Patent Publication Number: US-6982533-B2

Title: Method and apparatus to regulate loads

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   Not applicable. 
   STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
   Not applicable. 
   BACKGROUND OF THE INVENTION 
   The present invention relates to controllers providing adjustable frequency currents to loads and more specifically, to a method and apparatus to regulate torque provided to loads. 
   Induction Motors 
   Induction motors have broad application in industry, particularly when large horsepower is needed. A three phase induction motor receives three phases of electrical voltage to produce a rotating magnetic stator field. A rotor contained within the stator field experiences an induced current (hence the term induction) which generates a rotor field. The interaction of the rotor field and the stator field causes rotation of the rotor. 
   A common rotor design is a “squirrel cage winding” in which axial conductive bars are connected at either end by shorting rings to form a generally cylindrical structure. The flux of the stator field cutting across the conductive bars induces cyclic current flows through the bars and across the shorting rings. The cyclic current flows in turn produce the rotor field. 
   The use of this induced current to generate the rotor field eliminates the need for slip rings or brushes to provide power to the rotor, making the design relatively maintenance free. 
   Field Oriented Control of Induction Machines 
   To a first approximation, the torque and speed of an induction motor may be controlled by changing the frequency of the driving voltage and thus the angular rate of the rotating stator field. Generally, for a given torque, increasing the stator field rate will increase the speed of the rotor (which follows the stator field). Alternatively, for a given rotor speed, increasing the frequency of the stator field will increase the torque by increasing the slip, that is the difference in speed between the rotor and the stator field. An increase in slip increases the rate at which flux lines are cut by the rotor, increasing the rotor generated field and thus the force or torque between the rotor and stator fields. 
   Referring to  FIG. 1 , the rotating phasor  1  of the stator magneto motive force (“mmf”) will generally have some angle α with respect to the phasor of rotor flux  2 . The torque generated by the motor will be proportional to the magnitudes of these phasors  1  and  2  but also will be a function of their angle α. The maximum torque is produced when phasors  1  and  2  form a right angle to each other (e.g., α=90°) whereas zero torque is produced if these phasors are aligned (e.g., α=0°). Phasor  1  may therefore be usefully decomposed into a torque producing component  3  perpendicular to phasor  2  and a flux component  4  parallel to rotor flux phasor  2 . 
   These two components  3  and  4  of the stator mmf are proportional, respectively, to two stator currents i qs , a torque producing current and i ds , a flux producing current, which may be represented by orthogonal vectors in the rotating frame of reference (synchronous frame of reference) of the stator flux having slowly varying magnitudes. Accordingly, in controlling an induction motor, it is generally desired to control not only the frequency of the applied voltage (hence the speed of the rotation of the stator flux phasor  1 ) but also the phase of the applied voltage relative to the current flow and hence the division of the currents through the stator windings into the i qs  and i ds  components. Control strategies that attempt to independently control the currents i qs  and i ds  are generally termed field oriented control strategies (“FOC”). 
   While torque regulation has been contemplated in the past, unfortunately the regulation schemes adopted have not been very accurate. To this end, generally, at speeds below the rated motor speed, it has been assumed that the developed motor torque has been equal to a reference torque value. At speeds above rated speed, torque has been regulated in a pseudo open loop manner by dividing the torque reference value by an estimate of motor flux reduction value. More specifically, the torque reference is divided by a term proportional to the motor operating speed that is an estimate of the reduction in motor flux. Unfortunately, the term proportional to operating speed is a relatively inaccurate estimate of motor flux reduction and therefore torque regulation via one of these schemes is not very accurate. In addition, while system torque can change rapidly, operating frequency changes relatively slowly and therefore, in some cases, stability problems have been known to occur when operating frequency is used as an estimator of flux reduction. While such inaccurate torque regulators may work in some applications, such limited regulating capabilities are not acceptable for other applications. 
   Therefore, it would be advantageous to have a system that estimates torque quickly and accurately. 
   BRIEF SUMMARY OF THE INVENTION 
   It has been recognized that easily obtainable control system signals can be obtained and used to generate an essentially real time instantaneous torque estimate value that can in turn be used to drive a torque trim regulator thereby generating a torque command value that can in turn be used to trim a reference voltage value thus driving the torque applied to an induction machine toward a reference and desired torque value. The torque estimate can be derived by combining feedback current values with several different sets of obtainable system signals. Thus, a simple and accurate torque regulator can be configured. 
   Consistent with the above, at least some embodiments of the invention include a method for use with a controller for controlling a machine wherein a torque reference value is provided, the method comprising the steps of obtaining feedback current values corresponding to the currents provided to the machine, mathematically combining the feedback current values to generate an error value, mathematically combining the error value and the torque reference value to generate a torque command value and using the torque command value to control the machine. In some cases the step of obtaining feedback currents includes obtaining d and q-axis feedback currents and wherein the step of using the torque command value to control the machine includes generating a q-axis command voltage value as a function of the torque command value and using the q-axis command voltage value to drive the machine. In some cases the step of mathematically combining the error value and the torque reference value includes adding a derivative of the error value and a derivative of the torque reference value. 
   In at least some embodiments the step of mathematically combining the d and q-axis feedback current values to generate an error value includes mathematically combining the feedback current values to generate a torque estimate value and subtracting the torque estimate value from the torque reference value to provide the error value. 
   In some cases the method further includes the steps of determining the operating frequency of the machine, mathematically combining the operating frequency and the q-axis feedback current value to provide a d-axis flux estimate and deriving a d-axis command voltage value as a function of the d-axis flux estimate and, wherein, the step of mathematically combining the feedback current values to generate the torque estimate includes combining the feedback currents and the d and q-axis command voltage values to generate the torque estimate. 
