Patent Publication Number: US-7898197-B2

Title: Motor control device

Description:
This nonprovisional application claims priority under 35 U.S.C. §119(a) on Patent Application No. 2007-195544 filed in Japan on Jul. 27, 2007, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a motor control device for driving and controlling a motor. 
     2. Description of Related Art 
     In order to control a motor by supplying three-phase AC power to the motor, it is necessary to detect current values of two phases (e.g., U-phase current and V-phase current) among three phases including U-phase, V-phase and W-phase. Although two current sensors (current transformers or the like) are usually used for detecting current values of two phases, the use of two current sensors causes an increase of cost of the entire system equipped with the motor. 
     For this reason, there is proposed a conventional method in which bus current (DC current) between an inverter and a DC power supply is sensed by a single current sensor, and current values of two phases are detected from the sensed bus current. This method is also called a single shunt current detecting method. 
       FIG. 23  shows a general block diagram of a conventional motor driving system in which the single shunt current detecting method is adopted. An inverter (PWM inverter)  202  is equipped with half bridge circuits for three phases, each of which includes an upper arm and a lower arm, and it converts a DC voltage from a DC power supply  204  into a three-phase AC voltage by switching the individual arms in accordance with specified three-phase voltage values given by a controller  203 . The three-phase AC voltage is supplied to a three-phase permanent magnet synchronous motor  201 , so that the motor  201  is driven and controlled. 
     A line connecting the individual lower arms in the inverter  202  with the DC power supply  204  is called a bus line  213 . A current sensor  205  transmits a signal indicating bus current that flows in the bus line  213  to the controller  203 . The controller  203  does sampling of an output signal of the current sensor  205  at appropriate timing so as to detect phase current of a phase in which a voltage level becomes a maximum value (maximum phase) and phase current of a phase in which a voltage level becomes a minimum value (minimum phase), i.e., current values of two phases. 
     If voltage levels between different phase voltages are separated from each other sufficiently, current values of two phases can be detected from the output signal of the current sensor  205 . However, if the maximum phase and an intermediate phase of voltage become close to each other, or if the minimum phase and the intermediate phase of voltage become close to each other, it is difficult to detect current values of two phases (note that description of the single shunt current detecting method including description of a reason why it becomes difficult to detect current values of two phases will also appear later with reference to  FIG. 4  and the like). 
     Therefore, there is proposed a method in which if current values of two phases cannot be detected by the single shunt current detecting method in a certain period, a pulse width of a PWM signal for each arm in the inverter is corrected based on gate signals of three phases in the period. 
     A usual correction example of a specified voltage value (pulse width) that also supports the above-mentioned correction is shown in  FIG. 24 . In  FIG. 24 , the horizontal axis indicates time while  220   u ,  220   v  and  220   w  indicate voltage levels of the U-phase, the V-phase and the W-phase, respectively. Since a voltage level of each phase follows the specified voltage value (pulse widths) for each phase, they are considered to be equivalent. As shown in  FIG. 24 , the specified voltage value (pulse width) of each phase is corrected so that “maximum phase and intermediate phase” as well as “minimum phase and intermediate phase” of the voltage do not approach each other closer than a predetermined distance. Thus, voltages of individual phases do not become close to each other to the extent that current values of two phases cannot be detected, and current values of two phases can be detected stably. 
     When this type of voltage correction is performed, it is necessary to determine a correction quantity based on a relationship among specified voltage values (pulse widths) of three phases. If an applied voltage is low, in particular, the correction may be required for each of the three phases resulting in a complicated correction process. 
     On the other hand, a direct torque control is proposed as the control method that enables to reduce a torque ripple more than the case of performing a vector control.  FIG. 25  illustrates a block diagram of a general structure of the conventional motor driving system that realizes the direct torque control. 
     In the motor driving system shown in  FIG. 25 , an α-axis component φ α  and a β-axis component φ β  of a magnetic flux linkage of an armature winding of the motor are estimated based on two-phase current values (i α  and i β ) obtained from two current sensors and two-phase voltage values (v α  and v β ) obtained from two voltage detectors, and a generated torque T of the motor is estimated. In addition, a phase θ S   of the magnetic flux linkage vector viewed from the α-axis is calculated. These values are calculated in accordance with the equations (A-1) to (A-4) below. Here, R a  represents a resistance value of a one phase of the armature winding, P N  represents the number of pole pairs of the motor, and “φ α|t=0 ” and “φ β|t=0 ” represent values of the φ α  and φ β  at time t=0 (i.e., initial values of φ α  and φ β  ), respectively.
 
φ α =∫( v   α   −R   a   i   α ) dt+φ   α|t=0    (A-1)
 
φ β =∫( v   β   −R   a   i   β ) dt+φ   β|t=0    (A-2)
 
θ S =tan −1 (φ β /φ α )   (A-3)
 
 T=P   N (φ α   i   β −φ β   i   α )   (A-4)
 
