Patent Publication Number: US-9431935-B2

Title: Control device of AC motor

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is based on Japanese Patent Application No. 2013-170192 filed on Aug. 20, 2013, the disclosure of which is incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to a control device of an AC motor that senses a phase current of one phase among three phases by a current sensor and that controls a current flowing through an AC motor. 
     BACKGROUND 
     In recent years, from a social requirement of a lower fuel consumption and a less exhaust emission, an electric vehicle and a hybrid vehicle, each of which is mounted with an AC motor as a power source of a vehicle, is drawing attention. For example, in some of the hybrid vehicles, a DC power source made of a secondary battery or the like and an AC motor are connected to each other via an electric power conversion unit constructed of an inverter and the like, and a DC voltage of the DC power source is converted into an AC voltage by the inverter to thereby drive the AC motor. 
     In the control device of the AC motor mounted in the hybrid vehicle and the electric vehicle has been known the following technology (refer to, for example, a patent document 1): that is, a current sensor for sensing a phase current is provided only in one phase; and a current estimated value estimated on the basis of a current sensed value of the one phase is fed back, whereby a current flowing through an AC motor is controlled. Since the current sensor is provided only in the one phase, the number of the current sensor is reduced and the size of a portion near a three-phase output terminal of an inverter is reduced and the cost of a control system of the AC motor is reduced. 
     In the technique disclosed in the patent document 1, on the basis of a current sensed value of one phase (for example, U phase), which is sensed by the current sensor, and a d axis current command value and a q axis current command value and an electric angle of an AC motor, the current estimated values of the other two phases (for example, V phase and W phase) are calculated. Specifically, an angle (θ), which is formed by a rotator of the AC motor and a U phase axis of a stator, is added to a command current phase angle (α), which is acquired from a d axis current command value id* and a q axis current command value iq* to thereby find a U phase current phase angle θ′ (=θ+α). Then, a current amplitude Ia is calculated by the following formula (91) by the use of the U phase current phase angle θ′ and a U phase current sensed value Iu. Then, a sin value at an electric angle shifted by ±120 [°] from the U phase current phase angle θ′ is multiplied by the current amplitude Ia to thereby calculate the current estimated values Iv, Iw of the two other phases by the following formulas (92), (93).
 
 Ia=Iu /[√(⅓)×{−sin(θ′)}]  (91)
 
 Iv =√(⅓)× Ia ×{−sin(θ′+120°)}  (92)
 
 Iw =(⅓)× Ia ×{−sin(θ′+240°)}  (93)
 
     Then, the current sensed value Iu of one phase and the current estimated values Iv, Iw of the other two phases are dq transformed to thereby calculate a d axis current estimated value Id and a q axis current estimated value Iq. Then, the current flowing through the AC motor is controlled by a current feedback control mode of feeding back the d axis current estimated value Id and the q axis current estimated value Iq to a d axis current command value Id* and a q axis current command value Iq*. 
     In the technique of the patent document 1, when the U phase current phase angle θ′=0 [°] and sin(θ′)=0, in the calculation of the current amplitude Ia by the formula (91), Iu is divided by 0, that is, “zero division” is caused and hence the current amplitude Ia cannot be calculated correctly. For this reason, the current estimated values Iv, Iw of the other two phases cannot be calculated correctly. However, the patent document 1 never refers to measures against this “zero division”. Further, when the current sensed value Iu=0 [A], from the formulas (92) and (93), the current estimated values Iv, Iw of the other two phases are calculated as follows: Iv=0 [A] and Iw=0 [A]. Hence, there is a possibility that the control of the AC motor could not be performed. 
     Also in a technique other than the patent document 1, in the case where a variable to become 0 in a specified phase or at a specified timing is included, there is a possibility that a correct calculation could be impaired by “the zero division” of dividing something by 0 or “the zero multiplication” of multiplying something by 0 and hence the current estimated value could be varied.
     [Patent document 1] JP-A 2004-159391   

