Patent Publication Number: US-7719226-B2

Title: Highly responsive permanent magnet motor controller

Description:
CLAIM OF PRIORITY 
   The present application claims priority from Japanese application serial No. 2006-353651, filed on Dec. 28, 2006, the content of which is hereby incorporated by reference into this application. 
   FIELD OF THE INVENTION 
   The present invention relates to a position sensor-less vector control method applied to a permanent magnet motor. 
   BACKGROUND OF THE INVENTION 
   In technology for estimating axis error in a position sensor-less vector control method, as described in Japanese Patent Laid-open No. 2001-251889, voltage command values, detected current values, and a speed command value, which are outputs in vector control, are used to estimate axis error by calculation, and the calculated value is then used to estimate a frequency by calculation. The description in the control method also stipulates that command values for axis error are basically set to 0. 
   SUMMARY OF THE INVENTION 
   The method described in Japanese Patent Laid-open No. 2001-251889 can achieve highly responsive, highly stable control operation for motors having an electric time constant (ratio of an inductance to a resistance) that is small to a certain extent, i.e., for small- to medium-capacity motors. If the method is applied to motors having a comparatively large electric time constant, however, response in frequency estimation by calculation is restricted. 
   There has been a problem that when a speed command value is abruptly changed, excessive current is generated by large axis error caused during an acceleration or deceleration operation and thereby the operation efficiency is lowered. 
   An object of the present invention is to provide a highly responsive controller, for a permanent magnet motor, that can reduce axis error during an acceleration or deceleration operation to 0 and achieve a highly efficient operation, even for a motor having a electric time constant. 
   In one aspect of the invention, a current command value rather than a detected current value is used to estimate axis error by calculation. 
   In an another aspect of the invention, a command value for axis error is generated according to a speed command value, and a difference between the command value for axis error and an estimated axis error is used to control an estimated frequency value. 
   According to a preferred embodiment of the invention, axis error during an acceleration or deceleration operation can be reduced to 0 for motors having a small electric time constant (ratio of an inductance to a resistance) and motors having a large electric time constant, and thereby highly efficient operation can be achieved. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram showing an exemplary structure of a permanent magnet motor controller in an embodiment of the present invention. 
       FIG. 2  is graphs illustrating operation characteristics when a control response frequency F PLL , which is set in a frequency estimating part  6 , is low. 
       FIG. 3  is graphs illustrating operation characteristics when the control response frequency F PLL , which is set in the frequency estimating part  6 , is high. 
       FIG. 4  is graphs illustrating frequency characteristics in a range from an axis error command value Δθc* to an estimated value Δθc. 
       FIG. 5  is graphs illustrating operation characteristics when an embodiment of the present invention is used. 
       FIG. 6  is a block diagram showing an exemplary structure of a permanent magnet motor controller in another embodiment of the present invention. 
       FIG. 7  is graphs illustrating operation characteristics when the other embodiment of the present invention is used. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Embodiments of the present invention will be described below in detail with reference to the drawings. 
   First Embodiment 
     FIG. 1  is a block diagram showing an exemplary structure of the permanent magnet motor controller in an embodiment of the present invention. 
   The permanent magnet motor  1  outputs a motor torque obtained by synthesizing a torque component due to the magnetic flux of a permanent magnet and a torque component due to inductance of the winding of a armature. 
   The electric power converter  2  outputs a voltage proportional to three-phase AC voltage command values Vu*, Vv*, and Vw* to change the output voltage and revolutions of the permanent magnet motor  1 . 
   The DC power supply  21  supplies a DC voltage to the electric power converter  2 . 
   The current detector  3  detects three-phase AC currents Iu, Iv, and Iw of the permanent magnet motor  1 . 
   The coordinate converter  4  outputs a detected current value Idc of the d-axis and a detected current value Iqc of the q-axis according to detected values Iuc, Ivc, and Iwc of the three-phase AC currents Iu, Iv, and Iw and to an estimated phase value θc*. 
   The axis error estimating part  5  estimates axis error, which is a difference between the estimated phase value θc* and the phase value θ of the motor, by calculation according to voltage command values Vdc* and Vqc*, an estimated frequency value ω 1   c , low-pass filter output values Id*td and Iq*td of first current command values Id* and Iq*, and motor constants, and outputs an estimated value Δθc. 
   The frequency estimating part  6  outputs an estimated frequency value ω 1   c  from a difference between the estimated axis error Δθc and the axis error command value Δθc*, which is 0. 
   The phase estimating part  7  integrates the estimated frequency value ω 1   c  and outputs an estimated phase value θc* to coordinate converters  4  and  13 . 
   The speed control calculating part  8  outputs a first q-axis current command value Iq* from a difference between a speed command value ωr* and the estimated frequency value ω 1   c.    
   The d-axis current setting part  9  outputs a first d-axis current command value Id*. 
   The q-axis current control calculating part  10  outputs a second q-axis current command value Iq** from a difference between the first q-axis current command value Iq* and the detected current value Iqc. 
   The d-axis current control calculating part  11  outputs a second d-axis current command value Id** from a difference between the first d-axis current command value Id* and the detected current value Idc. 
   The vector control calculating part  12  outputs d-axis and q-axis voltage command values Vdc* and Vqc* according to electric constants of the permanent magnet motor  1 , the second current command values Id** and Iq**, and the estimated frequency value ω 1   c.    
   The coordinate converter  13  outputs three-phase current voltage command values Vu*, Vv*, and Vw* from the voltage command values Vdc* and Vqc* and the estimated phase value θc*. 
   The low-pass filter  14  receives the first d-axis and q-axis current command values Id* and Iq* and outputs current command values Id*td and Iq*td used by the axis error estimating part  5 . 
   A basic voltage and phase control method will be described first. 
   In a basic operation for voltage control, the d-axis current control calculating part  10  and q-axis current control calculating part  11  respectively use the first current command values Id* and Iq*, which are supplied from upstream, and the current detected values Idc and Iqc to calculate the second current command values Id** and Iq**, which are intermediate values used in vector control calculation. 
   The vector control calculating part  12  uses the second current command values Id** and Iq**, estimated frequency value ω 1   c  value, and motor constant settings to calculate the voltage command valued Vdc* and Vqc* indicated in equation (1), and controls the three-phase AC voltage command values Vu*, Vv*, and Vw* of the inverter. 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   [ 
                   