     Then, target values φ α * and φ β * of φ α  and φ β  are calculated based on a torque error ΔT(i.e., T*−T) between the estimated torque T and a specified torque value T*, a phase θ S , and a target value |φ S *| of a magnitude of the magnetic flux linkage vector made up of φ α  and φ β  (i.e., amplitude of the magnetic flux linkage), and magnetic flux control is performed so that φ α  and φ β  follow φ α * and φ β *. More specifically, the target values (v α * and v β *) of the two-phase voltage values (v α  and v β ) are calculated so that φ α  and φ β  follow φ α * and φ β *, and the specified three-phase voltage values (v u *, v v * and v w *) are generated from the target values of the two-phase voltage and are supplied to the inverter. 
     In the direct torque control, voltage and current to be used for estimating the magnetic flux are usually detected (sensed) by a detector (sensor). It is possible to calculate the voltage to be used for estimating the magnetic flux by using the specified voltage value. However, when trying to use the single shunt current detecting method for the direct torque control, it is necessary to correct the specified voltage value. Unless this is taken into account for making up the control system, the estimated magnetic flux will have an error. 
     The same is true on the case where the single shunt current detecting method is used for the motor control device performing estimation of the magnetic flux as well as the case where the single shunt current detecting method is used for the direct torque control. 
     SUMMARY OF THE INVENTION 
     A motor control device according to an embodiment of the present invention includes a motor current detector for detecting motor current flowing in a three-phase motor based on current flowing between an inverter driving the motor and a DC power supply, a specified voltage vector generating portion for generating a specified voltage vector indicating a voltage vector to which an applied voltage to the motor should follow based on a magnetic flux linkage of an armature winding of the motor, a specified voltage vector correcting portion for correcting the generated specified voltage vector, and a magnetic flux estimating portion for estimating the magnetic flux linkage based on the motor current and the specified voltage vector after the correction. The motor control device controls the motor via the inverter in accordance with the specified voltage vector after the correction. 
     More specifically, for instance, the specified voltage vector generated by the specified voltage vector generating portion is a specified voltage vector on a rotating coordinate, the specified voltage vector correcting portion corrects the specified voltage vector on the rotating coordinate in the process of converting the specified voltage vector on the rotating coordinate into specified three-phase voltage values on a three-phase fixed coordinate, and the motor control device supplies the specified three-phase voltage values corresponding to the specified voltage vector after the correction to the inverter so as to control the motor. 
     More specifically, for instance, the specified voltage vector generated by the specified voltage vector generating portion is a two-phase specified voltage vector on ab coordinates rotating step by step of 60 degrees of electrical angle in accordance with a phase of the specified voltage vector with respect to a predetermined fixed-axis. 
     More specifically, for instance, the specified voltage vector correcting portion decides whether or not the correction is necessary based on a magnitude of a coordinate axis component constituting the two-phase specified voltage vector on the ab coordinates, and if it is decided that the correction is necessary, the specified voltage vector correcting portion corrects the coordinate axis component so that the two-phase specified voltage vector on the ab coordinates is corrected. 
     More specifically, for instance, the motor control device further includes a coordinate converting portion for converting the two-phase specified voltage vector on the ab coordinates after the correction performed by the specified voltage vector correcting portion into a specified voltage vector on αβ coordinates having fixed α and β axes as its coordinate axes, and the magnetic flux estimating portion estimates the magnetic flux linkage based on the motor current and the specified voltage vector on the αβ coordinates. 
     Alternatively, for instance, the motor control device further includes a coordinate converting portion for converting the two-phase specified voltage vector on the ab coordinates after the correction performed by the specified voltage vector correcting portion into a specified voltage vector on αβ coordinates having fixed α and β axes as its coordinate axes, and the magnetic flux estimating portion estimates coordinate axis components of the magnetic flux linkage on the αβ coordinates based on coordinate axis components of the motor current on the αβ coordinates and the specified voltage vector on the αβ coordinates. 
     In addition, for instance, the motor control device further includes a torque estimating portion for estimating a torque generated by the motor based on the motor current and the estimated magnetic flux linkage, and the motor control device performs direct torque control of the motor based on the estimated torque. 
     Alternatively, for instance, the motor control device further includes a rotor position estimating portion for estimating a rotor position of the motor based on the estimated magnetic flux linkage, and the motor control device performs vector control of the motor based on the estimated rotor position. 
     A motor driving system according to an embodiment of the present invention includes a three-phase motor, an inverter for driving the motor, and the above-mentioned motor control device for controlling the inverter so as to control the motor. 
     Meanings and effects of the present invention will be apparent from the following description of embodiments. However, the embodiments described below are merely examples of the present invention, and the meanings of the present invention and terms of individual elements are not limited to those described in the following embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a general structure of a motor driving system according to an embodiment of the present invention. 
         FIG. 2  is a diagram illustrating a typical example of three-phase AC voltage to be applied to the motor shown in  FIG. 1 . 
         FIG. 3  is a diagram of a table showing a relationship between energizing patterns of the motor shown in  FIG. 1  and bus current. 
         FIG. 4  is a diagram illustrating a relationship between a voltage level of each phase voltage and a carrier signal in the motor shown  FIG. 1  and waveforms of a PWM signal and bus current corresponding to the relationship. 
       FIGS.  5 A-5D are equivalent circuit diagrams of armature windings and a periphery thereof shown in  FIG. 1  at each timing shown in  FIG. 4 . 
         FIG. 6  is a diagram of a table showing combinations (modes) of a relationship of phase voltage levels in the motor shown in  FIG. 1  and phases of current detected in the combinations. 
         FIG. 7  is a diagram illustrating a relationship among a U-phase axis, a V-phase axis, a W-phase axis, the α-axis and the β-axis. 
         FIG. 8  is a space vector diagram illustrating a relationship among the U-phase axis, the V-phase axis, the W-phase axis, the α-axis, the β-axis and the voltage vector according to a first example of the present invention. 
         FIG. 9  is a diagram for explaining an a-axis defined in the embodiment of the present invention. 
         FIG. 10  is a flowchart showing a procedure of a correction process of the voltage vector according to the embodiment of the present invention. 
         FIG. 11A  is a diagram illustrating a voltage vector locus on the ab coordinates before the correction process shown in  FIG. 10 . 
         FIG. 11B  is a diagram illustrating the voltage vector locus on the ab coordinates after the correction process shown in  FIG. 10 . 
         FIG. 12A  is a diagram illustrating a voltage vector locus on the αβ coordinates before the correction process shown in  FIG. 10 . 
         FIG. 12B  is a diagram illustrating the voltage vector locus on the αβ coordinates after the correction process shown in  FIG. 10 . 
         FIG. 13  is a diagram illustrating voltage waveforms of the U-phase voltage, the V-phase voltage and the W-phase voltage obtained after the correction process shown in  FIG. 10 . 
         FIG. 14  is a block diagram of a structure of a motor driving system according to a first example of the present invention. 
         FIG. 15  is an internal block diagram of a specified magnetic flux calculating portion shown in  FIG. 14 . 
         FIG. 16  is an internal block diagram of a specified voltage calculating portion shown in  FIG. 14 . 
         FIG. 17  is a vector diagram showing a relationship between the magnetic flux linkage and the voltage concerned with the calculation in the specified voltage calculating portion shown in  FIG. 14 . 
         FIG. 18  is a block diagram illustrating a structure of a motor driving system according to a second example of the present invention. 
         FIG. 19  is a diagram illustrating a relationship among the U-phase axis, the V-phase axis, the W-phase axis and the d-axis. 
         FIG. 20  is an internal block diagram of a position and speed estimator shown in  FIG. 18 . 
         FIG. 21  is an internal block diagram of a specified voltage calculating portion shown in  FIG. 18 . 
         FIG. 22  is a diagram illustrating a rotor phase (θ) decomposed by considering a relationship with the a-axis shown in  FIG. 9 . 
         FIG. 23  is a block diagram illustrating a general structure of a conventional motor driving system adopting the single shunt current detecting method. 
         FIG. 24  is a diagram illustrating a correction example of the specified voltage value (pulse width) in the conventional case where the single shunt current detecting method is adopted. 
         FIG. 25  is a block diagram illustrating a general structure of a conventional motor driving system that realizes a direct torque control. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, embodiments of the present invention will be described concretely with reference to the attached drawings. In the drawings to be referred to, the same portions are denoted by the same references so that overlapping descriptions for the same portions will be omitted as a general rule. Although first and second examples will be described later, items that are common to the examples and items to be referred to in each example will be described first. 
       FIG. 1  is a block structural diagram of a motor driving system according to an embodiment of the present invention. The motor driving system shown in  FIG. 1  includes a three-phase permanent magnet synchronous motor  1  (hereinafter referred to as a “motor 1” simply), a PWM (Pulse Width Modulation) inverter  2  (hereinafter referred to as an “inverter 2” simply), a controller  3 , a DC power supply  4  and a current sensor  5 . The DC power supply  4  delivers a DC voltage between a positive output terminal  4   a  and a negative output terminal  4   b  so that the negative output terminal  4   b  becomes a low voltage side. The motor driving system shown in  FIG. 1  adopts a single shunt current detecting method. 
     The motor  1  includes a rotor  6  to which a permanent magnet is provided and a stator  7  to which armature windings  7   u ,  7   v  and  7   w  of U-phase, V-phase and W-phase are provided. The armature windings  7   u ,  7   v  and  7   w  are connected at a neutral point  14  as a center in a form of Y-connection. Non-connection ends of the armature windings  7   u ,  7   v  and  7   w  that are opposite ends of the neutral point  14  are connected to terminals  12   u ,  12   v  and  12   w , respectively. 
     The inverter  2  is provided with a half bridge circuit for the U-phase, a half bridge circuit for the V-phase and a half bridge circuit for the W-phase. Each of the half bridge circuits includes a pair of switching elements. In each of the half bridge circuits, the pair of switching elements are connected in series between the positive output terminal  4   a  and the negative output terminal  4   b  of the DC power supply  4 , so that each of the half bridge circuits is supplied with a DC voltage from the DC power supply  4 . 
     The half bridge circuit for the U-phase is made up of a high voltage side switching element  8   u  (hereinafter referred to as an upper arm  8   u , too) and a low voltage side switching element  9   u  (hereinafter referred to as a lower arm  9   u , too). The half bridge circuit for the V-phase is made up of a high voltage side switching element  8   v  (hereinafter referred to as an upper arm  8   v , too) and a low voltage side switching element  9   v  (hereinafter referred to as a lower arm  9   v , too). The half bridge circuit for the W-phase is made up of a high voltage side switching element  8   w  (hereinafter referred to as an upper arm  8   w , too) and a low voltage side switching element  9   w  (hereinafter referred to as a lower arm  9   w , too). In addition, the switching elements  8   u ,  8   v ,  8   w ,  9   u ,  9   v  and  9   w  are respectively connected to diodes  10   u ,  10   v ,  10   w ,  11   u ,  11   v  and  11   w  in parallel so that the direction from the low voltage side to the high voltage side of the DC power supply  4  becomes the forward direction. Each of the diodes works as a freewheel diode. 
     The connection node of the upper arm  8   u  and the lower arm  9   u  that are connected in series, the connection node of the upper arm  8   v  and the lower arm  9   v  that are connected in series, the connection node of the upper arm  8   w  and the lower arm  9   w  that are connected in series are connected to the terminals  12   u ,  12   v  and  12   w , respectively. Note that field-effect transistors are shown as the switching elements in  FIG. 1 , but they can be replaced with IGBTs (Insulated Gate Bipolar Transistors) or the like. 
     The inverter  2  generates a PWM (Pulse Width Modulation) signal for each phase based on the specified three-phase voltage values supplied from the controller  3  and supplies the PWM signal to a control terminal (base or gate) of each switching element in the inverter  2 , so that each switching element performs switching action. The specified three-phase voltage values that are supplied from the controller  3  to the inverter  2  include a U-phase specified voltage value v u *, a V-phase specified voltage value v v * and a W-phase specified voltage value v w *. The specified voltage values v u *, v v * and v w * represent voltage levels (voltage values) of the U-phase voltage v u , V-phase voltage v v  and W-phase voltage v w , respectively. The U-phase voltage v u , the V-phase voltage v v  and the W-phase voltage v w  represent respectively voltages at the terminals  12   u ,  12   v  and  12   w  viewed from the neutral point  14  shown in  FIG. 1 . The inverter  2  controls on (conducting state) or off (nonconducting state) of the switching elements based on the specified voltage values v u *, v v * and v w *. 
     Ignoring a dead time for preventing the upper arm and the lower arm of the same phase from becoming the on state simultaneously, the upper arm is on when the lower arm is off in each half bridge circuit. On the contrary, the upper arm is off when the lower arm is on. In the following description, the above-mentioned dead time will be ignored. 
     The DC voltage applied to the inverter  2  by the DC power supply  4  is converted into a three-phase AC voltage that is PWM-modulated (pulse width modulated), for example, by the switching action of the switching elements in the inverter  2 . When the three-phase AC voltage is applied to the motor  1 , current corresponding to the three-phase AC voltage flows in the armature winding ( 7   u ,  7   v  and  7   w ) so that the motor  1  is driven. 
     The current sensor  5  senses current that flows in a bus line  13  of the inverter  2  (hereinafter referred to as “bus current”). The bus current includes a DC component, so it may be regarded as DC current. In the inverter  2 , the low voltage sides of the lower arms  9   u ,  9   v  and  9   w  are connected together to the negative output terminal  4   b  of the DC power supply  4 . The wiring line to which the low voltage sides of the lower arms  9   u ,  9   v  and  9   w  are connected together is the bus line  13 , and the current sensor  5  is inserted in the bus line  13  in series. The current sensor  5  transmits a signal indicating a current value of the bus current (detention current) to the controller  3 . The controller  3  refers to an output signal of the current sensor  5  and the like so as to generate and deliver the above-mentioned specified three-phase voltage values. Note that the current sensor  5  is a shunt resistor, a current transformer or the like, for example. In addition, it is possible to insert the current sensor  5  not in the wiring (bus line  13 ) between the low voltage sides of the lower arms  9   u ,  9   v  and  9   w  and the negative output terminal  4   b  but in the wiring between the high voltage sides of the upper arms  8   u ,  8   v  and  8   w  and the positive output terminal  4   a.    
     Here, with reference to  FIGS. 2 ,  3 ,  4 ,  5 A- 5 D, and  6 , a relationship between the bus current and the phase current flowing in the armature winding of each phase and the like will be described. The current flowing in the armature windings  7   u ,  7   v  and  7   w  are referred to as U-phase current, V-phase current and W-phase current, respectively, and each of them (or a generic name of them) is referred to as phase current (see  FIG. 1 ). Further, concerning the phase current, a polarity of the current direction flowing from the terminal  12   u ,  12   v  or  12   w  to the neutral point  14  is regarded as positive, while a polarity of the current direction flowing from the neutral point  14  outward is regarded as negative. 
       FIG. 2  shows a typical example of the three-phase AC voltage that is applied to the motor  1 . In  FIG. 2 , references  100   u ,  100   v  and  100   w  show waveforms of the U-phase voltage, the V-phase voltage and the W-phase voltage to be applied to the motor  1 , respectively. Each of the U-phase voltage, the V-phase voltage and the W-phase voltage (or a generic name of them) is referred to as phase voltage. When sinusoidal current is to be supplied to the motor  1 , an output voltage of the inverter  2  should be a sine wave. Although each of the phase voltages shown in  FIG. 2  is an ideal sine wave, a distortion is added to the sine wave in the present embodiment (as described later in detail). 
     As shown in  FIG. 2 , a relationship among the voltage levels of the U-phase voltage, the V-phase voltage and the W-phase voltage alters as time passes. This relationship is determined by the specified three-phase voltage values, and the inverter  2  decides an energizing pattern for each phase in accordance with the specified three-phase voltage values.  FIG. 3  shows this energizing pattern as a table. In  FIG. 3 , the first to the third columns from the left side indicate the energizing pattern. The fourth column will be described later. 
     The energizing pattern includes: 
     an energizing pattern “LLL” in which all the lower arms of the U, V and W-phases are turned on; 
     an energizing pattern “LLH” in which the upper arm of the W-phase is turned on while the lower arms of the U and V-phases are turned on; 
     an energizing pattern “LHL” in which the upper arm of the V-phase is turned on while the lower arms of the U and W-phases are turned on; 
     an energizing pattern “LHH” in which the upper arms of the V and W-phases are turned on while the lower arm of the U-phase is turned on; 
     an energizing pattern “HLL” in which the upper arm of the U-phase is turned on while the lower arms of the V and W-phases are turned on; 
     an energizing pattern “HLH” in which the upper arms of the U and W-phases are turned on while the lower arm of the V-phase is turned on; 
     an energizing pattern “HHL” in which the upper arms of the U and V-phases are turned on while the lower arm of the W-phase is turned on; and 
