame current of c phase; 
ide synchronous reference frame current of d-axis; 
i*de command current for d-axis in synchronous reference frame; 
i*ds command current for d-axis in stationary reference frame; 
iqe synchronous reference frame current of q-axis; 
i*qe command current for q-axis in synchronous reference frame; 
i*qs command current for q-axis in stationary reference frame; 
kff feed forward gain; 
ki integral gain; 
kp proportional gain; 
ks slip gain; 
Lm magnetizing inductance; 
Lr rotor inductance; 
Ls stator inductance; 
rs stator resistance; 
U switching control signals for generating a controlled PWM 
waveform; 
V*as command stationary reference frame voltage of a phase; 
Vas.sub.-- fbk 
feedback stationary reference frame voltage of a phase; 
V*bs command stationary reference frame voltage of b phase; 
Vbs.sub.-- fbk 
feedback stationary reference frame voltage of b phase; 
V*cs command stationary reference frame voltage of c phase; 
Vcs.sub.-- fbk 
feedback stationary reference frame voltage of c phase; 
V*de model reference voltage for d-axis in synchronous 
reference frame; 
Vde.sub.-- fbk 
feedback voltage for d-axis in synchronous reference frame; 
V*ds command stationary reference frame voltage for d-axis; 
Vds.sub.-- fbk 
stationary reference frame voltage feedback of d-axis; 
Vqe synchronous reference frame voltage of q-axis; 
Vqe.sub.-- fbk 
synchronous reference frame voltage feedback for q-axis; 
V*qs command stationary reference frame voltage of q-axis; 
Vqs.sub.-- fbk 
stationary reference frame voltage feedback of q-axis; 
.theta.e 
stator electrical angular position used in reference frame 
transformations; 
.lambda.de 
d-axis stator flux; 
.lambda.qe 
q-axis stator flux; 
.lambda.qr 
q-axis rotor flux; 
.sigma. 
inductance factor; 
.omega..sub.-- fbk 
speed (frequency) feedback. 
______________________________________ 
As illustrated in FIG. 1, command inputs to controller 10 include a voltage 
reference signal V*q for the q-axis and a speed reference signal .omega.*. 
Voltage reference signal V*q is determined by an autocommissioning 
procedure, such as by reference to a saturation curve for motor 12 or 
application of no-load current to motor 12. Speed reference signal 
.omega.* is set to a desired value by an operator, such as via a human 
interface module (not shown), or by a system controller or network with 
which controller 10 is interfaced. Flux regulating circuit 30 receives 
voltage reference signal V*q as well as a q-axis voltage feedback signal 
Vqe.sub.-- fbk and converts these signals to a d-axis current command 
signal i*de in the synchronous reference frame. Operation of flux 
regulating circuit 30 is described in greater detail in U.S. Pat. No. 
5,032,771, mentioned above, and U.S. Pat. No. 5,479,081, assigned to the 
assignee of the present invention and hereby incorporated herein by 
reference. In general, i*de is a fixed value within a constant torque 
operating range of motor 12. Speed regulating circuit 32 receives speed 
reference signal .omega.* as well as a speed feedback signal 
.omega..sub.-- fbk, and converts these signals to a q-axis current command 
signal i*qe in the synchronous reference frame. The operation of speed 
regulating circuit 32 is described in greater detail in U.S. Pat. No. 
5,032,771. In general, speed regulating circuit 32 is a closed loop PI 
controller of a type well known in the art. As will be appreciated to 
those skilled in the art, it should also be noted that, while for the 
purposes of the present description the current reference signal for the 
q-axis is generated by circuit 32 based upon a speed input, the q-axis 
current reference signal could also be based upon a frequency input or 
upon a torque input value. Current reference signals i*de and i*qe are 
then applied to synchronous-to-stationary transformation circuit 34 for 
conversion into the stationary reference frame in accordance with the 
following relationships: 
##EQU1## 
where .theta.e is the stator electrical angular position determined from 
the generated frequency fe as described below. Thus, transformation 
circuit 34 generates output signals i*ds and i*qs representative of 
command current for the d and q axes, respectively, in the stationary 
reference frame. 