                     
                       
                         
                           Vdc 
                           * 
                         
                       
                     
                     
                       
                         
                           Vqc 
                           * 
                         
                       
                     
                   
                   ] 
                 
                 = 
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               R 
                               * 
                             
                           
                           
                             
                               
                                 - 
                                 
                                   ω 
                                   1 
                                 
                               
                               · 
                               
                                 Lq 
                                 * 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ω 
                                 1 
                               
                               · 
                               
                                 Ld 
                                 * 
                               
                             
                           
                           
                             
                               R 
                               * 
                             
                           
                         
                       
                       ] 
                     
                     · 
                     
                       [ 
                       
                         
                           
                             
                               Id 
                               ** 
                             
                           
                         
                         
                           
                             
                               Iq 
                               ** 
                             
                           
                         
                       
                       ] 
                     
                   
                   + 
                   
                     [ 
                     
                       
                         
                           0 
                         
                       
                       
                         
                           
                             
                               ω 
                               1 
                             
                             · 
                             
                               Ke 
                               * 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
   where 
   R: resistance 
   Ld: d-axis inductance 
   Lq: q-axis inductance 
   Ke: induced voltage coefficient 
   *: setting 
   In a basic operation for phase control, the axis error estimating part  5  uses the voltage command values Vdc* and Vqc*, the low-pass filter output values Id*td and Iq*td of the first current command values Id* and Iq*, the estimated frequency value ω 1   c , and the motor constant setting to estimate axis error Δθ (=θc*−0), which is a difference between the estimated phase value θC* and motor phase value θ, from equation (2) 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     θ 
                     c 
                   
                 
                 = 
                 
                   
                     tan 
                     
                       - 
                       1 
                     
                   
                   ⁡ 
                   
                     [ 
                     
                       
                         
                           Vdc 
                           * 
                         
                         - 
                         
                           
                             R 
                             * 
                           
                           · 
                           
                             Id 
                             td 
                             * 
                           
                         
                         + 
                         
                           
                             ω 
                             
                               1 
                               ⁢ 
                               c 
                             
                           
                           · 
                           
                             Lq 
                             * 
                           
                           · 
                           
                             Iq 
                             td 
                             * 
                           
                         
                       
                       
                         
                           Vqc 
                           * 
                         
                         - 
                         
                           
                             R 
                             * 
                           
                           · 
                           
                             Iq 
                             td 
                             * 
                           
                         
                         - 
                         
                           
                             ω 
                             
                               1 
                               ⁢ 
                               c 
                             
                           
                           · 
                           
                             Lq 
                             * 
                           
                           · 
                           
                             Id 
                             td 
                             * 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   The frequency estimating part  6  controls the estimated frequency value ω 1   c  by calculation according to equation (3) so that the estimated axis error Δθc becomes 0. 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   ω 
                   