     an energizing pattern “HHH” in which all the upper arms of the U, V and W-phases are turned on (references of the upper arms and the lower arms ( 8   u  and the like) are omitted). 
       FIG. 4  shows a relationship between a voltage level of each phase voltage and a carrier signal in the case where three-phase modulation is performed and waveforms of the PWM signal and bus current corresponding to the relationship. The relationship between voltage levels of the individual phase voltages changes variously, but  FIG. 4  shows it by noting a certain timing  101  shown in  FIG. 2  for concrete description. More specifically,  FIG. 4  shows the case where a voltage level of the U-phase voltage is the maximum, and a voltage level of the W-phase voltage is the minimum. The phase having the maximum voltage level is referred to as a “maximum phase”, the phase having the minimum voltage level is referred to as a “minimum phase”, and the phase whose voltage level is not the maximum or the minimum is referred to as an “intermediate phase”. In the state shown in  FIG. 4 , the maximum phase, the intermediate phase and the minimum phase are the U-phase, the V-phase and the W-phase, respectively. In  FIG. 4 , reference CS denotes a carrier signal that is compared with a voltage level of each phase voltage. The carrier signal is a periodical signal of a triangular wave, and the period of the signal is referred to as a carrier period. Note that the carrier period is much shorter than a period of the three-phase AC voltage shown in  FIG. 2 . Therefore, if the triangular wave of the carrier signal shown in  FIG. 4  is added to the diagram of  FIG. 2 , the triangular wave will look like a single line. 
     Further with reference to  FIGS. 5A-5D , a relationship between the phase current and the bus current will be described.  FIGS. 5A-5D  are equivalent circuit diagrams of the armature windings and a periphery thereof at individual timings shown in  FIG. 4 . 
     A start timing of each carrier period, i.e., the timing when the carrier signal is a lowest level is referred to as T 0 . At the timing T 0 , the upper arms ( 8   u ,  8   v  and  8   w ) of the individual phases are turned on. In this case, as shown in  FIG. 5A , a short circuit is formed so that current from or to the DC power supply  4  becomes zero. Therefore, the bus current becomes zero. 
     The inverter  2  refers to v u *, v v * and v w * so as to compare a voltage level of each phase voltage with the carrier signal. In the increasing process of a level of the carrier signal (voltage level), when a voltage level of the minimum phase crosses the carrier signal at the timing T 1 , the lower arm of the minimum phase is turned on. Then, as shown in  FIG. 5B , current of the minimum phase flows as the bus current. In the example shown in  FIG. 4 , the lower arm  9   w  of the W-phase is in the turned-on state during the period from the timing T 1  to a timing T 2  that will be described later. Therefore, the W-phase current (having negative polarity) flows as the bus current. 
     Further when a level of the carrier signal increases and reaches the timing T 2  when a voltage level of the intermediate phase crosses the carrier signal, the upper arm of the maximum phase is turned on, and the lower arms of the intermediate phase and the minimum phase are turned on. Therefore, as shown in  FIG. 5C , current of the maximum phase flows as the bus current. In the example shown in  FIG. 4 , the upper arm  8   u  of the U-phase is in the turned-on state, and the lower arms  9   v  and  9   w  of the V-phase and the W-phase are turned on in the period from the timing T 2  to a timing T 3  that will be described later. Therefore, the U-phase current (having positive polarity) flows as the bus current. 
     Further when a level of the carrier signal increases and reaches the timing T 3  when a voltage level of the maximum phase crosses the carrier signal, the lower arms of all phases are turned on. Therefore, as shown in  FIG. 5D , a short circuit is formed so that current from or to the DC power supply  4  becomes zero. Therefore, the bus current becomes zero. 
     At a middle timing between the timing T 3  and a timing T 4  that will be described later, the carrier signal reaches the maximum level, and then a level of the carrier signal decreases. In the decreasing process of a level of the carrier signal, the states as shown in  FIGS. 5D ,  5 C,  5 B and  5 A appear one by one in this order. More specifically, in the decreasing process of a level of the carrier signal, it is supposed that a voltage level of the maximum phase crosses the carrier signal at the timing T 4 , a voltage level of the intermediate phase crosses the carrier signal at a timing T 5 , a voltage level of the minimum phase crosses the carrier signal at a timing T 6 , and a next carrier period starts at a timing T 7 . Then, the period between the timing T 4  and the timing T 5 , the period between the timing T 5  and the timing T 6 , the period between the timing T 6  and the timing T 7  have the same energizing patterns as the period T 2 -T 3 , the period T 1 -T 2  and the period T 0 -T 1 , respectively. 
     Therefore, if the bus current is sensed in the period T 1 -T 2  or T 5 -T 6 , the minimum phase current can be detected from the bus current. If the bus current is sensed in the period T 2 -T 3  or T 4 -T 5 , the maximum phase current can be detected from the bus current. Then, the intermediate phase current can be obtained by calculation utilizing the fact that a sum of the three phase current values becomes zero. The fourth column in the table shown in  FIG. 3  indicates a phase of current that flows as the bus current in each energizing pattern with a polarity of the current. For example, in the energizing pattern “HHL” corresponding to the eighth row in the table shown in  FIG. 3 , the W-phase current (having negative polarity) flows as the bus current. 
     Furthermore, the period obtained by removing the period between the timing T 1  and the timing T 6  from the carrier period indicates a pulse width of the PWM signal for the minimum phase. The period obtained by removing the period between the timing T 2  and the timing T 5  from the carrier period indicates a pulse width of the PWM signal for the intermediate phase. The period obtained by removing the period between the timing T 3  and the timing T 4  from the carrier period indicates a pulse width of the PWM signal for the maximum phase. 
     Although the above description exemplifies the case where the U-phase is the maximum phase and the W-phase is the minimum phase, there are six combinations of the maximum phase, the intermediate phase and the minimum phase.  FIG. 6  shows the combinations as a table. When the U-phase voltage, the V-phase voltage and the W-phase voltage are denoted by v u , v v  and v w , respectively, 
     the state that satisfies “v u &gt;v v &gt;v w ” is referred to as a first mode, 
     the state that satisfies “v v &gt;v u &gt;v w ” is referred to as a second mode, 
     the state that satisfies “v v &gt;v w &gt;v u ” is referred to as a third mode, 
     the state that satisfies “v w &gt;v v &gt;v u ” is referred to as a fourth mode, 
     the state that satisfies “v w &gt;v u &gt;v v ” is referred to as a fifth mode, and 
     the state that satisfies “v u &gt;v w &gt;v v ” is referred to as a sixth mode. The examples shown in FIGS.  4  and  5 A- 5 D correspond to the first mode. In addition,  FIG. 6  also indicates a phase of current sensed in each mode. 
     The U-phase specified voltage value v u *, the V-phase specified voltage value v v * and the W-phase specified voltage value v w * are specifically shown as set values of counter CntU, CntV and CntW, respectively. A larger set value is assigned to a higher phase voltage. For example, “CntU&gt;CntV&gt;CntW” holds in the first mode. 
     The counter (not shown) that is provided to the controller  3  increments its count value from zero every carrier period with reference to the timing T 0 . When the count value reaches CntW, the state in which the upper arm  8   w  of the W-phase is turned on is switched to the state in which the lower arm  9   w  is turned on. When the count value reaches CntV, the state in which the upper arm  8   v  of the V-phase is turned on is switched to the state in which the lower arm  9   v  is turned on. When the count value reaches CntU, the state in which the upper arm  8   u  of the U-phase is turned on is switched to the state in which the lower arm  9   u  is turned on. After the carrier signal reached the maximum level, the count value is decremented so that the switching action is performed reversely. 
     Therefore, in the first mode, the timing when the above-mentioned counter value reaches CntW corresponds to the timing T 1 . The timing when it reaches CntV corresponds to the timing T 2 . The timing when it reaches CntU corresponds to the timing T 3 . For this reason, in the first mode, while the counter value is incremented, the output signal of the current sensor  5  is sampled at a timing when the counter value is larger than CntW and is smaller than CntV, so that the W-phase current (having negative polarity) flowing as the bus current can be detected. Furthermore, the output signal of the current sensor  5  is sampled at a timing when the counter value is larger than CntV and is smaller than CntU, so that the U-phase current (having positive polarity) flowing as the bus current can be detected. 
     In the same manner, as shown in  FIG. 6 , in the second mode, the timing when the above-mentioned counter value reaches CntW corresponds to the timing T 1 . The timing when it reaches CntU corresponds to the timing T 2 . The timing when it reaches CntV corresponds to the timing T 3 . For this reason, in the second mode, while the counter value is incremented, the W-phase current (having negative polarity) can be detected from the bus current at the timing when the counter value is larger than CntW and is smaller than CntU. The V-phase current (having positive polarity) can be detected from the bus current at the timing when the counter value is larger than CntU and is smaller than CntV. The same is true on the third to the sixth modes. 
     In addition, sampling timing for sensing phase current of the minimum phase in the period T 1 -T 2  (e.g., mid-term between the timing T 1  and the timing T 2 ) is denoted by ST 1 , and sampling timing for sensing phase current of the maximum phase in the period T 2 -T 3  (e.g., mid-term between the timing T 2  and the timing T 3 ) is denoted by ST 2 . 
     Note that a pulse width (and a duty factor) of the PWM signal for each phase is specified by the set values CntU, CnuV and CntW of the counter as the specified three-phase voltage values (v u *, v v * and v w *). 
     When each phase current is detected from the bus current based on the above-mentioned principle, as understood from  FIG. 4 , if the voltage levels of the maximum phase and the intermediate phase approach each other for example, a time length between the period T 2 -T 3  and the period T 4 -T 5  becomes short. If the bus current is detected by converting an analog output signal from the current sensor  5  shown in  FIG. 1  into a digital signal and if this time length is extremely short, necessary time for A/D conversion or a converging time for a ringing (a current ripple that is caused by the switching) cannot be secured. As a result, phase current of the maximum phase cannot be sensed. In the same manner, if the voltage levels of the minimum phase and the intermediate phase approach each other, phase current of the minimum phase cannot be sensed. If the current values of two phases cannot be measured, phase current of three phases cannot be reproduced. As a result, a vector control of the motor  1  cannot be performed. 
     In the present embodiment, a voltage vector indicating an applied voltage to the motor  1  (specified voltage vector) is corrected so that a voltage level difference between the phase voltages is maintained to be larger than a predetermined value in the period in which it is considered that current values of two phases cannot be measured. Thus, the above-mentioned malfunction is resolved. 
     Prior to detailed description of this correction method, axes and state quantities (state variables) to be defined will be described.  FIG. 7  shows a relationship among the U-phase axis, the V-phase axis and the W-phase axis that are armature winding fixed axes of the U-phase, the V-phase and the W-phase, and the α-axis and the β-axis that are perpendicular to each other. A phase of the V-phase axis leads by 120 degrees of electrical angle with respect to the U-phase axis, and a phase of the W-phase axis leads by 120 degrees of electrical angle with respect to the V-phase axis. In a space vector diagram including the coordinate relationship diagram shown in  FIG. 7  and diagrams shown in  FIGS. 8 and 9  as described later, the counterclockwise direction corresponds to the leading direction of the phase. The α-axis matches with the U-phase axis, and the β-axis leads by 90 degrees of electrical angle with respect to the α-axis. The U-phase axis, the V-phase axis, the W-phase axis, the α-axis and the β-axis are fixed axes having no relationship with rotation of the rotor  6 . In addition, coordinates (coordinate system) having the α-axis and the β-axis selected as the coordinate axes are referred to as αβ coordinates (αβ coordinate system). 
     In addition, a whole motor voltage that is applied to the motor  1  from the inverter  2  is denoted by V a , and a whole motor current that is supplied to the motor  1  from the inverter  2  is denoted by I a . Then, an α-axis component and a β-axis component of the motor voltage V a  are expressed as an α-axis voltage v α  and a β-axis voltage v β , respectively. An α-axis component and a β-axis component of the motor current I a  are expressed as an α-axis current i α  and a β-axis current i β , respectively. A U-phase axis component, a V-phase axis component and a W-phase axis component of the motor voltage V a  are expressed as a U-phase voltage v u , a V-phase voltage v v  and a W-phase voltage v w , respectively. A U-phase axis component, a V-phase axis component and a W-phase axis component of the motor current I a  are expressed as a U-phase current i u , a V-phase current i v  and a W-phase current i w , respectively. 
     [Explanation of Correction Method] 
     A correction method of the voltage vector will be described.  FIG. 8  illustrates a space vector diagram indicating a relationship among the U-phase axis, the V-phase axis, the W-phase axis, the α-axis, the β-axis and the voltage vector. The vector denoted by numeral  110  is the voltage vector. A phase of the voltage vector  110  viewed from the β-axis in the counterclockwise direction is denoted by θ β , and a phase of the voltage vector  110  viewed from the α-axis in the counterclockwise direction is denoted by θ α . An angle quantity (nπ/3) shown in  FIG. 8  will be described later. 
     The voltage vector  110  is the voltage (motor voltage V a ) applied to the motor  1 , which is expressed as a two-dimensional vector quantity. For example, noting the αβ coordinates, the α-axis component and the β-axis component of the voltage vector  110  are v α  and v β , respectively. Actually, an α-axis specified voltage value and a β-axis specified voltage value indicating target values of the α-axis voltage and the β-axis voltage in the motor driving system are calculated, which express the voltage vector  110 . Therefore, the voltage vector is also translated into the specified voltage vector. 
     An asterisk region  111  with hatching that includes a vicinity of the U-phase axis, a vicinity of the V-phase axis and a vicinity of the W-phase axis indicates the region where current values of two phases cannot be detected. For example, if the V-phase voltage and the W-phase voltage are close to each other so that current values of two phases cannot be detected, the voltage vector  110  is located at a vicinity of the U-phase axis. If the U-phase voltage and the W-phase voltage are close to each other so that current values of two phases cannot be detected, the voltage vector  110  is located at a vicinity of the V-phase axis. 
     In this way, the region  111  where current values of two phases cannot be detected exist every 60 degrees of electrical angle with reference to the U-phase axis. If the voltage vector  110  exists in the region  111 , the current values of two phases cannot be detected. Therefore, if the voltage vector exists in the region  111 , the voltage vector should be corrected so that the voltage vector becomes a vector outside the region  111 . 
     In order to perform this correction, noting characteristic of the region  111  in which current values of two phases cannot be detected, it is supposed that coordinates (coordinate system) rotate in a stepping manner every 60 degrees of electrical angle. The coordinates are referred to as ab coordinates (The coordinate system is referred to as ab coordinate system). Note that dq coordinates that will be described later in a second example are coordinates that rotate continuously. The ab coordinates has an a-axis and a b-axis as coordinate axes perpendicular to each other.  FIG. 9  illustrates six axes each of which can be the a-axis. The a-axis becomes any one of a 1  to a 6  axes in accordance with a phase of the voltage vector  110  with respect to a predetermined fixed-axis. It is supposed that this predetermined fixed-axis is the U-phase axis (i.e., the α-axis ). Then, the a-axis becomes any one of a 1  to a 6  axes in accordance with the phase θ α . The a 1  axis, the a 3  axis and the a 5  axis match the U-phase axis, the V-phase axis and the W-phase axis, respectively. The a 2  axis, the a 4  axis and the a 6  axis match respectively an intermediate axis between the a 1  axis and the a 3  axis, an intermediate axis between the a 3  axis and the a 5  axis, and an intermediate axis between the a 5  axis and the a 1  axis. Note that a circle denoted by reference  131  will be described later. 
     If the voltage vector  110  is located in the range denoted by reference  121 , i.e., “11π/6≦θ α &lt;0” or “0≦θ α &lt;π/6” holds, the a-axis becomes the a 1  axis. 
     If the voltage vector  110  is located in the range denoted by reference  122 , i.e., “π/6≦θ α &lt;π/2” holds, the a-axis becomes the a 2  axis. 
     If the voltage vector  110  is located in the range denoted by reference  123 , i.e., “π/2≦θ α &lt;5 π/6” holds, the a-axis becomes the a 3  axis. 
     If the voltage vector  110  is located in the range denoted by reference  124 , i.e., “5 π/6≦θ α &lt;7π/6” holds, the a-axis becomes the a 4  axis. 
     If the voltage vector  110  is located in the range denoted by reference  125 , i.e., “7 π/6≦θ α &lt;3π/2” holds, the a-axis becomes the a 5  axis. 
     If the voltage vector  110  is located in the range denoted by reference  126 , i.e., “3 π/2≦θ α &lt;11 π/6” holds, the a-axis becomes the a 6  axis. 
     For example, if the voltage vector  110  is located at the position shown in  FIG. 9 , the a-axis becomes the a 4  axis. 
     In this way, the a-axis rotates in a stepping manner every 60 degrees along with rotation of the voltage vector, and the b-axis also rotates in a stepping manner every 60 degrees together with the a-axis that is orthogonal to the b-axis. The a-axis and the b-axis can be expressed to be coordinate axes that are digitized every 60 degrees and rotate every 60 degrees. For this reason, the a-axis is always located at the center of the region where current values of two phases cannot be detected. In this correction method, a voltage vector on the dq coordinates is converted into that on the ab coordinates. Then, the a-axis component and the b-axis component of the voltage vector converted into that on the ab coordinates are referred to and are corrected if necessary (for instance, the b-axis component is increased by the correction). 
     More concrete method of realizing this correction process will be described. A phase of the axis to which the voltage vector  110  is closest among the a 1  to a 6  axes is expressed by (nπ/3) with reference to the U-phase axis (see  FIG. 8 ). Here, “n” is a quotient that is obtained by dividing (θ β +2π/3) by π/3 or a quotient that is obtained by dividing (θ α +π/6) by π/3. The quotient is an integer of a value obtained by dividing a dividend by a divisor, when a remainder is omitted. θ β  and θ α  can be calculated in accordance with the equations (1-1a) and (1-1b) below.
 
