Patent Publication Number: US-10782636-B2

Title: Temperature control of heater in image forming apparatus

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to temperature control of a heater in an image forming apparatus. 
     Description of the Related Art 
     An image forming apparatus employing an electrophotographic process or an electrostatic printing process applies heat to a toner image to fix the toner image to a sheet. A fixing device performs so-called phase control in which the temperature of the fixing device is maintained at a target temperature by controlling the amount of alternating current to be supplied every half wave. In the phase control, a start phase angle at which supply of current is started is decided so that a difference between a target temperature and a measured temperature becomes small, and an alternating current is supplied to the heater during the period from the start phase angle to an end phase angle (Japanese Patent Laid-Open No. 2017-26858). 
     In Japanese Patent Laid-Open No. 2017-26858, it is proposed to reduce a harmonic current by providing a prohibited section in which a start phase angle cannot be set in a half period of an alternating current. In addition, in Japanese Patent Laid-Open No. 2017-26858, it is proposed to prevent a steep rise in a total amount of current supply of two heaters by shifting start phase angles of the two heaters. 
     In the prior art, there may be a case in which the harmonic current cannot be sufficiently reduced because the prohibited section, which is a range of phases in which an electrical connection start cannot be set in phase control, is fixed. In particular, as the range of basis weights of commercially available print materials has widened, higher output heaters have become necessary. If low power is continuously supplied to a high output heater for a low basis weight print material, a start phase angle at which a harmonic current is apt to be generated is used consecutively. This can occur, for example, in the case where a heater of 1000 W (100% supply rate) class is continuously used at 500 W (50% supply rate). If the prohibited section is widened in order to reduce the harmonic current, the temperature followability of the heater is lowered. 
     SUMMARY OF THE INVENTION 
     The present invention provides an image forming apparatus comprising the following elements. A fixing unit has a heater and is configured to fix a toner image to a sheet by applying heat from the heater. A temperature detector configured to detect a temperature of the fixing unit. A controller controls a supply of alternating current to the heater. The controller decides a supply rate for each control period that comprises a plurality of half periods in the alternating current, based on a difference between a target temperature of the fixing unit and the temperature detected by the temperature detector. In a case where the same supply rate over a plurality of the control period is decided, the controller decides a start phase angle that is a reference for a supply start corresponding to the supply rate so that the start phase angle is located outside a prohibited section and a combination of the start phase angle differs for each control period. For each of a plurality of half periods configuring the control period, the controller starts supply of the alternating current to the heater at the start phase angle, and stops supply of the alternating current to the heater when a zero cross point of the alternating current arrives. 
     Further features of the present invention 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 view for describing an image forming apparatus. 
         FIGS. 2A to 2C  are views for describing a method of reducing a harmonic current. 
         FIGS. 3A and 3B  are views for describing a method of reducing a harmonic current. 
         FIGS. 4A to 4C  are views for describing a method of reducing a harmonic current. 
         FIG. 5  is a block diagram for describing a controller. 
         FIG. 6  is a flow chart illustrating main phase control. 
         FIG. 7  is a flow chart illustrating first phase control. 
         FIG. 8  is a flow chart illustrating second phase control. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. Note that the following embodiments do not limit the invention according to the scope of the appended claims. Although a plurality of features are described in the embodiments, not all of the plurality of features are essential to the present invention, and the plurality of features may be arbitrarily combined. In addition, in the accompanying drawings, the same reference numerals are assigned to the same or similar components, and duplicate descriptions are omitted. 
     [Image Forming Apparatus] 
       FIG. 1  illustrates an intermediate transfer type image forming apparatus  1 . The image forming apparatus  1  may be an image forming apparatus that forms a single-color image, but here, it is an electrophotographic image forming apparatus that forms a multicolor image by mixing a plurality of colorants. The image forming apparatus  1  uses developers of four colors, such as yellow (Y), magenta (M), cyan (C), and black (BK). In  FIG. 1 , a character indicating a color is given to the end of a reference number, but this character is omitted when a matter common to four colors is described. 
     Photosensitive drums  6 C,  6 M,  6 Y, and  6 BK are arranged at equal intervals, and are image carriers for carrying electrostatic latent images and toner images. A primary charger  2  is an example of a charging unit for uniformly charging the image carrier. The primary charger  2  uniformly charges the surface of a photosensitive drum  6  by using a charging voltage. A scanning optical device  3  is an example of a scanning unit that forms an electrostatic latent image by scanning the surface of an image carrier with laser light. The scanning optical device  3  emits a luminous flux (a laser beam) L modulated based on an input image toward the photosensitive drum  6 . The luminous flux L forms an electrostatic latent image on the surface of the photosensitive drum  6 . A developing device  4  causes cyan, magenta, yellow, or black developer to adhere to the electrostatic latent image through a sleeve or blade to which a developing voltage is applied, respectively. As a result, the electrostatic latent image is developed, and a developer image (a toner image) is formed. 
     A feeding roller  8  feeds the sheets S accommodated in the feeding tray  7  one by one. A separation roller  9  separates one sheet S from the plurality of sheets S fed by the feeding roller  8 , and feeds the sheet S to the conveying path. A conveying roller  16  feeds the sheet S toward a secondary transfer portion in synchronization with an image write start timing. 