                     1 
                     ⁢ 
                     c 
                   
                 
                 = 
                 
                   
                     - 
                     Δθ 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     c 
                     · 
                     
                       [ 
                       
                         Kp 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Ki 
                           S 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 ( 
                 3 
                 ) 
               
             
           
         
       
     
   
   where 
   Kp: proportional gain 
   Ki: integral gain 
   The proportional gain Kp and integral gain Ki are set as in equation (4). 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 [ 
                 
                   
                     
                       
                         Kp 
                         = 
                         
                           2 
                           ⁢ 
                           
                             π 
                             · 
                             
                               F 
                               PLL 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         Ki 
                         = 
                         
                           
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 
                                   p 
                                   · 
                                   
                                     F 
                                     PLL 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                           N 
                         
                       
                     
                   
                 
                 ] 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   where 
   N: ratio of break points for the proportional gain and integral gain in the frequency estimating part  6  [times] 
   F PLL : control response frequency of the frequency estimating part  6  [Hz] 
   The phase estimating part  7  uses the estimated frequency value ω 1   c  to control the estimated phase value θc* by the calculation indicated by equation (5). 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   θ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     c 
                     * 
                   
                 
                 = 
                 
                   
                     ω 
                     1 
                   
                   ⁢ 
                   
                     c 
                     · 
                     
                       1 
                       S 
                     
                   
                 
               
             
             
               
                 ( 
                 5 
                 ) 
               
             
           
         
       
     
   
   This completes the explanation of the basic operation for phase control. 
   Now, effects provided by using the first current command values Id* and Iq*, which are a feature of the present invention, in the axis error estimating part  5  will be described. 
   Control characteristics in a conventional control method in which the detected current values Idc and Iqc are used will be described first. 
     FIG. 2  illustrates operation characteristics when the control response frequency F PLL , which is set in the frequency estimating part  6 , is low. 
   The drawing indicates that the estimated axis error Δθc amounts to −50 deg in the range A during which acceleration is carried out from a low-speed point “a” to a maximum-speed point “b” and that the motor current I 1  is 8 A. 
     FIG. 3  illustrates operation characteristics when the control response frequency F PLL  is high. 
   The drawing indicates that the estimated axis error Δθc is reduced to −20 deg in the range A and thereby the motor current I 1  is reduced from 8 A to 4.5 A. 
   In the region B in which the number of revolutions is kept maximized, the calculated value Δθc is always −50 deg and pulsation is generated in the motor speed ωr. 
   This pulsation is problematic because it causes noise and stops operation due to an overcurrent. 
   Accordingly, when a low control response frequency F PLL  is set in the frequency estimating part  6 , large axis error is generated, increasing the motor current I 1  and thereby reducing the motor efficiency. 
   When the F PLL  is high, the axis error tends to be suppressed, but it may become unstable. 
   The cause why the estimated Δθc becomes unstable when a high F PLL  is set will be then described below. 
   When there is a difference between the estimated phase value θc* and the phase value θ of the motor, i.e., axis error Δθ (=θc*−0), a matrix of conversion from the control side (dc−qc) to the motor axes (d−q) is obtained from equation (6). 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   [ 
                   
                     
                       
                         d 
                       
                     
                     
                       
                         q 
                       
                     
                   
                   ] 
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                               
                               ) 
                             
                           
                         
                         
                           
                             - 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 Δθ 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               Δθ 
                               ) 
                             
                           
                         
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               Δθ 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     [ 
                     
                       
                         
                           dc 
                         
                       
                       
                         
                           qc 
                         
                       
                     
                     ] 
                   
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   The d-axis and q-axis voltages Vd and Vq are represented by equation (8). 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   [ 
                   
                     
                       
                         Vd 
                       
                     
                     
                       
                         Vq 
                       
                     
                   
                   ] 
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                               
                               ) 
                             
                           
                         
                         
                           
                             - 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 Δθ 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               Δθ 
                               ) 
                             
                           
                         
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               Δθ 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     [ 
                     
                       
                         
                           
                             Vdc 
                             * 
                           
                         
                       
                       
                         
                           
                             Vqc 
                             * 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
         
       
     