θ β =tan −1 (− v   α   /v   β )   (1-1a)
 
θ α =tan −1 ( v   β   /v   α )   (1-1b)
 
     The ab coordinates correspond to coordinates obtained by rotating the αβ coordinates by an angle (nπ/3). Therefore, regarding that the voltage vector  110  is a voltage vector on the ab coordinates and that the a-axis component and the b-axis component of the voltage vector  110  are the a-axis voltage v a  and the b-axis voltage v b , the α-axis voltage v α , the β-axis voltage v β , the a-axis voltage v a  and the b-axis voltage v b  satisfy the coordinate conversion equation (1-2) below. 
     
       
         
           
             
               
                 
                   
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     Then, the correction process is performed by referring to the a-axis voltage v a  and the b-axis voltage v b  calculated in accordance with the equation (1-2).  FIG. 10  shows a flowchart indicating a procedure of this correction process. In the step S 1 , the coordinate conversion is performed in accordance with the equation (1-2). In the next step S 2 , the correction process with respect to v a  and v b  is performed. 
     In the step S 2 , it is decided first whether or not a value that indicates an amplitude of the b-axis voltage v b  (i.e., an absolute value of the b-axis voltage v b ) is smaller than a predetermined threshold value Δ (here, Δ&gt;0). In other words, it is decided whether or not the expression (1-3) as below is satisfied. Further, if the absolute value of the b-axis voltage v b  is smaller than the threshold value Δ and the b-axis voltage v b  is positive, the correction is performed so that v b  equals Δ. If the absolute value of the b-axis voltage v b  is smaller than the threshold value Δ and the b-axis voltage v b  is negative, the correction is performed so that v b  equals (−Δ). If the absolute value of the b-axis voltage v b  is more than or equal to the threshold value Δ, the correction is not performed with respect to v b . 
     Furthermore, in the step S 2 , it is also decided whether or not the a-axis voltage v a  satisfies the equation (1-4) below. If it satisfies the equation (1-4), the correction of v a  is performed so that v a  becomes equal to the right side of the equation (1-4). If v a  does not satisfy the equation (1-4) below, the correction is not performed with respect to v a . Note that the equation (1-4) is used for deciding whether the voltage vector  110  is included inside the circle  131  shown in  FIG. 9 . The state where the voltage vector  110  is included inside the circle  131  corresponds to the state where the phase voltages of three phases are close to each other. In this state, the current values of two phases cannot be detected regardless of a value of the b-axis voltage v b .
 
| v   b |&lt;   (1-3)
 
 v   a &lt;√{square root over (3)}   (1-4)
 
       FIGS. 11A and 11B  illustrate a locus of the voltage vector ( 110 ) on the ab coordinates before and after the correction process performed in the step S 2 . FIG.  11 A shows a voltage vector locus on the ab coordinates before the correction, and  FIG. 11B  shows a voltage vector locus on the ab coordinates after the correction. Note that the a-axis component and the b-axis component of the voltage vector  110  after the correction process in the step S 2  are denoted by v ac  and v bc , respectively (“v ac =v a ” and “v bc =v b ” hold if the correction is not performed actually).  FIGS. 11A and 11B  exemplify a case where the b-axis voltage is corrected. Each of  FIGS. 11A and 11B  illustrates a lot of plotted dots indicating voltage values at individual timings. The voltage vector before the correction corresponding to  FIG. 11A  can be located at a vicinity of the a-axis where current values of two phases cannot be detected, but the voltage vector after the correction corresponding to  FIG. 11B  is not located at a vicinity of the a-axis by the correction with respect to v b . 
     After the correction process in the step S 2 , the process goes to the step S 3  where the voltage vector  110  after the correction on the ab coordinates is converted into the voltage vector  110  on the αβ coordinates. When the α-axis component and the β-axis component of the voltage vector  110  after the correction process in the step S 2  are denoted respectively by v αc  and v βc , the coordinate conversion in the step S 3  is performed in accordance with the equation (1-5). 
     