The command current values generated by transformation circuit 34 are 
applied to current regulating circuit 36 for conversion into command 
voltages for the d and q axes in the stationary reference frame, V*ds and 
V*qs, respectively. For generating the required command voltage signals, 
current regulating circuit 36 receives a generated frequency signal fe 
from model and generating circuit 50, and current feedback signals for the 
d and q axes, ids.sub.-- fbk and iqs.sub.-- fbk. The generation of 
frequency signal fe will be described in greater detail below, with 
particular reference to FIGS. 2 and 3. The generation of current feedback 
signals ids.sub.-- fbk and iqs.sub.-- fbk are described below. The 
operation of and calculations performed by current regulating circuit 36 
are described in greater detail in U.S. Pat. No. 4,706,012, assigned to 
the assignee of the present invention and hereby incorporated herein by 
reference. 
From current regulating circuit 36, command voltage signals V*ds and V*qs 
are applied to two-to-three phase transformation circuit 38. 
Transformation circuit 38 converts the command voltage signals from d- and 
q-axes based signals into stationary reference frame voltage command 
signals for 3O three phases a, b and c in accordance with the following 
relationships: 
##EQU2## 
The stationary reference frame voltage command signals V*as, V*bs and V*cs 
are applied to PWM command circuit 28 for conversion into switching 
command signals, designated generally by the letter U, for altering the 
conductive state of switching devices within inverter circuit 20. The 
operation of PWM command circuit 28 is generally known in the art. In 
general, circuit 28 generates high frequency switching command signals 
timed to produce pulse-width-modulated output waveforms for the a, b and c 
phases that approximate sinusoidal AC power signals of a frequency, 
voltage and current level required to drive motor 12 at desired speeds. 
These controlled PWM output waveforms for the three electrical phases are 
then transmitted to motor 12 via conductors 22, 24 and 26. It should be 
noted that controller 10 could be configured differently from the 
preferred structure described above while nevertheless implementing the 
frequency generating and estimating techniques described herein. For 
example, circuits 34, 36 and 38 may be configured to control voltage 
rather than regulating current. 
Feedback signals required for operation of controller 10 are based upon 
sensed levels of voltage and current. As illustrated in FIG. 1, current 
feedback signals ias.sub.-- fbk and ics.sub.-- fbk are sensed from the 
corresponding conductors for these phases, 22 and 26, respectively. These 
current feedback signals are applied to phase signal generating circuit 40 
wherein a signal representative of the current in the third phase is 
derived from the relationship: 
EQU ibs.sub.-- fbk=-ias.sub.-- fbk-ics.sub.-- fbk. (5) 
The three phase current feedback signals are then applied to three-to-two 
phase transformation circuit 44 for resolution into current feeback 
components for the d and q axes in the stationary reference frame, 
ids.sub.-- fbk and iqs.sub.-- fbk, respectively, in accordance with the 
relationships: 
##EQU3## 
These current feedback signals are then applied to current regulating 
circuit 36 for use in generating d- and q-axes voltage command signals 
V*ds and V*qs. 
Voltage feedback signals for the a, b and c phases are generated from 
voltage sensed in conductors 22, 24 and 26, respectively. These sensed 
voltages, Vas.sub.-- fbk, Vbs.sub.-- fbk and Vcs.sub.-- fbk are applied to 
three-to-two phase transformation circuit 46 for resolution into voltage 
feedback signals for the d and q axes in the stationary reference frame in 
accordance with the relationships: 
##EQU4## 
To facilitate the control and generation functions of motor model and 
frequency generator circuit 50 voltage feedback signals for the d and q 
axes are converted to the synchronous reference frame by transformation 
circuit 48, in accordance with the relationships: 
##EQU5## 
The voltage feedback signal for the d-axis, Vde.sub.-- fbk, is then 
applied to motor model and frequency generator circuit 50, while the 
q-axis voltage feedback signal, Vqe.sub.-- fbk, is applied to flux 
regulating circuit 30 for use in generating the d-axis current command 
signal i*de. 
As illustrated diagrammatically in FIG. 2, motor model and frequency 
generator circuit 50 generally includes two functional circuits, motor 
model 52 and frequency generator 54. Motor model and frequency generator 
circuit 50 receives as inputs current command signals i*de and i*qe, and 
feedback voltage signal Vde.sub.-- fbk, and generates as output signals 
the stator electrical frequency fe and an estimated speed (or frequency) 
feedback signal .omega..sub.-- fbk. However, within circuit 50, motor 
model 52 determines a d-axis reference voltage signal V*de from the 
command current signals and from a filtered stator frequency signal 
generated by frequency generator 54. In turn, frequency generator 54 
receives the d-axis reference voltage signal V*de from model 52, the 
q-axis command current signal i*qe and the d-axis voltage feedback signal 
Vde.sub.-- fbk, and produces the frequency signal fe and speed feedback 
signal .omega..sub.-- fbk, as well as the filtered frequency signal 
fe.sub.-- ave required by model 52. 
