Patent Publication Number: US-11048206-B2

Title: Motor control apparatus and image forming apparatus to prevent a motor control operation from becoming unstable

Description:
BACKGROUND 
     Field 
     The present disclosure relates to a motor control technique for a motor control apparatus and an image forming apparatus. 
     Description of the Related Art 
     A control method called vector control has been known as a control method for controlling a motor by controlling a current value in a rotating coordinate system based on a rotation phase of a rotor of the motor. Specifically, a control method for controlling a motor by performing phase feedback control to control a current value in a rotating coordinate system so as to reduce a deviation between a command phase and a rotation phase of a rotor is known. A control method for controlling a motor by performing speed feedback control is also known. For a speed feedback control, a current value in a rotating coordinate system is controlled so as to reduce a deviation between a command speed and a rotational speed of a rotor. 
     In vector control, a drive current flowing through each winding of a motor is represented by a q-axis component (torque current component), which is a current component for generating torque for rotating the rotor, and a d-axis component (exciting current component), which is a current component that affects the intensity of a magnetic flux penetrating the winding of the motor. Torque required to rotate the rotor is efficiently generated by controlling the value of the torque current component according to a change in load torque applied to the rotor. As a result, an increase in motor sound and an increase in power consumption due to excess torque are suppressed. 
     In vector control, a configuration for determining the rotation phase of the rotor is required. US 2011/0285332 discusses a configuration for determining a rotation phase of a rotor based on an induced voltage generated, by rotation of the rotor, in windings of respective phases of a motor. 
     As the rotational speed of the rotor decreases, the magnitude of the induced voltage generated in the windings decreases. If the magnitude of the induced voltage generated in the windings is not sufficient to determine the rotation phase of the rotor, the rotation phase may not be determined accurately. In other words, the accuracy for determining the rotation phase of the rotor may degrade with decreasing rotation speed of the rotor. 
     In this regard, Japanese Patent Application Laid-Open No. 2005-39955 discusses a configuration in which constant current control for controlling a motor by supplying a predetermined current to windings of the motor is used when a command speed of the rotor is lower than a predetermined rotation speed of the rotor. In constant current control, neither phase feedback control nor speed feedback control is performed. Japanese Patent Application Laid-Open No. 2005-39955 also discusses a configuration in which vector control is used when the command speed of the rotor is more than or equal to the predetermined rotational speed. 
     An image forming apparatus including a toner container that contains toner and is detachably attachable to the image forming apparatus has heretofore been known. US 2014/0086639 discusses a driving coupling provided in an image forming apparatus and a driven coupling provided in a toner container as a configuration for transmitting a driving force from a motor provided in the image forming apparatus to the toner container. The driving coupling that is rotationally driven by the motor presses the driven coupling in a rotation direction, so that the driven coupling is rotated. In this manner, the driving force is transmitted to the toner container from the motor. 
     When pressing of the driven coupling by the driving coupling is started, load torque applied to the rotor of the motor that drives the driving coupling increases. For example, in a case where pressing of the driven coupling by the driving coupling is started immediately after a motor control method is switched from constant current control to vector control, the following matters may arise. 
     Specifically, if the load torque increases after pressing of the driven coupling by the driving coupling is started, the rotational speed of the rotor of the motor decreases. If the rotational speed of the rotor of the motor decreases immediately after the motor control method is switched from constant current control to vector control, the rotation phase of the rotor of the motor cannot be determined accurately. As a result, vector control cannot be performed accurately and thus the motor control operation may become unstable. 
     SUMMARY OF THE INVENTION 
     To address matters in this disclosure, the present disclosure is directed to preventing a motor control operation from becoming unstable. 
     According to an aspect of the present disclosure, an image forming apparatus that forms an image on a sheet includes a motor, a first coupling configured to transmit a driving force from the motor, an attachable/detachable unit configured to be detachably attachable to the image forming apparatus, wherein the attachable/detachable unit includes a second coupling configured to transmit the driving force from the first coupling to a rotary member included in the attachable/detachable unit, a detector configured to detect a drive current flowing through a winding of the motor, a phase determiner configured to determine a rotation phase of a rotor of the motor based on the drive current detected by the detector, and a controller including a first control mode for controlling the drive current flowing through the winding to reduce a deviation between a command phase representing a target phase of the rotor and the rotation phase determined by the phase determiner, and a second control mode for controlling the drive current flowing through the winding based on a current of a predetermined magnitude, wherein one of the first coupling and the second coupling includes a projecting portion, and the other one of the first coupling and the second coupling includes a recessed portion corresponding to the projecting portion, wherein, in a state where the projecting portion is fit to the recessed portion, the second coupling is rotated by being pressed in a rotation direction by the first coupling rotationally driven by the motor, wherein the controller starts driving of the motor in the second control mode, and wherein, in a state where the second control mode is executed in a case where a value corresponding to load torque applied to the rotor is greater than a first predetermined value and a value corresponding to a rotational speed of the rotor is greater than a second predetermined value, the controller switches a control mode for controlling the drive current from the second control mode to the first control mode. 
     Further features of the present disclosure will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a sectional view illustrating an image forming apparatus according to a first exemplary embodiment. 
         FIG. 2  is a block diagram illustrating a control configuration of the image forming apparatus. 
         FIG. 3  illustrates a relationship between a two-phase motor having an A-phase and a B-phase, and a rotating coordinate system represented by a d-axis and a q-axis. 
         FIG. 4  is a block diagram illustrating a configuration of a motor control apparatus according to the first exemplary embodiment. 
         FIG. 5  is a block diagram illustrating a configuration of a command generator. 
         FIG. 6  is a graph illustrating an example of a method for carrying out a micro-step driving method. 
         FIG. 7  illustrates a configuration of a developing device. 
         FIG. 8  illustrates a configuration of a driven coupling. 
         FIG. 9  illustrates a configuration of a driving coupling. 
         FIGS. 10A, 10B, and 10C  each illustrate a rotation phase of the driving coupling and a rotation phase of the driven coupling. 
         FIGS. 11A and 11B  are perspective views each illustrating the driving coupling and the driven coupling. 
         FIGS. 12A and 12B  are graphs each illustrating load torque applied to a rotor of the motor and a rotational speed of the rotor of the motor. 
         FIG. 13  is a block diagram illustrating a configuration of a control switch. 
       .  14  is a flowchart illustrating a method for controlling the motor by the motor control apparatus. 
         FIG. 15  is a block diagram illustrating the configuration of the motor control apparatus that performs speed feedback control. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Preferred exemplary embodiments of the present disclosure will be described below with reference to the accompanying drawings. The shapes of components described in the exemplary embodiments, the relative arrangement of the components, and the like should be appropriately modified in accordance with the configuration of an apparatus to which the present disclosure is applied and various conditions, and the scope of the present disclosure is not limited to the following exemplary embodiments. Moreover, the following exemplary embodiments illustrate a case where a motor control apparatus is provided in an image forming apparatus  100 . However, the motor control apparatus is not necessarily provided in the image forming apparatus  100 . For example, the motor control apparatus may also be used as a sheet conveying device that conveys a recording medium and a sheet such as a document. 
     [Image Forming Apparatus] 
       FIG. 1  is a sectional view illustrating a configuration of a monochromatic electrophotographic copying machine  100  (hereinafter referred to as an image forming apparatus  100 ) including a sheet conveying device used in a first exemplary embodiment. The image forming apparatus  100  is not limited to a copying machine, but instead may be, for example, a facsimile apparatus, a printing machine, or a printer. The recording method is not limited to an electrophotographic method, but instead may be, for example, an inkjet method. Further, the type of the image forming apparatus  100  may be a monochrome type or a color type. 
     The configuration and functions of the image forming apparatus  100  will be described below with reference to  FIG. 1 . As illustrated in  FIG. 1 , the image forming apparatus  100  includes a document reading device  200  and an image printing device  301 . 
     &lt;Document Reading Device&gt; 