     SUMMARY 
     It is an object of the present disclosure to provide a control device of an AC motor that senses a phase current of one phase among three phases by a current sensor and that controls a current flowing through an AC motor and that prevents a current estimated value from being varied by “zero division” or “zero multiplication” in a calculation formula. 
     According to an aspect of the present disclosure, a control device of a three-phase AC motor includes: an inverter that drives the AC motor; a current sensor that senses a current flowing in a sensor phase among three phases of the AC motor as a sensor phase current; and a controller that switches on and off a switching element of the inverter to control a current flowing through the AC motor. The controller includes: a current estimation device that estimates a d-axis current estimated value and a q-axis current estimated value based on the sensor phase current and an electric angle of the AC motor; and a zero-crossing interpolation device that interpolates a command value relating to a voltage of the AC motor when the sensor phase current is in a predetermined zero cross range, which includes a zero point. When the sensor phase current is in the zero cross range, the zero-crossing interpolation device interpolates the command value with a continuous variable value. 
     According to the above device, when the sensor phase current crosses zero, the command value relating to the voltage of the AC motor is interpolated, whereby “zero division” of dividing something by 0 and “zero multiplication” of multiplying something by 0 are prevented from being caused in the calculation formula for a current estimation. Hence, when the sensor phase crosses zero, variation in the current estimated value can be prevented. 
     The above device interpolates the command value relating to the voltage of the AC motor by “the continuous variable values” to thereby continuously change the interpolated values in accordance with the driving state of the AC motor during the zero-crossing period. Hence, when the zero-crossing period is finished, the difference between the optimal voltage command value for the driving state of the AC motor and the interpolated value can be prevented. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, features and advantages of the present disclosure will become more apparent from the following detailed description made with reference to the accompanying drawings. In the drawings: 
         FIG. 1  is a diagram to show a construction of an electric motor drive system to which a control device of an AC motor according to an embodiment of the present disclosure is applied; 
         FIG. 2  is a general construction diagram of the control device of an AC motor according to the embodiment of the present disclosure; 
         FIG. 3  is a block diagram to show a construction of a control section of a current feedback control mode according to a first embodiment of the present disclosure; 
         FIG. 4  is a block diagram to show a construction of another phase current estimation part of  FIG. 3 ; 
         FIG. 5  is a chart to illustrate a fixed coordinate system (α-β coordinate system) based on a sensor phase; 
         FIGS. 6A and 6B  are waveform charts to illustrate a movement of another phase current estimated value when a sensor phase current crosses zero; 
         FIG. 7  is a schematic chart to show an example of interpolating a d axis voltage command value and a q axis voltage command value when a sensor phase current crosses zero; 
         FIG. 8  is a flow chart of current estimation processing according to the first embodiment of the present disclosure; 
         FIG. 9  is a subordinate flow chart of zero-crossing interpolation processing of another phase current estimated value; 
         FIG. 10  is a flow chart of current estimation processing according to a modified example of the first embodiment; 
         FIG. 11  is a block diagram to show a construction of a control section of a torque feedback control mode according to a second embodiment of the present disclosure; 
         FIG. 12  is a schematic chart to show an example of interpolating a voltage phase command value when a sensor phase current crosses zero; and 
         FIG. 13  is a flow chart of current estimation processing according to the second embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, embodiments of a control device of an AC motor according to the present disclosure will be described on the basis of the drawings. First, a construction common to a plurality of embodiments will be described with reference to  FIG. 1  and  FIG. 2 . An electric motor control device  10  as “a control device of an AC motor” according to an embodiment is applied to an electric motor drive system  1  for driving a hybrid vehicle. 
     [Construction of Control Device of AC Motor] 
     As shown in  FIG. 1 , the electric motor drive system  1  has an AC motor  2 , a DC power source  8 , and the electric motor control device  10 . The AC motor  2  is an electric motor for generating torque for driving the driving wheels  6  of an electrically driven vehicle. The AC motor  2  of the present embodiment is a three-phase AC motor of a permanent magnet synchronous type. 
     The electrically driven vehicle includes a vehicle for driving the driving wheels  6  by an electric energy such as a hybrid vehicle, an electric vehicle, and a fuel cell electric vehicle. The electrically driven vehicle of the present embodiment is a hybrid vehicle provided with an engine  3  and the AC motor  2  is a so-called motor generator (designated by “MG” in the drawings) having a function as an electric motor for generating torque to drive the driving wheels  6  and a function as a generator which is driven by the kinetic energy of the vehicle, transmitted from the engine  3  and the driving wheels  6 , and which can generate electricity. 
     The AC motor  2  is coupled to an axle  5  via a gear  4 , for example, a transmission. In this way, a driving force of the AC motor  2  rotates the axle  5  via the gear  4  to thereby drive the driving wheels  6 . 
     The DC power source  8  is an electricity storage device that can charge and discharge electricity, for example, a secondary battery such as a nickel metal hydride battery or a lithium ion battery, and an electric double-layer capacitor. The DC power source  8  is connected to an inverter  12  (refer to  FIG. 2 ) of the electric motor control device  10 , that is, the DC power source  8  is so constructed as to supply electricity to the AC motor  2  and to be supplied with electricity from the AC motor  2  via the inverter  12 . 
     A vehicle control circuit  9  is constructed of a microcomputer and the like and is provided therein with a CPU, a ROM, an I/O, and a bus line for connecting these elements, all of which are not shown in the drawings. The vehicle control circuit  9  controls the whole of the electrically driven vehicle by software processing, which is performed by executing previously stored programs by the CPU, and by hardware processing, which is performed by a dedicated electronic circuit. 
     The vehicle control circuit  9  is so constructed as to be able to acquire signals from various kinds of sensors and switches such as an accelerator signal from an accelerator sensor, a brake signal from a brake switch, a shift signal from a shift switch, and a vehicle speed signal relating to a speed of the vehicle, all of which are not shown in the drawings. Further, the vehicle control circuit  9  detects a driving state of the vehicle on the basis of these acquired signals and outputs a torque command value trq* responsive to the driving state to the electric motor control device  10 . Further, the vehicle control circuit  9  outputs a command signal to an engine control circuit (not shown) for controlling the drive of the engine  3 . 
     As shown in  FIG. 2 , the electric motor control device  10  includes the inverter  12 , a current sensor  13 , and a control section  15  as “a controller.” 
     The inverter  12  has a boost voltage of the DC power source by a boost converter (not shown) inputted thereto as a system voltage VH. The inverter  12  has six switching elements (not shown) connected in a bridge mode. As to the switching element, for example, an IGBT (Insulated Gate Bipolar Transistor), a MOS (Metal Oxide Semiconductor) transistor, and a bipolar transistor can be used. The switching elements are switched on and off on the basis of PWM signals UU, UL, VU, VL, WU, WL outputted from a PWM signal generation part  25  of the control section  15 , whereby the drive of the AC motor  2  is controlled on the basis of three phase AC voltages vu, w, vw to be impressed on the AC motor  2 . 
     The current sensor  13  is provided in any one phase of the AC motor  2 . In the present embodiment, the current sensor  13  is provided in a W phase. Hereinafter, the W phase in which the first current sensor  13  is provided is referred to as “a sensor phase”. The current sensor  13  senses a phase current of the W phase as a current sensed value iw_sns of the sensor phase and outputs the current sensed value iw_sns to the control section  15 . Hereinafter, in the description of the present embodiment, the description will be made on the premise of a construction in which the sensor phase is the W phase. However, in the other embodiments, a U phase or a V phase may be the sensor phase. 
     A rotation angle sensor  14  is provided near a rotor (not shown) of the AC motor  2  and senses an electric angle θe and outputs the sensed electric angle θe to the control section  15 . Further, the number of revolutions N of a rotor of the AC motor  2  is calculated on the basis of the electric angle θe sensed by the rotation angle sensor  14 . Hereinafter, “the number of revolutions N of the rotor of the AC motor  2 ” is simply referred to as “the number of revolutions N of the AC motor  2 ”. The rotation angle sensor  14  of the present embodiment is a resolver. However, in the other embodiments, the rotation angle sensor  14  may be other kind of sensor, for example, a rotary encoder. 
     The control section  15  is constructed of a microcomputer and the like and is provided therein with a CPU, a ROM, an I/O, and a bus line for connecting these elements, all of which are not shown in the drawings. The control section  15  controls an action of the AC motor  2  by software processing, which is performed by executing previously stored programs by the CPU, and by hardware processing, which is performed by a dedicated electronic circuit. 
     According to the number of revolutions N of the AC motor  2  based on the electric angle θe sensed by the rotation angle sensor  14  and to a torque command value trq* from the vehicle control circuit  9 , the electric motor control device  10  drives the AC motor  2  as an electric motor, whereby the AC motor  2  performs “a powering operation as an electric motor” and consumes electricity, or drives the AC motor  2  as a generator, whereby the AC motor  2  performs “a regenerating operation as a generator” and generates electricity. Specifically, according to the number of revolutions N and whether the torque command value trq* is plus or minus, the electric motor control device  10  switches the action of the AC motor  2  into the following four patterns: 
     &lt;1. Normal rotation/powering operation&gt; when the number of revolutions N is plus and the torque command value trq* is plus, the AC motor  2  consumes electricity; 
     &lt;2. Normal rotation/regenerating operation&gt; when the number of revolutions N is plus and the torque command value trq* is minus, the AC motor  2  generates electricity; 
     &lt;3. Reverse rotation/powering operation&gt; when the number of revolutions N is minus and the torque command value trq* is minus, the AC motor  2  consumes electricity; and 
     &lt;4. Reverse rotation/regenerating operation&gt; when the number of revolutions N is minus and the torque command value trq* is plus, the AC motor  2  generates electricity. 
     In the case where the number of revolutions N&gt;0 (normal rotation) and the torque command value trq*&gt;0, or the number of revolutions N&lt;0 (reverse rotation) and the torque command value trq*&lt;0, the inverter  12  converts a DC electricity supplied from the DC power source  8  to an AC electricity by the switching operation of the switching elements and supplies the AC electricity to the AC motor  2 , whereby the AC motor  2  is driven in such a way as to output torque (to perform a powering operation). 
     On the other hand, in the case where the number of revolutions N&gt;0 (normal rotation) and the torque command value trq*&lt;0, or the number of revolutions N&lt;0 (reverse rotation) and the torque command value trq*&gt;0, the inverter  12  converts an AC electricity generated by the AC motor  2  to a DC electricity by the switching operation of the switching elements and supplies the DC electricity to the DC power source  8 , whereby the AC motor  2  performs a regenerating operation. 
     [Construction and Operation &amp; Effect of Control Section] 
     Hereinafter, the construction and the operation, and effect of the control section  15  will be described for each embodiment. A control section  151  of a first embodiment controls a current flowing through the AC motor  2  by a current feedback control mode, whereas a control section  153  of a second embodiment controls a current flowing through the AC motor  2  by a torque feedback control mode. 
     First Embodiment 
     The control section  151  of the first embodiment of the present disclosure will be described with reference to  FIG. 3  to  FIG. 10 . The current feedback control mode is a control mode for feeding back a d axis current estimated value id_est and a q axis current estimated value iq_est to a d axis current command value id* and a q axis current command value iq*, respectively, and includes a so-called sine wave control mode and an overmodulated control mode. 
     As shown in  FIG. 3 , the control section  151  includes a dq axis current command value operation part  21 , a current subtractor  22 , a PI operation part  23 , an inverse dq transformation part  24 , a PWM signal generation part  25 , a current estimation part  301 , and a voltage command value zero-crossing interpolation part  27  as “a zero-crossing interpolation device”. 
     The dq axis current command value operation part  21  operates a d axis current command value id* and a q axis command value iq* in a rotary coordinate system (d-q coordinate system) of the AC motor  2  on the basis of the torque command value trq* acquired from the vehicle control circuit  9 . In the present embodiment, the d axis current command value id* and the q axis command value iq* are operated with reference to a map stored previously. In the other embodiments, the dq axis current command value operation part  21  may be constructed in such a way that the d axis current command value id* and the q axis command value iq* are operated from a mathematical formula or the like. 
     The current subtractor  22  has a d axis current subtractor  221  and a q axis current subtractor  222 . The d axis current subtractor  221  calculates a d axis current deviation Δid of a difference between the d axis current estimated value id_est, which is calculated by the current estimation part  301  and is fed back, and the d axis current command value id*. Further, the q axis current subtractor  222  calculates a q axis current deviation Δiq of a difference between the q axis current estimated value iq_est, which is calculated by the current estimation part  301  and is fed back, and the q axis current command value iq*. 
     The PI operation part  23  has a d axis PI operation part  231  and a q axis PI operation part  232 . The d axis PI operation part  231  calculates a d axis voltage command value vd* by a PI operation in such a way that the d axis current deviation Δid converges to 0 so as to make the d axis current estimated value id_est follow the d axis current command value id*. Further, the q axis PI operation part  232  calculates a q axis voltage command value vd* by a PI operation in such a way that the q axis current deviation Δiq converges to 0 so as to make the q axis current estimated value iq_est follow the q axis current command value iq*. 
     The d axis voltage command value vd* and the q axis voltage command value vq*, which are operated by the PI operation part  23 , are inputted to the inverse dq transformation part  24  as a d axis voltage command value (fixed value) vd*_fix and a q axis voltage command value (fixed value) vq*_fix via the voltage command value zero-crossing interpolation part  27 . The construction of the voltage command value zero-crossing interpolation part  27  will be described later. The inverse dq transformation part  24  transforms the d axis voltage command value (fixed value) vd*_fix and the q axis voltage command value (fixed value) vq*_fix to a U phase voltage command value vu*, a V phase voltage command value vv*, and a W phase voltage command value vw* on the basis of the electric angle θe acquired from the rotation angle sensor  14 . 
     The PWM signal generation part  25  calculates PWM signals UU, UL, VU, VL, WU, WL, which relate to switching on or off the switching elements of the inverter  12 , on the basis of the three phase voltage command values vu*, w*, vw* and the system voltage VH impressed on the inverter  12 . When the switching elements of the inverter  12  are switched on or off on the basis of the PWM signals UU, UL, VU, VL, WU, WL, the three phase AC voltages vu, w, vw are generated. Then, when the three phase AC voltages vu, w, vw are impressed on the AC motor  2 , the drive of the AC motor  2  is controlled in such a way that a torque corresponding to the torque command value trq* is outputted. 
     The current estimation part  301  includes another phase current estimation part  31  and a dq transformation part  34 . In the case of an electric motor control device having the current sensors  13  provided in two phases, a current in one remaining phase in which the current sensor  13  is not provided can be easily calculated by the Kirchhoff&#39;s law. On the other hand, in the present embodiment in which the current sensor  13  is provided only in one phase (W phase), the other phase current estimation part  31  of the current estimation part  301  estimates a current of one phase among the U phase and the V phase which are not provided with the current sensor  13 . Hereinafter, a phase for which a current is estimated is referred to as “an estimated phase”. In the description of the present embodiment, the description will be made on the premise of a construction in which the estimated phase is the U phase. 
     The dq transformation part  34  dq transforms the current sensed value iw_sns of the sensor phase and a current estimated value iu_est of the estimated phase, which is estimated by the other phase current estimation part  31 , to thereby calculate a d axis current estimated value id_est and a q axis estimated value iq_est. In this regard, in  FIG. 3 , a case in which the estimated phase is the V phase will be shown in a parenthesis such as [iu(v)_est] for the other phase current estimated value outputted to the dq transformation part  34  from the other phase current estimation part  31  and, in the same way, [u(v)w→dq] for the dq transformation part  34 . 
     Next, a construction will be described in which the other phase current estimation part  31  estimates a current estimated value iu_est of the estimated phase. Here, in the current feedback control mode, the d axis current command value id* and the q axis current command value iq* are used for the control. Hence, the other phase current estimation part  31  of the present embodiment calculates the current estimated value iu_est of the estimated phase on the basis of the information on the current sensed value iw_sns of the sensor phase, the electric angle θe, and the d axis current command value id* and the q axis current command value iq*. In particular, the present embodiment is characterized in that the current estimated value iu_est of the estimated phase is calculated from a sensor phase reference current phase θx calculated on the basis of an α axis current iα and a β axis current iβ in an α-β coordinate system. 
     The other phase current estimation part  31  of the present embodiment, as shown in a detailed construction of  FIG. 4 , includes another phase current reference value calculation part  32  and another phase current zero-crossing interpolation part  33 . The other phase current reference value calculation part  32  acquires the d axis current command value id* and the q axis current command value iq*, which are calculated by the dq axis current command value operation part  21 , and the electric angle θe, and calculates a current command value iv* of the V phase, which is not the estimated phase, by an inverse dq transformation. In this regard, in the case where the estimated phase is the V phase in the other embodiment, the other phase current reference value calculation part  32  may calculate a current command value iu* of the U phase or may calculate the current command values iu*, iv* of the U phase and the V phase. 
     Next, the other phase current reference value calculation part  32  calculates the α axis current iα and the β axis current iβ by the use of the V phase current command value iv* calculated in this manner and the current sensed value iw_sns of the sensor phase and then calculates the sensor phase reference current phase θx defined in the α-β coordinate system. 
     As shown in  FIG. 5 , an α axis corresponds to an axis of the W phase of the sensor phase and a β axis is orthogonal to the α axis. The sensor phase reference current phase θx is an angle, which is formed by the α axis and a current vector (Ia∠θx) of a current amplitude Ia and is synchronous with the current sensed value iw_sns of the sensor phase. In the state of a normal rotation and a powering operation of a plus torque, the sensor phase reference current phase θx when a waveform of a W phase current iw crosses zero from minus to plus is 0 [°], whereas the sensor phase reference current phase θx when the waveform of the W phase current iw crosses zero from plus to minus is 180 [°]. 
     Here, the α axis current iα and the β axis current iβ, which are used for calculating the sensor phase reference current phase θx, will be described. When the α axis current iα and the β axis current iβ are expressed by the use of the respective phase currents iu, iv, iw, the α axis current iα and the β axis current iβ are shown by formulas (1), (2). Here, K in the formulas is a transformation coefficient. 
     