     A primary transfer roller  5  transfers the toner image carried on the photosensitive drum  6  to an intermediate transfer belt  10 . A primary transfer voltage is applied to the primary transfer roller  5  to transfer the toner image onto the intermediate transfer belt  10 . The intermediate transfer belt  10  functions as an intermediate transfer member. A driving roller  11  is a roller for rotating the intermediate transfer belt  10 . The secondary transfer portion has a secondary transfer roller  14 . In the secondary transfer portion, the intermediate transfer belt  10  and the secondary transfer roller  14  convey the sheet S while sandwiching the sheet S therebetween, whereby a multi-color toner image carried on the intermediate transfer belt  10  is transferred onto the sheet S. The secondary transfer voltage facilitates transfer of the toner image to the sheet S. Thereafter, the sheet S is conveyed to a fixing device  12 . The fixing device  12  applies pressure and heat to the toner image carried on the sheet S to fix it. A discharge roller  13  discharges the sheet S on which the image has been formed. Note that, the primary transfer roller  5 , the intermediate transfer belt  10 , and the secondary transfer roller  14  are examples of a transfer unit for transferring a toner image onto a sheet. The fixing device  12  is an example of a fixing unit for fixing a toner image carried on a sheet. 
     The fixing device  12  has a pressure roller  21  and a fixing belt  22 . A ceramic heater  23  for heating the toner image is provided inside the fixing belt  22 . The ceramic heater  23  has a first heater  24 A and a second heater  24 B whose longitudinal directions are the rotation axis of the fixing belt  22 . The first heater  24 A and the second heater  24 B are arranged side by side in parallel, and have different heat generation distributions in the longitudinal direction. A controller  15  measures the temperature of the ceramic heater  23  using a thermistor  25  as a temperature detector, and controls the amount of power to be supplied to the ceramic heater  23  according to the difference between the measured temperature and a target temperature. Note that, by using a plurality of heaters having different heat generation distributions such as the first heater  24 A and the second heater  24 B, temperature unevenness of the ceramic heater  23  is reduced. 
     &lt;Concept of Phase Control&gt; 
       FIG. 2A  is a diagram for describing phase control for an alternating current waveform. The horizontal axis represents time t. The vertical axis of the upper graph represents voltage V. The vertical axis of the lower graph represents the state of supply (on/off). The phase control is control of the power supplied to the heater by turning on the heater at an particular phase angle within one half wave of the alternating current waveform and turning off the heater at the next zero cross point T 0 . The zero cross point is a point at which the amplitude (voltage) of the alternating current waveform becomes 0 [V]. The phase angles corresponding to the zero cross points are, for example, 0 degrees (360 degrees) and 180 degrees. In this case, phase control is performed using four half waves W 1 , W 2 , W 3 , and W 4  as a set. In other words, one control period corresponds to two periods of the alternating current waveform. The controller  15  decides a target temperature in accordance with sheet information (e.g.: basis weight) of the sheet S, and decides the amount of power supplied to the ceramic heater  23  for each control period so that the difference between the target temperature and the measured temperature becomes small. The sheet information is information used for deciding the fixing temperature, and is, for example, information that designates the size of the sheet P, the presence or absence of a coating, the basis weight, and simplex/duplex printing. As a control parameter for the heater, here, a concept of a supply rate, which is a parameter correlated with the amount of power, is introduced. The supply rate is a ratio of the amount of power actually supplied in one control period with respect to the maximum amount of power that can be supplied in one control period. The supply rate may be expressed as a percentage for convenience of description. The controller  15  decides the supply rate so that the difference between the target temperature and the measured temperature becomes small, and decides start phase angles θ 1 , θ 2 , θ 3 , and θ 4  of the four half waves W 1 , W 2 , W 3 , and W 4 , respectively, so that the decided supply rate is achieved. According to the  FIG. 2A , in the half wave W 1  (the first half wave), supply is started at the start phase angle θ 1 , and supply ends at the next zero cross point T 0 . In the half wave W 2  (the second half wave), supply is started at the start phase angle θ 2 , and supply ends at the next zero cross point T 0 . In the half wave W 3  (the third half wave), supply is started at the start phase angle θ 3 , and supply ends at the next zero cross point T 0 . In the half wave W 4  (the fourth half wave), supply is started at the start phase angle θ 4 , and supply ends at the next zero cross point T 0 . In other words, hatched portions in  FIG. 2A  and the like mean the supply regions. Incidentally, a triac may be used as an element for switching between supply of power and stoppage. Once the triac is turned on, it is not switched off until the input voltage becomes 0V. Therefore, the triac terminates the supply at the zero cross point T 0 . 
     For example, in a case where the start phase angle θ is set to 180 [degrees], the supply rate in the half wave W becomes 0 [%]. In a case where the start phase angle θ is set to 0 [degrees], the supply rate in the half wave W becomes 100 [%]. In a case where the start phase angle θ is set to 90 [degrees], the supply rate in the half wave W becomes 50 [%]. Also, in a case where one control period is configured by four half waves, the supply rate in one control period is the average value of the supply rates of the four half waves. 
     For example, it is assumed that the start phase angle θ 1  of the first half wave W 1  and the start phase angle θ 2  of the second half wave W 2  are set so that the supply rate becomes 30 [%]. It is assumed that the start phase angle θ 3  of the third half wave W 3  and the start phase angle θ 4  of the fourth half wave W 4  are set so that the supply rate becomes 70 [%]. In this case, the supply rate in one control period is 50 [%]. 
     &lt;Harmonic Current&gt; 
     A harmonic current is a noise current generated by performing phase control on the ceramic heater  23 . In phase control, harmonic currents are generated due to the following three factors.
         First factor: when supply of the alternating current is started in the vicinity of the phase angles of 90 [degrees] or 270 [degrees], current change before and after supply becomes a maximum, and a harmonic current is generated.   Second factor: In a case where supply of the alternating current to a plurality of heaters is started at the same phase angle, current change over the entire fixing device becomes large, and a harmonic current is generated.   Third factor: If the supply is continued at the same phase angle over a plurality of control periods, a level of a harmonic current spectrum corresponding to the phase angle becomes high. Specifically, in a case where a high power heater is periodically supplied with low power (e.g.: supply rate=50[%]) in accordance with phase control, the average value of the harmonic current increases.       