     The document reading device  200  is provided with a document feeding device that feeds a document to a reading position. Documents P stacked on a document stacking portion  2  of the document feeding device  201  are fed one by one by a pickup roller  3  and are then conveyed by a sheet teed roller  4 . A separation roller  5  that is in pressure contact with the sheet feed roller  4  is provided at a position opposed to the sheet feed roller  4 . The separation roller  5  is configured to rotate when load torque more than or equal to predetermined torque is applied to the separation roller  5 , and has a function for separating documents fed in a state where two sheets are superimposed. 
     The pickup roller  3  and the sheet feed roller  4  are coupled by a rocking arm  12 . The rocking arm  12  is supported by a rotating shaft of the sheet feed roller  4  so that the rocking arm  12  can be rotated about the rotating shaft of the sheet feed roller  4 . 
     Each document P is conveyed by the sheet feed roller  4  and the like and is then discharged onto a discharge tray  10  by a discharge roller  11 . As illustrated in  FIG. 1 , the document stacking portion  2  is provided with a document setting sensor SS 1  that detects whether a document is stacked on the document stacking portion  2 . In addition, a sheet sensor SS 2  that detects a leading edge of a document (detects whether a document is present) is provided at a conveyance path through which the document passes. 
     The document reading device  200  is provided with a document reading portion  16  that reads an image on a first surface of the conveyed document. Image information obtained by reading the image by the document reading portion  16  is output to the image printing device  301 . 
     The document reading device  200  is also provided with a document reading portion  17  that reads an image on a second surface of the conveyed document. Image information obtained by reading the image by the document reading portion  17  is output to the image printing device  301  in the same manner as the document reading portion  16  described above. 
     A document reading operation is carried out as described above. That is, the document feeding device  201  and a reading device  202  function as the document reading device  200 . 
     A first reading mode and a second reading mode are used as document reading modes. The first reading mode is a mode for reading an image on a conveyed document by the above-described method. The second reading mode is a mode in which an image on a document placed on a document glass  214  of the reading device  202  is read by the document reading portion  16  that moves at a constant speed. In a normal operation, an image on a sheet-like document is read in the first reading mode, and images on bound documents, such as a book or booklet, are read in the second reading mode. 
     Sheet accommodating trays  302  and  304  are provided in the image printing device  301 . Different types of recording media can he accommodated in the sheet accommodating trays  302  and  304 , respectively. For example, A4-size plain paper is accommodated in the sheet accommodating tray  302 , and A4-size thick paper is accommodated in the sheet accommodating tray  304 . Each of the recording media is a medium on which an image is formed by the image forming apparatus  100 . Examples of the recording media include a sheet, a resin sheet, cloth, an overhead projector (OHP) sheet, and a label. 
     The recording media accommodated in the sheet accommodating tray  302  are fed by a sheet feed roller  303  and delivered to registration rollers  308  by conveyance rollers  306 . The recording media accommodated in the sheet accommodating tray  304  are fed by a sheet feed roller  305  and conveyance rollers  307  and delivered to the registration rollers  308  by the conveyance rollers  306 . Alternatively, sheet S may be fed from a sheet feed tray  327  by rollers  328  and  329  as supported by rocking arm  330  and delivered to the registration rollers  308  by the conveyance rollers  306 . 
     An image signal output from the document reading device  200  is input to an optical scanning device  311  including a semiconductor laser and a polygon mirror. An outer peripheral surface of a photosensitive drum  309  serving as a photosensitive member is charged by a charger  310 . After the outer peripheral surface of the photosensitive drum  309  is charged, laser light corresponding to the image signal input from the document reading device  200  to the optical scanning device  311  passes through the polygon mirror and a mirror  312  and  313  from the optical scanning device  311 , and is then applied to the outer peripheral surface of the photosensitive drum  309 . As a result, an electrostatic latent image is formed on the outer peripheral surface of the photosensitive drum  309 . 
     A developing device  314  serving as a developing unit includes a developing roller  350  serving as a developer bearing member. The electrostatic latent image formed on the outer peripheral surface of the photosensitive drum  309  is developed by developer (toner) borne on the developing roller  350 , so that a toner image is formed on the outer peripheral surface of the photosensitive drum  309 . The toner image formed on the photosensitive drum  309  is transferred onto a recording medium by a transfer charger  315  serving as a transfer portion provided at a position (transfer position) opposed to the photosensitive drum  309 . In accordance with this transfer timing, the recording medium is fed to the transfer position by the registration rollers  308 . 
     As described above, the recording medium to which the toner image is transferred is fed to a fixing unit  318  by a conveyance belt  317  and is heated and pressurized by the fixing unit  318 , so that the toner image is fixed onto the recording medium. In this manner, an image is formed on the recording medium by the image forming apparatus  100 . 
     In the case of forming an image in a single-sided printing mode, the recording medium which has passed through the fixing unit  318  is discharged onto a discharge tray (not illustrated) by discharge rollers  319  and discharge rollers  324 . In the case of forming an image in a double-sided printing mode, a fixing processing is performed on the first surface of the recording medium by the fixing unit  318 . Then, the recording medium is conveyed to a reverse path  325  by the discharge rollers  319 , conveyance rollers  320 , and inverting rollers  321 . After that, the recording medium is conveyed to the registration rollers  308  again by conveyance rollers  322  and conveyance rollers  323  along path  326 , so that an image is formed on the second surface of the recording medium by the above-described method. Then, the recording medium is discharged onto the discharge tray (not illustrated) by the discharge rollers  319  and the discharge rollers  324 . 
     In a case where the recording medium having an image formed on the first surface is discharged to the outside of the image forming apparatus  100  in a state where the first surface of the recording medium faces downward, the recording medium which has passed through the fixing unit  318  passes through the discharge rollers  319  and is then conveyed toward the conveyance rollers  320 . After that, the rotation of the conveyance rollers  320  is reversed immediately before a trailing edge of the recording medium passes through a nip portion between the conveyance rollers  320 , so that the recording medium passes through the discharge rollers  324  in a state here the first surface of the recording medium faces downward and is then discharged to the outside of the image forming apparatus  100 . 
     The configuration and functions of the image forming apparatus  100  are described above. 
       FIG. 2  is a block diagram illustrating an example of a control configuration of the image forming apparatus  100 . As illustrated in  FIG. 2 , a system controller  151  includes a central processing unit (CPU)  151   a , a read-only memory (ROM)  151   b , and a random access memory (RAM)  151   c . The system controller  151  is connected to each of an image processing unit  112 , an operation unit  152 , an analog-to-digital (A/D) converter  153 , a high-voltage control unit  155 , a motor control apparatus  157 , sensors  159 , and an alternating current (AC) driver  160 . The system controller  151  can transmit and receive data and commands to and from each of the connected units. 
     The CPU  151   a  reads out various programs stored in the ROM  151   b  and executes the programs to thereby execute various sequences related to a predetermined image formation sequence. 
     The RAM  151   c  is a storage device. The RAM  151   c  stores various data, such as setting values for the high-voltage control unit  155 , command values for the motor control apparatus  157 , and information received from the operation unit  152 . 
     The system controller  151  transmits setting value data, which is used for various devices provided in the image forming apparatus  100  to execute image processing in the image processing unit  112 , to the image processing unit  112 . Further, the system controller  151  receives signals from the sensors  159 , and sets setting values for the high-voltage control unit  155  based on the received signals. 
     The high-voltage control unit  155  supplies a high-voltage unit  156  (the charger  310 , the developing device  314 , the transfer charger  315 , etc.) with a required voltage depending on the setting values set by the system controller  151 . The sensors  159  include a sensor for detecting a recording medium to be conveyed by the conveyance rollers. 
     The motor control apparatus  157  controls a stepping motor  509 , which drives a load, according to a command output from the CPU  151   a .  FIG. 2  illustrates only the stepping motor  509  as a motor for the image forming apparatus  100 . However, in practice, the image forming apparatus  100  is provided with a plurality of motors. Alternatively, a single motor control apparatus may be configured to control a plurality of motors.  FIG. 2  illustrates only one motor control apparatus  157 . However, in practice, the image forming apparatus  100  may be provided with a plurality of motor control apparatuses. 
     The A/D converter  153  receives a detection signal detected by a thermistor  154  for detecting the temperature of a fixing heater  161 , converts the detection signal from an analog signal into a digital signal, and transmits the digital signal to the system controller  151 . The system controller  151  controls the AC driver  160  based on the digital signal received from the A/D converter  153 . The AC driver  160  controls the fixing heater  161  so that the temperature of the fixing heater  161  reaches a temperature for fixing processing. The fixing heater  161  is a heater that is used for fixing processing and included in the fixing unit  318 . 