In the presently preferred embodiment of controller 10, motor model 52 
generates reference voltage signal V*de based upon the following 
relationship: 
EQU V*de=(rs)*(i*de)!-(2.pi.*fe.sub.-- 
ave)*.sigma.*Ls*(i*qe)!=rs*(i*de)!-2.pi.*fe.sub.-- ave*.lambda.qe!.(11) 
The value of a may be determined from the following relationship: 
(12) 
In the presently preferred embodiment, the values of rs and a being 
predetermined from an autocommissioning procedure that is generally beyond 
the scope of the present invention. In addition, it should be noted that 
the value of the q-axis voltage signal Vqe may be determined based upon 
the relationship: 
EQU Vqe=rs*iqe!+2.pi.*fe.sub.-- ave*Ls*ide!=rs*iqe!+2.pi.*fe.sub.-- ave* 
.lambda.de!. (13) 
As illustrated in FIGS. 2 and 3, frequency generator 54 generally includes 
a feed forward portion 56, a feedback portion 58, a converter circuit 60 
and a filter circuit 62. Feed forward portion 56 of generator 54 derives 
an intermediate frequency signal f' from the q-axis current command signal 
i*qe, the d-axis feedback voltage signal Vde.sub.-- fbk and the model 
reference voltage V*de as described below. Feedback portion 58 derives 
stator electrical frequency fe from intermediate frequency signal f' and 
from the q-axis current command signal i*qe. Feedback portion 58 also 
produces a filtered rotor frequency estimate fr.sub.-- ave that is used by 
converter 60 as a basis for generating speed feedback signal 
.omega..sub.-- fbk. Moreover, intermediate frequency signal f' is filtered 
by circuit 62 and algebraically combined with the filtered rotor frequency 
estimate at a summer 64 to produce filtered stator frequency fe.sub.-- 
ave. 
FIG. 3 diagrammatically illustrates in greater detail the internal signal 
flow between the various functional components of frequency generator 54. 
As shown in FIG. 3, model reference voltage V*de is applied to the feed 
forward portion 56 of generator 54 and the difference between this signal 
and the d-axis feedback voltage signal Vde.sub.-- fbk is determined by a 
summing point 66 to generate an error or difference signal Verr. This 
voltage error signal is applied to a coherence element 67 wherein the 
signal is assigned a positive or negative sign depending upon the value of 
re.sub.-- ave. In particular, if the value of re.sub.-- ave is equal to or 
greater than 0, error signal Verr is multiplied by a weighting factor of 
+1. If the value of fe.sub.-- ave is less than 0, Verr is multiplied by a 
weighting factor of -1 at block 67. The resulting signal is then 
multiplied by a non-linear gain Gn at element 68. In the presently 
preferred embodiment, gain Gn is varied as illustrated in FIG. 4. As shown 
in FIG. 4, the value of Gn is held constant at a value of (fe.sub.-- 
base/fe.sub.-- min) within a first range of values of re, as indicated by 
reference numeral 100, where re.sub.-- base is the rated frequency of 
motor 12 and fe.sub.-- min is a lower frequency determined empirically and 
set to provide the desired response while maintaining stability of 
control. Within a region 102 of operation between the frequency fe.sub.-- 
min and the rated frequency fe.sub.-- base, the value of gain Gn is 
decreased non-linearly (proportional to the inverse of re) to a value of 
unity at rated frequency fe.sub.-- base. This preferred feature of 
generator 54 affords compensation for the linear ramp in voltage below 
rated or base frequency fe.sub.-- base, as compared to motor flux which is 
constant below base speed. Likewise, the q-axis stator flux can be 
approximated as the ratio of the d-axis synchronous reference frame 
voltage to the electrical operating frequency in radians. Once the base 
frequency fe.sub.-- base is exceeded during operation of controller 10 
gain Gn is held constant to maintain stable control. As will be 
appreciated to those skilled in the art, the approximation of flux values 
from voltage values afforded by the use of gain element Gn eliminates the 
need for integration techniques of the type used in known motor control 
devices. 