       
         
           
             
               
                 
                   
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       FIGS. 12A and 12B  illustrate a locus of the voltage vector ( 110 ) on the αβ coordinates before and after the correction process described above.  FIG. 12A  shows a voltage vector locus on the αβ coordinates before the correction, and  FIG. 12B  shows a voltage vector locus on the αβ coordinates after the correction. This correction process makes a region where a voltage vector is not located exist every 60 degrees of electrical angle in the αβ coordinates as fixed coordinates. The voltage vector (specified voltage vector) after the correction is converted into individual voltage components of the U-phase, the V-phase and the W-phase finally.  FIG. 13  illustrates waveforms of voltages v u , v v  and v w  obtained after the above-mentioned correction process, in which the horizontal axis represents time. In  FIG. 13 , plotted dots  142   u  arranged on a distorted sine wave shows a locus of the voltage v u , plotted dots  142   v  arranged on a distorted sine wave shows a locus of the voltage v v , and plotted dots  142   w  arranged on a distorted sine wave shows a locus of the voltage v w . As understood from  FIG. 13 , a voltage difference between phase voltages is secured to be larger than a predetermined value by the above-mentioned correction process. 
     Hereinafter, first and second examples are described as examples to which the correction process (correction method) described above is applied. Note that items described in one example (e.g., the first example) can be applied to another example, as long as no contradiction arises. 
     FIRST EXAMPLE 
     The first example will be described.  FIG. 14  is a block diagram illustrating a structure of a motor driving system according to the first example. In the motor driving system shown in  FIG. 14 , so-called direct torque control is performed. If an interior permanent magnet motor or the like is used, magnetic flux of a permanent magnet or an inductance distribution may have harmonics in many cases. For instance, the magnetic flux of the permanent magnet linking with the U-phase armature winding traces a waveform of a sine wave with respect to a change in rotor phase ideally, but actually the waveform includes harmonics, which causes a distortion of an induction voltage (electromotive force) generated by rotation of the permanent magnet. In the same manner, a d-axis inductance and a q-axis inductance of the armature winding also include harmonics. It is known that such harmonics can cause a torque ripple. 
     When the vector control is performed so that the d-axis current and the q-axis current become constant, the generated torque becomes constant if the magnetic flux of the permanent magnet and the inductance distribution have no harmonic. Actually, however, they usually have harmonics, so the generated torque has a ripple. In the direct torque control, the magnetic flux linking with the armature winding of the stator is estimated, and a torque is estimated based on the estimated magnetic flux and the motor current so that the torque is controlled directly. Since the estimated magnetic flux is affected by the harmonics, the estimation of the torque is also affected by the harmonics. Since the direct torque control is performed based on the estimated torque, the torque ripple can be reduced even if the magnetic flux of the permanent magnet or the inductance distribution has harmonics. 
     A motor control system shown in  FIG. 14  includes a motor  1 , an inverter  2 , a DC power supply  4  and a current sensor  5 . It also includes individual portions denoted by reference numerals  21  to  30 . In the first example, the controller  3  shown in  FIG. 1  is made up of individual portions denoted by reference numerals  21  to  30 . 
     As described above, the current sensor  5  senses the bus current and outputs a signal indicating a current value of the bus current. A current detecting portion  21  refers to the specified three-phase voltage values v u *, v v * and v w * delivered from the coordinate converter  30  so as to specify the maximum phase, the intermediate phase and the minimum phase. Based on the specified three-phase voltage values v u *, v v * and v w *, it also decides the timings ST 1  and ST 2  (see  FIG. 6 ) for sampling the output signal of the current sensor  5 , so as to calculate and deliver the U-phase current i u  and the V-phase current i v  from current values of the bus current (output signal values of the current sensor  5 ) obtained at the timings ST 1  and ST 2 . On this occasion, a relational expression “i u +i v +i w =0” is used if necessary. 
     As described above with reference to  FIG. 6 , v u *, v v  and v w * are expressed as counter set values CntU, CntV and CntW, respectively. The current detecting portion  21  compares the counter set values CntU, CntV and CntW with each other based on v u *, v v * and v w * so as to specify which of the first to the sixth modes the present time belongs to, and it determines the timings ST 1  and ST 2  when the bus current should be detected with the specified mode taken into account. For instance, if “CntU&gt;CntV&gt;CntW” holds, the present time is decided to belong the first mode, so that the timing corresponding to a value between the set values CntW and CntV is defined to be ST 1  while the timing corresponding to a value between the set values CntV and CntU is defined to be ST 2 . If the present time belongs to the first mode, bus current values detected at the timings ST 1  and ST 2  are −i w  and i u , respectively. 
     The coordinate converter  22  converts the three-phase current detected by the current detecting portion  21  into two-phase current on the αβ coordinates. More specifically, i u  and i v  as the U-phase axis component and the V-phase axis component of the motor current I a  are converted into i α  and i β  as the α-axis component and the β-axis component of the motor current I a . The current components i α  and i β  obtained from this conversion are supplied to a magnetic flux and torque estimator  23 . 
     An α-axis component and a β-axis component of the magnetic flux linkage of the armature windings ( 7   u ,  7   v  and  7   w ) shown in  FIG. 1  are referred to as an α-axis magnetic flux φ α  and a β-axis magnetic flux φ β , respectively. Similarly to the motor driving system shown in  FIG. 25 , the magnetic flux and torque estimator  23  performs an estimation of the magnetic flux based on the α-axis current, the β-axis current and the specified voltage vector. As the specified voltage vector for this estimation, the specified voltage vector after the correction process described above is used. More specifically, the magnetic flux and torque estimator  23  estimates the α-axis magnetic flux φ α  and the β-axis magnetic flux φ β  based on i α  and i β  from the coordinate converter  22  and v αc * and v βc * from a specified voltage calculating portion  29 . The symbols v αc * and v βc * represent target values to which v αc  and v βc  appearing in the above equation (1-5) should follow. The symbols v αc * and v βc * are coordinate axis components forming the specified voltage vector after the correction on the αβ coordinates, and the meaning thereof will be apparent from description of the specified voltage calculating portion  29  that will be described later. 
     More specifically, the magnetic flux and torque estimator  23  estimates φ α  and φ β  in accordance with the equation (2-1) and (2-2). After that, the magnetic flux and torque estimator  23  calculates a phase θs of the magnetic flux linkage vector made up of φ α  and φ β  with respect to the α-axis based on φ α  and φ β  estimated by itself in accordance with the equation (2-3) below, and it estimates a torque T generated by the motor  1  in accordance with the equation (2-4) below. The integrals in the right-hand sides of the equations (2-1) and (2-2) are integrals with respect to time t, and the integral interval is from a reference time (t=0) to the present time.
 
φ α =∫( v   αc   *−R   a   i   α ) dt+φ   α|t=0    (2-1)
 
φ β =∫( v   βc   *−R   a   i   β ) dt+φ   β|t=0    (2-2)
 
θ S =tan −1 (φ β /φ α )   (2-3)
 
 T=P   N (φ α   i   β −φ β   i   α )   (2-4)
 
     Here, R a  represents a resistance value of one phase of the armature windings ( 7   u ,  7   v  and  7   w ), P N  represents the number of pole pairs of the motor  1 , and “φ α|t=0 ” and “φ β|t=0 ” represent values of the φ α  and φ β  at time t=0 (i.e., initial values of φ α  and φ β ), respectively. 
     In addition, a state quantity that will appear in equations or the like that will be described later is defined here. Symbols L d  and L q  represent respectively a d-axis inductance (d-axis component of an inductance of the armature windings of the motor  1 ) and a q-axis inductance (q-axis component of an inductance of the armature windings of the motor  1 ), and a symbol (Φ a  represents the magnetic flux linkage of an armature due to the permanent magnet of the rotor  6  of the motor  1 . Symbols i d  and i q  represent respectively a d-axis current as a d-axis component and a q-axis current as a q-axis component of the motor current I a . 
     The d-axis is defined in the direction of the north pole of the permanent magnet of the rotor  6 , and the q-axis leads the d-axis by π/2. The d-axis and the q-axis will be further described later in a description of the second example. Note that R a , L d , L q , Φ a , P N , “φ α|t=0 ” and “φ β|t=0 ” are determined in advance in a designing stage of the motor driving system. 
     The subtracter  24  calculates a torque error ΔT (=T*−T) between the torque T estimated by the magnetic flux and torque estimator  23  and the specified torque value T* indicating a target value of the torque T. As to the direct torque control, it is necessary to give a specified value of the amplitude of the magnetic flux linkage together with the specified torque value T*. The specified value of the amplitude is represented by |φ S *|. The specified value |φ S *| indicates a target value of a magnitude of the magnetic flux linkage vector made up of φ α  and φ β  (i.e., amplitude of the magnetic flux linkage). In general, an amplitude |φ S | of the magnetic flux linkage and the torque T are expressed by the equation (2-5) and the equation (2-6) below. Therefore, in order to realize a maximum torque control, for instance, the calculation equation (2-7) of the d-axis current for realizing the maximum torque control is substituted into the equation (2-5) and the equation (2-6), so that table data indicating a relationship between |φ S | and T are generated in advance. The table data are stored in the table  25  shown in  FIG. 14 , and |φ S | and T are dealt with as |φ S *| and T*. Then, the table  25  is used for calculating |φ S *| from the specified torque value T*. 
     
       
         
           
             
               
                 
                   
                      
                     
                       ϕ 
                       S 
                     
                      
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 L 
                                 d 
                               
                               ⁢ 
                               
                                 i 
                                 d 
                               
                             
                             + 
                             
                               Φ 
                               a 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             
                               L 
                               q 
                             
                             ⁢ 
                             
                               i 
                               q 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
             
               
                 
                   T 
                   = 
                   
                     
                       P 
                       N 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             Φ 
                             a 
                           
                           ⁢ 
                           
                             i 
                             q 
                           
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 L 
                                 q 
                               
                               - 
                               
                                 L 
                                 d 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             i 
                             d 
                           
                           ⁢ 
                           
                             i 
                             q 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     i 
                     d 
                   
                   = 
                   
                     
                       
                         Φ 
                         a 
                       
                       
                         2 
                         ⁢ 
                         
                           ( 
                           
                             
                               L 
                               q 
                             
                             - 
                             
                               L 
                               d 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         
                           
                             Φ 
                             a 
                             2 
                           
                           
                             4 
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   
                                     L 
                                     q 
                                   
                                   - 
                                   
                                     L 
                                     d 
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                         + 
                         
                           i 
                           q 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     7 
                   
                   ) 
                 
               
             
           
         
       
     
     The specified value |φ S *| obtained from the table  25  is supplied to the specified magnetic flux calculating portion  26 . However, if flux-weakening control is required in the case where the motor  1  is rotating at high speed or in other cases, |φ S *| is calculated in accordance with the equation (2-8) below and is supplied to the specified magnetic flux calculating portion  26 . Here, ω represents an electrical angle speed in rotation of the rotor  6  of the motor  1  (electrical angle speed of the d-axis), and V om  represents a limitation value of the motor voltage V a  that should be limited by the flux-weakening control. 
     