       
         
           
             
               
                 
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     Further, as described above, the sum of instantaneous values of three phase currents iu, iv, iw becomes 0 by the Kirchhoff&#39;s law, that is, the following formula (3) holds.
 
 iu+iv+iw= 0  (3)
 
     Here, when the formula (1) is deformed by the use of the formula (3), the following formula (4) is obtained. 
     
       
         
           
             
               
                 
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     In other words, as shown in the formula (4), the α axis current is can be calculated on the basis of only the W phase current iw of the sensor phase. Here, when the current sensed value iw_sns of the sensor phase is used as the W phase current iw, an α axis current sensed value iα_sns can be expressed by a formula (5). 
     
       
         
           
             
               
                 
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     Further, when the formula (2) is referred to, in the case where the current command value iu* is used as the U phase current iu and the current command value iv* is used as the V phase current iv, a β axis current estimated value iβ_est can be expressed by a formula (6). 
     
       
         
           
             
               
                 
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     In the formula (6), the β axis current estimated value iβ_est is calculated from the current command values iu*, iv* and does not include a component of the current sensed value iw_sns of the sensor phase, which is sensed by the current sensor  13 . For this reason, the β axis current estimated value iβ_est calculated by the formula (6) is not always information reflecting an actual current with high accuracy. Hence, when the formula (6) is deformed in such a way that the β axis current estimated value iβ_est includes the current sensed value iw_sns of the sensor phase by the use of the Kirchhoff&#39;s law (formula (3)), the following formula (7) can be obtained. 
     
       
         
           
             
               
                 
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                             - 
                             
                               3 
                             
                           
                           × 
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             v 
                             * 
                           
                         
                         - 
                         
                           
                             
                               3 
                             
                             2 
                           
                           ⁢ 
                           iw_sns 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     As shown by the formula (7), when the β axis current estimated value iβ_est is made to include the current sensed value iw_sns of the sensor phase, which is an actual current, it is possible to respond to variations in control and hence to narrow a region in which a W phase axis component is small and is hard to converge. Hence, the accuracy of the β axis current estimated value iβ_est can be improved. In other words, a sensing accuracy of the sensor phase reference current phase θx calculated by the use of the β axis current estimated value iβ_est can be improved. Subsequently, the sensor phase reference current phase θx is calculated by a formula (8) on the basis of the α axis current sensed value iα_sns calculated by the formula (5) and the β axis current estimated value iβ_est calculated by the formula (6) or the formula (7). 
     Here, in the case where the sensor phase reference current phase θx is calculated by an arc tangent function (tan −1 ) by the use of the formula (8), depending on the definition of the α axis current iα and the β axis current iβ, there could be a case where the sensor phase reference current phase θx does not become an angle synchronous with the sensor phase (W phase). This is caused by the definition of an axis (for example, an interchange or a sign inversion of the α axis and the β axis). 
     In this case, it is assumed that the calculation method can be changed as required in such a way that: the sensor phase reference current phase θx when the current sensed value iw_sns of the sensor phase in a normal rotation and a normal torque crosses zero from minus to plus becomes 0 [°]; and the sensor phase reference current phase θx when the current sensed value iw_sns of the sensor phase crosses zero from plus to minus becomes 180 [°], in other words, in such a way that the sensor phase reference current phase θx becomes an angle synchronous with the sensor phase current sensed value iw_sns. For example, the sensor phase reference current phase θx may be calculated after operating the signs of the α axis current iα and the β axis current iβ, or the α axis current iα and the β axis current iβ may be interchanged between them, or a phase difference 90 [°] caused by an orthogonal relationship between the α axis and the β axis may be added to or subtracted from the calculated sensor phase reference current phase θx. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     θ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     x 
                   
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         iβ_est 
                         iα_sns 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Next, the current estimated value iu_est of the U phase of the estimated phase is calculated by the use of the sensor phase reference current phase θx and the current sensed value iw_sns of the sensor phase. Here, when the current sensed value iw_sns of the sensor phase and the current estimated value iu_est of the U phase of the estimated phase are expressed by the use of the sensor phase reference current phase θx, because a phase difference between the respective phases is 120 [°], the current sensed value iw_sns of the sensor phase and the current estimated value iu_est of the U phase of the estimated phase are expressed by formulas (9) and (10), respectively. Here, Ia in the formulas (9), (10) is a current amplitude.
 
 iw _ sns=Ia ×sin(θ x )  (9)
 
 iu _ est=Ia ×sin(θ x− 120°)  (10)
 
     Further, when the formula (10) is deformed by the use of an addition theorem, the U phase current estimated value iu_est can be expressed by the following formula (11) by the use of the sensor phase reference current phase θx and the current sensed value iw_sns of the sensor phase. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         iu_est 
                         = 
                           
                         ⁢ 
                         
                           Ia 
                           × 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   θ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   x 
                                 
                                 - 
                                 
                                   120 
                                   ⁢ 
                                   ° 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               
                                 1 
                                 2 
                               
                             
                             × 
                             Ia 
                             × 
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   θ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   x 
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             
                               
                                 3 
                               
                               2 
                             
                             × 
                             Ia 
                             × 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   θ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   x 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               
                                 1 
                                 2 
                               
                             
                             × 
                             iw_sns 
                           
                           - 
                           
                             
                               
                                 3 
                               
                               2 
                             
                             × 
                             
                               
                                 Ia 
                                 × 
                                 sin 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     θ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   ) 
                                 
                               
                               
                                 tan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     x 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             { 
                             
                               
                                 - 
                                 
                                   1 
                                   2 
                                 
                               
                               - 
                               
                                 
                                   
                                     3 
                                   
                                   2 
                                 
                                 × 
                                 
                                   1 
                                   
                                     tan 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         θ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         x 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             } 
                           
                           × 
                           iw_sns 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Further, when an estimation coefficient iu_kp is defined by a formula (12), the U phase current estimated value iu_est can be expressed also by a formula (13) by the use of the estimation coefficient iu_kp. Here, the estimation coefficient iu_kp may be directly operated by a formula (12), or a part or all of the formula (12) may be mapped in advance on the basis of the sensor phase reference current phase θx and then the estimation coefficient iu_kp may be calculated with reference to this map. 
     In the case where the control section  151  is constructed of a conventional electronic control circuit (microcomputer), when the control section  151  is mounted with an operation formula, the operation formula is processed not in continuous time but in discrete time and hence the sensor-sensed value and the respective operated values are treated also as discrete values based on a specified resolution (LSB). Here, “the control section  151  is mounted with an operation formula” means that the control section  151  includes a program of software and a construction of a hardware circuit. In order to avoid multiplication and division of large processing load, it is effective to map the estimation coefficient iu_kp or a term of {1/tan(θx)} in the estimation coefficient iu_kp by using the sensor phase reference current phase θx as an argument. This mapping makes it easy to apply the control section  151  to a discrete system, which results in minimizing the processing load of the microcomputer and hence eliminating the need for using an expensive microcomputer having a high operation processing capacity. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Mathematical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   iu_kp 
                   = 
                   
                     
                       - 
                       
                         1 
                         2 
                       
                     
                     - 
                     
                       
                         
                           3 
                         
                         2 
                       
                       × 
                       
                         1 
                         
                           tan 
                           ⁡ 
                           
                             ( 
                             
                               θ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               x 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   iu_est 
                   = 
                   