     The system controller  151  controls the operation unit  152  so that an operation screen used for a user to set, for example, a type of a recording medium to be used (hereinafter referred to as a sheet type), is displayed on a display unit provided on the operation unit  152 , The system controller  151  receives information set by the user from the operation unit  152 , and controls operation sequences for the image forming apparatus  100  based on the information set by the user. Further, the system controller  151  transmits information indicating the state of the image forming apparatus  100  to the operation unit  152 . Examples of the information indicating the state of the image forming apparatus  100  include the number of images to be formed, a progress status of an image formation operation, and information about jamming, double feeding, or the like of sheets in the document reading device  200  and the image printing device  301 . The operation unit  152  displays the information received from the system controller  151  on the display unit. 
     As described above, the system controller  151  controls the operation sequences for the image forming apparatus  100 . 
     [Motor Control Apparatus] 
     Next, the motor control apparatus  157  according to the present exemplary embodiment will be described. The motor control apparatus  157  according to the present exemplary embodiment can control the stepping motor  509  by using two control methods, i.e., a vector control method as a first control mode and a constant current control method as a second control mode. In the following exemplary embodiment, the control operation is performed as described below based on a rotation phase θ as an electrical angle, a command phase θ_ref, a current phase, and the like. However, for example, the control operation may be performed as described below based on a mechanical angle converted from an electrical angle. 
     &lt;Vector Control&gt; 
     A method in which the motor control apparatus  157  according to the present exemplary embodiment performs vector control will now be described with reference to  FIGS. 3 and 4 . In the following exemplary embodiment, the stepping motor  509  is not provided with any sensor such as a rotary encoder for detecting a rotation phase of a rotor of the stepping motor  509 . 
       FIG. 3  illustrates a relationship between the stepping motor  509  (hereinafter referred to as the motor  509 ) having two phases, i.e., an A-phase (first phase) and a B-phase (second phase), and a rotating coordinate system represented by a d-axis and a q-axis. As illustrated in  FIG. 3 , an a-axis corresponding to an A-phase winding  401   a / 401   c  and a  3 -axis corresponding to a B-phase winding  401   b / 401   d  are defined in a stationary coordinate system. As illustrated in  FIG. 3 , a d-axis is defined along the direction of a magnetic flux generated by magnetic poles of a permanent magnet used as a rotor  402 , and a q-axis is defined along the direction which leads the d-axis by 90 degrees in a counterclockwise direction (along the direction perpendicular to the d-axis). An angle formed between the a-axis and the d-axis is defined as θ, and the rotation phase of the rotor  402  is represented by the angle θ. In vector control, the rotating coordinate system based on the rotation phase θ of the rotor  402  is used. Specifically, in vector control, a q-axis component (torque current component) that generates torque in the rotor  402  and a d-axis component (exciting current component) that affects the intensity of the magnetic flux penetrating the windings are used. The q-axis component and the d-axis component are current components in the rotating coordinate system of current vectors corresponding to drive currents flowing through the windings. 
     The vector control is a control method for controlling the motor  509  by performing phase feedback control for controlling the value of the torque current component and the value of the exciting current component so as to reduce a deviation between the command phase θ_ref representing a target phase of the rotor  402  and an actual rotation phase. In addition, a method for controlling the motor  509  by performing speed feedback control for controlling the value of the torque current component and the value of the exciting current component so as to reduce a deviation between a command speed representing a target speed of the rotor  402  and an actual rotational speed can be used. 
       FIG. 4  is a block diagram illustrating an example of the configuration of the motor control apparatus  157  that controls the motor  509 . The motor control apparatus  157  is configured using at least one application specific integrated circuit (ASIC), and executes functions to be described below. 
     As illustrated in  FIG. 4 , the motor control apparatus  157  includes a constant current controller  517  that performs constant current control, and a vector controller  518  that performs vector control. 
     The motor control apparatus  157  includes, as one or more circuits for performing vector control, a phase controller  502 , a current controller  503 , a coordinate inverse transformer  505 , a coordinate transformer  511 , and a pulse-width modulation (PWM) inverter  506  for supplying drive currents to the windings of the motor  509 . The coordinate transformer  511  transforms the current vector corresponding to the drive currents flowing through the A-phase winding  401   a / 401   c  and  13 -phase windings  401   b / 401   d  of the motor  509  from the stationary coordinate system represented by the α-axis and β-axis into the rotating coordinate system represented by the q-axis and d-axis. As a result, the drive currents flowing through the windings can be represented by a current value (q-axis current) of the q-axis component and a current value (d-axis current) of the d-axis component, which are current values in the rotating coordinate system. The q-axis current corresponds to the torque current that generates torque in the rotor  402  of the motor  509 . The d-axis current corresponds to the exciting current that affects the intensity of the magnetic flux penetrating the windings of the motor  509 . The motor control apparatus  157  can independently control the q-axis current and the d-axis current. As a result, the motor control apparatus  157  controls the q-axis current depending on the load torque applied to the rotor  402 , thereby making it possible to efficiently generate torque for rotating the rotor  402 . That is, in vector control, the magnitude of the current vector illustrated in  FIG. 3  varies depending on the load torque applied to the rotor  402 . 
     The motor control apparatus  157  determines the rotation phase θ of the rotor  402  of the motor  509  by the following method, and performs vector control based on the determination result. The CPU  151   a  outputs driving pulses as commands for driving the motor  509  to a command generator  500  based on the operation sequence for the motor  509 . The operation sequence (motor driving pattern) for the motor  509  is stored in, for example, the ROM  151   b , and the CPU  151   a  outputs the driving pulses based on the operation sequences stored in the ROM  151   b.    
     The command generator  500  generates the command phase θ_ref representing the target phase of the rotor  402  based on the driving pulses output from the CPU  151   a , and outputs the generated command phase θ_ref. The configuration of the command generator  500  will be described below. 
     A subtractor  101  calculates a deviation between the rotation phase θ and the command phase θ_ref of the rotor  402 . of the motor  509 , and outputs the calculated deviation. 
     The phase controller  502  acquires a deviation Δθ for a cycle  200   i ts). The phase controller  502 . generates a q-axis current command value iq_ref and a d-axis current command value id_ref based on proportional control (P), integral control (I), and differential control (D) so as to reduce the deviation Δθ acquired from the subtractor  101 , and outputs the generated q-axis current command value iq_ref and d-axis current command value id_ref. Specifically, the phase controller  502  generates the q-axis current command value iq_ref and the d-axis current command value id_ref based on the P-control, the I-control, and the D-control so that the deviation Δθ acquired from the subtractor  101  becomes zero, and outputs the generated q-axis current command value iq_ref and d-axis current command value id_ref. The P-control is a control method for controlling a value to be controlled based on a value proportional to a deviation between a command value and an estimated value. The I-control is a control method for controlling a value to be controlled based on a value proportional to a time integral of a deviation between a command value and an estimated value. The D-control is a control method for controlling a value to be controlled based on a value proportional to a time change of a deviation between a command value and an estimated value. The phase controller  502  according to the present exemplary embodiment generates the q-axis current command value iq_ref and d-axis current command value id_ref based on the P-control. the I-control, and the D-control. However, the configuration of the phase controller  502  according to the present exemplary embodiment is not limited to this example. For example, the phase controller  502  may generate the q-axis current command value iq_ref and d-axis current command value id_ref based on the P-control and the I-control. In the present exemplary embodiment, the d-axis current command value id_ref that affects the intensity of the magnetic flux penetrating the windings is set to “0”. However, the present exemplary embodiment is not limited to this example. 
     The drive current flowing through the A-phase winding  401   a / 401   c  of the motor  509  is detected by a current detector  507 , and is then converted from an analog value into a digital value by an A/D converter  510 . The drive current flowing through the B-phase winding  401   b / 401   d  of the motor  509  is detected by a current detector  508  and is then converted from an analog value into a digital value by the A/D converter  510 . A cycle at which the current detectors  507  and  508  detect a current is, for example, a cycle (e.g.,  25  μs) that is less than or equal to the cycle T in which the deviation Δθ is acquired by the phase controller  502 . 
     The current values of the drive currents converted from the analog value into the digital value by the A/D converter  510  are represented as current values iα and iβ in the stationary coordinate system by the following formulas using a phase θe of the current vector illustrated in  FIG. 1 . The phase θe of the current vector is defined as an angle formed between the α-axis and the current vector. I represents the magnitude of the current vector
 