       
         
           
             
               
                 
                   
                      
                     
                       ϕ 
                       S 
                       * 
                     
                      
                   
                   = 
                   
                     
                       V 
                       om 
                     
                     ω 
                   
                 
               
               
                 
                   ( 
                   
                     2 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 15  illustrates an internal block diagram of the specified magnetic flux calculating portion  26 . The specified magnetic flux calculating portion  26  shown in  FIG. 15  includes individual portions denoted by reference numerals  35  to  37 . The specified magnetic flux calculating portion  26  calculates and delivers an α-axis specified magnetic flux value φ α * and a β-axis specified magnetic flux value φ β * that are target values of φ α  and φ β  based on |φ S *| obtained as described above, θs from the magnetic flux and torque estimator  23  and ΔT from the subtracter  24 . 
     More specifically, a PI controller  35  performs proportional-plus-integral control for converging ΔT to zero so as to calculate a phase correction quantity Δθ S * corresponding to ΔT. An adder  36  calculates a sum (θ S +Δθ S *) of θ S  and Δθ S *. This sum is supplied to a vector generating portion  37  as a phase specified value θ S * (i.e., (θ S +Δθ S *)). The vector generating portion  37  calculates φ α * and φ β * based on |φ S *| and θ S * in accordance with the equations (2-9a) and (2-9b) below.
 
φ α *=|φ S *|cos θ S *   (2-9a)
 
φ β *=|φ S *|sin θ S *   (2-9b)
 
     The values φ α * and φ β * calculated by the specified magnetic flux calculating portion  26  and the values φ α  and φ β  estimated by the magnetic flux and torque estimator  23  are supplied to the subtracters  27  and  28 . The subtracters  27  and  28  calculates deviations (φ α *−φ α ) and (φ β *−φ β ) and supplies them to the specified voltage calculating portion  29 . In addition, i α  and i β  obtained by the coordinate converter  22  are also supplied to the specified voltage calculating portion  29  (omitted in  FIG. 14 ). 
       FIG. 16  illustrates an internal block diagram of the specified voltage calculating portion  29 . The specified voltage calculating portion  29  shown in  FIG. 16  includes individual portions denoted by reference numerals  41  to  44 . A precorrection voltage calculating portion  41  calculates an α-axis specified voltage value v α * and a β-axis specified voltage value v β * based on (φ α *−φ α ), (φ β *−φ β ) i α  and i β  so that φ α  tracks φ α * and that φ β  tracks φ β *. The symbols v α * and v β * represent respectively target values of v α and v β for converging both (φ α *−φ α ) and (φ β *−φ β ) to zero. The values v α * and v β * are calculated so that a specified voltage vector (v αβ *) made up of v α * and v β * becomes a sum of a time differential of a magnetic flux linkage vector (φ αβ ) made up of φ α  and φ β  and a voltage drop vector due to R a  and a current vector (i αβ ) made up of i α  and i β  (see the equation (2-10) below). When the individual values generated in the motor driving system are regarded as discrete values, this calculation method can be embodied. The embodied calculation method will be described later. 
     
       
         
           
             
               
                 
                   
                     v 
                     
                       α 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       β 
                     
                     * 
                   
                   = 
                   
                     
                       
                         ⅆ 
                         
                             
                         
                         ⁢ 
                         
                           ϕ 
                           
                             α 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             β 
                           
                         
                       
                       
                         ⅆ 
                         t 
                       
                     
                     + 
                     
                       
                         R 
                         a 
                       
                       · 
                       
                         i 
                         
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     A coordinate rotating portion  42  converts v α * and v β * into v a  and v b  in accordance with the above equation (1-2). More specifically, it converts two-phase specified voltage vector represented by v α * and v β * on the αβ coordinates into two-phase specified voltage vector represented by v a  and v b  on the ab coordinates (the specified voltage vectors correspond to the voltage vector  110  shown in  FIG. 8 ). In addition, a value of n that is used for calculation of the equation (1-2) is calculated by using the above equation (1-1 a ) or (1-1 b ). A value of n calculated by the coordinate rotating portion  42  is used also for calculation in the coordinate rotating portion  44 . Note that the coordinate rotating portion  42  uses v α * and v β * as v α  and v β , respectively, in the right-hand sides of the equation (1-1 a ), (1-1 b ) and (1-2). 
     A component correcting portion  43  performs the correction process in the step S 2  of  FIG. 10  on v a  and v b , so as to output v a  and v b  after the correction as v ac  and v bc , respectively. However, if the correction is not necessary, “v ac =v a ” and “v bc =v b ” hold. 
     The coordinate rotating portion  44  converts the a-axis voltage v ac  and the b-axis voltage v bc  after the correction into the α-axis voltage v αc  and the β-axis voltage v β c after the correction in accordance with the above equation (1-5), so as to output the obtained v αc and v βc  as v αc * and v βc *, respectively. In other words, it converts the two-phase specified voltage vector expressed by v ac  and v bc  on the ab coordinates after the correction into the two-phase specified voltage vector expressed by v αc * and v βc * on the αβ coordinates after the correction. The symbols v αc * and v βc * represent respectively the α-axis component and the β-axis component of the specified voltage vector after the correction. 
     The specified voltage values v αc * and v βc * calculate by the specified voltage calculating portion  29  (coordinate rotating portion  44 ) are supplied to the coordinate converter  30  shown in  FIG. 14 . The coordinate converter  30  converts v αc * and v βc * into the specified three-phase voltage values v u *, v v * and v w * and outputs the specified three-phase voltage values to the inverter  2 . The inverter  2  supplies three-phase AC current to the motor  1  in accordance with the specified three-phase voltage values. The values v u *, v v * and v w * calculated by the coordinate converter  30  correspond to the U-phase axis component, the V-phase axis component and the W-phase axis component of the specified voltage vector expressed by v αc * and v βc *. 
     [Calculation Equation with Discretization] 
     Calculations in the motor driving system are performed based on discrete instantaneous values of individual state quantities, actually. Therefore, it is considered that input values and output values of individual portions denoted by reference numerals  21  to  30  are made discrete values by a discrete period T S , and operations of the individual portions will be further described. 
     It is supposed that the reference time (t=0) belongs to the 0th period, and that the present time belongs to the m-th period (m is a natural number). Then, i u  and i v  in the m-th period are represented by i[m] and i v [m], respectively, and i α  and i β  based on i u [m] and i v [m] are represented by i α [m] and i β [m], respectively. Then, v αc * and v βc * output from the specified voltage calculating portion  29  in the m-th period are represented by v αc *[m] and v βc *[m], respectively, and φ α , φ β , θ S  and T based on i α [m], i β [m], v αc *[m] and v βc *[m] are represented by φ α [m], φ β [m], θ S [m] and T[m], respectively. Further, T* in the m-th period is represented by T*[m], and |φ S *| based on T*[m] is represented by |φ S *|[m]. In addition, ΔT based on T*[m] and T[m] is represented by ΔT[m]. 
     In this case, the magnetic flux and torque estimator  23  calculates φ α [m], φ β [m], θ S [m] and T[m] in accordance with the equations (3-1) to (3-4) below, which correspond to the above equations (2-1) to (2-4). 
     
       
         
           
             
               
                 
                   
                     
                       ϕ 
                       α 
                     
                     ⁡ 
                     
                       [ 
                       m 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         m 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               
                                 v 
                                 
                                   α 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   c 
                                 
                                 * 
                               
                               ⁡ 
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                             - 
                             
                               
                                 R 
                                 a 
                               
                               ⁢ 
                               
                                 
                                   i 
                                   α 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   k 
                                   ] 
                                 
                               
                             
                           
                           ) 
                         
                         · 
                         
                           T 
                           S 
                         
                       
                     
                     + 
                     
                       ϕ 
                       
                         
                           α 
                           | 
                           t 
                         
                         = 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ϕ 
                       β 
                     
                     ⁡ 
                     
                       [ 
                       m 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         m 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               
                                 v 
                                 
                                   β 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   c 
                                 
                                 * 
                               
                               ⁡ 
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                             - 
                             
                               
                                 R 
                                 a 
                               
                               ⁢ 
                               
                                 
                                   i 
                                   β 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   k 
                                   ] 
                                 
                               
                             
                           
                           ) 
                         
                         · 
                         
                           T 
                           S 
                         
                       
                     
                     + 
                     
                       ϕ 
                       
                         
                           β 
                           | 
                           t 
                         
                         = 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       θ 
                       S 
                     
                     ⁡ 
                     
                       [ 
                       m 
                       ] 
                     
                   
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             ϕ 
                             β 
                           
                           ⁡ 
                           
                             [ 
                             m 
                             ] 
                           
                         
                         / 
                         
                           
                             ϕ 
                             α 
                           
                           ⁡ 
                           
                             [ 
                             m 
                             ] 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     T 
                     ⁡ 
                     
                       [ 
                       m 
                       ] 
                     
                   
                   = 
                   
                     
                       P 
                       N 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               ϕ 
                               α 
                             
                             ⁡ 
                             
                               [ 
                               m 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               i 
                               β 
                             
                             ⁡ 
                             
                               [ 
                               m 
                               ] 
                             
                           
                         
                         - 
                         
                           
                             
                               ϕ 
                               β 
                             
                             ⁡ 
                             
                               [ 
                               m 
                               ] 
                             
                           
                           ⁢ 
                           
                             
                               i 
                               α 
                             
                             ⁡ 
                             
                               [ 
                               m 
                               ] 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     Then, the specified magnetic flux calculating portion  26  calculates φ α *[m+1] and φ α *[m+1] based on ΔT[m], θ S [m] and |φ S *|[m], and the subtracters  27  and  28  calculate the deviations (φ α *[m+1]−φ α [m]) and (φ 62  *[m+1]−φ β [m]). In other words, target values of φ α  and φ β  of the next period are determined based on ΔT, θ S  and |φ S *| in the m-th period, and a deviation between the target value and an instantaneous value of the magnetic flux linkage at the present time is determined. 
     The precorrection voltage calculating portion  41  (see  FIG. 16 ) in the specified voltage calculating portion  29  calculates the specified voltage vector necessary for matching the φ α  and φ β  in the (m+1)th period with φ α *[m+1] and φ β *[m+1]. In other words, the precorrection voltage calculating portion  41  calculates v α *[m+1] and v β *[m+1] in accordance with the equation (3-5) below, which corresponds to the above equation (2-10). After that, the specified voltage calculating portion  29  calculates v αc *[m+1] and v βc *[m+1] indicating voltage to be applied to the motor  1  in the (m+1)th period from v α *[m+1] and v β *[m+1] through the correction process and supplies them to the inverter  2  through the coordinate conversion performed by the coordinate converter  30 . 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             v 
                             α 
                             * 
                           
                         
                         
                           
                             [ 
                             
                               m 
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                       
                         
                           
                             v 
                             β 
                             * 
                           
                         
                         
                           
                             [ 
                             
                               m 
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         1 
                         
                           T 
                           S 
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     ϕ 
                                     α 
                                     * 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       m 
                                       + 
                                       1 
                                     
                                     ] 
                                   
                                 
                                 - 
                                 
                                   
                                     ϕ 
                                     α 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     m 
                                     ] 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     ϕ 
                                     β 
                                     * 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       m 
                                       + 
                                       1 
                                     
                                     ] 
                                   
                                 
                                 - 
                                 
                                   
                                     ϕ 
                                     α 
                                   
                                   ⁡ 
                                   
                                     [ 
                                     m 
                                     ] 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                     + 
                     