   The method may also include the steps of identifying a system operating frequency, mathematically combining the operating frequency and the torque reference value to generate a power reference value and, wherein, the step of mathematically combining to generate an error value includes combining the feedback current values to generate a power estimate and subtracting the power estimate from the power reference value. Here, the step of mathematically combining the error value and the torque reference value to generate a torque command value may include the steps of combining derivatives of each of the power reference value and the power error value to generate the torque reference value. 
   In at least some embodiments the error value is a power error value and the step of mathematically combining the error value and the torque reference value to generate a torque command value includes the steps of converting the torque reference value into a power reference value and combining derivatives of each of the power reference value and the power error value to generate the torque reference value to generate the torque command value. In some cases the step of converting the torque reference value to a power reference value includes the step of multiplying the torque reference value by a system operating frequency. 
   The invention also includes an apparatus for use with a controller for controlling a machine wherein a torque reference value is provided, the apparatus for identifying an error indicative of the difference between the reference torque value and the torque applied to the machine and using the error value to modify control of the machine, the apparatus comprising sensors for obtaining current values corresponding to the currents provided to the machine and a processor running software to mathematically combine the current values to generate an error value, mathematically combine the error value and the torque reference value to generate a torque command value and use the torque command value to control the machine. 
   The invention further includes an apparatus for use with a controller providing command voltage signals to drive a pulse width modulated (PWM) inverter linked to a machine wherein a torque reference value is provided, the apparatus for identifying an error indicative of the difference between the reference torque value and the torque applied to the machine and using the error value to modify a q-axis command voltage value used to control the machine, the apparatus comprising sensors for obtaining d and q-axis feedback current values corresponding to the currents provided to the machine, an estimator for mathematically combining the d and q-axis feedback current values to generate an error value, a torque regulator for mathematically combining the error value and the torque reference value to generate a torque command value and a processor using the torque command value to generate the q-axis command voltage value. 
   Moreover, the invention includes a method for use with a controller for controlling a machine, the method comprising the steps of receiving a reference torque value, obtaining feedback signals from the machine during machine operation, deriving an estimate indicative of torque applied to the machine and controlling the machine as a function of both the reference torque value and the estimate. 
   These and other objects, advantages and aspects of the invention will become apparent from the following description. In the description, reference is made to the accompanying drawings which form a part hereof, and in which there is shown a preferred embodiment of the invention. Such embodiment does not necessarily represent the full scope of the invention and reference is made therefore, to the claims herein for interpreting the scope of the invention. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       FIG. 1  is a schematic diagram illustrating the relationships between various currents and magnetic fields in an induction machine; 
       FIG. 2  is a schematic diagram illustrating an exemplary control system according to at least one embodiment of the present invention; 
       FIG. 3  is a schematic diagram illustrating components of the torque estimator of  FIG. 2  according to at least one embodiment of the present invention; 
       FIG. 4  is similar to  FIG. 3 , albeit illustrating components of a torque estimator according to a different embodiment of the present invention; 
       FIG. 5  is similar to  FIG. 3 , albeit illustrating a torque error estimator according to another embodiment of the invention; 
       FIG. 6  is similar to  FIG. 3 , albeit illustrating one other torque error estimator; 
       FIG. 7  is a flow chart illustrating a general method according to the present invention; 
       FIG. 8  is a graph illustrating a command torque value, a resulting shaft torque value, a torque error value and a torque regulator control signal when an inventive system is driven at a first operating frequency; 
       FIG. 9  is a graph similar to  FIG. 8 , albeit illustrating the signals when the system is driven at a second operating frequency that is higher than the first operating frequency; 
       FIG. 10  is a schematic diagram of yet another inventive embodiment; and 
       FIG. 11  is a schematic diagram of one other inventive embodiment. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Hereinafter, unless indicated otherwise, an “*” will indicate a command signal, a “qs” subscript will indicate a signal associated with a stator q-axis in a d-q frame of reference, a “ds” subscript will indicate a signal corresponding to the d-axis in a d-q frame of reference, a “s” subscript will indicate a signal associated with a motor stator, a “ref” subscript will be used to indicate a reference signal that incorporates some quantities determined and programmed during a commissioning procedure, an “est” subscript will be used to refer to an estimated value, a “fb” subscript will be used to refer to a feedback signal, “u” subscript and “v” subscripts will be used to refer to signals associated with two of the three phases of a motor and a “reg” subscript will be used to refer to a regulated value. 
   In addition, note that the term “derivative” is used herein to refer to two different mathematical concepts and that the context of the text in which the term appears should be used to determine which of the two meanings should be applied. First, derivative is used to refer to a change with respect to time as in Equations 2 and 3 below. Second, in some cases, the term derivative is used to refer to any derivation from an initial value. For instance, applying a proportional or proportional-integral gain to an initial value may result in a derivative of the initial value. Hereinafter the terms “value” and “signal” are generally used interchangeable. 
   While the present invention may be employed with adjustable frequency controllers to deliver current to any of several different types of loads including AC motors, generators, grid-tie inverters, etc., in the interest of simplifying this explanation, unless indicated otherwise, the invention will be described in the context of a system providing currents to an AC motor. 
   A. Theory 
   As a fundamental basis for the present invention, the electromagnetic torque of an AC motor can be expressed by the following equation: 
             T   =       3   2     ·     (     P   2     )     ·     (         λ   ds     ·     i   qs       -       λ   qs     ·     i   ds         )               Eq   .           ⁢   1             
 