From element 68, the product of error signal and gain Gn is applied to 
proportional and integral gain elements 70 and 72 to be multiplied by 
gains kp and ki. In the presently preferred embodiment, gains kp and ld 
are varied as illustrated in FIG. 5. It should be noted that FIG. 5 shows 
several different traces for gains kp and ki (normalized to a running 
value of unity) for different rated slip frequencies of motor 12, 
including trace 104 for a synchronous machine (slip frequency of zero), 
and traces 106, 108 and 110 for machines having rated slip frequencies of 
1.0, 2.0 and 3.0 hertz respectively. In addition, the traces shown in FIG. 
5 are presented based upon a per unit of stator electrical frequency 
basis. In the presently preferred embodiment of generator 54, gains kp and 
ld are ramped at a constant rate until a desired minimum shaft speed is 
reached (such as approximately 1/120 of rated speed), and are thereafter 
increased to unity. The point of step increase of gains kp and ki is 
determined by reference to the filtered rotor frequency value fr.sub.-- 
ave, although the d-axis voltage feedback signal Vde.sub.-- fbk value 
could also serve as the basis for this step change. 
In addition to manipulation of the reference and feedback voltage signals, 
feed forward portion 56 of generator 54 also receives the torque current 
command signal i*qe and multiplies the value of this quantity by a 
feedforward gain kff at element 74. In the presently preferred embodiment, 
gain kff is ramped up to a steady state value at a predetermined rate 
after startup of motor 12 as illustrated in FIG. 6. As shown in FIG. 6, 
the value of kff is ramped at a constant rate and reaches its full running 
value at a preset time after startup, such as 250 ms. The specific ramp 
rate and steady state value of this feed forward gain value will typically 
be adjusted for the specific motor ratings, particularly the motor rated 
slip. Moreover, the value of feedforward gain kff is preferably maintained 
at a fairly high level during running to ensure rapid response of 
controller 10 to changes in loading on motor 12. 
From elements 70, 72 and 74, the values generated are algebraically summed 
at summer 76 to produce a frequency signal f'. This signal is then applied 
to filter element 62, as discussed more fully below, and to feedback 
portion 58 at a summing point 78, where it is algebraically summed with a 
filtered rotor frequency signal fr.sub.-- ave. As illustrated in FIG. 3, 
the combination of frequency signal f' and rotor frequency signal 
fr.sub.-- ave produces the stator electrical frequency signal fe. This 
value is transmitted from generator 54 to current regulating circuit 36 
for use in determining d and q-axes voltage command signals V*ds and V*qs 
as discussed above. In addition to producing stator electrical frequency 
signal fe, feedback portion 58 receives torque current signal i*qe and 
multiplies this signal by a slip gain ks at block 80. Slip gain ks is 
preferably provided by the nameplate information or an adaption mechanism 
for motor 12. In addition, controller 10 could be configured to adapt slip 
gain ks to compensate for thermal changes in motor 12 during operation or 
in a constant horsepower region of operation of motor 12 to improve the 
speed estimate provided by circuit 54. The resulting signal is then 
applied to a summer 82 along with the stator electrical frequency signal 
fe to generate a difference signal fr corresponding to a rotor electrical 
frequency estimate. The rotor electrical frequency signal is then applied 
to a filter element 84 to produce filtered rotor frequency signal 
fr.sub.-- ave. 
Similar to the PI gains kp and ki, in the presently preferred embodiment, 
filter element 84 has bandwidth characteristics that are varied during 
starting and running periods of operation of motor 12. The frequency 
characteristics of filter 84 are graphically depicted in FIG. 7 for 
machines of different rated slip frequencies, including, curve 112 for a 
synchronous machine (slip frequency of zero), and curves 114, 116 and 118 
for machines having rated slip frequencies of 1.0, 2.0 and 3.0 hertz 
respectively. The curves shown in FIG. 7 are presented based upon a per 
unit of stator electrical frequency basis. In addition, lines 120 in FIG. 
7 represent the shaft speed of motor 12 per unit of stator frequency for 
each of the slip frequency ratings. It should be noted that, in the 
preferred embodiment the bandwidth of filter 84 is increased linearly as a 
function of the filtered stator electrical frequency fe.sub.-- ave during 
a first phase of running and until a minimum value of rotor electrical 
frequency fr.sub.-- ave is reached. Thereafter, the bandwidth of filter 84 
is increased rapidly to a steady state running bandwidth normalized in 
FIG. 7 to a value of unity. As indicated by the line segments redecending 
from the unity value in FIG. 7, as the speed of motor 12 is reduced during 
operation, the bandwidth value for filter 84 is ramped along a line 
between unity and a normalized value of 0.5. 