     The harmonic current related to the first factor is reduced by setting the vicinity of the phase angle 90 [degrees] and the vicinity of 270 [degrees] to prohibited sections for a start phase angle. In addition, the harmonic current related to the second factor is reduced by making the start phase angles different so that power is supplied to the plurality of heaters at different timings. The harmonic current for the third factor is reduced by deciding the start phase angle such that the same combination of start phase angles does not continue over a plurality of control periods. 
       FIG. 2B  illustrates that prohibited sections X are set in the vicinity of phase angles at which the amplitudes of the alternating currents are a maximum. The controller  15  sets prohibited sections X in the vicinity of phase angles at which the amplitude of the alternating current becomes a maximum. In this example, prohibited sections X that have a predetermined width are set so as to include 90 degrees, 270 degrees, 450 degrees, and 630 degrees, respectively. In particular, the start phase angle θ of the half waves W 1  to W 4  is set so as to coincide with the end of the prohibited section X. As a result, the harmonic current related to the first factor is reduced. 
       FIG. 2C  illustrates a method of reducing harmonic currents associated with the first factor. The controller  15  corrects the start phase angle θ by a shift amount D so that the start phase angle θ decided in accordance with the supply rate is located outside the prohibited section X. Correction is performed by +D for the half waves W 1  and W 2 . Correction is performed by −D for the half waves W 3  and W 4 . The reason why the signs of the shift amounts of the half waves W 1  and W 2  and the half waves W 3  and W 4  are different from each other is to maintain the average supply rate in one control period as much as possible. 
       FIG. 3A  illustrates a method of reducing harmonic currents associated with the second factor for the first heater  24 A.  FIG. 3B  illustrates a method of reducing harmonic currents associated with the second factor for the second heater  24 B. The controller  15  decides the start phase angle θa of the first heater  24 A and the start phase angle θb of the second heater  24 B based on the supply rate. Further, the controller  15  sets prohibited sections X for the first heater  24 A and the second heater  24 B, respectively. Note that, in consideration of the first factor, the controller  15  decides the start phase angle such that the start phase angle corresponding to the supply rate is located outside the prohibited section X. For example, the controller  15  may decide shift amounts Da and Db based on the supply rates and the prohibited section X. For the half waves W 1  and W 2 , the start phase angle θa′ after correction of the first heater  24 A is θa+Da, and the start phase angle after correction of the second heater  24 B is θb−Db. For the half waves W 3  and W 4 , the start phase angle θa′ after correction of the first heater  24 A is θa−Da, and the start phase angle after correction of the second heater  24 B is θb+Db. In this manner, the distance between the start phase angle θa′ and the start phase angle θb′ is sufficiently secured, so that the harmonic current related to the second factor is reduced. Other methods can be used as long as the distance between the start phase angle θa′ and the start phase angle θb′ is sufficiently secured. 
     In order to describing the method of reducing the harmonic current by the third factor,  FIGS. 4A to 4C  are referred to.  FIG. 4A  illustrates a first control period,  FIG. 4B  illustrates a second control period which is a control period next to the first control period, and  FIG. 4C  illustrates a third control period which is a control period that follows the second control period. The first control period comprises a first period and a second period of the alternating current. The second control period comprises a third period and a fourth period of the alternating current. The third control period comprises a fifth period and a sixth period of the alternating current. Here, it is illustrated that a plurality of control periods each having a supply rate of 50% (corresponding to a start phase angle of) 90° are consecutive. In the first control period, the supply rate of the first half wave W 1  and the supply rate of the second half wave W 2  are 30% (start phase angle θ 1 - 1 ), respectively, and the supply rate of the third half wave W 3  and the supply rate of the fourth half wave W 4  are 70% (start phase angle θ 1 - 2 ), respectively. In the second control period, the supply rate of the first half wave W 1  and the supply rate of the second half wave W 2  are 25% (start phase angle θ 2 - 1 ), respectively, and the supply rate of the third half wave W 3  and the supply rate of the fourth half wave W 4  are 75% (start phase angle θ 2 - 2 ), respectively. In the third control period, the supply rate of the first half wave W 1  and the supply rate of the second half wave W 2  are 20% (start phase angle θ 3 - 1 ), respectively, and the supply rate of the third half wave W 3  and the supply rate of the fourth half wave W 4  are 80% (start phase angle θ 3 - 2 ), respectively. As described above, the combination of the start phase angle applied to the first half wave and the second half wave and the start phase angle applied to the third half wave and the fourth half wave is changed for each control period, thereby reducing the harmonic current due to the third factor. In this example, each time the control period changes, the supply rate applied in the first half of the control period gradually decreases, and the supply rate applied in the first half of the control period gradually increases. Additionally, the minimum value of the supply rate is assumed to be 5%, and the maximum value of the supply rate is assumed to be 95%. In this example, in a case where the supply rate applied to the first half of a control period reaches 5% and the supply rate applied to the second half of the control period reaches 95%, the supply rate of the first half of the next control period is increased and the supply rate of the second half of the next control period is decreased. Finally, in a case where the first half supply rate becomes 95% and the second half supply rate becomes 5%, the first half supply rate shifts from increase to decrease and the second half supply rate shifts from decrease to increase. Here, the rate of change of the supply rate for each control period is set to 5%, but this is merely an example. This rate of change may be, for example, 1%. 
     If the supply rate per one control period is 40%, the combination of the first half supply rate and the second half supply rate changes, for example, from 20% and 60%, to 15% and 65%, and then to 10% and 70%. Incidentally, in a case where the prohibited region is set to a range of 70° to 110° for one half wave (range of 0° to 180°), the supply rate becomes approximately 38 to 62%. 