where,
 
   P is the number of motor poles; 
   i qs  is motor current aligned with the q-axis and typically reflects motor load; 
   i ds  is motor current aligned with the d-axis and typically motor flux current; 
   λ ds  is motor flux aligned with the d-axis; and 
   λ qs  is motor flux aligned with the q-axis. 
   As well known in the art, the voltage equations in a dq frame of reference for an induction machine can be expressed as:
 
 V   qs   =r   s   ·i   qs +ω e ·λ ds   +pλ   qs   Eq. 2
 
 V   ds   =r   s   ·i   ds −ω e ·λ qs   +pλ   ds   Eq. 3
 
where,
 
   r s  is the stator resistance; and 
   p is derivative operator 
         ⅆ     ⅆ   t       .       
 
In steady state the last terms in each of Equations 2 and 3 drops out. Thus, in steady state, Equations 1 through 3 can be combined to express motor torque T using the following equation: 
             T   =       3   2     ·     (     P   2     )     ·     (         (         V   qs     -       r   s     ·     i   qs           ω   e       )     ·     i   qs       +       (         V   ds     -       r   s     ·     i   ds           ω   e       )     ·     i   ds         )               Eq   .           ⁢   4             
 
Equation 4 can be rewritten using values that are generally easy to obtain in a control system. To this end, most control systems generate both d and q-axis command voltage values V ds * and V qs * and, generally, d and q-axis feedback current values i dsfb  and i qsfb  are available.
 
   Thus, Equation 4 can be rewritten as follows: 
                     T   est     =       ⁢       3   2     ·     (     P   2     )     ·     (         (         V   qs   *     -       r   s     ·     i   qsfb           ω   e       )     ·     i   qsfb       +                         ⁢       (         V   ds   *     -       r   s     ·     i   dsfl           ω   e       )     ·     i   dsfb       )                 Eq   .           ⁢   5             
 
Referring to Equation 5, it should be appreciated that the values required to solve Equation 5 can be readily ascertained and used to identify an essentially instantaneous and real time torque estimate T est . Where a torque reference or control value T ref  is provided to a system indicating a desired torque, the instantaneous applied torque estimate T est  can be compared to the input torque value and the difference can be used to adjust the voltages applied to the load thereby causing the torque to converge toward the reference torque value T ref .
 