In addition to contributing to the derivation of the stator electrical 
frequency value re, filtered rotor frequency signal if.sub.-- ave is 
applied to convening circuit 60 where it is multiplied by a constant 
conversion factor to produce speed feedback signal .omega..sub.-- fbk. 
This speed feedback signal is used by speed regulating circuit 32 of 
controller 10 to generate torque current command signal i*qe as described 
above. Moreover, as illustrated in FIG. 1, stator electrical frequency 
signal fe is applied to an integrator 126 to generate values of .theta.e 
for use in transformation circuits 34 and 48 as indicated above with 
reference to relationships (1) and (10). 
Returning to FIG. 3, frequency signal f' is applied to filter 62 prior to 
being combined algebraically with filtered rotor frequency signal 
if.sub.-- ave. In the presently preferred embodiment, filter 62 passes a 
constant bandwidth equal to the normalized unity bandwidth of filter 84. 
Once filtered at element 62, the two signals are combined at summer 64 to 
generate filtered stator electrical frequency estimate signal fe.sub.-- 
ave. This signal is then transmitted to model 52 for use in deriving the 
d-axis voltage command signal V*de as described above. 
It should be noted that several important advantages flow from the 
preferred structure and operation of controller 10, and particularly of 
frequency generator 54. For example, the frequency signals produced by 
generator 54 are all performed in the synchronous reference frame, based 
upon reference values of current and voltage, and upon feedback voltage 
signals only. Thus, controller 10 is able to properly adjust output 
control signals to maintain proper field oriented control without recourse 
to sensed speed signals. Moreover, it has been found that the preferred 
embodiment described above provides enhanced performance at lower speeds 
than heretofore known variable frequency drives, and eliminates or reduces 
the need to compensate or cancel unwanted effects of drift and offset 
common in analog circuitry. 
It should also be noted that the foregoing preferred embodiment provides 
improved startup characteristics, particularly by virtue of controlled 
variation of gains kff, kp and ki, and due to the preferred relationship 
between the bandwidths of filters 64 and 84, as described above. In 
particular, when controller 10 is commanded to start motor 12, lower gains 
are preferred and change as the stator electrical frequency increases, 
such that motor 12 can start and voltage can be established on the motor, 
resulting in a detectable value of d-axis voltage feedback signal 
Vde.sub.-- fbk. Feed forward gain kff is subsequently altered depending 
upon operating conditions and provides rapid adaptability to changing load 
conditions. However, during startup, PI gains kp and ki are maintained 
low, requiring ramping up of feed forward gain kff to prevent pull-out 
during a start. Moreover, filter 84 effectively acts as a "Wacking filter" 
which holds the rotor frequency estimate of the motor and tracks this 
frequency. Upon startup of motor 12, the bandwidth of filter 84 is 
maintained low as compared to that of filter 62, effectively resulting in 
dominance of the feedforward component f' of the frequency estimate 
fe.sub.-- ave during this phase of operation. Thereafter, because the 
bandwidth of filter 84 is gradually increased, the feedforward component 
f' and feedback component fr.sub.-- ave of the filtered stator frequency 
estimate fe.sub.-- ave approach parity as an acceptable or minimum rotor 
frequency estimate is determined. 
In addition to the advantages mentioned above, those skilled in the art 
will note that because controller 10 transforms feedback voltages to the 
synchronous reference frame (see element 48 described above), and performs 
subsequent operations on values in the synchronous reference frame, phase 
shifting inherent in operations performed in the stationary or a-b-c 
reference frames due to the required filtering is effectively avoided. 
Moreover, while known motor controllers may function as speed regulating 
drives by operating on an input or reference speed signal, such devices 
typically feed forward the speed reference signal and feedback a speed 
feedback signal, and thus cannot function effectively as torque regulating 
drives. In the system described above, the preferred form of feedback 
portion 58, including filter 84, provides tracking capability when 
controller 10 is operated as either a speed or torque regulating drive 
system. 
While the embodiments illustrated in the FIGURES and described above are 
presently preferred, it should be understood that these embodiments are 
offered by way of example only and may be adapted to various other 
structures. For example, rather than stepped increases in PI gains kp and 
ld, more gradual increases may be implemented following an initial startup 
ramping. Moreover, while filter 84 above has been described as a low pass 
filter having bandwidth characteristics varying with frequency, a lag-lead 
or lead-lag filter may be provided to perform a similar rotor frequency 
"tracking" function.