     In this manner, in a case where the same supply rate is decided over a plurality of control periods, the controller  15  decides the start phase angle such that the start phase angle corresponding to the supply rate is located outside the prohibited sections X and a combination of start phase angles differs for each control period. Further, the controller  15  may change the prohibited sections X for each control period to thereby reduce harmonic currents associated with the third factor. For example, a prohibited section X 1  for a first control period and a prohibited section X 2  for a second control period are different. Similarly, the prohibited section X 2  for the second control period and a prohibited section X 3  for a third control period are different. Note that the prohibited section X for the first heater  24 A and the prohibited section X for the second heater  24 B may coincide with each other or may be different from each other. 
     &lt;Controller&gt; 
       FIG. 5  is a view for describing functions of the controller  15 . The CPU  30  realizes various functions by executing programs stored in a ROM region of a storage unit  31 . Note that part or all of these functions may be realized by hardware such as an ASIC or an FPGA. ASIC is an abbreviation for Application Specific Integrated Circuit. FPGA is an abbreviation for Field Programmable Gate Array. A host apparatus  28  is a computer, an image scanner, a digital camera, or the like that transmits sheet information to the image forming apparatus  1 . A target deciding unit  32  decides a target temperature Tt of the fixing device  12  based on the sheet information. For example, the target deciding unit  32  decides the target temperature Tt to be relatively high for a sheet S having a large basis weight, and decides the target temperature Tt to be relatively low for a sheet S having a low basis weight. A difference unit  33  acquires a difference dT between a target temperature Tt and a measured temperature Tm obtained by the thermistor  25 . The supply rate deciding unit  34  decides a supply rate P corresponding to the difference dT. For example, the supply rate deciding unit  34  decides a supply rate Pa of the first heater  24 A and a supply rate Pb of the second heater  24 B. A table or a function (formula) for deciding the supply rates Pa and Pb may be stored in the storage unit  31  in advance. A first phase control unit  35  decides the start phase angle θa of the first heater  24 A based on the supply rate Pa, and decides the start phase angle θb of the second heater  24 B based on the supply rate Pb. A table or a function (formula) for deciding the start phase angle θa from the supply rate Pa may be prepared in advance and stored in the storage unit  31 . Similarly, a table or a function (formula) for deciding the start phase angle θb from the supply rate Pb may be stored in advance in the storage unit  31 . Further, the first phase control unit  35  decides the shift amount Da of the first heater  24 A and the shift amount Db of the second heater  24 B. A prohibited section changing unit  37  changes the prohibited section Xv for each control period, and outputs it to the second phase control unit  36 . The second phase control unit  36  decides the corrected start phase angles θa′, θb′ based on the start phase angles θa, θb and the prohibited section Xv. In other words, the shift amounts Da and Db are decided such that the start phase angles θa′ and θb′ are located outside the prohibited section Xv. Further, if the start phase angles θa′ and θb′ do not coincide with each other, an effect of reducing harmonic currents is further enhanced. The second phase control unit  36  turns on the driving circuit  26 A at the start phase angle θa′ to supply an alternating current to the first heater  24 A, and turns off the driving circuit  26 A at the zero cross point T 0 . The second phase control unit  36  turns on the driving circuit  26 A at the start phase angle θb′ to supply an alternating current to the second heater  24 A, and turns off the driving circuit  26 A at the zero cross point T 0 . The detection circuit  38  detects the alternating current zero cross point T 0  and notifies the CPU  30  of the zero cross point T 0 . The CPU  30  recognizes the phase angle of the alternating current based on the zero cross point T 0  detected by the detection circuit  38 . In addition, the CPU  30  may calculate the length of the half period of the alternating current by measuring the times of two adjacent zero cross points T 0 . 
     &lt;Flow Chart&gt; 
       FIG. 6  is a flow chart illustrating main phase control.
         In step S 101 , the CPU  30  (as target deciding unit  32 ) receives sheet information from the host apparatus  28 .   In step S 102 , the CPU  30  (as target deciding unit  32 ) decides the target temperatures Tt corresponding to the sheet information.   In step S 103 , the CPU  30  acquires the measured temperature Tm from the thermistor  25 .   In step S 104 , the CPU  30  (as difference unit  33 ) calculates the difference dT between the target temperature Tt and the measured temperature Tm.   In step S 105 , the CPU  30  (as supply rate deciding unit  34 ) decides the supply rates Pa and Pb such that the difference dT becomes small.   In step S 106 , the CPU  30  (as first phase control unit  35 ) performs the first phase control based on the supply rates Pa and Pb, and decides the start phase angles θa and θb and the shift amounts Da and Db. The first phase control unit  35  executes the first phase control based on the supply rate Pa, and decides the start phase angle θa and the shift amount Da. The first phase control unit  35  executes the first phase control based on the supply rate Pb, and decides the start phase angle θb and the shift amount Db. Note that the first phase control unit  35  may decide a minimum value Damin and a maximum value Damax that can be taken by the shift amount Da. The first phase control unit  35  may decide a minimum value Dbmin and a maximum value Dbmax that can be taken by the shift amount Db. In other words, the first phase control unit  35  may select, as the shift amount Da, an arbitrary shift amount that is greater than or equal to the minimum value Damin and less than or equal to the maximum value Damax, or may output both the minimum value Damin and the maximum value Damax. Here, it is assumed that the first phase control unit  35  outputs the minimum value Damin and the maximum value Damax to the second phase control unit  36 , and the second phase control unit  36  decides the final shift amount Da. Similarly, the first phase control unit  35  may select, as the shift amount Db, an arbitrary shift amount that is greater than or equal to the minimum value Dbmin and less than or equal to the maximum value Dbmax, or may output both the minimum value Dbmin and the maximum value Dbmax. Here, it is assumed that the first phase control unit  35  outputs the minimum value Dbmin and the maximum value Dbmax to the second phase control unit  36 , and the second phase control unit  36  decides the final shift amount Db.   In step S 107 , the CPU  30  (as prohibited section changing unit  37 , second phase control unit  36 ) changes the prohibited section Xv for each control period, and decides the corrected start phase angles θa′, θb′ based on the prohibited section Xv, the start phase angles θa, θb, and the shift amounts Da, Db.   In step S 108 , the CPU  30  (as second phase control unit  36 ) drives the driving circuit  26 A based on the corrected start phase angle θa′ and drives the driving circuit  26 B based on the corrected start phase angle θb′.   In step S 109 , the CPU  30  determines whether or not printing has ended. If printing has not ended, the CPU  30  advances the process to step S 103  and repeats execution of step S 103  to step S 109 .       