   
   Equation (8) indicates that the d-axis voltage Vd includes information about the q-axis voltage command value Vqc*. 
   When the voltage Vd changes, the d-axis current Id, the q-axis voltage Vq, and the q-axis current Iq also change in that order. Since the axis error estimating part  5  uses the detected current values Idc and Iqc for calculation, an unstable loop related to the estimated axis error Δθc is generated. 
   A loop transfer function GΔθ(s) from the axis error command value Δθc* to the estimated axis error Δθc is obtained as follows. 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   
                     G 
                     θ 
                   
                   ⁡ 
                   
                     ( 
                     s 
                     ) 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     
                       π 
                       · 
                       
                         F 
                         PLL 
                       
                       · 
                       
                         
                           ω 
                           r 
                           2 
                         
                         _ 
                       
                       · 
                       Ld 
                       · 
                       
                         Lq 
                         * 
                       
                     
                   
                   
                     
                       Ld 
                       · 
                       Lq 
                       · 
                       
                         S 
                         3 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           Ld 
                           + 
                           Lq 
                         
                         ) 
                       
                       · 
                       R 
                       · 
                       
                         S 
                         2 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             R 
                             2 
                           
                           + 
                           
                             
                               
                                 ω 
                                 r 
                                 2 
                               
                               _ 
                             
                             · 
                             Ld 
                             · 
                             Lq 
                           
                         
                         ) 
                       
                       · 
                       S 
                     
                   
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
   where 
   ωr: average motor speed 
     FIG. 4  illustrates frequency characteristics obtained by setting the average motor speed ωr to a maximum number of revolutions in equation (8) and assigning the control response frequency F PLL  set for the characteristics in  FIGS. 2 and 3  to equation (8). 
   The characteristics set in  FIG. 2  and the characteristics set in  FIG. 3  are represented by a dotted line and a solid line, respectively. 
   The characteristics in  FIG. 4  indicates that, at point c (=−180 deg) in the phase characteristics, the characteristics (dotted line) set in  FIG. 2  is stable at 0 dB (=1) or less and the characteristics (solid line) set in  FIG. 3  is unstable at 0 dB (=1) or more. 
   That is, when the detected current values Idc and Iqc are used to estimate a frequency, if F PLL  is high, the estimated axis error Δθc becomes unstable. 
   To make the estimated axis error Δθc stable, estimated current values are used to estimate a frequency. 
   The first current command values Id* and Iq* rather than the detected current values Idc and Iqc are used here to obtain primary delay signals Id*td and Iq*td indicated in equation (9) by calculation. 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   [ 
                   
                     
                       
                         
                           Id 
                           td 
                           * 
                         
                       
                     
                     
                       
                         
                           Iq 
                           td 
                           * 
                         
                       
                     
                   
                   ] 
                 
                 = 
                 
                   [ 
                   
                     
                       
                         
                           
                             1 
                             
                               1 
                               + 
                               
                                 Tacr 
                                 · 
                                 S 
                               
                             
                           
                           · 
                           
                             Id 
                             * 
                           
                         
                       
                     
                     
                       
                         
                           
                             1 
                             
                               1 
                               + 
                               
                                 Tacr 
                                 · 
                                 S 
                               
                             
                           
                           · 
                           
                             Iq 
                             * 
                           
                         
                       
                     
                   
                   ] 
                 
               
             
             
               
                 ( 
                 9 
                 ) 
               
             
           
         
       
     
   
   where 
   Tacr: Delay in current control response 
   The axis error estimating part  5  calculates the estimated Δθc as obtained from equation (3) above. 
     FIG. 5  shows characteristics when signals Id*td and Iq*td output from the low-pass filter  14  are used to estimate axis error (the same value as the F PLL  in  FIG. 3  is set). 
   Although the use of the detected current values Idc and Iqc has made operation unstable, the use of the signals Id*td and Iq*td output from the low-pass filter  14  ensures stable operation even in the region B. 
   Although, in this embodiment, the axis error estimating part  5  uses the signals output from the low-pass filter  14 , if the control gains in the d-axis current command generating part  9  and speed control calculating part  8  are low and the motions of Id* and Iq*, which are output signals thereof, are slow, Id* and Iq* may be used instead of Id*td and Iq*td to estimate Δθc by calculation. 
   Second Embodiment 
   In the method described in the first embodiment, to reduce axis error during acceleration or deceleration, the axis error command value Δθc* has been set to 0, and the current command values Id*td and Iq*td output from the low-pass filter have been used to estimate axis error. In this embodiment, an axis error command value Δθc* is generated from the speed command value ωr* to further reduce the axis error. 
     FIG. 6  shows this embodiment. 
   The elements having reference numerals  1  to  14  and  21  in the drawing are identical to the elements having the same reference numerals in  FIG. 1 . 
   The axis error command calculating part  15  uses the speed command value ωr* to output the axis error command value Δθc*. 
   The principle of operation of the axis error estimating part  15 , which is a feature of the present invention, will be described. 
   Described first is the value of the axis error Δθ (=estimated value Δθc) generated in the acceleration or deceleration region when the axis error estimating part  15  is not provided (Δθc*=0). 
   The frequency estimating part  6  uses the estimated axis error Δθc to calculate an estimated frequency value ω 1   c  from equation (3). 
   The relation between a change Δωr in motor speed and a differential torque Δτ between the motor torque and the load torque is represented by equation (10). 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ω 
                     r 
                   