 iα=I *cos θ e    (1)
 
 iβ=I *sin θ e    (2)
 
     These current values iα and iβ are input to each of the coordinate transformer  511 , a coordinate transformer  519 , and an induced voltage determiner  512 . 
     The coordinate transformer  511  converts the current values iα and iβ in the stationary coordinate system into a current value iq of the q-axis current and a current value id of the d-axis current, respectively, in the rotating coordinate system by the following formulas.
 
 id =cos θ* i α+sin θ* iβ   (3)
 
 iq =−sin θ* i α+cos θ* iβ   (4)
 
     The coordinate transformer  511  outputs the converted current value iq to a subtractor  102 . The coordinate transformer  511  outputs the converted current value id to a subtractor  103 . 
     The subtractor  102  calculates a deviation between the q-axis current command value iq_ref and the current value iq, and outputs the deviation to the current controller  503 . 
     The subtractor  103  calculates a deviation between the d-axis current command value id_ref and the current value id, and outputs the deviation to the current controller  503 . 
     The current controller  503  generates drive voltages Vq and Vd based on the P-control, the I-control, and the D-control so as to reduce the deviation to be input. Specifically, the current controller  503  generates the drive voltages Vq and Vd so that the deviation to be input becomes zero, and outputs the generated drive voltages Vq and Vd to the coordinate inverse transformer  505 . The current controller  503  according to the present exemplary embodiment generates the drive voltages Vq and Vd based on the P-control, the I-control, and the D-control. However, the configuration of the current controller  503  according to the present exemplary embodiment is not limited to this example. For example, the current controller  503  may generate the drive voltages Vq and Vd based on the P-control and the I-control. 
     The coordinate inverse transformer  505  inversely transforms the drive voltages Vq and Vd in the rotating coordinate system output from the current controller  503  into drive voltages Vα and Vβ, respectively, in the stationary coordinate system by the following formulas.
 
 V α=cos θ* Vd −sin θ* Vq    (5)
 
 Vβ= sin θ* Vd +cos θ* Vq    (6)
 
     The coordinate inverse transformer  505  outputs the inversely transformed drive voltages Vα and Vβ to each of the induced voltage determiner  512  and the PWM inverter  506 . 
     The PWM inverter  506  includes a full-bridge circuit. The full-bridge circuit is driven by a PWM signal based on the drive voltages Vα and Vβ received from the coordinate inverse transformer  505 . As a result, the PWM inverter  506  generates the drive currents iα and iβ corresponding to the drive voltages Vα and Vβ, respectively, and supplies the generated drive currents iα and iβ to the windings of respective phases of the motor  509 , thereby driving the motor  509 . In the present exemplary embodiment, the PWM inverter  506  includes a full-bridge circuit, but instead may include a half-bridge circuit or the like. 
     Next, a configuration for determining the rotation phase θ will be described. To determine the rotation phase θ of the rotor  402 , values of induced voltages Eα and Eβ induced to the A-phase winding  401   a / 401   c  and B-phase winding  401   b / 401   d  of the motor  509  by rotation of the rotor  402  are used. The values of the induced voltages Eα and Eβ are determined (calculated) by the induced voltage determiner  512 . Specifically, the induced voltages Eα and Eβ are determined by the following formulas based on the current values iα and iβ input to the induced voltage determiner  512  from the A/D converter  510  and the drive voltages Vα and Vβ input to the induced voltage determiner  512  from the coordinate inverse transformer  505 .
 
 Eα=Vα−R*iα−L*diα/dt    (7)
 
 Eβ=Vβ−R*iβ−L*diβ/dt    (8)
 
     In formulas (7) and (8), R represents a winding resistance and L represents a winding inductance. The values of the winding resistance R and the winding inductance L are values unique to the motor  509  to be used, and are preliminarily stored in the ROM  151   b,  a memory (not illustrated) provided in the motor control apparatus  157 , or the like. 
     The induced voltages Eα and Eβ determined by the induced voltage determiner  512  are output to a phase determiner  513 . 
     The phase determiner  513  determines the rotation phase θ of the rotor  402  of the motor  509  by the following formula based on a ratio between the induced voltage Eα and the induced voltage Eβ output from the induced voltage determiner  512 .
 
θ=tan{circumflex over ( )}−1(− Eβ/E α)   (9)
 