     •First Phase Control 
       FIG. 7  is a flow chart illustrating details of the first phase control in step S 106 .
         In step S 201 , the CPU  30  (as first phase control unit  35 ) decides a start phase angle θa that meets the supply rate Pa in one half wave and decides a start phase angle θb that meets the supply rate Pb in one half wave.   In step S 202 , the CPU  30  (as first phase control unit  35 ) decides a shift range (Damin to Damax) which is a range that the shift amount Da can take, and a shift range (Dbmin to Dbmax) of the shift amount Db. For example, Damin may be −Da, and Damax may be +Da, as  FIG. 3A  illustrates. Dbmin may be −Db, and Dbmax may be +Db, as  FIG. 3B  illustrates.       

     •Second Phase Control 
     In the present embodiment, two constraints may be employed to reduce harmonic current. The first constraint is that the start phase angle θ′ acquired by correcting the start phase angle θ by the shift amount D, and the start phase angle θ exist in the same half wave. The second constraint is that the start phase angle θ′ is not included in the prohibited section X. The CPU  30  decides the shift range (Damin to Damax) so that these two constraints are met. 
     For example, Dmax may be decided as follows. 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 0 ≤ P ≤ x/2 
                 Dmax = p 
               
               
                   
                 x/2 ≤ P ≤ (1 − x)/2 
                 Dmax = −p + X 
               
               
                   
                 (1 − x)/2 ≤ P ≤ 0.5 
                 Dmax = p 
               
               
                   