   B. First Embodiment Implementation 
   Referring now to the drawings wherein like symbols and numerals are used to refer to similar elements throughout the several views and, more specifically, referring to  FIG. 2 , the present invention will be described in the context of an exemplary motor control system  50  that, in general, receives both a torque reference signal T ref  and a d-axis flux reference signal λ dsref  and uses those two signals to generate AC voltages on three separate supply lines  95 ,  97 ,  99  linked to motor  92 . System  50  includes various feedback loops that enable essentially instantaneous and real time control of torque applied to motor  92  so that the applied torque can be made essentially equal to the reference torque value T ref . In  FIG. 2 , two current sensors  94  and  96  (e.g., Hall effect sensors) are coupled to two of the three supply lines (e.g.,  95  and  97 ) that are linked to motor  92  to sense currents passing therethrough and generate feedback current signals i ufb  and i vfb  which are provided to a two-three-two transformer  86 . 
   Transformer  86  first uses feedback signals i ufb  and i vfb  to identify the current passing through third line  99  linked to motor  92  thereby transforming the two feedback currents into three feedback currents. Next, transformer  86  transforms the three phase currents into d and q-axis two-phase currents i dsfb  and i qsfb . d and q-axis feedback currents i dsfb  and i qsfb  are provided to other system  50  components to determine how to alter the voltages applied to motor  92  via the three supply lines  95 ,  97  and  99  to drive motor  92  as desired. 
   Referring still to  FIG. 2  and, more specifically, according to the present invention, system  50  includes both a torque estimator  70  and a torque regulator  71 . Estimator  70  receives the d and q-axis feedback signals i dsfb  and i qsfb , respectively, and uses those signals along with other system specific values identified during a commissioning procedure to, among other things, generate an instantaneous torque estimate value T est  representative of the instantaneous torque applied to motor  92 . Torque estimate T est  is provided to torque regulator  71  which uses estimate T est  and the torque reference value T ref  to generate a torque command value T* which is trimmed or adjusted so as to, essentially in real time, cause the torque applied to motor  92  to be equal to the input torque value T ref . 
   Prior to operation of system  50  and, during a commissioning procedure, the system specific values that are determined and then programmed for subsequent use by system  50  include a value P (hereinafter the “pole count”) indicating the number of poles associated with motor  92 , a flux reference λ dsref , a transient inductance value L σ  and the stator resistance value r s . Various algorithms exist for identifying system specific inductance value L σ , resistance value r s , and d-axis flux reference λ dsref  and any of those algorithms may be used here. 
   Referring still to  FIG. 2 , in addition to estimator  70 , regulator  71 , motor  92 , sensors  94  and  96  and transformer  86 , system  50  includes a q-axis command voltage determiner  21 , four summer blocks  64 ,  72 ,  78  and  82 , a q-axis torque to current converter  62 , a frequency determiner  66 , a flux regulator  74 , a flux to d-axis current converter  76 , a d-axis current regulator  80 , a two-to-three phase transformer  88  and PWM controller/inverter module  90  and a d-axis reference voltage determiner  23 . 
   Determiner  66  uses a q-axis error value i qserr  to determine an operating frequency ω e  that is provided to each of determiners  21  and  23  and to estimator  70 . In addition to receiving frequency ω e , determiner  21  also obtains resistance value r s  and receives q-axis command current i qs *, d-axis command current i ds * and d-axis flux reference λ dsref  and solves the following equation to identify q-axis command voltage V qsref  which is:
 
 V   qs   *=r   s   i   qs *+ω e λ dsrf   Eq. 6
 
   As indicated above, torque regulator  71  receives each of the torque reference value T ref  and the torque estimate T est  and uses those values to generate torque command value T*. Command value T* is provided to torque to q-axis current converter  62 . 
   Converter  62  scales the received torque command value T* providing the q-axis current command value i qs * to summer  64 . In addition to receiving the q-axis current command value i qs *, summer  64  also receives the q-axis feedback signal i qsfb  described above and subtracts the q-axis feedback signal i qsfb  from the q-axis command signal i qs * providing the q-axis current error signal i qserr . 
   Referring yet again to  FIG. 2 , summer  72  receives each of the d-axis flux estimate λ dsest  and the d-axis flux reference value λ dsref  and subtracts estimated value λ dsest  from reference value λ dsref  and provides the difference to flux regulator  74 . In at least some embodiments, flux regulator  74  is a PI regulator. Regulator  74  converts the received value to a command flux value λ*. Flux to d-axis current converter  76  scales the command flux value λ* thereby generating a d-axis command current value i ds *. 
   Summer  78  receives each of the d-axis command current signal i ds * and d-axis feedback current signal i dsfb  and subtracts feedback signal i dsfb  from command signal i ds * thereby generating a d-axis current error signal i dserr . d-axis current regulator  80  is, in at least some embodiments, a PI regulator. Regulator  80  converts its input to a regulated d-axis voltage value V dsreg  which is provided to summer  82 . 
   In addition to receiving frequency ω e , determiner  23  also obtains resistance value r s  and inductance value L σ  and receives q-axis and d-axis command currents i qs * and i ds *, respectively, and solves the following equation to identify d-axis reference voltage V dsref :
 