                       
                         R 
                         a 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   i 
                                   α 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   m 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   i 
                                   β 
                                 
                                 ⁡ 
                                 
                                   [ 
                                   m 
                                   ] 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
     The equation (3-5) (as well as the above equation (2-10)) is derived from a difference equation indicating a relationship between the magnetic flux linkage and the voltage corresponding to  FIG. 17 . In  FIG. 17 , φ αβ [m] represents a vector made up of φ α [m] and φ β [m], and φ αβ *[m+1] represents a vector made up of φ α *[m+1] and φ β *[m+1]. 
     In this way, the first example enables to detect the motor current with reliability by the step of correcting the voltage vector (specified voltage vector). Furthermore, since this correction process is performed on the ab coordinates that can support a easy correction, a necessary correction can be realized simply and securely. Since it is sufficient to correct the coordinate axis components v a  and v b  of the voltage vector (specified voltage vector) independently on the ab coordinates, contents of the correction can be simple. In particular, the correction is required for all the three phases if the applied voltage is low, but it is easy to determine correction quantities in this case. 
     In addition, it is possible to reduce a torque ripple by the direct torque control even if the motor that is used has harmonics in the magnetic flux of the permanent magnet or the inductance distribution. Note that it is possible to use a synchronous reluctance motor or a induction motor as the motor  1  instead of the interior permanent magnet motor. The synchronous reluctance motor and the induction motor also have harmonics in the magnetic flux of the permanent magnet or the inductance distribution, so the effect of reducing the torque ripple can be obtained by the direct torque control. 
     In the first example, the specified voltage values are corrected for detecting the motor current with reliability. If the specified voltage values before the correction are used for estimation of the magnetic flux, an estimation error may occur. In the first example, the specified voltage values (v αc * and v βc *) after the correction are used for estimating the magnetic flux, so the estimation error due to the correction does not occur. In addition, since the correction process is performed on the stage of the voltage vector, the specified voltage vector after the correction to be used for estimating the magnetic flux can be obtained easily. Therefore, the step of inverse conversion of the three-phase voltage is not necessary, and the voltage detector for detecting the three-phase voltage is not necessary unlike the motor driving system shown in  FIG. 25 . 
     SECOND EXAMPLE 
     Next, a second example will be described. The symbols and the like defined in the first example are also used in the second example.  FIG. 18  is a block diagram showing a structure of the motor driving system according to the second example. In the motor driving system shown in  FIG. 18 , the vector control is performed by estimating a rotor position from an estimated value of the magnetic flux linkage. 
     Prior to description of individual portions shown in  FIG. 18 , axes defined in the second example will be described, and calculation equations concerned with operations in the second example will be derived.  FIG. 19  is referred to.  FIG. 19  is an analytic model diagram of the motor  1 .  FIG. 19  shows the U-phase axis, the V-phase axis and the W-phase axis. Numeral  6   a  denotes a permanent magnet provided to the rotor  6  of the motor  1 . In the rotating coordinate system rotating at the same speed as the magnetic flux of the permanent magnet  6   a , the direction of the magnetic flux of the permanent magnet  6   a  is regarded as the d-axis. In addition, it is supposed that the q-axis is at the phase leading the d-axis by 90 degrees of electrical angle, though it is not illustrated. The d-axis and the q-axis are coordinate axes of the rotating coordinate system, and the coordinates (coordinate system) having them as its coordinate axes is referred to as the dq coordinates (dq coordinate system). 
     The d-axis (as well as the q-axis) is rotating, and its rotation speed (electrical angle speed) is represented by ω. In addition, a phase of the d-axis in the counterclockwise direction viewed from the armature winding fixed-axis of the U-phase is represented by θ. The counterclockwise direction corresponds to the phase leading direction. Since the phase θ is usually called a rotor position, it is referred to as the rotor position in the following description. 
     A d-axis component and a q-axis component of the entire motor voltage V a  applied to the motor  1  from the inverter  2  are referred to as a d-axis voltage v d  and a q-axis voltage V q , respectively. In addition, as described above in the first example, the d-axis component and the q-axis component of the entire motor current I a  supplied from the inverter  2  to the motor  1  are referred to as a d-axis current i d  and a q-axis current i q . 
     Specified values with respect to the d-axis voltage v d  and the q-axis voltage v q  are referred to as a d-axis specified voltage value v d * and a q-axis specified voltage value v q *, respectively. The specified values v d * and v q * are voltage values (target voltage values) to which v d  and v q  should follow, respectively. 
     The specified value with respect to the d-axis current i d  and the q-axis current i q  are referred to as a d-axis specified current value i d * and a q-axis specified current value i q *, respectively. The specified values i d * and i q * are current values (target current values) to which i d  and i q  should follow, respectively. 
     An extended induction voltage equation (in other words, an extended electromotive force equation) on the dq coordinates is expressed by the equation (4-1), and an extended induction voltage (in other words, an extended electromotive force) E ex  is expressed by the equation (4-2). Note that “p” in the equations below is a differential operator. When the equation (4-1) is rewritten with respect to the αβ coordinates, the equation (4-3) is obtained. Furthermore, the fact that the equation (4-3) holds is also described in the document “Sensorless Controls of Salient-Pole Permanent Magnet Synchronous Motors Using Extended Electromotive Force Models” by Ichikawa and four others, Institute of Electrical Engineers Papers D, 2002, Vol. 122, No. 12, pp. 1088-1096. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             v 
                             d 
                           
                         
                       
                       
                         
                           
                             v 
                             q 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   R 
                                   a 
                                 
                                 + 
                                 
                                   pL 
                                   d 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   ω 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   L 
                                   q 
                                 
                               
                             
                           
                           
                             
                               
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   L 
                                   q 
                                 
                               
                             
                             
                               
                                 
                                   R 
                                   a 
                                 
                                 + 
                                 
                                   pL 
                                   d 
                                 
                               
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 i 
                                 d 
                               
                             
                           
                           
                             
                               
                                 i 
                                 q 
                               
                             
                           
                         
                         ] 
                       
                     
                     + 
                     
                       [ 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             
                               E 
                               ex 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     E 
                     ex 
                   
                   = 
                   
                     
                       ω 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 
                                   L 
                                   d 
                                 
                                 - 
                                 
                                   L 
                                   q 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               i 
                               d 
                             
                           
                           + 
                           
                             Φ 
                             a 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         ( 
                         
                           
                             L 
                             d 
                           
                           - 
                           
                             L 
                             q 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           pi 
                           q 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             v 
                             α 
                           
                         
                       
                       
                         
                           
                             v 
                             β 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   R 
                                   a 
                                 
                                 + 
                                 
                                   pL 
                                   d 
                                 
                               
                             
                             
                               
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       L 
                                       d 
                                     
                                     - 
                                     
                                       L 
                                       q 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   - 
                                   ω 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       L 
                                       d 
                                     
                                     - 
                                     
                                       L 
                                       q 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   R 
                                   a 
                                 
                                 + 
                                 
                                   pL 
                                   d 
                                 
                               
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 i 
                                 α 
                               
                             
                           
                           
                             
                               
                                 i 
                                 β 
                               
                             
                           
                         
                         ] 
                       
                     
                     + 
                     
                       
                         E 
                         ex 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   - 
                                   sin 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                               
                             
                           
                           
                             
                               
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     The matrix in the first term of the right-hand side of the equation (4-3) is moved to the left-hand side of the same, and then each side is integrated with respect to time. Thus, the equations (4-4) and (4-5) are obtained (since “θ=ωt” holds, the integral of −sin θ is cos θ/ω while the integral of cos θ is sin θ/ω). On this occasion, however, the differential term of i q  of the extended induction voltage E ex  (i.e., the second term of the right-hand side of the equation (4-2)) is omitted.
 
∫( v   α   −R   a   i   α −ω( L   d   −L   q ) i   β ) dt−L   d   i   α =(( L   d   −L   q ) i   d +Φ a )cos θ=φ exα   (4-4)
 
∫( v   β +ω( L   d   −L   q ) i   α   −R   a   i   β ) dt−L   d   i   β =(( L   d   −L   q ) i   d +Φ a )sin θ=φ exβ   (4-5)
 
     Supposing “E ex =φ ex /ω” holds, E ex  represents an induction voltage (electromotive force) generated by magnetic flux linkage φ ex  of the armature winding and rotation of the rotor  6  of the motor  1 . If E ex  is regarded as an induction voltage vector in the rotating coordinate system, the induction voltage vector becomes a vector on the q-axis. Similarly, if φ ex  is regarded as a magnetic flux linkage vector in the rotating coordinate system, the magnetic flux linkage vector becomes a vector on the d-axis. Symbols φ exα  and φ exβ  appearing also in the equations (4-4) and (4-5) represent respectively an α-axis component and a β-axis component of φ ex . 
     A phase θ ex  of the magnetic flux linkage vector φ ex  with respect to the α-axis is expressed by the equation (4-6) below. In the motor driving system according to the second example, the α-axis component φ exα  and the β-axis component φ exβ  of the magnetic flux linkage vector φ ex  are estimated, and base on the estimated values the phase θ ex  is estimated. As described above, since the magnetic flux linkage vector φ ex  is to be a vector on the d-axis, the estimated θ ex  is identical to θ ideally. Therefore, PLL (Phase Locked Loop) control is performed based on a difference (axial error) between the estimated θ ex  and θ to be used for the coordinate conversion, so that the rotation speed and the rotor position are estimated. The rotation speed ω and the rotor position θ are estimated in accordance with the equations (4-7) and (4-8) below. Here, K p  and K i  respectively represent a proportional coefficient and an integral coefficient in the proportional-plus-integral control, and s is the Laplace operator.
 