                 0.5 ≤ P ≤ (1 + x)/2 
                 Dmax = −p + 1 
               
               
                   
                 (1 + X)/2 ≤ P ≤ 1 − x/2 
                 Dmax = p − (1 − X) 
               
               
                   
                 1 − x/2 ≤ P ≤ 1 
                 Dmax = −p + 1 
               
               
                   
                   
               
            
           
         
       
     
     For example, Dmin may be decided as follows. 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 P &lt; 0.5 
                 Dmin = −p + (1 − X) 
               
               
                   
                 0.5 ≤ P 
                 Dmin = p − X 
               
               
                   
                   
               
            
           
         
       
     
     Where p is the phase angle (p=P×180 degrees) corresponding to the supply rate P. x is the supply rate (x=X/180) corresponding to the prohibited section X. 
     The CPU  30  decides a final shift amount D from the shift range (Damin to Damax) based on the start phase angles θ of the plurality of heaters. The controller  15  decides the shift amounts Da and Db so that the start phase angle θa′ of the first heater  24 A and the start phase angle θb′ of the second heater  24 B in the same half wave are sufficiently separated from each other. For example, as illustrated in  FIGS. 3A and 3B , the sign of the shift amount Da and the sign of the shift amount Db in the same half wave may be reversed. 
       FIG. 8  is a flow chart illustrating details of the second phase control in step S 107 . It is sufficient if the start phase angle is located outside the prohibited section Xv and is different for each control period. For example, the prohibited section Xv may be fixed, and the shift amount of the start phase angle may be changed each control period. As another method, a method of changing the prohibited section Xv for each control period can be considered. However, since it is sufficient to decide the combination of the start phase angles so as to be located outside the prohibited section Xv and different for each control period, still other decision methods may be adopted. 
     In step S 301 , the CPU  30  (as prohibited section changing unit  37 ) changes the prohibited section Xv for each control period. Thereby, harmonic currents are reduced compared to the prior art. For example, the prohibited section changing unit  37  changes the prohibited section Xv within a variable range of the prohibited section that is determined in advance. The storage unit  31  may store a plurality of prohibited sections Xv. In this case, the prohibited section changing unit  37  may randomly select one prohibited section Xv from a plurality of prohibited sections Xv. Alternatively, the plurality of prohibited sections Xv may be assigned a respective order. In this case, the prohibited section changing unit  37  may select, in accordance with an order, one prohibited section Xv from a plurality of prohibited sections Xv. The prohibited section Xv may be decided such that the center phase angle of the half wave W (90 degrees+n×180 degrees) is the center. Alternatively, the center of the prohibited section Xv may be shifted from the center phase angle of the half wave W. However, even in this case, it is assumed that the prohibited section Xv includes the center phase angle of a half wave W. 
     In step S 302 , the CPU  30  (as second phase control unit  36 ) determines whether or not Damax and Dbmax meet a first requirement. As illustrated in  FIG. 3A , the second phase control unit  36  obtains θa′ using Damax (half waves W 1 , W 2 : θa′=θa+Damax; half waves W 3 , W 4 : θa′=θa−Damax). As illustrated in  FIG. 3B , the second phase control unit  36  obtains θb′ using Dbmax (half waves W 1 , W 2 : θb′=θb−Dbmax; half waves W 3 , W 4 : θb′=θb+Dbmax). Here, the first requirement is that the distance |θa′−θb′| exceeds the distance |θa−θb| in all of the four half waves. In other words, if the distance between the start phase angle of the first heater  24 A and the start phase angle of the second heater  24 B is increased by the shift (correction) of the start phase angle, the harmonic current is reduced. If the first requirement is met, the CPU  30  advances the processing to step S 320 . In step S 320 , the CPU  30  (as second phase control unit  36 ) selects Damax as the shift amount Da, selects Dbmax as the shift amount Db, and advances the processing to step S 306 . Meanwhile, if the first requirement is not met, the CPU  30  advances the processing to step S 303 . 
     In step S 303 , the CPU  30  (as second phase control unit  36 ) determines whether or not the start phase angle θa is inside the prohibited section Xv. The start phase angle θa being inside the prohibited section Xv means that the start phase angle θa is included in the prohibited section Xv. If the start phase angle θa is inside the prohibited section Xv, the CPU  30  advances the processing to step S 330 . In step S 330 , the CPU  30  (as second phase control unit  36 ) determines whether or not Damax and Dbmax meet a second requirement. As illustrated in  FIG. 3A , the second phase control unit  36  obtains θa′ using Damax (half waves W 1 , W 2 : θa′=θa+Damax; half waves W 3 , W 4 : θa′=θa−Damax). As illustrated in  FIG. 3B , the second phase control unit  36  obtains θb′ using Dbmax (half waves W 1 , W 2 : θb′=θb−Dbmax; half waves W 3 , W 4 : θb′=θb+Dbmax). Here, the second requirement is that the distance between the start phase angle θa′ and the start phase angle θb′ exceeds a threshold value θth in all four half waves. If the second requirement is met, the CPU  30  advances the processing to step S 320 . In other words, Damax is selected as the shift amount Da, and Dbmax is selected as the shift amount Db. If the second requirement is not met, the CPU  30  advances the processing to step S 331 . In step S 331 , the CPU  30  (as second phase control unit  36 ) selects Damin as the shift amount Da, selects Dbmax as the shift amount Db, and advances the processing to step S 306 . Meanwhile, if the start phase angle θa is not inside the prohibited section Xv, the CPU  30  advances the processing to step S 304 . 