     In the present exemplary embodiment, the phase determiner  513  determines the rotation phase θ by the calculation based on formula (9), but instead may determine the rotation phase θ by other methods. For example, the phase determiner  513  may determine the rotation phase θ by referring to a table that is stored in the ROM  151   b  or the like and represents the relationship between the induced voltages Eα and Eβ and the rotation phase θ corresponding to the induced voltages Eα and Eβ. 
     The rotation phase θ of the rotor  402 . obtained as described above is input to each of the subtractor  101 , the coordinate inverse transformer  505 , and the coordinate transformers  511  and  519 . 
     In the case of performing vector control, the motor control apparatus  157  repeatedly performs the above-described control operation. 
     As described above, the motor control apparatus  157  according to the present exemplary embodiment performs vector control using the phase feedback control for controlling the current values in the rotating coordinate system so as to reduce the deviation between the command phase θ_ref and the rotation phase θ. The vector control prevents the motor  509  from entering a step-out state and suppresses an increase in motor sound and an increase in power consumption due to excess torque. 
     &lt;Constant Current Control&gt; 
     Next, constant current control according to the present exemplary embodiment will be described. 
     In constant current control, a predetermined current is supplied to each winding of the motor  509 , to thereby control the drive current flowing through the winding. Specifically, in constant current control, a drive current having a magnitude (amplitude) corresponding to torque obtained by adding a predetermined margin to torque assumed to be required for rotating the rotor  402  is supplied to the winding so as to prevent the motor  509  from entering a step-out state even when the load torque applied to the rotor  402  fluctuates. This is because, in constant current control, the configuration in which the magnitude of the drive current is controlled based on the determined (estimated) rotation phase and rotational speed is not used (feedback control is not performed), and thus the drive current cannot be adjusted depending on the load torque applied to the rotor  402 . As the magnitude of a current increases, torque to be applied to the rotor  402  increases. The amplitude of a current corresponds to the magnitude of a current vector. 
     In the following exemplary embodiment, when the constant current control is executed, the motor  509  is controlled by supplying a current of a predetermined magnitude to each winding of the motor  509 . In contrast, for example, when the constant current control is executed, the motor  509  may be controlled by supplying the current of the predetermined magnitude, which is determined depending on acceleration or deceleration of the motor  509 , to each winding of the motor  509 . 
     Referring to  FIG. 4 , the command generator  500  outputs the command phase θ_ref to the constant current controller  517  based on the driving pulses output from the CPU  151   a . The constant current controller  517  generates current command values iα_ref and iβ_ref in the stationary coordinate system corresponding to the command phase θ_ref output from the command generator  500 , and outputs the generated current command values iα_ref and iβ_ref, In the present exemplary embodiment, the magnitudes of current vectors corresponding to the current command values iα_ref and iβ_ref in the stationary coordinate system are constant. 
     The drive currents flowing through the A-phase winding  401   a / 401   c  and B-phase winding  401   b / 401   d  of the motor  509  are detected by the current detectors  507  and  508 , respectively. As described above, the detected drive currents are each converted from an analog value into a digital value by the A/D converter  510 . 
     The subtractor  102  receives the current value iα output from the A/D converter  510  and the current command value iα_ref output from the constant current controller  517 . The subtractor  102  calculates a deviation between the current command value iα_ref and the current value iα, and outputs the deviation to the current controller  503 . 
     The subtractor  103  receives the current value iβ output from the A/D converter  510  and the current command value iβ_ref output from the constant current controller  517 . The subtractor  103  calculates a deviation between the current command value iβ_ref and the current value iβ, and outputs the deviation to the current controller  503 . 
     The current controller  503  outputs the drive voltages Vα and Vβ based on the P-control, the I-control, and the D-control so as to reduce the deviation to be input. Specifically, the current controller  503  outputs the drive voltages Vα and Vβ so that the deviation to be input approaches zero. 
     The PWM inverter  506  drives the motor  509  by supplying the drive currents to the windings of the respective phases of the motor  509  based on the input drive voltages Vα and Vβ the above-described method. 
     Thus, in constant current control according to the present exemplary embodiment, neither phase feedback control nor speed feedback control is performed. In other words, in constant current control according to the present exemplary embodiment, the drive currents to be supplied to the windings are not adjusted depending on the rotating status of the rotor  402 . Accordingly, in constant current control, a current obtained by adding a predetermined margin to a current for rotating the rotor  402  is supplied to the windings so as to prevent the motor  509  from entering a step-out state. 
     &lt;Command Generator&gt; 
       FIG. 5  is a block diagram illustrating the configuration of the command generator  500  according to the present exemplary embodiment. As illustrated in  FIG. 5 , the command generator  500  includes a speed generator  500   a  that generates a rotational speed ω_ref in place of a command speed, and a command value generator  500   b  that generates the command phase θ_ref based on the driving pukes output from the CPU  151   a.    
     The speed generator  500   a  generates the rotational speed ω_ref based on a time interval of falling edges of continuous driving pulses, and outputs the generated rotational speed ω_ref. That is, the rotational speed ω_ref varies at the cycle corresponding to the cycle of driving pulses. 
     The command value generator  500   b  generates the command phase θ_ref by the following formula (10) based on the driving pulses output from the CPU  151   a , and outputs the generated command phase θ_ref
 
θ_ref=θ ini +θstep* n    (10)
 
     In formula (10), θini represents a phase (initial phase) of the rotor  402  when driving of the motor  509  is started, θstep represents an increased amount (variation) of θ_ref per driving pulse, and n represents the number of pulses input to the command value generator  500   b.    
     &lt;Micro-Step Driving Method&gt; 
     In the present exemplary embodiment, a micro-step driving method is used in constant current control. The driving method used in constant current control is not limited to the micro-step driving method, but instead may be, for example, a driving method such as a full-step driving method. 
       FIG. 6  is a graph illustrating an example of a method for carrying out the micro-step driving method.  FIG. 6  illustrates the driving pulses output from the CPU  151   a , the command phase θ_ref generated by the command value generator  500   b , and the current flowing through the A-phase winding  401   a / 401   c  and B-phase winding  401   b / 401   d.    
     The micro-step driving method according to the present exemplary embodiment will be described below with reference to  FIGS. 5 and 6 . The driving pulses and command phases illustrated in  FIG. 6  indicate a state where the rotor  402  is rotated at a constant speed. 
     In the micro-step driving method, the lead amount of the command phase θ_ref equals the amount (90°/N) obtained by dividing 90 degrees, which is the lead amount of the command phase θ_ref in the full-step driving method, by N is a positive integer). As a result, the current waveform smoothly changes in the shape of a sine wave as illustrated in  FIG. 6 , which makes it possible to more finely control the rotation phase θ of the rotor  402 . 
     In the case of performing micro-step driving, the command value generator  500   b  generates the command phase θ_ref by the following formula (11) based on the driving pulse output from the CPU  151   a , and outputs the generated command phase θ_ref.
 
θ_ref=45°+90/ N°*n    (11)
 