                     iu_kp 
                     × 
                     iw_sns 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     When the formula (11) or the formula (13) is referred to, in the case of calculating the U phase current estimated value iu_est by the use of the sensor phase reference current phase θx and the current sensed value iw_sns of the sensor phase, the current amplitude Ia is not used. Hence, in the current estimation, the current amplitude Ia does not need to be found and hence variables to be operated can be reduced. 
     The U phase current estimated value iu_est, which is calculated on the basis of the sensor phase reference current phase θx and the current sensed value iw_sns of the sensor phase, is outputted as a current estimated value (reference value) iu_est_ref of the estimated phase to the other phase current zero-crossing interpolation part  33 . 
     Here, as shown in  FIGS. 6A and 6B , the current sensed value iw_sns of the sensor phase changes in the shape of a sine wave and interchanges between plus and minus across 0 [A] every phase of 180 [°]. In this way, not only when the current sensed value iw_sns of the sensor phase is strictly 0 [A] but also when the current sensed value iw_sns of the sensor phase is within a specified range Az including 0 [A] is referred to as “when the sensor phase current crosses zero”. Further, in the following descriptions, when the current value or the like includes not only a value of strict 0 but also a value within a range substantially equivalent to 0 in terms of a control operation in which a sensing error and the resolution of a device are taken into consideration, the current value or the like will be described as “zero”. 
     “A value within a specified range Az including 0 [A]” means that an absolute value of the current sensed value iw_sns of the sensor phase is not more than a specified value or that an absolute value of the estimation coefficient iu_kp is not less than a specified value. Here, “a specified value” may be set by a current value of, for example, ±5 [A], or may be set on the basis of a resolution of, for example, 5 [LSB] in the discrete system, or may be set by a mathematical formula or the like. Further, since the current sensed value iw_sns of the sensor phase is synchronous with the sensor phase reference current phase θx, “a specified value” may be set by a value of the sensor phase reference current phase θx. 
     As shown in  FIG. 6B , a state where the current sensed value iw_sns of the sensor phase is within the specified range Az corresponds to a zero-crossing phase range Pzx on a phase axis. The zero-crossing phase range Pzx can be also converted to “a zero-crossing period Tzx” (refer to  FIG. 7  and the like, which will be described later) on a time axis. As for a method for converting the zero-crossing phase range Pzx to the time axis, any method may be used: for example, a method for calculating the number of revolutions of the AC motor  2  as a coefficient, and a method for measuring the time that elapses between two points of a starting point and an ending point of the zero-crossing phase range Pzx by a timer or the like in the microcomputer. 
     When the sensor phase current crosses zero, from the formula (5), an α axis current sensed value iα_sns becomes zero and a tangent tan(θx) of the sensor phase reference current phase θx becomes infinite in the formula (8). Then, when the current sensed value iw_sns of the sensor phase becomes zero or the tangent tan(θx) of the sensor phase reference current phase θx becomes infinite in the formula (11), “zero multiplication” of multiplying something by zero” is caused. Further, when the tangent tan(θx) of the sensor phase reference current phase θx becomes zero in the formula (11), “zero division” of dividing something by zero is caused. For this reason, the current estimated value iu_est of the U phase of the estimated phase might be varied. 
     Hence, in the present embodiment, the other phase current zero-crossing interpolation part  33  interpolates the current estimated value (reference value) iu_est_ref to thereby mask the zero division and the zero multiplication. In this regard, as to the zero division, in order to prevent the current estimated value from being calculated to be an unintentional value by the effect of the discrete system in the formula (13), it is possible to take measures against the zero division also by setting a limited value for the estimated coefficient iu_kp or for a term of {1/tan(θx)} in the estimated coefficient iu_kp. Further, in the case where the control section  151  is mounted with the formula (13), it is also effective to map the estimated coefficient iu_kp or the term of {1/tan (θx)} of the estimated coefficient iu_kp. In this case, it is possible to take measures against the zero division also by setting a limited value in the map. 
     The other phase current zero-crossing interpolation part  33  includes a zero-crossing determination part  331  and a last value holding part  332 . The zero-crossing determination part  331  determines whether or not the present time is the time “when the sensor phase current crosses zero”. In other words, when the current sensed value iw_sns of the sensor phase is within the specified range Az including 0 [A], the zero-crossing determination part  331  determines that the present time is the time when the sensor current crosses zero. 
     In the case where the zero-crossing determination part  331  determines that the present time is not the time when the sensor phase current crosses zero, the zero-crossing determination part  331  outputs the current estimated value (reference value) iu_est_ref calculated by the other phase current reference value calculation part  32 , as it is, as a current estimated value (fixed value) iu_est_fix to the dq transformation part  34 . 
     On the other hand, in the case where the zero-crossing determination part  331  determines that the present time is the time when the sensor phase current crosses zero, the zero-crossing determination part  331  acquires a current estimated value (interpolated value) iu_est_cmp from the last value holding part  332  and outputs the current estimated value (interpolated value) iu_est_cmp as the current estimated value (fixed value) iu_est_fix to the dq transformation part  34 . 
     The last value holding part  332  holds a value of the last time in advance, and in the case where the zero-crossing determination part  331  determines that the present time is the time when the sensor phase current crosses zero, the last value holding part  332  calculates the current estimated value (interpolated value) iu_est_cmp and outputs the current estimated value (interpolated value) iu_est_cmp to the zero-crossing determination part  331 . 
     For example, the last value holding part  332  holds a specified number of nearest previous current estimated values (fixed values) iu_est_fix, which are calculated previously, as current estimated values (held values) iu_est_hld. Then, in the case where the zero-crossing determination part  331  determines that the present time is the time when the sensor phase current crosses zero, the last value holding part  332  makes the current estimated value (held value) iu_est_hld, which is a value of the last time or a value before the last time, the current estimated value (interpolated value) iu_est_cmp (hereinafter, this operation is referred to as “zero-crossing interpolate, or “zero-crossing interpolation”) and outputs the current estimated value (interpolated value) iu_est_cmp to the zero-crossing determination part  331 . 
     Further, for example, the last value holding part  332  holds a specified number of nearest previous d axis current estimated values id_est and q axis current estimated values iq_est, which are previously calculated by the dq transformation part  34 , as d axis current estimated values (held values) id_est_hld and q axis current estimated values (held values) iq_est_hld. Then, in the case where the zero-crossing determination part  331  determines that the present time is the time when the sensor phase current crosses zero, the last value holding part  332  calculates a U phase estimated value as a current estimated value (interpolated value) iu_est_cmp by the inverse dq transformation of the d axis current estimated values (held values) id_est_hld and the q axis current estimated values (held values) iq_est_hld, which are the values of the last time or the values before the last time, and outputs the current estimated value (interpolated value) iu_est_cmp to the zero-crossing determination part  331 . 
     In this way, when the sensor phase current crosses zero, by interpolating the current estimated value iu_est of the estimated phase, a sudden variation in the current estimated value iu_est of the estimated phase, which is caused by “the zero division” or the “zero multiplication” in the formula (11), can be avoided. In this regard, a method of zero-crossing interpolating the current estimated value iu_est of the estimated phase, which is performed by the other phase current zero-crossing interpolation part  33 , may be a method other than the method described above, or the zero-crossing interpolation of the current estimated value iu_est of the estimated phase may be not performed as required. 
     The dq transformation part  34  calculates the d axis current estimated value id_est and the q axis current estimated value iq_est by the dq transformation by the use of the current estimated values (fixed values) iu_est_fix acquired from the other phase zero-crossing interpolation part  33 , the current sensed value iw_sns of the sensor phase, and the electric angle θe. The calculation of the d axis current estimated value id_est and the q axis current estimated value iq_est in the dq transformation part  34  will be described. First, a general formula of the dq transformation will be shown in the following formula (14). 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Mathematical 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       formula 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       9 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           id_est 
                         
                       
                       
                         
                           iq_est 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         
                           2 
                           3 
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     e 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       θ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       e 
                                     
                                     - 
                                     
                                       120 
                                       ⁢ 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       θ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       e 
                                     
                                     + 
                                     
                                       120 
                                       ⁢ 
                                       ° 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       θ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       e 
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 - 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         e 
                                       
                                       - 
                                       
                                         120 
                                         ⁢ 
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 - 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         e 
                                       
                                       + 
                                       
                                         120 
                                         ⁢ 
                                         ° 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               u 
                             
                           
                         
                         
                           
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               v 
                             
                           
                         
                         
                           
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               w 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Here, iv=−iu−iw by the Kirchhoff&#39;s law (refer to formula (3)), and when iu=iu_est and iw=iw_sns are substituted for the formula (14), the following formula (15) can be acquired. Here, in the present embodiment, the current estimated value (fixed value) iu_est_fix, which is zero-crossing interpolated, is used as the iu_est. 
     
       
         
           
             [ 
             
               Mathematical 
               ⁢ 
               
                   
               
               ⁢ 
               formula 
               ⁢ 
               
                   
               
               ⁢ 
               10 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           
                             [ 
                             
                               
                                 
                                   id_est 
                                 
                               
                               
                                 
                                   iq_est 
                                 
                               
                             
                             ] 
                           
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 
                                   2 
                                   3 
                                 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 cos 
                                                 ⁢ 
                                                 
                                                   ( 
                                                   
                                                     θ 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     e 
                                                   
                                                   ) 
                                                 
                                               
                                               - 
                                             
                                           
                                         
                                         
                                           
                                             
                                               cos 
                                               ⁡ 
                                               
                                                 ( 
                                                 
                                                   
                                                     θ 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     e 
                                                   
                                                   - 
                                                   
                                                     120 
                                                     ⁢ 
                                                     ° 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               
                                                 cos 
                                                 ⁢ 
                                                 
                                                   ( 
                                                   
                                                     
                                                       θ 
                                                       ⁢ 
                                                       
                                                           
                                                       
                                                       ⁢ 
                                                       e 
                                                     
                                                     + 
                                                     
                                                       120 
                                                       ⁢ 
                                                       ° 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                               - 
                                             
                                           
                                         
                                         
                                           
                                             
                                               cos 
                                               ⁡ 
                                               
                                                 ( 
                                                 
                                                   
                                                     θ 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     e 
                                                   
                                                   - 
                                                   
                                                     120 
                                                     ⁢ 
                                                     ° 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   - 
                                                   sin 
                                                 
                                                 ⁢ 
                                                 
                                                   ( 
                                                   
                                                     θ 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     e 
                                                   
                                                   ) 
                                                 
                                               
                                               + 
                                             
                                           
                                         
                                         
                                           
                                             
                                               sin 
                                               ⁡ 
                                               
                                                 ( 
                                                 
                                                   
                                                     θ 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     e 
                                                   
                                                   - 
                                                   
                                                     120 
                                                     ⁢ 
                                                     ° 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               
                                                 
                                                   - 
                                                   sin 
                                                 
                                                 ⁢ 
                                                 
                                                   ( 
                                                   
                                                     
                                                       θ 
                                                       ⁢ 
                                                       
                                                           
                                                       
                                                       ⁢ 
                                                       e 
                                                     
                                                     + 
                                                     
                                                       120 
                                                       ⁢ 
                                                       ° 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                               + 
                                             
                                           
                                         
                                         
                                           
                                             
                                               sin 
                                               ⁡ 
                                               
                                                 ( 
                                                 
                                                   
                                                     θ 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     e 
                                                   
                                                   - 
                                                   
                                                     120 
                                                     ⁢ 
                                                     ° 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     iu_est 
                                   
                                 
                                 
                                   
                                     iw_sns 
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 2 
                                 3 
                               
                             
                             × 
                             
                               
                                 
                                   3 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           cos 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 θ 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 e 
                                               
                                               + 
                                               
                                                 30 
                                                 ⁢ 
                                                 ° 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           - 
                                           
                                             cos 
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 
                                                   θ 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   e 
                                                 
                                                 - 
                                                 
                                                   90 
                                                   ⁢ 
                                                   ° 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           - 
                                           
                                             sin 
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 
                                                   θ 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   e 
                                                 
                                                 + 
                                                 
                                                   30 
                                                   ⁢ 
                                                   ° 
                                                 