                 
                 = 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     t 
                     · 
                     
                       1 
                       
                         J 
                         · 
                         S 
                       
                     
                     · 
                     Pm 
                   
                 
               
             
             
               
                 ( 
                 10 
                 ) 
               
             
           
         
       
     
   
   where 
   Pm: number of pole pairs of the motor 
   J: Synthesized inertia of the motor and machine [kgm 2 ] 
   When equation (3) is equalized to equation (10), equation (4) is assigned to them, and the resulting equation is rewritten about the estimated value Δθc, equation (11) is obtained. 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   Δθ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   c 
                 
                 = 
                 
                   - 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         t 
                         · 
                         
                           1 
                           J 
                         
                         · 
                         Pm 
                         · 
                         
                           N 
                           
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 
                                   π 
                                   · 
                                   
                                     F 
                                     PLL 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             N 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 
                                   π 
                                   · 
                                   
                                     F 
                                     PLL 
                                   
                                 
                               
                               ) 
                             
                           
                           · 
                           S 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 ( 
                 11 
                 ) 
               
             
           
         
       
     
   
   This equation indicates that the estimated value Δθc is related to the ratio N of break points for the proportional gain and integral gain in the frequency estimating part  6  and to the control response frequency F PLL . 
   When ωr* is equalized to ωr and equation (10) is differentiated, equation (12) is obtained. 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   
                     Δω 
                     r 
                     * 
                   
                   · 
                   S 
                 
                 = 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     t 
                     · 
                     
                       1 
                       J 
                     
                     · 
                     Pm 
                   
                 
               
             
             
               
                 ( 
                 12 
                 ) 
               
             
           
         
       
     
   
   Equation (12) is then assigned to equation (11), and an axis error command value Δθc*, indicated in equation (13), that cancels the estimated value Δθc is generated. 
   
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   Δθ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     c 
                     * 
                   
                 
                 = 
                 
                   
                     
                       N 
                       
                         
                           ( 
                           
                             2 
                             ⁢ 
                             
                               π 
                               · 
                               
                                 F 
                                 PLL 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                     · 
                     
                       Δω 
                       r 
                       * 
                     
                     · 
                     S 
                   
                   
                     [ 
                     
                       1 
                       + 
                       
                         
                           N 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               
                                 π 
                                 · 
                                 
                                   F 
                                   PLL 
                                 
                               
                             
                             ) 
                           
                         
                         · 
                         S 
                       
                     
                     ] 
                   
                 
               
             
             
               
                 ( 
                 13 
                 ) 
               
             
           
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   Δθ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     c 
                     * 
                   
                 
                 = 
                 
                   
                     
                       N 
                       
                         
                           ( 
                           
                             2 
                             ⁢ 
                             
                               π 
                               · 
                               
                                 F 
                                 PLL 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                     · 
                     Δ 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ω 
                       r 
                       * 
                     
                     · 
                     S 
                   
                 
               
             
             
               
                 ( 
                 14 
                 ) 
               
             
           
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   [ 
                   
                     
                       
                         
                           Vdc 
                           * 
                         
                       
                     
                     
                       
                         
                           Vqc 
                           * 
                         
                       
                     
                   
                   ] 
                 
                 = 
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               R 
                               * 
                             
                           
                           
                             
                               
                                 - 
                                 
                                   ω 
                                   
                                     1 
                                     ⁢ 
                                     c 
                                   
                                 
                               
                               · 
                               
                                 L 
                                 * 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ω 
                                 
                                   1 
                                   ⁢ 
                                   c 
                                 
                               
                               · 
                               
                                 Ld 
                                 * 
                               
                             
                           
                           
                             
                               R 
                               * 
                             
                           
                         