θ ex =tan −1 (φ exβ /φ exα )   (4-6)
 
ω=( K   p   +K   i   /s )(θ ex −θ)   (4-7)
 
θ=ω/ s    (4-8)
 
     A concrete operation of the motor driving system shown in  FIG. 18  will be described. The motor control system shown in  FIG. 18  includes a motor  1 , an inverter  2 , a DC power supply  4 , a current sensor  5 , and individual portions denoted by reference numerals  61 - 70 . In the second example, the controller  3  shown in  FIG. 1  is made up of the individual portions denoted by the reference numerals  61 - 70 . 
     As described above, the current sensor  5  senses bus current and outputs a signal indicating a current value of the bus current. A current detecting portion  61  and a coordinate converter  62  are similar respectively to the current detecting portion  21  and the coordinate converter  22  shown in  FIG. 14 . More specifically, the current detecting portion  61  calculates and outputs the U-phase current i u  and the V-phase current i v  based on the output signal value of the current sensor  5  and the specified three-phase voltage values v u *, v v * and v w * similarly to the current detecting portion  21  shown in  FIG. 14 . However, the specified three-phase voltage values v u *, v v * and v w * with respect to the current detecting portion  61  are supplied from the coordinate converter  70 . The coordinate converter  62  converts i u  and i v  calculated in the current detecting portion  61  into i α  and i β . 
     A magnetic flux estimator  63  estimates the magnetic flux linkage of the motor  1  based on i α  and i β  obtained by the coordinate converter  62  and v αc * and v βc * from the specified voltage calculating portion  69  in accordance with the above equations (4-4) and (4-5) (in other words, it calculates the α-axis component φ exα  and the β-axis component φ exβ of the magnetic flux linkage vector φ ex ). On this occasion, v αc * and v βc * are used respectively as v α  and v β  in the equations (4-4) and (4-5). In addition, ω estimated by the position and speed estimator  64  is also used. 
       FIG. 20  illustrates an internal block diagram of the position and speed estimator  64 . The position and speed estimator  64  shown in  FIG. 20  includes individual portions denoted by reference numerals  75  to  78 . A θ ex  calculating portion  75  calculates the phase θ ex  based on the φ exα  and φ exβ  calculated by the magnetic flux estimator  63  in accordance with the above equation (4-6). A subtracter  76  subtracts θ supplied by an integrator  78  from θ ex  supplied by the θ ex  calculating portion  75  so as to calculate an axial error (θ ex −θ). A PI controller  77  performs proportional-plus-integral control so that the axial error (θ ex −θ) converges to zero. In other words, the calculation is performed in accordance with the above equation (4-7), so that the rotation speed ω is calculated. The integrator  78  integrates ω calculated by the PI controller  77  in accordance with the above equation (4-8), so as to calculate the rotor position θ. The values ω and θ calculated by the PI controller  77  and the integrator  78  are the rotation speed and the rotor position estimated by the position and speed estimator  64 . 
     A (αβ/dq converter  65  converts i α  and i β  obtained by the coordinate converter  62  into i d  and i q  that are current components on the dq coordinates in accordance with θ estimated by the position and speed estimator  64 . 
     A specified current calculating portion  66  generates and delivers the d-axis specified current value i d * and the q-axis specified current value i q *. For instance, it generates i q * so that the rotation speed ω follows a speed specified value ω* supplied from the outside and refers to i q * and the like, if necessary, so as to generate i d * so that a desired vector control (e.g., maximum torque control) can be realized. 
     Subtracters  67  and  68  calculates current errors (i d *−i d ) and (i q *−i q ) based on i d  and i q  from the (αβ/dq converter  65  and i d * and i q * from the specified current calculating portion  66 , and a result of the calculation is supplied to the specified voltage calculating portion  69 . 
       FIG. 21  illustrates an internal block diagram of the specified voltage calculating portion  69 . The specified voltage calculating portion  69  shown in  FIG. 21  includes individual portions denoted by reference numerals  81  to  84 . A precorrection voltage calculating portion  81  calculates the d-axis specified voltage value v d * and the q-axis specified voltage value v q * so that the current errors (i d *−i d ) and (i q *−i q ) converge to zero by the proportional-plus-integral control. The values v d * and v q * are target values of v d  and v q  for converging both of (i d *−i d ) and (i q *−i q ) to zero. 
     A coordinate rotating portion  82  converts v d * and v q * into v a  and v b  based on θ estimated by the position and speed estimator  64 . Referring to  FIG. 22 , this conversion method will be further described.  FIG. 22  is a space vector diagram showing a relationship among the U-phase axis, the V-phase axis, the W-phase axis, the d-axis, the q-axis and the voltage vector  110 . A phase of the voltage vector  110  viewed from the q-axis is represented by ε. A phase of the voltage vector  110  with respect to the U-phase axis is expressed by (θ+ε+π/2). In addition, a phase of the axis closest to the voltage vector  110  among axes a 1  to a 6  (see  FIG. 9 ) is expressed by “(n′+2)π/3” with respect to the U-phase axis. Here, n′ represents a quotient obtained by dividing (θ+ε) by π/3. 
     For convenience sake, θ is decomposed into the above-mentioned phase (n′+2)π/3 and a difference phase θ D  between the phase (n′+2)π/3 and θ as shown in  FIG. 22 . A relationship between these phases is expressed by the equation (5-1) below. Then, v d  and v q  expressing the voltage components on the dq coordinates are converted into v a  and v b  expressing the voltage components on the ab coordinates by the equation (5-2) below. In addition, ε is expressed by the equation (5-3) below. 
     
       
         
           
             
               
                 
                   θ 
                   = 
                   
                     
                       θ 
                       D 
                     
                     + 
                     
                       
                         
                           ( 
                           
                             
                               n 
                               ′ 
                             
                             + 
                             2 
                           
                           ) 
                         
                         ⁢ 
                         π 
                       
                       3 
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             v 
                             a 
                           
                         
                       
                       
                         
                           
                             v 
                             b 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 θ 
                                 D 
                               
                             
                           
                           
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 θ 
                                 D 
                               
                             
                           
                         
                         
                           
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 θ 
                                 D 
                               
                             
                           
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 θ 
                                 D 
                               
                             
                           
                         
                       
                       ] 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               v 
                               d 
                             
                           
                         
                         
                           
                             
                               v 
                               q 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   ɛ 
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           - 
                           
                             v 
                             d 
                           
                         
                         
                           v 
                           q 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     The coordinate rotating portion  82  converts v d * and v q * into v a  and v b  in accordance with the above equations (5-1) to (5-3). On this occasion, however, v d * and v q * are used respectively as v d  and v q  in the equations (5-2) and (5-3). More specifically, n′ is determined from ε obtained from the equation (5-3) and the estimated θ, and then θ and the determined n′ are substituted into the equation (5-1) so as determine θ D . After that, using the determined θ D , v d * and v q * is converted into v a  and v b  in accordance with the equation (5-2). The equation “n′+2=n” holds between n′ and n described in the first example (see  FIG. 8 ). The value obtained by adding 2 to n′ determined in the coordinate rotating portion  82  (i.e., the value of n) is used for calculation in a coordinate rotating portion  84 . 
     The values v a  and v b  obtained in the coordinate rotating portion  82  are sent to a component correcting portion  83 . The component correcting portion  83  and the coordinate rotating portion  84  are similar to the component correcting portion  43  and the coordinate rotating portion  44  shown in  FIG. 16 . More specifically, the component correcting portion  83  performs the correction process in the step S 2  in  FIG. 10  on v a  and v b , and it delivers v a  and v b  after the correction as v ac  and v bc , respectively. If the correction is not necessary, however, “v ac =v a ” and “v bc =v b ” hold. 
     The coordinate rotating portion  84  converts the a-axis voltage v ac  and the b-axis voltage v bc  after the correction into the α-axis voltage v αc  and the β-axis voltage v βc  after the correction in accordance with the above equation (1-5), so as to deliver the obtained v αc  and v βc  as v αc * and v βc *, respectively. 
     The values v αc * and v βc * calculate by the specified voltage calculating portion  69  (the coordinate rotating portion  84 ) are supplied to the coordinate converter  70  shown in  FIG. 18 . The coordinate converter  70  converts V αc * and v βc * into the specified three-phase voltage values v u *, v v * and v w * and delivers the specified three-phase voltage values to the inverter  2 . The inverter  2  supplies three-phase AC current to the motor  1  in accordance with the specified three-phase voltage values. 
     In the second example too, the step of correcting the voltage vector (specified voltage vector) is provided, so the motor current can be detected with reliability. Since the correction process is performed on the ab coordinates that can support a easy correction, a necessary correction can be realized simply and securely. Since it is sufficient to correct the coordinate axis components v a  and v b  of the voltage vector (specified voltage vector) independently on the ab coordinates, contents of the correction can be simple. In particular, the correction is required for all the three phases if the applied voltage is low, but it is easy to determine correction quantities in this case. 
     In the second example, the specified voltage values are corrected for detecting the motor current with reliability. If the specified voltage values before the correction are used for estimation of the magnetic flux, an estimation error may occur. In the second example, the specified voltage values (v αc * and v βc *) after the correction are used for estimating the magnetic flux, so the estimation error due to the correction does not occur. In addition, since the correction process is performed on the stage of the voltage vector, the specified voltage vector after the correction to be used for estimating the magnetic flux can be obtained easily. Therefore, the step of inverse conversion of the three-phase voltage is not necessary, and the voltage detector for detecting the three-phase voltage is not necessary unlike the motor driving system shown in  FIG. 25 . 
     Although the examples of the motor driving system to which the present invention is applied are described above, the present invention can include various variations (or other examples). Note 1 to Note 5 will be described below as the variations (or other examples) or annotations. The contents of the individual notes can be combined arbitrarily as long as no contradiction arises. 
     Note 1: Although the case where the inverter  2  uses a three-phase modulation is handled in the above description, the present invention does not depend on the modulation method. For instance, if the inverter  2  performs a two-phase modulation, the energizing pattern is different from that of the three-phase modulation shown in  FIG. 3 . In the two-phase modulation, since the lower arm having the minimum phase is always turned on, the energizing pattern corresponding to the period between the timings T 0  and T 1  and the period between the timings T 6  and T 7  shown in  FIG. 4  does not exist. After all, however, if the bus current is detected in the energizing pattern corresponding to the period between the timings T 1  and T 2  and the period between the timings T 2  and T 3 , current in the maximum phase and the minimum phase can be detected. 
     Note 2: In the motor driving system according to the present embodiment, the method for obtaining each of the values including the above-mentioned various specified values (φ α *, v d * and the like) and other state quantities (φ α , φ exα  and the like) to be derived is arbitrary. For instance, they may be obtained by calculation in the controller  3  (see  FIG. 1 ) or by looking up table data that are set in advance. 
     Note 3: In addition, a part or the whole of the functions of the controller  3  (see  FIG. 1 ) may be realized by using software (a program) incorporated in a general-use microcomputer or the like. When the controller  3  is realized by using software, the block diagram showing the structure of individual portions of the controller  3  expresses a functional block diagram. Of course, it is possible to constitute the controller  3  only by hardware without using software (a program). 
     Note 4: For instance, it is possible to consider as described below. The controller  3  works as a motor control device. The motor control device may be considered to include the current sensor  5  shown in  FIG. 1  or the like. The motor current detector for detecting the motor current based on an output signal of the current sensor  5  includes the current detecting portion  21  shown in  FIG. 14  or the current detecting portion  61  shown in  FIG. 18 . In addition, for instance, the precorrection voltage calculating portion  41  and the coordinate rotating portion  42  shown in  FIG. 16 , or the precorrection voltage calculating portion  81  and the coordinate rotating portion  82  shown in  FIG. 21  work as a specified voltage vector generating portion. In addition, for instance, the component correcting portion  43  shown in  FIG. 16  or the component correcting portion  83  shown in  FIG. 21  works as a specified voltage vector correcting portion. 
     Note 5: Note that only a symbol (like i α ) is used for expressing a state quantity (state variable) or the like corresponding to the symbol in some cases for a simple description in this specification. Therefore, for example, “i α ” and “α-axis current i α ” indicate the same thing in this specification. 
     The present invention can be preferably applied to any electric equipment using a motor. In particular, the present invention can be preferably applied to an compressor of a refrigerator, an air conditioner for a vehicle, an electric car or the like.