                                               
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     As shown in the formula (15), the d axis current estimated value id_est and the q axis current estimated value iq_est can be calculated by the dq transformation by the use of the current values (sensed values or estimated values) of two phases among three phases. Hence, the other phase current estimation part  31  needs to calculate only the current estimated value of one phase (U phase) among two phases other than the sensor phase and does not need to calculate the current estimated value of the other phase (V phase). 
     Returning to  FIG. 3 , the description will be made continuously. The d axis current estimated value id_est and the q axis current estimated value iq_est, which are estimated in the above manner by the current estimation part  301 , are fed back to the subtractor  22 . Then, the PI operation part  23  calculates the d axis voltage command value vd* and the q axis voltage command value vq* by the PI operation on the basis of the d axis current deviation Δid and the q axis current deviation Δiq. Incidentally, when the sensor phase current crosses zero, if the other phase current zero-crossing interpolation part  33  interpolates the current estimated value iu_est of the estimated phase, there is a possibility that the d axis voltage command value vd* and the q axis voltage command value vq* are varied by the error of the current estimated value iu_est of the estimated phase, which is caused by the interpolation, and hence that the current feedback control could be made unstable. Hence, the voltage command value zero-crossing interpolation part  27  performs the zero-crossing interpolation of the d axis voltage command value vd* and the q axis voltage command value vq* apart from the zero crossing interpolation of the current estimated value iu_est of the estimated phase, thereby preventing the d axis voltage command value vd* and the q axis voltage command value vq* from being varied. 
     The voltage command value zero-crossing interpolation part  27  determines on the basis of the current sensed value iw_sns of the sensor phase and the electric angle θe whether or not the present time is the time when the sensor phase current crosses zero, as is the case with the zero-crossing determination part  331  of the other phase current zero-crossing interpolation part  33 . Alternatively, the voltage command value zero-crossing interpolation part  27  may use the determination result of the zero-crossing determination part  331 . In the case where the voltage command value zero-crossing interpolation part  27  determines that the present time is not the time when the sensor phase current crosses zero, the voltage command value zero-crossing interpolation part  27  outputs the d axis voltage command value vd* and the q axis voltage command value vq*, which are operated by the PI operation part  23 , as they are, as the d axis voltage command value (fixed value) vd*_fix and the q axis voltage command value (fixed value) vq*_fix to the inverse transformation part  24 . 
     On the other hand, in the case where the voltage command value zero-crossing interpolation part  27  determines that the present time is the time when the sensor phase current crosses zero, the voltage command value zero-crossing interpolation part  27  interpolates the d axis voltage command value vd* and the q axis voltage command value vq*, which are operated by the PI operation part  23 , by continuous variable values and outputs the interpolated values as the d axis voltage command value (fixed value) vd*_fix and the q axis voltage command value (fixed value) vq*_fix to the inverse transformation part  24 . Here, “to interpolate the d axis voltage command value vd* and the q axis voltage command value vq* by continuous variable values” means that the d axis voltage command value vd* and the q axis voltage command value vq* are not fixed at constant values such as the values of the last time, respectively, but that the interpolated values of the d axis voltage command value vd* and the q axis voltage command value vq* are repeatedly updated during the zero-crossing period. 
     A specific example of interpolating the d axis voltage command value vd* and the q axis voltage command value vq* by “continuous variable values” will be described with reference to  FIG. 7 . A horizontal axis of  FIG. 7  designates time and a vertical axis designates voltage. The time of the horizontal axis correlates to the sensor phase reference current phase θx. In other words, the zero-crossing phase range Pzx of  FIG. 6B  corresponds to “a zero-crossing period Tzx” from a time is when the sensor phase current starts crossing zero till a time te when the sensor phase current finishes crossing zero. Voltage values shown by solid lines are the d axis voltage command value vd* and the q axis voltage command value vq* which are operated by the PI operation part  23  by the current feedback control in the time except for the zero-crossing period Tzx. In the zero-crossing period Tzx, the d axis voltage command value vd* and the q axis voltage command value vq* are interpolated respectively by a d axis voltage command interpolated value vd*_cmp and a q axis voltage command interpolated value vq*_cmp, which are shown by broken lines. 
     The d axis voltage command interpolated value vd*_cmp and the q axis voltage command interpolated value vq*_cmp are repeatedly operated at specified operation intervals by filtering processing, an exterpolation method, or the like. For example, in the exterpolation method, a value of this time is estimated by exterpolating the operated value of the last time but one and the operated value of the last time or the past operated values other than these operated values in combination. Further, in the other method, a d axis voltage command reference value vd*_ref and a q axis voltage command reference value vq*_ref, which are shown by single-dot and dash lines, are made target values and the interpolated values are operated in such a way that the present values are brought closer to the target values. These reference values are calculated, for example, by a feedforward operation based on a voltage equation of an electric motor. 
     In the feedforward operation, the d axis voltage command value vd* and the q axis voltage command value vq* are calculated by the use of formulas (16.1), (16.2) on the basis of the d axis current command value id* and the q axis current command value iq*.
 
 vd*=Ra×id*+Ld× ( d/dt ) id*−ω×Lq×iq*   (16.1)
 
 vq*=Ra×iq*+Lq× ( d/dt ) iq*+ω×Ld×id*+ω×ψ   (16.2)
 