     Thus, upon receiving one driving pulse, the command value generator  500   b  adds 90/N° to the command phase θ_ref, thereby updating the command phase θ_ref. That is, the number of driving pulses output from the CPU  151   a  corresponds to the command phase. The cycle (frequency) of driving pulses output from the CPU  151   a  corresponds to a target speed (command speed) of the rotor  402  of the motor  509 . 
     &lt;Configuration of Developing Device&gt; 
       FIG. 7  illustrates the configuration of the developing device  314  according to the present exemplary embodiment. 
     The developing device  314  includes the developing roller  350  serving as a rotary member, a container  351 , a roller support portion  352 , a driven coupling  353  serving as a second coupling, and an urging member  354 . 
     The developing roller  350  is supported by the roller support portion  352 , which is provided in the container  351 , so that the developing roller  350  is rotated about an axis parallel to a Y-axis illustrated in  FIG. 7 . 
     At one end of the developing roller  350 , the driven coupling  353  that rotates integrally with the developing roller  350  is provided. 
     At the one end of the developing roller  350 , the urging member  354  that urges the driven coupling  353  against a driving portion  355  is provided in the Y-axis direction. 
     The driving portion  355  includes a driving coupling  356  serving as a first coupling, a drive transmission gear  357 , and the motor  509 . The driving force from the motor  509  is transmitted to the driving coupling  356  through the drive transmission gear  357 . 
     In the present exemplary embodiment, the developing device  314  corresponds to an attachable/detachable unit which can be inserted into or removed from the image printing device  301  (inserted into or removed from the driving portion  355 ) in the Y-axis direction illustrated in  FIG. 7 , that is, can be detachably attachable to the image printing device  301 . 
     &lt;Configuration for Driving Developing Device  314 &gt; 
       FIG. 8  illustrates the configuration of the driven coupling  353 . The driven coupling  353  includes first projecting portions  361   a ,  361   b , and  361   c  each serving as a projecting portion that projects in an inserting direction (in a direction toward the driving coupling  356  from the driven coupling  353 ) when the developing device  314  is attached to the image printing device  301 . In the present exemplary embodiment, an angle formed in the rotation direction between the center of the first projecting portion  361   a  in the rotation direction and the center of the first projecting portion  361   b  in the rotation direction, an angle formed in the rotation direction between the center of the first projecting portion  361   b  in the rotation direction and the center of the first projecting portion  361   c  in the rotation direction, and an angle formed in the rotation direction between the center of the first projecting portion  361   c  in the rotation direction and the center of the first projecting portion  361   a  in the rotation direction are equal. Specifically, in the present exemplary embodiment, the angle formed in the rotation direction between the center of the first projecting portion  361   a  in the rotation direction and the center of the first projecting portion  361   b  in the rotation direction, the angle formed in the rotation direction between the center of the first projecting portion  361   b  in the rotation direction and the center of the first projecting portion  361   c  in the rotation direction, and the angle formed in the rotation direction between the center of the first projecting portion  361   c  in the rotation direction and the center of the first projecting portion  361   a  in the rotation direction are  120  degrees. That is, the first projecting portions  361   a,    361   b , and  361   c  are provided at equal intervals in the rotation direction. However, the arrangement of the first projection portions is not limited to this example. In the present exemplary embodiment, the driven coupling  353  includes three first projecting portions  361   a ,  361   b , and  361   c . However, the number of the first projection portions is not limited to three. That is, the number of the first projecting portions  361   a,    361   b , and  361   c  provided on the driven coupling  353  may be one or more. 
       FIG. 9  illustrates the configuration of the driving coupling  356 . The driving coupling  356  includes second projecting portions  360   a ,  360   b , and  360   c  that project in a direction opposite to the inserting direction (in a direction toward the driven coupling  353  from the driving coupling  356 ). In the present exemplary embodiment, an angle formed in the rotation direction between the center of the second projecting portion  360   a  in the rotation direction and the center of the second projecting portion  360   b  in the rotation direction, an angle formed in the rotation direction between the center of the second projecting portion  360   b  in the rotation direction and the center of the second projecting portion  360   c  in the rotation direction, and an angle formed in the rotation direction between the center of the second projecting portion  360   c  in the rotation direction and the center of the second projecting portion  360   a  in the rotation direction are equal. Specifically, in the present exemplary embodiment, the angle formed in the rotation direction between the center of the second projecting portion  360   a  in the rotation direction and the center of the second projecting portion  360   b  in the rotation direction, the angle formed in the rotation direction between the center of the second projecting portion  360   b  in the rotation direction and the center of the second projecting portion  360   c  in the rotation direction, and the angle formed in the rotation direction between the center of the second projecting portion  360   c  in the rotation direction and the center of the second projecting portion  360   a  in the rotation direction are 120 degrees. That is, the second projecting portions  360   a ,  360   b , and  360   c  are provided at equal intervals in the rotation direction. However, the arrangement of the second projecting portions  360   a ,  360   b , and  360   c  is not limited to this example. In the present exemplary embodiment, the driving coupling  356  includes three second projecting portions  360   a ,  360   b , and  360   c . However, the number of the second projecting portions is not limited to three. That is, the number of the second projecting portions provided on the driving coupling  356  may be one or more. 
       FIGS. 10A, 10B, and 10C  each illustrate the rotation phase of the driving coupling  356  and the rotation phase of the driven coupling  353  when the driven coupling  353  is viewed from the driving coupling  356  in the Y-axis direction. In the following description, reference symbols “a”, “b”, “c” for each of the first projecting portion  361  and the second projecting portion  360  are omitted. 
       FIGS. 10A and 11B  each illustrate a state where at least a part of the first projecting portion  361  overlaps the second projecting portion  360  in the rotation direction of the driving coupling  356 .  FIG. 10C  illustrates a state where the first projecting portion  361  does not overlap the second projecting portion  360  in the rotation direction of the driving coupling  356 . In the present exemplary embodiment, the driving coupling  356  is rotated counterclockwise in  FIGS. 10A, 10B, and 10C . However, the configuration of the driving coupling  356  is not limited to this example. 
     In the present exemplary embodiment, the rotation phase of the first projecting portion  361  when the developing device  314  is attached to the image printing device  301  is not uniquely determined. Accordingly, as illustrated in  FIGS. 10A, 10B, and 10C , when the developing device  314  is attached to the image printing device  301 , the following situationmay occur. That is, at least a part of the first projecting portion  361  overlaps the second projecting portion  360  in the rotation direction, or the first projecting portion  361  does not overlap the second projecting portion  360  in the rotation direction. 
       FIGS. 11A and 11B  are perspective views each illustrating the driving coupling  356  and the driven coupling  353 .  FIG. 11A  is a perspective view illustrating a state where at least a part of the first projecting portion  361  overlaps the second projecting portion  360  in the rotation direction when the developing device  314  is attached to the image printing device  301 .  FIG. 11B  is a perspective view illustrating a state where the first projecting portion  361  does not overlap the second projecting portion  360  in the rotation direction when the developing device  314  is attached to the image printing device  301 . 
     As illustrated in  FIG. 11A , when at least a part of the first projecting portion  361  overlaps the second projecting portion  360  in the rotation direction, a regulated surface  365  of the first projecting portion  361  contacts a regulating surface  364  of the second projecting portion  360 . The regulated surface  365  and the regulating surface  364  are surfaces crossing each other in the Y-axis direction (inserting direction). The regulated surface  365  and the regulating surface  364  may be planar surfaces or curved surfaces. 
     In a state where the regulated surface  365  of the first projecting portion  361  contacts the regulating surface  364  of the second projecting portion  360 , the driven coupling  353  is urged toward the driving coupling  356  by the urging member  354 . 
     When driving of the motor  509  is started in the state illustrated in  FIG. 11A , the driving coupling  356  is rotated while frictionally sliding along the driven coupling  353  in a stopped state (while the regulating surface  364  is frictionally sliding along the regulated surface  365 ). That is, the driving force from the motor  509  is not transmitted to the driven coupling  353 . 
     After that, when the second projecting portion  360  is rotated to a position where the second projecting portion  360  does not overlap the first projecting portion  361  in the rotation direction, the driven coupling  353  moves toward the driving coupling  356  by the urging force of the urging member  354 . As a result, as illustrated in  FIG. 11B , each first projecting portion  361  is fit to and corresponds with a recessed portion  370  which is formed between the second projecting portion  360  in the rotation direction. 
     When the first projecting portion  361  is fit to the recessed portion  370  and the driving coupling  356  is further rotated in the rotation direction, as illustrated in  FIG. 10C , a contact surface  362  of the second projecting portion  360  contacts a contacted surface  363  of the first projecting portion  361 . Further, when the contact surface  362  presses the contacted surface  363  in the rotation direction, the driven coupling  353  is rotated in the rotation direction. That is, the driving force from the motor  509  is transmitted to the driven coupling  353 . 
     As described above, the driving coupling  356  and the driven coupling  353  are coupled together and the driving force from the motor  509  is transmitted to the developing device  314 . The contact surface  362  and the contacted surface  363  may be curved surfaces or planar surfaces. 
     &lt;Switching between Vector Control and Constant Current Control&gt; 
     A length of a period D from a time when driving of the driving coupling  356  is started to a time when the driving force from the motor  509  is transmitted to the driven coupling  353  (this period is hereinafter referred to as an idling period) varies depending on the phase of the driven coupling  353  and the phase of the driving coupling  356  when the developing device  314  is attached to the image printing device  301 . Specifically, for example, an idling period D_c in the state illustrated in  FIG. 10C  is shorter than an idling period D_b in the state illustrated in  FIG. 10B , and the idling period D_b in the state illustrated in  FIG. 10B  is shorter than an idling period D_a in the state illustrated in  FIG. 10A . 
       FIGS. 12A and 12B  each illustrate the load torque applied to the rotor  402  of the motor  509  and the rotational speed of the motor  509 .  FIG. 12B  illustrates a state an actual rotational speed (indicated by a dashed-dotted line) before time t 1  overlaps a target speed (indicated by a solid line). 
     As illustrated in  FIG. 12A , during the idling period D, that is, in a state where the driving force from the motor  509  is not transmitted to the driven coupling  353 , load torque T 1  for driving the driving coupling  356  is applied to the rotor  402  of the motor  509 . At time t 1  after the lapse of the idling period D, that is, when the driving force from the motor  509  is transmitted to the driven coupling  353 , the load torque applied to the rotor  402  of the motor  509  increases. This is because the load torque for rotating the developing roller  350  in the stopped state is further applied to the rotor  402  of the motor  509 . As a result, the actual rotational speed of the rotor  402  of the motor  509  decreases. 
     In a case where the transmission of the driving force from the motor  509  to the driven coupling  353  is started at a time after time ts, which is when the motor control method is switched from constant current control to vector control, that is, in a case where time ts is later than time  0 , the following situation may occur. Specifically, at time t 1 , the actual rotational speed of the rotor  402  of the motor  509  is smaller than a threshold ωth, which makes it difficult to accurately determine the rotation phase of the rotor  402  of the motor  509 . As a result, vector control cannot be accurately performed and thus the motor control operation may become unstable. 
     Accordingly, in the present exemplary embodiment, the following configuration is applied to prevent the motor control operation from becoming unstable. A method for switching the motor control method according to the present exemplary embodiment will be described below. 
     As illustrated in  FIG. 4 , the motor control apparatus  157  according to the present exemplary embodiment includes a configuration for switching constant current control and vector control. Specifically, the motor control apparatus  157  includes a control switch  515  and selection switches  516   a,    516   b,  and  516   c.  During a period in which constant current control is performed, the induced voltage determiner  512 , the phase determiner  513 , and the coordinate transformer  519  are operated. During a period in which vector control is performed, one or more circuits for performing constant current control may be operated or suspended. 