 V   dsref   =r   s   i   ds *−ω e   L   σ   i   qs *  Eq. 7
 
   d-axis reference voltage signal V dsref  is provided to summer  82 . Summer  82  adds received values thereby generating a d-axis command voltage signal V ds *. As illustrated, each of the d and q-axis command voltage signals V ds * and V qs * are provided to two-to-three phase transformer  88 . Transformer  88  converts the d and q-axis command voltage signals V ds * and V qs * to three phase command signals V u *, V v * and V W * which are provided to controller/inverter module  90 . Module  90  uses the three phase command voltage values to generate voltages on, and associated currents through, supply lines  95 ,  97  and  99  linked to motor  92  as well known in the art. 
   Referring again to  FIG. 2 , torque regulator  71  includes summers  56  and  60  and a trim regulator  58 . As illustrated, the reference torque value T ref  is provided to each of summer  60  and summer  56 . In addition to receiving the reference torque value T ref , summer  56  also receives the torque estimate value T est . Summer  56  subtracts estimated value T est  from reference torque value T ref  thereby generating a torque error value T err  which is provided to trim regulator  58 . Regulator  58  is, in at least some embodiments, a PI regulator. The output of regulator  58  is provided as a second input to summer  60 . Summer  60  adds the value received from trim regulator  58  and the torque reference value T ref  thereby generating the torque command value T* described above. Thus, where the estimate T est  of applied torque is lower than the reference value T ref , regulator  71  has the effect of increasing the torque command value T* thereby stepping up the applied torque and causing the applied torque value to converge on the reference value T ref . 
   Referring still to  FIG. 2 , in addition to receiving the d and q-axis feedback currents i dsfb  and i qsfb , respectively, torque estimator  70  accesses pole count value P and stator resistance value r s . Moreover, the d and q-axis command voltage values V ds * and V qs * output by summers  82  and  68  are fed back to torque estimator  70  and an output frequency value ω e  is obtained. Estimator  70  mathematically combines all of the received values to generate torque estimate T est . In addition, estimator  70  combines some of the values accessed or received to generate the d-axis flux estimate λ dsest . 
   To identify torque estimate T est , estimator  70  evaluates Equation 5 above. To this end, referring to  FIG. 3 , estimator  70  includes a gain block  120 , five multipliers  122 ,  128 ,  132 ,  134  and  140 , three summers  124 ,  130  and  136  and two dividers  126  and  138 . Value P corresponding to the number of poles associated with motor  92  is provided to block  120  which multiplies value P by ¾ and provides its output to multiplier  132 . Stator resistance value r s , is provided to each of multipliers  122  and  134 . Multiplier  122  also receives the q-axis feedback current signal i qsfb  and multiplies feedback signal i qsfb  by resistance value r s providing its output to summer  124 . Summer  124  subtracts the output of multiplier  122  from the q-axis command voltage value V qs * and provides its output to divider  126 . Divider  126  divides the output of summer  124  by frequency ω e  and provides its output to multiplier  128 . Multiplier  128  multiplies the output of divider  126  by the q-axis feedback signal i qsfb  and provides its output to summer  130 . 
   Multiplier  134  multiplies the d-axis feedback current signal i dsfb  by the stator resistance value r s , and provides its output to summer  136 . Summer  136  subtracts the output of multiplier  134  from the d-axis command voltage value V ds * and provides its output to divider  138 . Divider  138  divides the output of summer  136  by frequency ω e  and provides its output to multiplier  140 . Multiplier  140  multiplies the output of divider  138  by the d-axis feedback current signal i dsfb  and provides its output to summer  130 . Summer  130  adds the outputs of multipliers  128  and  140  and provides its output to multiplier  132 . Multiplier  132  multiplies the outputs of block  120  and summer  130  thereby generating the torque estimate value T est  which is provided to torque regulator  71  in  FIG. 2 . 