                       
                       ] 
                     
                     · 
                     
                       [ 
                       
                         
                           
                             
                               Id 
                               * 
                             
                           
                         
                         
                           
                             
                               Iq 
                               * 
                             
                           
                         
                       
                       ] 
                     
                   
                   + 
                   
                     [ 
                     
                       
                         
                           0 
                         
                       
                       
                         
                           
                             
                               ω 
                               
                                 1 
                                 ⁢ 
                                 c 
                               
                             
                             · 
                             
                               Ke 
                               * 
                             
                           
                         
                       
                     
                     ] 
                   
                   + 
                   
                     [ 
                     
                       
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               Vd 
                               * 
                             
                           
                         
                       
                       
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               Vq 
                               * 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             
               
                 ( 
                 15 
                 ) 
               
             
           
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
                 ⁢ 
                 
                     
                 
               
             
             
               
                   
               
             
           
           
             
               
                 
                   [ 
                   
                     
                       
                         
                           Vdc 
                           * 
                         
                       
                     
                     
                       
                         
                           Vqc 
                           * 
                         
                       
                     
                   
                   ] 
                 
                 = 
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               R 
                               * 
                             
                           
                           
                             
                               
                                 - 
                                 
                                   ω 
                                   r 
                                   * 
                                 
                               
                               · 
                               
                                 L 
                                 * 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ω 
                                 r 
                               
                               · 
                               
                                 Ld 
                                 * 
                               
                             
                           
                           
                             
                               R 
                               * 
                             
                           
                         
                       
                       ] 
                     
                     · 
                     
                       [ 
                       
                         
                           
                             
                               Id 
                               * 
                             
                           
                         
                         
                           
                             
                               Iqc 
                               td 
                             
                           
                         
                       
                       ] 
                     
                   
                   + 
                   
                     [ 
                     
                       
                         
                           0 
                         
                       
                       
                         
                           
                             
                               ω 
                               r 
                               * 
                             
                             · 
                             
                               Ke 
                               * 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
             
             
               
                 ( 
                 16 
                 ) 
               
             
           
         
       
     
   
   Frequency estimation is controlled so that the estimated value Δθc matches the command value Δθc*. 
     FIG. 7  illustrates characteristics when the axis error command value Δθc* is used (the F PLL  used in  FIG. 3  is set). 
   The drawing indicates that the axis error command value Δθc*, indicated by a dashed line, that is calculated in the range A has a value of 20 deg on the positive side so that the Δθc in  FIG. 5  is cancelled. 
   In this case, the estimated value Δθc (the actual axis error Δθ also has the same value) is 0 even in the range A and the motor current I 1  is reduced down to 4 A, indicating that highly efficient operation can be performed. 
   Although the axis error command value Δθc* is calculated from equation (13) in this embodiment, the axis error can also be reduced by an approximate calculation as indicated by equation (14). 
   In the first and second embodiments, the first current command values Id* and Iq* and the detected current values Idc and Iqc have been used to generate the second current command values Id** and Iq**, and the generated current command values have been used to perform calculation for vector control. However, it is also possible to apply these embodiments to: 
   1) a vector control calculation method in which the first current command values Id* and Iq* and the detected current values Idc and Iqc are used to generate voltage compensated values ΔVd* and ΔVq* and the generated voltage compensated values and the first current command values Id* and Iq*, the estimated frequency value ω 1   c , and the electric constants of the permanent magnet motor  1  are used to calculate the voltage command values Vdc* and Vqc* according to equation (15), and 
   2) a control calculation method in which the first d-axis current command value Id* (=0), the primary delay signal Iqctd of the detected q-axis current value Iqc, the speed command value ωr*, and the electric constants of the permanent magnet motor  1  are used to calculate the voltage command values Vdc* and Vqc* according to equation (16). 
   In the methods in the first and second embodiments, an expensive current detector  3  has been used to detect three-phase AC currents Iu, Iv, and Iw. However, these embodiments can also be applied to a low-cost system in which DC current flowing in a one shunt resistor mounted to detect an overcurrent in the electric power converter  2  is used to reproduce three-phase motor currents Iu^, Iv^, and Iw^ and the reproduced current values are used. 
   As described above, the present invention can suppress axis error during an acceleration or deceleration operation to 0 for motors having a small electric time constant (ratio of an inductance to a resistance) and motors having a large electric time constant, and can thereby achieve a highly efficient operation. 
   The present invention can also provide a highly responsive permanent magnet motor controller that can also be applied to an inexpensive current detecting system.