       FIG. 13  is a block diagram illustrating the configuration of the control switch  515 . As illustrated in  FIG. 13 , the control switch  515  includes a first determination unit  515   a,  a second determination unit  515   b,  and a generation unit  515   c.    
     The first determination unit  515   a  will be described below. The first determination unit  515   a  receives the rotational speed ω_ref output from the speed generator  500   a . The first determination unit  515   a  compares the rotational speed ω_ref with the threshold ωth, and outputs the comparison result to the generation unit  515   c.    
     The threshold ωth according to the present exemplary embodiment is set to a value greater than a rotational speed ω_min which is a minimum speed among the rotational speeds at which the rotation phase θ can be determined accurately. That is, in vector control, the rotation phase θ can be determined accurately. Also, in constant current control, the rotation phase θ can be determined accurately if the rotational speed of the rotor  402  of the motor  509  is more than or equal to ω_min. 
     If the rotational speed ω_ref is more than or equal to the threshold wth (ω_ref≥ωth), the first determination unit  515   a  outputs a signal A=“H” as the comparison result. On the other hand, if the rotational speed ω_ref is less than the threshold cosh (ω_ref&lt;ωth), the first determination unit  515   a  outputs the signal A=“L” as the comparison result. The first determination unit  515   a  outputs the signal A, for example, at the same cycle as the cycle Tin which the CPU  151   a  outputs the rotational speed ω_ref. 
     Next, the second determination unit  515   b  will be described. The second determination unit  515   b  receives a current value iq′ output from the coordinate transformer  519 . The current value iq′ corresponds to the parameter corresponding to the load torque applied to the rotor  402  of the motor  509 . 
     The second determination unit  515   b  compares the current value iq′ input after a lapse of a predetermined time from the time when the driving of the motor  509  is started with a threshold iqth as a predetermined value, and outputs the comparison result to the generation unit  515   c.  The threshold iqth according to the present exemplary embodiment is set to, for example, a value greater than the current value iq corresponding to the load torque applied to the rotor  402  of the motor  509  during the idling period Further, the threshold iqth is set to, for example, a value smaller than the current value iq corresponding to the load torque applied to the rotor  402  of the motor  509  in a state where the motor  509  drives the developing device  314  at a constant speed during the image formation operation. The threshold iqth is, for example, an experimentally obtained value. The predetermined time is, for example, is a time longer than a period from a time when driving of the motor  509  is started to a time when the rotational speed ω_ref reaches ω_min. Further, the predetermined time is, for example, a longest time among the times required for starting the transmission of the driving force from the motor  509  to the driven coupling  353  after driving of the motor  509  is started, that is, a time shorter than an idling period D_max in a case where the idling period D is longest. The predetermined time is, for example, an experimentally obtained time. The idling period D_max is longer than a time for the rotational speed ω_ref to reach ω_min after driving of the motor  509  is started. 
     If the current value iq′ is more than or equal to the threshold iqth (iq′≤iqth), the second determination unit  515   b  outputs a signal B=“H” as the comparison result. On the other hand, if the current value iq′ is less than the threshold (iq′&lt;iqth), the second determination unit  515   b  outputs the signal B=“L” as the comparison result. The second determination unit  515   b  outputs the signal B=“L” during a period from a time when driving of the motor  509  is started to a time when a predetermined time has passed. Further, the second determination unit  515   b  outputs the signal B, for example, at the same cycle as the cycle T in which the CPU  151   a  outputs the rotational speed ω_ref. 
     Next, the generation unit  515   c  will be described. As illustrated in  FIG. 13 , the generation unit  515   c  includes a timer  515   d  that measures time. 
     In the case of performing constant current control, the generation unit  515   c  sets a switch signal to “L”, and in the case of performing vector control, the generation unit  515   c  sets the switch signal to “H”. As illustrated in  FIG. 4 , the switch signal is input to each of the selection switches  516   a ,  516   b , and  516   c . The generation unit  515   c  outputs the switch signal, for example, at the same cycle as the cycle T in which the CPU  151   a  outputs the rotational speed ω_ref. 
     In a state where constant current control is executed, in a case where time t_m that has elapsed after driving of the motor  509  is started is longer than the idling period D_max, the generation unit  515   c  outputs the switch signal=“H”, regardless of the signal A and the signal B. As a result, the state of each of the selection switches  516   a ,  516   b , and  516   c  is switched according to the switch signal, and vector control is performed by the vector controller  518 . 
     In the state where constant current control is executed, if time t_m is less than or equal to the idling period D_max and the signal A=“H” and signal B=“H” are output, the generation unit  515   c  outputs the switch signal=“H”. As a result, the state of each of the selection switches  516   a ,  516   b , and  516   c  is switched according to the switch signal, and vector control is performed by the vector controller  518 . 
     In the state where constant current control is executed, when time t_m is less than or equal to the idling period D_max and at least one of the signal A or the signal B is set to “L”, the generation unit  515   c  outputs the switch signal=“L”. As a result, the state of each of the selection switches  516   a ,  516   b , and  516   c  is maintained, and constant current control is continued by the constant current controller  517 . 
     In a state where vector control is executed, when signal A=“H” is output, the generation unit  515   c  outputs the switch signal=“H”. As a result, the state of each of the selection switches  516   a ,  516   b , and  516   c  is maintained, and vector control is continued by the vector controller  518 . 
     In the state where vector control is executed, when the signal A=“L” is output, the generation unit  515   c  outputs the switch signal=“L”. As a result, the state of each of the selection switches  516   a ,  516   b , and  516   c  is switched according to the switch signal, and constant current control is performed by the constant current controller  517 . 
       FIG. 14  is a flowchart illustrating a method for controlling the motor  509  by the motor control apparatus  157 . A control operation for the motor  509  according to the present exemplary embodiment will be described below with reference to  FIG. 14 , Processing in this flowchart is executed by the motor control apparatus  157  that has received an instruction from the CPU  151   a.    
     First, when the CPU  151   a  outputs an enable signal “H” to the motor control apparatus  157 , the motor control apparatus  157  starts driving of the motor  509  based on a command output from the CPU  151   a . The enable signal is a signal for permitting or prohibiting the operation of the motor control apparatus  157 . When the enable signal is at a low level (L), the CPU  151   a  prohibits the operation of the motor control apparatus  157 . That is, the control operation for the motor  509  by the motor control apparatus  157  is terminated. Further, when the enable signal is at a high level (H), the CPU  151   a  permits the operation of the motor control apparatus  157  and the motor control apparatus  157  controls the motor 509  based on a command output from the CPU  151   a.    
     Next, in step S 1001 , the generation unit  515   c  outputs the switch signal “L” so that driving of the motor  509  can be controlled by the constant current controller  517 . As a result, constant current control is performed by the constant current controller  517 . 
     After that, in step S 1002 , if the CPU  151   a  outputs the enable signal “L” to the motor control apparatus  157  (YES in step S 1002 ), the motor control apparatus  157  terminates driving of the motor  509 . 
     In step S 1002 , if the CPU  151   a  outputs the enable signal “H” to the motor control apparatus  157  (NO in step S 1002 ), the processing proceeds to step S 1003 . 
     Next, in step S 1003 , if the signal A “L” is output (NO in step S 1003 ), the processing returns to step S 1001 . That is, the state where constant current control is performed by the constant current controller  517  is maintained. 
     In step S 1003 , if the signal A=“H” is output (YES in step S 1003 ), the processing proceeds to step S 1004 . 
     In step S 1004 , if the signal B=“H” is output (YES in step S 1004 ), the processing proceeds to step S 1005 . In step S 1005 , the switch signal “H” is output to each of the selection switches  516   a ,  516   b , and  516   c . As a result, vector control is performed by the vector controller  518 . 
     On the other hand, in step  51004 , if the signal B=“L” is output (NO in step S 1004 ), the processing proceeds to step S 1006 . 
     In step S 1006 , if time t_m is less than or equal to max (NO in step S 1006 ), the processing returns to step S 1001 . That is, the state where constant current control is performed by the constant current controller  517  is maintained. 
     In step S 1006 , if time t_m is more than D_max (YES in step S 1000  the processing proceeds to step S 1005 . 
     In step S 1007 , if the signal A=“H” is output (YES in step S 1007 ), the processing returns to step S 1005 . That is, the state where vector control is performed by the vector controller  518  is maintained. 
     In step S 1007 , if the signal A=“L” is output (NO in step S 1007 ), the processing returns to step S 1001 . In step S 1001 , the switch signal “L” is output to each of the selection switches  516   a ,  516   b , and  516   c . As a result, constant current control is performed by the constant current controller  517 . 
     Then, the motor control apparatus  157  repeatedly performs the above-described control operation until the CPU  151   a  outputs the enable signal “L” to the motor control apparatus  157 . Also, when vector control is being executed, if the CPU  151   a  outputs the enable signal “L” to the motor control apparatus  157 , the motor control apparatus  157  suspends the motor control operation. 
     As described above, in the present exemplary embodiment, the motor control method is switched from constant current control to vector control after the transmission of the driving force from the motor  509  to the developing device  314  is resumed. Consequently, it is possible to prevent the motor controloperation from becoming unstable. 
     The present exemplary embodiment described above illustrates a configuration for switching the motor control method for controlling the motor  509  that rotationally drives the developing device  314 . However, the configuration for switching the control method according to the present exemplary embodiment is not applied only to the developing device  314 . For example, the configuration for switching the control method according to the present exemplary embodiment is also applicable to a unit (e.g., a drum unit including a photosensitive drum) that can be inserted into or removed from the image printing device  301  and is rotationally driven when the unit is attached to the image printing device  301 . 
     In the present exemplary embodiment, the driving force is transmitted from the driving coupling  356  to the driven coupling  353  in a state where the first projecting portion  361  provided on the driven coupling  353  is fit to the recessed portion  370  provided on the driving coupling  356 . However, the present exemplary embodiment is not limited to this example. For example, the driving force may be transmitted from the driving coupling  356  to the driven coupling  353  in a state where a projecting portion provided on the driving coupling  356  is fit to the recessed portion  370  provided on the driven coupling  353 . In other words, any configuration may be employed as long as one of the driving coupling  356  and the driven coupling  353  includes a projecting portion, and the other one of the driving coupling  356  and the driven coupling  353  includes the recessed portion  370 . 
     Further, in the present exemplary embodiment, the length of the projecting portion  361  in the rotation direction is shorter than the length of the recessed portion  370  in the rotation direction. However, the present exemplary embodiment is not limited to this example, For example, the length of the projecting portion  361  in the rotation direction may be the same as the length of the recessed portion  370  in the rotation direction. 
     In the present exemplary embodiment, the urging member  354  that urges the driven coupling  353  against the driving portion  355  in the Y-axis direction is provided at one end of the developing roller  350 . However, the present exemplary embodiment is not limited to this example. For example, the driving portion  355  may be provided with the urging member  354  in such a manner that the urging member  354  urges the driving coupling  356  against the developing device  314  in the Y-axis direction. 
     In vector control according to the present exemplary embodiment, the motor  509  is controlled by performing phase feedback control. However, the present exemplary embodiment is not limited to this configuration. For example, a configuration in which the motor  509  is controlled by feeding back a rotational speed w of the rotor  402  may be employed. Specifically, as illustrated in  FIG. 15 , the CPU  151   a  outputs a command speed ω_ref representing the target speed of the rotor  402 . Further, a speed determiner  514  provided in the motor control apparatus  157  determines the rotational speed w based on a time change of the rotation phase θ output from the phase determiner  513 . To determine the speed, the following formula (12) is used.
 