   C. Experimental Results 
     FIG. 8  illustrates the effects of operation with and without the inventive torque regulator described above. To generate the waveforms in  FIG. 8 , a 5 HP, 460 V, 60 Hz, 6.5 Arms, 1780 RPM induction motor was operated in a torque regulation mode at 900 RPM. The torque reference was set to 100% of the name plate torque for the system used and the torque regulator described above was initially enabled. At approximately 3 seconds, the regulator was disabled and the change in torque error, torque command and measured shaft torque illustrated occurred. The resulting error was approximately 3% of the rated motor torque. At 7.2 seconds the regulator was re-enabled and the torque error was again eliminated. 
     FIG. 9  contains experimental results similar to those described above with respect to  FIG. 8  except that the operating frequency used to generate the waveforms in  FIG. 9  was 2400 RPM instead of 900 RPM. Again, the torque regulator was initially enabled, was disabled at 3 seconds and then was re-enabled at 7.2 seconds. Here, the torque command signal was increased above the rated operating speed to compensate for field weakening effects. The torque reference value T ref  (not illustrated) remained at 100% of the name plate torque value. 
   D. Additional Exemplary Embodiments 
   The example above assumes that an encoder or other type of speed feedback device is not provided to generate a rotor speed signal useable to determine the operating frequency of the system. Some systems will include a speed feedback device. In these cases a slightly different topographical control system may be employed, albeit the torque regulator and torque estimator operating in the same manner as described above in at least some embodiments. To this end, referring now to  FIG. 10 , an exemplary control system  200  that includes a speed feedback device is illustrated. In  FIG. 10 , many of the components are similar to the components described above with respect to  FIG. 2  and therefore are not described again here in detail. To indicate similarity, some of the components are identified by numbers as above followed by a “′”. For instance, the PWM converter/inverter in  FIG. 10  is identified by numeral  90 ′ the 2-3 phase transfer is identified by numeral  88 ′ and so on. In addition, components  21 ,  71 ,  62 ,  64 ,  70 ,  72 ,  74 ,  76 ,  78 ,  80 ,  82 ,  23  and  86  in  FIG. 2  have been lumped together in  FIG. 10  as block  202  to simplify  FIG. 10 . 
   Referring to  FIG. 10 , an encoder  204  is attached to motor  92 ′ for determining rotor speed and generating a rotor speed signal ω r  indicative thereof. Referring also to  FIG. 2 , the d-axis voltage command signal V ds * from summer  82  and the d-axis reference signal V dsref  from determiner  23  are provided to slip frequency determiner  25  which uses those signals to generate a slip frequency signal ω s . A summer  206  adds the rotor and slip frequency values to determine operating frequency ω e  which is provided along with other values (e.g., L σ , r s , etc.) to block  202 . 
   Referring still to  FIGS. 2 and 10 , determiner  21  solves Equation 6 to identify a q-axis reference voltage V qsref . The q-axis current error i qserr  is provided to a q-axis current regulator  208  which generates a regulated q-axis voltage value V qsreg . A summer  68  adds the q-axis regulated and reference voltages to generate the q-axis command voltage V qs *. As in  FIG. 2 , in  FIG. 10  the d and q-axis command voltages are provided to 2-3 phase transformer  88 ′ and are used thereby to drive converter/inverter  90 ′. 
   One alternative embodiment of the present invention uses the outputs of current regulators  80  and  208  (see again  FIGS. 2 and 10 ) to adjust the torque estimate T est  instead of using the command voltage values V ds * and V qs *. 
   To this end, it has been recognized that the general torque Equation 1 can be rewritten as follows: 
               T   ref     =       3   2     ·     (     P   2     )     ·     (         λ   dsref     ·     i   qs       -       λ   qsref     ·     i   ds         )               Eq   .           ⁢   8             
 