     Here, the symbols are as follows. 
     Ra: armature resistance 
     Ld, Lq: d axis self inductance, q axis self inductance 
     ω: electric angular speed 
     ψ: armature interlinkage magnetic flux of permanent magnet 
     The armature resistance Ra, the d axis self inductance Ld, the q axis self inductance Lq, and the armature interlinkage magnetic flux ψ, which are device constants of the AC motor  2 , may be fixed values or may be operated by calculation. Further, these device constants may be operated in the following manner: that is, values close to actual characteristics and actually measured values are put into a map; and these device constants are operated from the map on the basis of the torque command value trq*, or the d axis current command value id* and the q axis command value iq*. 
     Further, the reference value that is a target value to which the interpolated value is brought closer may be calculated not only by the feedforward operation but also by the use of a value calculated by the other operation. Still further, processing of bringing the present value closer to the reference value may be performed by filtering the interpolated values for the reference value and may be performed by the use of another method for changing a value continuously. In this way, the present embodiment is characterized in that the d axis voltage command value vd* and the q axis voltage command value vq* are not fixed at constant values, thereby being interpolated, but are interpolated by the continuous variable values in the zero-crossing period Tzx. 
     Next, a current estimation processing routine of the first embodiment will be described with reference to  FIG. 8  and  FIG. 9 . In the description of the following flow charts, a symbol S designates “step”. Further, as described above, in the present embodiment, a construction has been described by way of example in which the W phase is selected as the sensor phase from among three phases and in which the U phase is selected as the estimated phase in which the current is estimated, so that also in the description of the flow charts, the description will be made on the premise of the construction described above. 
     A current estimation routine is repeatedly performed at specified operation intervals during a period in which the power of the control section  151  is on. When the present routine is started, in the first step S 10 , the current sensed value iw_sns of the sensor phase, which is sensed by the current sensor  13 , is acquired and the electric angle θe of the AC motor  2 , which is sensed by the rotation angle sensor  14 , is acquired. 
     Then, in the first embodiment, the reference value calculation part  32  of the other phase current estimation part  31  calculates the α axis current iα and the β axis current iβ in S 22 , S 23  and then calculates the sensor phase reference current phase θx in S 28 . In S 22 , the current command value iv* of the V phase is calculated by the electric angle θe of the AC motor  2  and by the inverse transformation based on the d axis current command value id* and the q axis current command value iq*. The V phase in this case is a phase which is not the estimated phase among two phases other than the sensor phase. Here, in the other embodiment, the current command values iu*, iv* of the U phase and the V phase may be calculated. 
     In S 23 , the α axis current iα_sns is calculated by the formula (5) by the use of the current sensed value iw_sns of the sensor phase. In S 24 , the β axis current iβ_est is calculated by the formula (7) by the use of the current command value iv* of the other one phase and the current sensed value iw_sns of the sensor phase. In S 28 , the sensor phase reference current phase θx is calculated by the formula (8) by the use of the α axis current iα and the β axis current iβ. 
     In S 40 , the current estimated value (reference value) iu_est_ref of the U phase is calculated by the formula (11) by the use of the sensor phase reference current phase θx and the current sensed value iw_sns of the sensor phase. At this time, the current estimated value (reference value) iu_est_ref of the U phase may be calculated by the formula (13) by the use of the estimated coefficient iu_kp, which is calculated by the formula (12) or is acquired from the map, and the current sensed value iw_sns of the sensor phase. 
     In S 50 , the other phase current zero-crossing interpolation part  33  performs interpolation processing when the sensor phase current crosses zero for the current estimated value (reference value) of the U phase. In a subordinate flow chart of  FIG. 9 , in S 51 , the zero-crossing determination part  331  determines whether or not the present time is the time when the sensor phase current crosses zero. This determination is made, for example, by determining whether or not the current sensed value iw_sns of the sensor phase is a value within the specified range Az including 0 [A]. 
     In the case where it is determined in S 51  that the present time is not the time when the sensor phase current crosses zero (NO), the routine proceeds to S 52  where the current estimated value (reference value) iu_est_ref of the U phase, which is calculated in S 40 , is outputted as it is, as the current estimated value (fixed value) iu_est_fix of the U phase. 
     On the other hand, in the case where it is determined in S 51  that the present time is the time when the sensor phase current crosses zero (YES), the routine proceeds to S 54 . In S 54 , the current estimated value (interpolated value) iu_est_cmp of the U phase is acquired from the last value holding part  332  and then the current estimated value (interpolated value) iu_est_cmp of the U phase is outputted as the current estimated value (fixed value) iu_est_fix of the U phase. 
     Returning to  FIG. 8 , in S 60 , the dq transformation part  34  dq transforms the current sensed value iw_sns of the sensor phase and the current estimated value iu_est of the U phase by the formula (15) on the basis of the electric angle θe to thereby calculate the d axis current estimated value id_est and the q axis current estimated value iq_est. The d axis current estimated value id_est and the q axis current estimated value iq_est, which are calculated in this way, are fed back to the d axis current command value id* and the q axis current command value iq* by the subtractor  22 . Then, the PI operation part  23  operates the d axis voltage command value vd* and the q axis voltage command value vq* in such a way that the d axis current deviation Δid and the q axis current deviation Δiq converges to 0. 
     Next, in S 71  to S 73 , the voltage command value zero-crossing interpolation part  27  performs interpolation processing when the sensor phase current crosses zero for the d axis voltage command value vd* and the q axis voltage command value vq*. In S 71 , it is determined whether or not the present time is the time when the sensor phase current crosses zero. The determination result in S 51  may be employed for this determination. In the case where it is determined that the present time is not the time when the sensor phase current crosses zero (S 71 : NO), the routine proceeds to S 72 . In S 72 , the d axis voltage command value vd* and the q axis voltage command value vq*, which are operated by the PI operation part  23 , are outputted, as they are, as the d axis voltage command value (fixed value) vd*_fix and the q axis voltage command value (fixed value) vq*_fix. Then, the routine is finished. 
     On the other hand, in the case where it is determined that the present time is the time when the sensor phase current crosses zero (S 71 : YES), the routine proceeds to S 73 . In S 73 , the d axis voltage command value vd* and the q axis voltage command value vq* are interpolated by the continuous variable values and the interpolated values are outputted as the d axis voltage command value (fixed value) vd*_fix and the q axis voltage command value (fixed value) vq*_fix. Then, the routine is finished. 
     Further, in a modified example shown in a flow chart of  FIG. 10 , in addition to S 73 , S 74  is performed in which the d axis current estimated value id_est and the q axis current estimated value iq_est, which are calculated in S 60 , are interpolated. In S 74 , the d axis current estimated value id_est and the q axis current estimated value iq_est may be fixed respectively at the values of the last time or the values before the last time, thereby being interpolated, or may be interpolated by the continuous variable values. 
     Effects of First Embodiment 
     (1) The electric motor control device  10  of the present embodiment is a device for sensing a phase current of one phase among three phases by the current sensor  99  and for estimating phase currents of the other two phases. The current sensor  13  is provided only in the sensor phase and hence the number of the current sensor  13  can be reduced. In this way, a portion near a three-phase output terminal of the inverter  12  can be reduced in size and the cost of the electric motor control device  10  can be reduced. Further, by reducing the number of the current sensor  13  to one, the effect of a gain error of the current sensor, which could be caused in a conventional control system of an AC motor using a plurality of current sensors, can be eliminated. In this way, in the AC motor  2 , an output torque variation caused by the gain error of the plurality of current sensors can be eliminated, which leads to eliminating a vehicle vibration, for example, in the case of an AC motor for a vehicle and to removing an element of reducing the product marketability of the vehicle. 
     (2) When a current flowing through the AC motor  2  is controlled by the current feedback control mode in the electric motor control device  10  having the current sensor  13  provided only in one phase, by interpolating the current estimated value iu_est of the estimated phase when the sensor phase current crosses zero, a state can be avoided in which calculation cannot be performed because of “the zero division” and “the zero multiplication” in the formula (11). Hence, it is possible to prevent the current estimated value iu_est of the estimated phase from being suddenly changed. 
     (3) When the sensor phase current crosses zero, by interpolating the d axis voltage command value vd* and the q axis voltage command value vq* as “a command value relating to the voltage of the AC motor”, for example, variations in the d axis voltage command value vd* and the q axis voltage command value vq*, which are caused by the estimation error developed by the zero-crossing interpolation of the current estimated value iu_est of the estimated phase, can be prevented. Hence, it is possible to avoid the current feedback control of the AC motor  2  from being made unstable. 
     (4) In the interpolation method in which the d axis voltage command value vd* and the q axis voltage command value vq* are fixed on the basis of only information at the time is when the zero-crossing period Tzx starts, a change in the d axis voltage command value vd* and the q axis voltage command value vq*, which are operated during the zero-crossing period Tzx, is not taken into consideration. Hence, when the zero-crossing period Tzx is finished, an optimal voltage command value for the driving state of the electric motor is different from the interpolated value, so that when the current estimation processing returns from the processing when the sensor phase current crosses zero, the d axis voltage command value vd* and the q axis voltage command value vq* might be changed discontinuously. 
     In contrast to this, by interpolating the d axis voltage command value vd* and the q axis voltage command value vq* by the continuous variable values on the basis of the information changed during the zero-crossing period Tzx, the interpolated values can be continuously changed in accordance with the driving state of the electric motor during the zero-crossing period Tzx, which can prevent the difference between the optimal voltage command value for the driving state of the electric motor when the zero-crossing period Tzx is finished and the interpolated value. 
     (5) As shown by the modified example (refer to  FIG. 10 ), when the sensor phase current crosses zero, by interpolating not only the d axis voltage command value vd* and the q axis voltage command value vq* but also the d axis current estimated value id_est and the q axis current estimated value iq_est, variations in the d axis current estimated value id_est and the q axis current estimated value iq_est can be prevented. Hence, in the other control and determination, which are performed by the use of the d axis current estimated value id_est and the q axis current estimated value iq_est, other than the current feedback control, the effect of an erroneous determination and a malfunction can be avoided. 
     (6) As a conventional technique for estimating the current of a phase other than the sensor phase in an electric motor control device having a current sensor provided only in one phase, the technique described in the patent document 1 (JP-A 2004-159391) is a technique for estimating the current of the phase other than the sensor phase on the basis of a d axis current command value and a q axis current command value. 
     By the way, a current vector of an AC motor follows a command current vector while changing with respect to a command current vector corresponding to a current command value by the effect of a control error and a feedback control. For this reason, there is caused “a difference” between an actual current phase and a command current phase and hence the command current phase does not become information reflecting the actual current phase with high accuracy. In this point, the conventional technique of the patent document 1 does never take the actual current phase into consideration and calculates the current estimated values of the other two phases by the use of a U phase current phase angle found from a command current phase angle. Hence, especially in the case where a change in torque and a change in rotation speed are required, as is the case with an AC motor for a vehicle, the current estimated values cannot be calculated with high accuracy, which causes a possibility that the control of the AC motor cannot be established. 
     In contrast to this, the current estimation part  301  of the present embodiment calculates the sensor phase reference current phase θx on the basis of the α axis current iα and the β axis current iβ in the fixed coordinate system (α-β coordinate system) based on the sensor phase and hence can calculate an actual current phase θx based on the sensor phase. Further, the current estimation part  301  of the present embodiment calculates the current estimated value iu_est of the estimated phase on the basis of the sensor phase reference current phase θx and the current sensed value iw_sns of the sensor phase and hence can calculate the current estimated value iu_est of the estimated phase with accuracy in consideration of the effects of the higher harmonic wave component of the actual current phase θx and variations usually developed. 
     (7) In the present embodiment in which the current flowing through the AC motor  2  is controlled by the use of the current feedback control mode, the β axis current iβ is calculated by the formula (6) or the formula (7) on the basis of two phase current values among the current command values iu*, iv* of the phases other than the sensor phase, which can be acquired by inverse dq transforming the d axis current command value id* and the q axis current command value iq*, and the current sensed value iw_sns of the sensor phase. In particular, it is preferable that the β axis current iβ is calculated by the formula (7) on the basis of the current command values iv* of one phase other than the sensor phase and the current sensed value iw_sns of the sensor phase. 
     In this case, in the α-β coordinate system, “a region in which the effect of the current sensed value is large and in which a calculation error of the sensor phase reference current phase θx is small” can be expanded. Hence, the effect of the current sensed value of the sensor phase can be included in the β axis current iβ. As a result, a calculation accuracy of the sensor phase reference current phase θx can be improved. In this way, periodic control variations in the d axis current and the q axis current can be reduced, and at a transient time when the current command values are changed or the like, a calculation accuracy of the current estimated value iu_est, in other words, convergence to a true value of the current estimated value iu_est can be improved. 
     Second Embodiment 
     Next, a control section  153  of a second embodiment of the present disclosure will be described with reference to  FIG. 11  to  FIG. 13 . In the description of a control block diagram and a flow chart of the second embodiment, the substantially same constructions or the substantially same steps as the first embodiment will be denoted by the same reference symbols and their descriptions will be omitted. A torque feedback control mode is a control mode of feeding back a torque estimated value tr_est to a torque command value trq*. Specifically, a square wave control mode of controlling a phase of a square wave voltage is known as a control mode of the torque feedback control mode (for example, refer to JP-A 2010-124544). Here, a square wave in this case means a waveform of one pulse in one cycle of current. 
     As shown in  FIG. 11 , the control section  153  includes a torque subtractor  52 , a PI operation part  53 , a square wave generator  54 , a signal generator  55 , a current estimation part  303 , a torque estimation part  56 , and a voltage phase command value zero-crossing interpolation part  57  as “a zero-crossing interpolation device”. The torque subtractor  52  calculates a torque deviation Δtrq of a difference between a torque estimated value trq_est, which is fed back from the torque estimation part  56 , and a torque command value trq*. 
     The PI operation part  53  calculates a voltage phase command value Vψ, which is a phase command value of a voltage vector, in such a way that the torque deviation Δtrq converges to 0 so as to make the torque estimated value trq_est follow the torque command value trq*. The voltage phase command value Vψ operated by the PI operation part  53  is inputted to the square wave generator  54  as a voltage phase command value (fixed value) Vψ_fix via the voltage phase command value zero-crossing interpolation part  57 . The construction of the voltage phase command value zero-crossing interpolation part  57  will be described later. 
     The square wave generator  54  generates a square wave on the basis of the voltage phase command value Vψ and the electric angle θe and outputs a U phase voltage command value vu*, a V phase voltage command value vv*, and a W phase voltage command value vw*. The signal generator  55  generates voltage command signals UU, UL, VU, VL, WU, WL, which relate to switching on/off the switching elements of the inverter  12 , on the basis of the U phase voltage command value vu*, the V phase voltage command value vv*, and the W phase voltage command value vw* and outputs the generated voltage command signals UU, UL, VU, VL, WU, WL to the inverter  12 . The switching elements of the inverter  12  are switched on/off on the basis of the voltage command signals UU, UL, VU, VL, WU, WL, whereby three phase AC voltages vu, vv, vw are generated. Then, the three phase AC voltages vu, vv, vw are impressed on the AC motor  2  and hence the drive of the AC motor  2  is controlled so as to output torque corresponding to the torque command value trq*. 
     The current estimation part  303  estimates the d axis current estimated value id_est and the q axis current estimated value iq_est on the basis of the current sensed value iw_sns of the sensor phase, which is sensed by the current sensor  13 , and the electric angle θe, which is acquired from the rotation angle sensor  14 . In the torque feedback control mode, unlike the current feedback control mode, the d axis current command value id* and the q axis current command value iq* or the current command values iu*, iv* of the phases (U phase and V phase) other than the sensor phase, which can be obtained by inverse dq transforming the d axis current command value id* and the q axis current command value iq*, cannot be used for the current estimation. Hence, the current estimation part  303  of the present embodiment estimates the d axis current estimated value id_est and the q axis current estimated value iq_est on the basis of the information on the current sensed value iw_sns of the sensor phase and the electric angle θe without using these current command values. 
     In particular, in the present embodiment, as is the case with the first embodiment, first, the other phase current estimation part calculates the current estimated value iu_est of the estimated phase by the use of the α-β coordinate system. Here, the present embodiment is characterized by focusing attention on that the α axis current iα and the β axis current iβ are in the relationship between “a sine wave and a cosine wave” and that a phase difference between the α axis current iα and the β axis current iβ is 90 [°] and by calculating the β axis current iβ on the basis of a differential value Δiα of the α axis current. Then, the present embodiment is characterized by dq transforming the current sensed value iw_sns of the sensor phase and the current estimated value iu_est of the estimated phase to thereby calculate the d axis current estimated value id_est and the q axis current estimated value iq_est. 
     The differential value Δiα of the α axis current is calculated by the following formula (17) on the basis of “an amount of change in the α axis current iα to an electric angle movement Δθe [rad] between timings when the α axis current iα is calculated”, that is, “a difference between a value of this time and a value of the last time of the α axis current iα”.
 