     In step S 304 , the CPU  30  (as second phase control unit  36 ) determines whether or not the start phase angle θb is inside the prohibited section Xv. The start phase angle θb being inside the prohibited section Xv means that the start phase angle θb is included in the prohibited section Xv. If the start phase angle θb is inside the prohibited section Xv, the CPU  30  advances the processing to step S 310 . In step S 310 , the CPU  30  (as second phase control unit  36 ) determines whether or not Damax and Dbmax meet the second requirement. This determination process is similar to step S 330 . If the second requirement is met, the CPU  30  advances the processing to step S 320 . In other words, Damax is selected as the shift amount Da, and Dbmax is selected as the shift amount Db. If the second requirement is not met, the CPU  30  advances the processing to step S 311 . In step S 311 , the CPU  30  (as second phase control unit  36 ) selects Damax as the shift amount Da, selects Dbmin as the shift amount Db, and advances the processing to step S 306 . Meanwhile, if the start phase angle θb is not inside the prohibited section Xv, the CPU  30  advances the processing to step S 305 . 
     In step S 305 , the CPU  30  (as second phase control unit  36 ) selects 0 degrees as the shift amount Da, selects 0 degrees as the shift amount Db, and advances the processing to step S 306 . This means that the start phase angle is not substantially corrected (shifted). 
     In step S 306 , the CPU  30  (as second phase control unit  36 ) decides the start phase angle θa′ using the shift amount Da selected in step S 305 , S 311 , S 320  or S 331 . Furthermore, the CPU  30  (as second phase control unit  36 ) decides the start phase angle θb′ using the shift amount Db selected in step S 305 , S 311 , S 320  or S 331 . 
     In this manner, the controller  15  decides the start phase angles θa′ and θb′ while changing the prohibited section Xv for each control period. Thereby, harmonic currents are reduced. 
     &lt;Summary&gt; 
     As illustrated in  FIG. 1 , the ceramic heater  23  is an example of a heating unit. The fixing device  12  is an example of a fixing unit that fixes a toner image to a sheet S by applying heat in accordance with the heating unit. The thermistor  25  is an example of an acquisition unit (a temperature detector) for acquiring a measured temperature of the heating unit. The controller  15  is an example of a control unit for controlling the supply of an alternating current to the heating unit. As illustrated in step S 105 , the controller  15  decides the supply rate for each control period, which comprises a plurality of half periods, of the alternating current based on the difference between the target temperature and the measured temperature of the heating unit. As indicated in steps S 106  and S 201 , the controller  15  decides start phase angles which are references of the start of supply corresponding to a supply rate. The same supply rate may be decided over a plurality of control periods. For example, the controller  15  decides that the start phase angles, which are references for the start of supply corresponding to the supply rate, is located outside the prohibited section, and a combination of start phase angles differs for each control period. As illustrated in  FIGS. 4A to 4C , the combination of start phase angles is a combination of the start phase angle applied to the first half of the control period (first half wave and second half wave) and the start phase angle applied to the second half of the control period (third half wave and fourth half wave). As step S 108  illustrates, for each of the plurality of half periods that configure the control period, the controller  15  starts supply of current to the heating unit at a start phase angle. Further, the controller  15  is configured to stop the power supply to the heating unit when the zero cross point of the alternating current arrives. Note that, the controller  15  may have a detection circuit for detecting the zero cross point of the alternating current. Although the harmonic current can be reduced by providing a wide fixed prohibited section, the temperature followability is lowered. In a case where a fixed prohibited section having a narrow width is provided, the temperature followability is improved, but the effect of reducing the harmonic current is reduced. On the other hand, since the controller  15  of the present embodiment changes the combination of start phase angles for each control period, it becomes possible to achieve both temperature followability and a reduction of harmonic currents. 
     For example, as indicated in step S 301 , the controller  15  decides a prohibited section that is changed each control period and is applied to each of a plurality of half periods in the alternating current that configures the control period. As indicated in steps S 305 , S 311 , S 320 , and S 311  the predetermined shift amount is decided so that the start phase angle corrected by the predetermined shift amount is located outside of the prohibited section. As step S 306  illustrates, for each of the plurality of half periods that configure the control period, the controller  15  corrects the start phase angle by a predetermined shift amount. As step S 108  illustrates, for each of the plurality of half periods that configure the control period, the controller  15  starts supply of the alternating current to the heating unit at the start phase angle which has been corrected by the predetermined shift amount. As described above, the controller  15  according to the present embodiment may change the prohibited section Xv for each control period to achieve both temperature followability and a reduction of harmonic currents. 
     Several methods for making the prohibited section variable may be considered. For example, the controller  15  may change the prohibited section for each control period within a predetermined range. In addition, the storage unit  31  may be used as a storage unit that stores a plurality of prohibited sections. In this case, the controller  15  selects one prohibited section from a plurality of prohibited sections stored in the storage unit for each control period. As a result, the prohibited section may be changed each control period. In this case, the controller  15  may select one prohibited section from a plurality of prohibited sections according to a predetermined selection rule. As the selection rule, for example, a rule for randomly selecting one prohibited section from a plurality of prohibited sections may be employed. Further, the prohibited section may be changed by adding or subtracting a triangular wave to or from a basic prohibited section. 