Referring again to  FIGS. 2 and 10 , q-axis command voltage V qs * is equal to the sum of the q-axis regulated voltage value V qsreg  and the q-axis reference voltage value V qsref  and the d-axis command voltage V ds * is equal to the sum of the d-axis regulated voltage value V dsreg  and the d-axis reference voltage value V dsref . Thus, Equation 4 above can be rewritten as follows: 
               T   est     =       3   2     ·     (     P   2     )     ·     [               (         V   qsref     +     V   qsref     -       r   s     ·     i   qsfb           ω   e       )     ·     i   qsfb       +                 (         V   dsref     +     V   dsref     -       r   s     ·     i   dsfb           ω   e       )     ·     i   dsfb             ]               Eq   .           ⁢   9             
 
   Thus, in at least one other inventive embodiment, the torque estimator may obtain and receive each of values P, ω e , r s , V qsref , V dsref , V qsreg , V dsreg , i qsfb  and i dsfb  and use those values to resolve Equation 9 to identify an instantaneous torque estimate T est  essentially in real time. To this end, referring to  FIG. 4 , an exemplary second torque estimator  70 ′ is illustrated that may be used to replace estimator  70  is  FIG. 1 . Here and in other exemplary systems described hereinafter, while the sources for the values obtained and received by estimator  70 ′ (and other estimates described below) are not specifically illustrated, it should be apparent from a perusal of  FIG. 2  where the values originate. For instance, the output of determiner  21  provides q-axis reference voltage value V qsref , the output of regulator  66  provides q-axis regulated voltage value V qsreg  and so on. 
   As illustrated in  FIG. 4 , the output of estimator  70 ′ is provided to trim regulator  58  (see also  FIG. 2 ). Estimator  70 ′ includes a scalar block  142 , five multipliers  144 ,  148 ,  152 ,  156 , and  162 , five summers  145 ,  150 ,  154 ,  158  and  164  and two dividers  146  and  160 . Multiplier  144  multiplies the stator resistance value r s , by the q-axis feedback current value i qsfb  and provides its output to summer  145 . Summer  154  adds the q-axis regulated voltage value V qsreg  and the q-axis reference voltage value V qsref  and provides its output to summer  145 . Summer  145  subtracts the output of multiplier  144  from the output of summer  154  and provides its output to divider  146 . Divider  146  divides the output of summer  145  by the operating frequency ω e  and provides its output to multiplier  148 . Multiplier  148  multiplies the output of divider  146  by the q-axis feedback current value i qsfb  and provides its output to summer  150 . 
   Referring still to  FIG. 4 , summer  164  adds the d-axis regulated voltage value V dsreg  and the d-axis reference voltage value V dsref  and provides its output to summer  158 . Multiplier  156  multiplies the stator resistance value r s , and the d-axis feedback current value i dsfb  and provides its output to summer  158 . Summer  158  subtracts the output of multiplier  156  from the output of summer  164  and provides its output to divider  160 . Divider  160  divides the output of summer  158  by operating frequency ω e  and provides its output to multiplier  162 . Multiplier  162  multiplies the output of divider  160  by the d-axis feedback current value i dsfb  and provides its output to summer  150 . Summer  150  adds the outputs of multipliers  148  and  162  and provides its output to multiplier  152 . 
   Scalar block  142  multiplies pole count value P by ¾ and provides its output to multiplier  152 . Multiplier  152  multiplies the output of block  142  and the output of summer  150  and provides the estimated torque value T est  pursuant to Equation 9 above. The estimated torque value T est  is provided to summer  56  where estimated value T est  is subtracted from torque reference value T ref  . 
   According to one additional exemplary embodiment of the present invention, it has been recognized that when the current regulators used in a system are capable of regulating the d and q-axis current errors to zero values in steady state, a simplified torque estimating algorithm may be employed to identify value T est . To this end, as well known in the motor controls industry, the q-axis reference flux value λ qsref  can be expressed as follows:
 
λ qsref   =L   σ   i   qs *  Eq. 10
 
Combining Equations 7 and 10, the d-axis reference voltage V dsref  can be expressed as:
 
 V   dsref   =r   s   i   ds *−ω e λ qsref   Eq. 11
 
   Torque error T err  (i.e., T ref −T est ) can be represented by combining the terms in Equations 8, 9 and 11 to yield the following equation: 
               T   err     =       3   2     ·     P   2     ·     [               (       λ   dsref     -         r   s     ·     i   qsfb         ω   e         )     ·     (       i   qs   *     -     i   qsfb       )       -                     V   qsreg     ·     i   qsfb         ω   e       -       (       λ   qsref     -         r   s     ·     i   dsfb         ω   e         )     ·                   (       i   ds   *     -     i   dsfb       )     -         V   dsreg     ·     i   dsfb         ω   e               ]               Eq   .           ⁢   12             
 
   Examining Equation 12, it has been recognized that when there is zero current error, several of the terms in Equation 12 are eliminated yielding the following equation: 
               T   err     =       3   2     ·     P   2     ·     [       -         V   qsreg     ·     i   qsfb         ω   e         -         V   dsreg     ·     i   dsfb         ω   e         ]               Eq   .           ⁢   13             
 