Δ iα=−{iα ( n )− i α( n− 1)}/Δθ e   (17)
 
     Here, the electric angle movement Δθe is a value of expressing an electric angle movement from the current sensing timing of the last time to the current sensing timing of this time by a unit of radian. Further, iα ( n ) is the value of this time of the α axis current iα and iα (n−1) is the value of the last time of the α axis current iα. In this regard, the current sensing timing may be set at “a switching timing”, which is the timing when the switching elements of any one phase of the inverter  12  is switched on/off every electric angle 60 [°], and at “an intermediate timing” between consecutive switching timings. 
     Further, in the case where an operation in the control section  153  is performed in a discrete system, the differential value Δiα of the α axis current iα is delayed by the half of the electric angle movement Δθe with respect to an actual β axis current iβ. It is preferable in consideration of this point that a correction amount H, which is obtained by multiplying an average value of the value of last time and the value of this time of the α axis current iα by the half of the electric angle movement Δθe (Δθe/2), is calculated from a formula (18) and that the correction amount H is added to the differential value Δiα of the α axis current iα by a formula (19).
 
 H={iα ( n− 1)+ i α( n )}/2×(Δθ e/ 2)  (18)
 
 iβ _ est=Δiα+H   (19)
 
     Then, the sensor phase reference current phase θx is calculated by the formula (8) by the use of the α axis current iα and the β axis current iβ. Here, in the case where a sign is reversed by the definition of the α axis current iα and the β axis current iβ in the formula (17), the sign may be operated if necessary in such a way as to be appropriate for the calculation of “tan −1  (iβ/iα)” by the formula (8). Alternatively, in the case where as the result of the calculation, the sensor phase reference current phase θx is not synchronous with the current sensed value iw_sns of the sensor phase, not only the sign is operated but also a phase difference of 90 [°] may be appropriately added to or subtracted from the calculated sensor phase reference current phase θx. This is the same as the current feedback control mode. 
     Further, it is assumed that the other phase current estimation part of the current estimation part  303  of the present embodiment has the same detailed construction as the other phase current estimation part  31  of the first embodiment shown in  FIG. 4  except for a point that the other phase current reference value calculation part  32  has the d axis current command value id* and the q axis current command value iq* inputted thereto. The other phase current reference value calculation part  32  calculates the current estimated value (reference value) iu_est_ref of the estimated phase by the formula (11) or the formula (13) on the basis of the current sensed value iw_sns of the sensor phase and the sensor phase reference current phase θx. Then, when the sensor phase current crosses zero, the other phase current zero-crossing interpolation part  33  (refer to  FIG. 4 ) zero-crossing interpolates the current estimated value iu_est of the estimated phase to thereby calculate the current estimated value (fixed value) iu_est_fix of the estimated phase. When the current estimated value (fixed value) iu_est_fix of the estimated phase is calculated in this way, the current estimation part  303  calculates the d axis current estimated value id_est and the q axis current estimated value iq_est by the formula (15). 
     The torque estimation part  56  operates the torque estimated value trq_est by a formula (20) or a map or the like on the basis of the d axis current estimated value id_est and the q axis current estimated value iq_est, which are estimated by the current estimation part  303 , and then feeds back the torque estimated value trq_est to the torque subtractor  52 ,
 
 trq _ est=p×{iq _ est ×ψ+( Ld−Lq )× id _ est×iq _ est}   (20)
 