     The heating unit may include the first heater  24 A and the second heater  24 B. The controller  15  decides a first supply rate (for example: Pa) which is a supply rate for the first heater  24 A and a second supply rate (for example: Pb) which is a supply rate for the second heater  24 B. The controller  15  decides a first phase angle (for example: θa), which is a start phase angle corresponding to the first supply rate, and a second phase angle (for example: θb), which is a start phase angle corresponding to the second supply rate. The controller  15  decides a first shift amount (for example: Da) which is a shift amount for the first heater, and a second shift amount (for example: Db) which is a shift amount for the second heater. The controller  15  corrects the first phase angle by the first shift amount, and corrects the second phase angle by the second shift amount. The controller  15  starts supply of the alternating current to the first heater at the first phase angle corrected by the first shift amount for each of the plurality of half periods configuring the control period, and stops supply of the alternating current to the first heater when a zero cross point of the alternating current arrives. The controller  15  starts supply of the alternating current to the second heater at the second phase angle corrected by the second shift amount, and stops supply of the alternating current to the second heater when a zero cross point of the alternating current arrives. 
     The controller  15  obtains the distance |θa−θb| between the first phase angle θa and the second phase angle θb, and the distance |θa′−θb′| between the first phase angle θa−Da where correction is by the first shift amount Da and the second phase angle θb−Db where correction is by the second shift amount Db. The controller  15  may decide the first shift amount Da and the second shift amount Db so that the distance |θa′−θb′| becomes larger than the distance |θa−θb|. Thus, the peak of the harmonic current in the total of the first heater  24 A and the second heater  24 B is reduced. 
     There may be a case where there is no first shift amount and the second shift amount such that the distance |θa′−θb′| becomes larger than the distance |θa−θb|. In this case, the controller  15  may decide the first shift amount and the second shift amount such that the distance between the first phase angle corrected by the first shift amount and the second phase angle corrected by the second shift amount is larger than a predetermined threshold value. 
     The controller  15  may select the first shift amount Da from between the first minimum shift amount (e.g.: Damin) and the first maximum shift amount (e.g.: Damax). The controller  15  may select the second shift amount Db from between the second minimum shift amount (e.g.: Dbmin) and the second maximum shift amount (e.g.: Dbmax). 
     The controller  15  may determine whether or not the first requirement is met. The first requirement is a requirement that the distance between the first phase angle (θa−Damax) corrected by the first maximum shift amount and the second phase angle (θb−Dbmax) corrected by the second maximum shift amount is larger than the distance between the first phase angle and the second phase angle. If the first requirement is met, the controller  15  may select the first maximum shift amount as the first shift amount and select the second maximum shift amount as the second shift amount. 
     If the first requirement is not met, controller  15  may determine whether or not the first phase angle is inside the prohibited section. If the first phase angle is inside the prohibited section, the controller  15  may determine whether or not the second requirement is met. The second requirement is that the distance between the first phase angle corrected by the first maximum shift amount and the second phase angle corrected by the second maximum shift amount is larger than a predetermined threshold value. If the second requirement is met, the controller  15  may select the first maximum shift amount as the first shift amount and select the second maximum shift amount as the second shift amount. 
     If the second requirement is not met, the controller  15  may select the first minimum shift amount as the first shift amount and select the second maximum shift amount as the second shift amount. 
     If the first phase angle is not inside the prohibited section, the controller  15  may determine whether or not the second phase angle is inside the prohibited section. The controller  15  may select  0  as the first shift amount and select  0  as the second shift amount in a case where the second phase angle is inside the prohibited section. 
     The controller  15  may determine whether or not the second requirement is met if the second phase angle is not inside the prohibited section. If the second requirement is met, the controller  15  may select the first maximum shift amount as the first shift amount and select the second maximum shift amount as the second shift amount. 
     If the second phase angle is not inside the prohibited section and the second requirement is not met, the controller  15  may select the first maximum shift amount as the first shift amount and select the second minimum shift amount as the second shift amount. 
     In a case where any element in the claims is given a reference sign, the reference sign merely indicates an example of the element in the specification and the drawings. Therefore, reference signs should not be used as a basis for a limiting interpretation. 
     Other Embodiments 
     Embodiment(s) of the present invention 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 comprise 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 invention has been described with reference to exemplary embodiments, it is to be understood that the invention 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. 2019-007173, filed Jan. 18, 2019 which is hereby incorporated by reference herein in its entirety.