ω= dθ/dt    (12)
 
     A speed controller  600  is configured to generate the q-axis current command value iq_ref so as to reduce a deviation between the rotational speed ω and the command speed ω_ref and output the generated q-axis current command value iq_ref. The motor  509  may be controlled by performing speed feedback control in this manner. In the configuration in which the rotational speed is fed back as described above, the rotational speed of the rotor  402  can be controlled to a predetermined speed. 
       FIG. 15  is a block diagram illustrating the configuration of the motor control apparatus that performs speed feedback control. In the present exemplary embodiment, the first determination unit  515   a . compares the target speed ω_ref of the rotor  402  with the threshold wth, and outputs the signal A. However, the configuration of the first determination unit  515   a  according to the present exemplary embodiment is not limited to this example. For example, the first determination unit  515   a  may compare the rotational speed ω determined by the speed determiner  514  illustrated in  FIG. 15  with the threshold ωth, and may output the signal A. 
     The motor control apparatus  157  according to the present exemplary embodiment corresponds to the portion (the current controller  503 , the PWM inverter  506 , and the like) that is partially shared between one or more circuits for performing vector control and one or more circuits for performing constant current control. However, the configuration of the motor control apparatus  157  is not limited to this example. For example, one or more circuits for performing vector control and one or more circuits for performing constant current control may be independently provided. 
     The rotational speed ω_ref may be determined based on, for example, a cycle in which the magnitude of periodic signals, such as the drive current iα or iβ, the drive voltage Vα or Vβ, and the induced voltage Eα or Eβ, which have a correlation with the rotation cycle of the rotor  402  becomes zero. 
     Further, in the present exemplary embodiment, a stepping motor is used as the motor  509  that drives a load. However, other motors such as a direct current (DC) motor or a brushless DC motor may be used. The motor is not limited to a two-phase motor. The present exemplary embodiment is also applicable to other motors such as a three-phase motor. 
     Further, in the present exemplary embodiment, a permanent magnet is used as the rotor  402 . However, the rotor  402  is not limited to a permanent magnet. 
     According to an aspect of the present disclosure, it is possible to prevent a motor control operation from becoming unstable. 
     Embodiment(s) of the present disclosure can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be referred to more fully as a ‘non-transitory computer-readable storage medium’) to perform the functions of one or more of the above-described embodiment(s) and/or that includes one or more circuits (e.g., application specific integrated circuit (ASIC)) for performing the functions of one or more of the above-described embodiment(s), and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiment(s) and/or controlling the one or more circuits to perform the functions of one or more of the above-described embodiment(s). The computer may include one or more processors (e.g., central processing unit (CPU), micro processing unit (MPU)) and may include a network of separate computers or separate processors to read out and execute the computer executable instructions. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™, a flash memory device, a memory card, and the like. 
     While the present disclosure has been described with reference to exemplary embodiments, it is to be understood that the disclosure is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2019-108892, filed Jun. 11, 2019, which is hereby incorporated by reference herein in its entirety.