     Here, symbols are as follows: 
     p: number of pairs of poles of AC motor 
     Ld, Lq: d axis self inductance, q axis self inductance 
     ψ: armature interlinkage magnetic flux of permanent magnet 
     The voltage phase command value zero-crossing interpolation part  57  determines whether or not the present time is the time when the sensor phase current crosses zero on the basis of the current sensed value iw_sns of the sensor phase and the electric angle θe, as is the case with the zero-crossing determination part  331  of the other phase current zero-crossing interpolation part  33  (refer to  FIG. 4 ). Alternatively, the voltage phase command value zero-crossing interpolation part  57  may use the determination result of the zero-crossing interpolation part  331 . 
     In the case where the voltage phase command value zero-crossing interpolation part  57  determines that the present time is not the time when the sensor phase current crosses zero, the voltage phase command value zero-crossing interpolation part  57  outputs the voltage phase command value Vψ, which is operated by the PI operation part  53 , as it is, as a voltage phase command value (fixed value) Vψ_fix to the square wave generator  54 . 
     On the other hand, in the case where the voltage phase command value zero-crossing interpolation part  57  determines that the present time is the time when the sensor phase current crosses zero, the voltage phase command value zero-crossing interpolation part  57  interpolates the voltage phase command value Vψ, which is operated by the PI operation part  53 , by continuous variable values and outputs the interpolated voltage phase command value Vψ as the voltage phase command value (fixed value) Vψ_fix to the square wave generator  54 . Here, “to interpolate the voltage phase command value Vψ by continuous variable values” means that the voltage phase command value Vψ is not fixed at a constant value such as the value of the last time but the interpolated values are repeatedly updated during the zero-crossing period. 
     A specific example in which the voltage phase command value Vψ is interpolated by “the continuous variable values” will be described with reference to  FIG. 12  corresponding to  FIG. 7  of the first embodiment.  FIG. 12  is the same as  FIG. 7  except for that a vertical axis designates a phase (angle). A phase shown by a solid line shows the voltage phase command value Vψ, which is operated by the PI operation part  53  by the torque feedback control in the time other than the zero-crossing period Tzx. In the zero-crossing period Tzx, the voltage phase command value Vψ is interpolated by a voltage phase command interpolated value Vψ_cmp shown by a broken line. 
     The voltage phase command interpolated value Vψ_cmp is repeatedly operated at specified operation intervals by filtering processing or an exterpolation method, as is the case with the first embodiment. For example, in a method for bringing a present value closer to a target value, an interpolated value is operated in such a way as to bring the present value closer to the target value of a voltage phase command value Vψ_ref shown by a single dot and dash line. In this case, a reference value to which the present value is brought closer may be calculated by a calculation formula on the basis of the torque command value trq* and the number of revolutions of the AC motor  2  or may be calculated with reference to a map or the like. 
     Subsequently, a current estimation processing routine of the second embodiment will be described with reference to  FIG. 13 . A flow chart shown in  FIG. 13  is different from the flow chart shown in  FIG. 8  of the first embodiment in the following points: the α axis current iα and the β axis current iβ are calculated by S 25  to S 27  in place of S 22  to S 24 ; and in the case where it is determined that the present time is not the time when the current sensed value iw_sns of the sensor phase crosses zero (S 71 : NO), S 75  is performed in place of S 72 , whereas in the case where it is determined that the present time is the time when the current sensed value iw_sns of the sensor phase crosses zero (S 71 : YES), S 76  is performed in place of S 73 . 
     In S 25 , the α axis current iα is calculated by the formula (5) by the use of the current sensed value iw_sns of the sensor phase. In S 26 , the differential value Δiα of the α axis current iα is calculated by the formula (17) on the basis of a change amount of the α axis current iα to the electric angle movement Δθe between the current sensing timings of the α axis current iα. In S 27 , the correction amount H is added to the differential value Δiα of the α axis current iα by the formulas (18), (19) to thereby calculate the β axis current estimated value iβ_est. 
     In S 75 , the voltage phase command value Vψ, which is operated by the PI operation part  53 , is outputted, as it is, as the voltage phase command value (fixed value) Vψ_fix. Then, the current estimation processing routine is finished. In S 76 , the voltage phase command value Vψ is interpolated by the continuous variable values and the interpolated voltage phase command value Vψ is outputted as the voltage phase command value (fixed value) Vψ_fix. Then, the current estimation processing routine is finished. 
     Further, as is the case with S 74  in the modified example of the first embodiment shown in  FIG. 10 , the d axis current estimated value id_est and the q axis current estimated value iq_est may be interpolated in addition to S 76  shown in  FIG. 13 . In this case, the d axis current estimated value id_est and the q axis current estimated value iq_est may be fixed at the values of the last time or the values before the last time, thereby being interpolated, or may be interpolated by the continuous variable values. 
     Effect of Second Embodiment 
     The second embodiment has the effects (1), (2) of the first embodiment in common and has the following effects (3′), (4′), (5′) in place of the effects (3), (4), (5) of the first embodiment. Further, the second embodiment has an effect (8) specific to the second embodiment. 
     (3′) When the sensor phase current crosses zero, by interpolating the voltage phase command value Vψ as “a command value relating to the voltage of the AC motor”, for example, variations in the voltage phase command value Vψ, which are caused by an estimated error caused by the zero-crossing interpolation of the current estimated value iu_est, can be prevented. Hence, it is possible to prevent the torque feedback control of the AC motor  2  from being made unstable. 
     (4′) In the interpolation method for fixing the voltage phase command value Vψ on the basis of only information at the time ts when the zero crossing period Tzx starts, a change in the voltage phase command value Vψ operated during the zero-crossing period Tzx is not taken in consideration, so that when the zero-crossing period Tzx is finished, the optimal voltage phase command value to the driving state of the electric motor is different from the interpolated value and hence, when the current estimation processing returns from the processing when the sensor phase current crosses zero, the voltage phase command value Vψ might be changed discontinuously. In contrast to this, by interpolating the voltage phase command value Vψ by the continuous variable values on the basis of the information changing during the zero-crossing period Tzx, the interpolated values can be continuously changed in accordance with the driving state of the electric motor during the zero-crossing period Tzx, which can hence prevent the optimal voltage phase command value to the driving state of the electric motor from being different from the interpolated value when the zero-crossing period Tzx is finished. 
     (5′) In the case where not only the voltage phase command value Vψ but also the d axis current estimated value id_est and the q axis current estimated value iq_est are interpolated when the sensor phase current crosses zero, variations in the d axis current estimated value id_est and the q axis current estimated value iq_est can be prevented. Hence, in the other control and determination, which are performed by the use of the d axis current estimated value id_est and the q axis current estimated value iq_est, other than the torque feedback control, the effect of an erroneous determination and a malfunction can be avoided. 
     (8) In the present embodiment, when the control section  153  performs the torque feedback control mode, the β axis current iβ can be calculated on the basis of the differential value Δiα of the α axis current iα without using the current command values iu*, iv* of the other phases. Hence, also in the torque feedback control mode, an optimal current estimation by the α-β coordinate system can be performed as is the case with the current feedback control mode. 
     Other Embodiments 
     (A) A method by which the current estimation device estimates the current estimated value iu(v)_est of the estimated phase, the d axis current estimated value id_est, and the q axis current estimated value iq_est on the basis of the current sensed value iw_sns of the sensor phase of one phase and the electric angle θe is not limited to the method based on the α axis current iα and the β axis current iβ in the α-β coordinate system as the embodiment described above. For example, in a current estimation method using a current command value, the technique of the JP-A 2004-159391 (patent document 1) of a conventional technique may be employed if it can be understood that the effect (6) of the first embodiment cannot be obtained. 
     Further, it is also recommended to employ a current estimation method that estimates a d-axis current estimated value id_est and a q axis current estimated value iq_est without estimating a current estimated value of a phase other than a sensor phase on the basis of the current sensed value iw_sns of a sensor phase of one phase and the electric angle θe and that could cause “the zero division” or “the zero multiplication” in an estimation operation for a specified phase or at a specified timing. A current estimation part of employing this method is constructed in such a way as to, first, estimate the d axis current estimated value id_est and the q axis current estimated value iq_est and then to calculate a current estimated value of the other phase by the inverse dq transformation, as required. 
     (B) When the sensor phase current crosses zero, not only the feedforward operated value described above but also the other calculated value may be used as the reference value of the target value to which the d axis voltage command value vd* and the q axis voltage command value vq* or the voltage phase command value Vψ are or is brought closer (refer to  FIG. 7  and  FIG. 12 ). Further, as a method for setting an interpolated value as a continuous variable value, another method capable of changing a value continuously may be used in addition to the filtering processing or the exterpolation method for the reference value. For example, an operation of continuously changing the d axis current estimated value id_est and the q axis current estimated value iq_est during the zero-crossing period Tzx is equivalent to an operation of continuously changing the d axis voltage command value vd* and the q axis voltage command value vq*. 
     (C) The sensor phase for sensing the sensor current by the current sensor may be not only the W phase of the embodiment described above but also the U phase or the V phase. Further, the estimated phase for calculating the current estimated value from the current sensed value of the sensor phase and the sensor phase reference current phase θx may be not only the U phase of the embodiment described above but also the V phase or the W phase. 
     (D) “The current feedback control mode” is not limited to the sine wave PWM control mode or the overmodulated PWM control mode but may be any control mode of using a current command value and feeding back a current sensed value or a current estimated value based on the current sensed value to the current command value. Further, “the torque feedback control mode” is not limited to the square wave control mode of the embodiment described above but may be any control mode of feeding back a torque estimated value based on the current sensed value relating to the drive of an AC motor to the torque command value. 
     (E) The AC motor of the embodiments described above is the three-phase AC motor of a permanent magnet synchronous type but may be an induction motor or another synchronous motor in the other embodiments. Further, the AC motor of the embodiments described above may be the so-called motor generator having a function as an electric motor and a function as a generator but may be not have the function as the generator in the other embodiment. 
     (F) The control device of the AC motor according to the present disclosure is not limitedly applied to the system having one set of an inverter and an AC motor as the embodiments described above but may be applied to a system having two sets of an inverter and an AC motor. Further, the control device of the AC motor according to the present disclosure may be applied to a system of an electric train having a plurality of AC motors connected in parallel to one inverter. 
     (G) The control device of the AC motor according to the present disclosure is not limitedly applied to the AC motor of the hybrid vehicle having the construction shown in  FIG. 1  but may be applied to an AC motor of an electrically driven vehicle having any construction. Further, the control device of the AC motor according to the present disclosure may be applied to an AC motor other than the AC motor of the electrically driven vehicle. 
     The present disclosure is not limited to the embodiments described above but can be put into practice in various modes within a scope not departing from the gist of the present disclosure. 
     The above disclosure has the following aspects. 
     According to an aspect of the present disclosure, a control device of a three-phase AC motor includes: an inverter that drives the AC motor; a current sensor that senses a current flowing in a sensor phase among three phases of the AC motor as a sensor phase current; and a controller that switches on and off a switching element of the inverter to control a current flowing through the AC motor. The controller includes: a current estimation device that estimates a d-axis current estimated value and a q-axis current estimated value based on the sensor phase current and an electric angle of the AC motor; and a zero-crossing interpolation device that interpolates a command value relating to a voltage of the AC motor when the sensor phase current is in a predetermined zero cross range, which includes a zero point. When the sensor phase current is in the zero cross range, the zero-crossing interpolation device interpolates the command value with a continuous variable value. 
     Here, “the AC motor” includes an AC-driven motor, a generator, and a motor generator. For example, a motor generator that is used as a main unit of a hybrid vehicle and an electric vehicle and that generates a torque for driving driving wheels corresponds to “the AC motor”. Further, for example, an electric motor control device for driving the motor generator corresponds to “a control device of an AC motor”. 
     A specific example of “a command value relating to a voltage of an AC motor”, for example, “a d axis voltage command value and a q axis voltage command value”, in a current feedback control mode of feeding back a d axis current estimated value and a q axis estimated value to a d axis current command value and a q axis current command value. Further, in a torque feedback control mode of feeding back a torque estimated value, which is calculated from a d axis current estimated value and a q axis estimated value, to a torque command value, “a voltage phase command value” corresponds to “a command value relating to a voltage of an AC motor”. In addition, “a command value relating to a voltage of an AC motor” includes all voltage command values relating to the control of the AC motor, for example, three-phase AC voltage command values, and amplitude command values of a voltage vector. 
     According to the present disclosure, when the sensor phase current crosses zero, the command value relating to the voltage of the AC motor is interpolated, whereby “zero division” of dividing something by 0 and “zero multiplication” of multiplying something by 0 are prevented from being caused in the calculation formula for a current estimation. Hence, when the sensor phase crosses zero, variation in the current estimated value can be prevented. 
     In particular, the present disclosure is characterized in that the time when the sensor phase crosses zero is regarded as “a zero-crossing period” of a specified time duration and that the command value relating to the voltage of the AC motor is repeatedly updated and interpolated by “continuous variable values” during the zero-crossing period. 
     A method for fixing the command value relating to the voltage of the AC motor at an interpolated value set when the zero-crossing period starts is proposed as a method opposite to the interpolation method of the present disclosure. In the case where the command value relating to the voltage of the AC motor is fixed at the interpolated value, since a change in the voltage command value that could be caused during the zero crossing period is not taken into consideration, when the zero crossing period is finished, an optimal command value to a driving state of the AC motor might be different from the interpolated value, so that when current estimation processing returns from the processing when the sensor phase current crosses zero, the voltage command value might be discontinuously changed. 
     On the other hand, the present disclosure interpolates the command value relating to the voltage of the AC motor by “the continuous variable values” to thereby continuously change the interpolated values in accordance with the driving state of the AC motor during the zero-crossing period. Hence, when the zero-crossing period is finished, the difference between the optimal voltage command value for the driving state of the AC motor and the interpolated value can be prevented. 
     Here, specific processing for interpolating the command value relating to the voltage of the AC motor by “the continuous variable values” may be performed, for example, by setting a reference value for a voltage command value by a feedforward operation or the like and then by filtering the interpolated values for the reference value. Alternatively, an interpolated value of this time may be calculated by exterpolating a value of the last time but one or a value before the last time but one and a value of the last time. 
     Further, there are the following constructions in which the current estimation means “further estimates a current estimated value of a phase other than a sensor phase”. A first construction is a construction in which: a current estimated value of a phase other than a sensor phase is calculated; and then the current sensed value of the sensor phase and the current estimated value of the other phase are dq transformed to thereby calculate a d axis current estimated value and a q axis current estimated value. A second construction is a construction in which: the d axis current estimated value and the q axis current estimated value are calculated; and then a current estimated value of the other phase is calculated by an inverse dq transformation. Further, a construction in which these constructions are combined to each other can be formed. In this construction, when the sensor phase current crosses zero, preferably, the current estimated value of the other phase is further interpolated to thereby prevent the current estimated value of the other phase from being suddenly changed. 
     In addition, when the sensor phase current crosses zero, the d axis current estimated value and the q axis current estimated value, which are estimated by the current estimation means, may be interpolated. This can prevent the d axis current estimated value and the q axis current estimated value from being varied. Hence, in the other control and determination performed by the use of the d axis current estimated value and the q axis current estimated value, the effects of an erroneous determination and a malfunction can be avoided. 
     Alternatively, the current estimation device may further estimate a current estimated value of another phase other than the sensor phase, and, when the sensor phase current is in the zero cross range, the current estimation device interpolates a current estimated value of the another phase. Further, the controller may control the current flowing through the AC motor based on a d-axis voltage command value and a q-axis voltage command value. The d-axis voltage command value is calculated by feeding back the d-axis current estimated value with respect to the d-axis current command value, and the q-axis voltage command value is calculated by feeding back the q-axis current estimated value with respect to the q-axis current command value. When the sensor phase current is in the zero cross range, the zero-crossing interpolation device interpolates the d-axis voltage command value and the q-axis voltage command value, as command values relating to the voltage of the AC motor, with continuous variable values. Further, the controller may control the current flowing through the AC motor based on a voltage phase command value, and the voltage phase command value is calculated by feeding back a torque estimated value, which is calculated from the d-axis current estimated value and the q-axis current estimated value, with respect to a torque command value. When the sensor phase current is in the zero cross range, the zero-crossing interpolation device interpolates the voltage phase command value as the command value relating to the voltage of the AC motor with the continuous variable value. Furthermore, when the sensor phase current is in the zero cross range, the controller may further interpolate the d-axis current estimated value and the q-axis current estimated value, which are estimated by the current estimation device. 
     It is noted that a flowchart or the processing of the flowchart in the present application includes sections (also referred to as steps), each of which is represented, for instance, as S 10 . Further, each section can be divided into several sub-sections while several sections can be combined into a single section. Furthermore, each of thus configured sections can be also referred to as a device, module, or means. 
     While the present disclosure has been described with reference to embodiments thereof, it is to be understood that the disclosure is not limited to the embodiments and constructions. The present disclosure is intended to cover various modification and equivalent arrangements. In addition, while the various combinations and configurations, other combinations and configurations, including more, less or only a single element, are also within the spirit and scope of the present disclosure.