   Thus, referring again to  FIG. 2 , torque error T err  may be determined according to Equation 13 when the current error is regulated to zero. 
   Referring now to  FIG. 5 , an exemplary torque error estimator  70 ″ and torque regulator  71 ″ are illustrated that, it is contemplated, would be used to replace the torque estimator and regulator of  FIG. 2 . Here, consistent with Equation 13, torque estimator  70 ″ receives operating frequency ω e , pole count P, d-axis and q-axis regulated voltage values V dsreg  and V qsreg , respectively, and d and q-axis feedback current values i dsfb  and i qsfb , respectively, and, uses those signals to evaluate Equation 13 thereby providing torque error value T err . As illustrated in  FIG. 5 , in this case, torque error T err  is provided directly to trim regulator  58 . Components  58  and  60  in  FIG. 5  operate in an identical manner to the similarly labeled components of  FIG. 2  and therefore will not be described here in detail. As illustrated, regulator  71 ″ generates torque command value T* which is provided to converter  62 . 
   In yet one additional embodiment of the present invention, a torque error value T err  like the error generated by Equation 13 may, instead, be generated using Equation 12 above when the system current regulators cannot regulate the d and q-axis current errors to zero in steady state. In this regard, referring now to  FIG. 6 , yet one additional torque estimator  70 ′″ and associated torque regulator  71 ′″ are illustrated. The torque regulator  71 ′″ in  FIG. 6  operates in a fashion identical to regulator  71 ″ in  FIG. 5  and therefore will not be described here in detail. As illustrated, estimator  70 ′″ receives operating frequency ω e , pole count P, resistance value r s , q-axis reference flux value λ qsref , d-axis reference flux value λ dsref , d and q-axis command current values i ds * and i qs *, respectively, and d and q-axis feedback current values i dsfb  and i qsfb , and uses those values to evaluate Equation 12. 
   Referring now to  FIG. 7 , an exemplary general method  190  according to the present invention is illustrated. In this regard, after various system specific parameters have been identified and stored during a commissioning procedure and, during normal system operation, at block  192  feedback values and other calculated values are determined, identified or received and are used to identify an instantaneous torque error value T err . At block  194 , the instantaneous torque error value T err  is used to trim the torque reference signal T ref  thereby providing the command torque value T*. Next, at block  196 , the command torque signal T* is used to trim the q-axis reference voltage signal V qsref  thereby generating the q-axis command voltage value V qs *. This process is repeated during normal system operation. 
   Referring again to Equation 5, it should be appreciated that as the operating frequency ω e  approaches zero, the torque estimate T est  quickly approaches an extremely large value that does not accurately reflect system torque. Thus, at low operating speeds some other algorithm for regulating torque may be required. In this regard, it has been recognized that power P can be expressed as:
 
 P=Tω   e   Eq. 14
 
Thus, a power estimate Pest may be expressed by combining Equations 5 and 14 as: 
               P   est     =       3   2     ·     (     P   2     )     ·     (         (       V   qs   *     -       r   s     ⁢     i   qsfb         )     ·     i   qsfb       +       (       V   ds   *     -       r   s     ⁢     i   dsfb         )     ·     i   dsfb         )               Eq   .           ⁢   15             
 
   The reference torque T ref  can be converted to a reference power value P ref  by multiplying value T ref  by the operating frequency ω e . Thereafter, the reference power value P ref  and the power estimate P est  can be used to drive the torque regulator as above. 
   Referring now to  FIG. 11 , a portion of one system  212  for comparing power values instead of torque values is illustrated. System  212  is meant to be used in conjunction with other components from  FIG. 2  as indicated. The sub-system of  FIG. 11  includes a multiplier  222 , a power estimator  210  and a torque regulator  71 ″″. Referring also to  FIG. 2 , operating frequency ω e  from block  66  is provided to multiplier  222  along with torque reference T ref . Multiplier  222  multiplies frequency ω e  and reference T ref  to generate a power reference signal P ref  consistent with Equation 14 above. 
   Power estimator  210  receives all of the values indicated and generates power estimate P est  by evaluating Equation 15 above, estimate P est  is provided to torque regulator  71 ″″ along with power reference P ref . Regulator  71 ″″ scales reference P ref  via block  214  and provides the scaled value to a summer  220 . Another summer  216  subtracts power estimate P est  from reference P ref  to generate power error P err . Error P err  is regulated by a regulator  218  (e.g., a PI regulator) and the output of regulator  218  is provided to summer  220 . Summer  220  adds received values and outputs a command torque value T* which is provided to converter  62  in  FIG. 2  as illustrated. 
   It should be appreciated that, in addition to using power values in the embodiment of  FIG. 2 , power values may be substituted in any of the other embodiments described above by simply multiplying the reference torque by the operating frequency and altering the torque estimate equations by replacing the operating frequency with a one value. 
   It should be understood that the methods and apparatuses described above are only exemplary and do not limit the scope of the invention, and that various modifications could be made by those skilled in the art that would fall under the scope of the invention. For example, while various components are described above as performing various functions and steps of overall processes, it should be appreciated that a single programmable processor will often be employed to perform many of the steps. In addition, while described above as used with an FOC controller, the inventive methods and systems are also useable with non-FOC drives operating in steady state. Moreover, while the invention is described above in the context of induction motor control, the invention may be used to control both synchronous and permanent magnet motors. In these cases the slip frequency ω s  would be zero.