Patent Publication Number: US-9423751-B2

Title: Image forming apparatus for controlling toner density in developing unit

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an image forming apparatus, and in particular relates to replenishment control for maintaining a toner density in a developing unit at a target density. 
     2. Description of the Related Art 
     A developing unit using a two-component developer including a toner and a carrier detects toner density by a sensor to maintain toner density at a target density (Japanese Patent Laid-Open No. H08-110696). When toner is used for an image formation, the toner is replenished from a toner tank to the developing unit, and the toner and the carrier are mixed by a mixer. 
     In recent years, there is a demand for miniaturization, a reduction in capacity or the like in developing units. If a developing unit is miniaturized, the amount of replenished toner per time increases with respect to the capacity of the developing unit, and there are cases in which the toner and the carrier are not mixed sufficiently. In particular, toner density outputted by a sensor tends to fluctuate immediately after the toner is replenished. This is especially noticeable for a small-scale developing unit. An output value of the sensor repeatedly increases/decreases and finally converges to the actual toner density. Accordingly, if the toner is replenished using toner density acquired from the sensor when the toner and the carrier are not mixed sufficiently, the toner density cannot be controlled to the target density. 
     SUMMARY OF THE INVENTION 
     The present invention controls replenishment of toner to a developing unit at a higher precision. 
     The present invention provides an image forming apparatus comprising a photosensitive member, a latent image forming unit, a developing unit, a circulating unit, a drive unit, a replenishment unit, a detection unit, an aquisition unit, a determining unit, a correction unit, and a controller. The latent image forming unit forms an electrostatic latent image on the photosensitive member. The developing unit includes a container that stores a toner. The circulating unit conveys the toner in a predetermined direction in order to cause the toner to circulate in the container. The developing unit develops the electrostatic latent image using the toner in the container. The drive unit drives the circulating unit. The replenishment unit replenishes the developing unit with toner. The detection unit detects a density of the toner in the container. The acquisition unit acquires information related to a circulation period at which the circulating unit causes the toner to circulate. The determining unit determines a correction condition based on the information acquired by the acquisition unit. The correction unit corrects a detection result of the detection unit based on the correction condition determined by the determining unit. The controller controls the replenishment unit based on the detection result corrected by the correction unit. 
     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 illustrating an example of an image forming apparatus. 
         FIG. 2  is an overview cross-sectional view for illustrating an example of a developing unit. 
         FIG. 3  is a block diagram for illustrating an example of a replenishment controller. 
         FIG. 4  is a flowchart for illustrating an example of a replenishment control. 
         FIGS. 5A and 5B  are views for illustrating an example of characteristics of a bandstop filter. 
         FIG. 6  is a flowchart for illustrating an example of an approach to determining a replenishment amount based on a toner consumption amount. 
         FIGS. 7A and 7B  are views for explaining an effect of an averaging unit. 
         FIG. 8  is a flowchart for illustrating an example of averaging and mask processing. 
         FIG. 9  is a block diagram for illustrating the replenishment controller of a comparative example 1. 
         FIGS. 10A to 10D  are views for explaining an effect of an embodiment. 
         FIGS. 11A to 11D  are views for explaining an effect of an embodiment. 
         FIG. 12  is a block diagram for illustrating a function for adjusting a stopband in accordance with a process speed. 
         FIG. 13  is a flowchart for illustrating a method for adjusting a stopband in accordance with a process speed. 
         FIG. 14  is a flowchart for illustrating a method for adjusting a stopband in accordance with a process speed. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     &lt;Image Forming Apparatus&gt; 
     The present embodiment can be applied to an image forming apparatus for forming an image by an electrophotographic method, an electrostatic recording method, or the like, on an image carrier using for example a photosensitive member, a dielectric or the like. The image forming apparatus forms a latent image corresponding to an image signal on an image carrier, and forms a visible image (toner image) by developing the latent image by a developing apparatus using a two-component developer. Toner particles and carrier particles are principal components of the two-component developer. A visible image is transferred onto a transfer material such as a paper by the image forming apparatus, and is fixed on the transfer material by a fixing apparatus. Also, the image forming apparatus may be any product such as a printer, a copying machine, a multi function peripheral, or a facsimile machine. 
     In  FIG. 1 , an image of an original  31  to be copied is projected to an image sensor  33  such as CCD (Charge Coupled Device) by a lens  32 . The image sensor  33  divides the image of the original  31  into a large number of pixels, and generates a photoelectric conversion signal corresponding to a density (luminance) of each pixel. An analog image signal outputted from the image sensor  33  is transmitted to an image processing circuit  34 . The image processing circuit  34  converts the analog image signal to a pixel image signal having an output level for each pixel that corresponds to the density of the pixel, and transmits that to a pulse width modulation circuit  35 . The pulse width modulation circuit  35  forms and outputs a laser driving pulse for each inputted pixel image signal with a width (duration) corresponding to this level. A driving pulse with a wider width is generated for a high density pixel image signal, and a driving pulse with a narrower width is generated for a low density pixel image signal. A laser driving pulse outputted from the pulse width modulation circuit  35  is supplied to a semiconductor laser  36  which is a latent image forming unit. The semiconductor laser  36  emits only at a time corresponding to the pulse width. Accordingly, the semiconductor laser  36  is driven for a longer time for a high density pixel, and driven for a shorter time for a low density pixel. 
     A rotational polygonal mirror  37  deflects and scans a laser beam  81  emitted from the semiconductor laser  36 . The laser beam  81  is caused to form a spot on a photosensitive drum  40  by a lens  38  such as an f/G lens and a fixed mirror  39 . Then, the laser beam  81  scans on the photosensitive drum  40  in a direction (main scanning direction) substantially parallel to a rotation axis of the photosensitive drum  40 , and thereby forms an electrostatic latent image. Note, there are devices that use a light source other than the semiconductor laser  36  in the present embodiment such as an LED (Light Emitting Diode) array as a latent image forming unit, and the present invention may also be suitably applied to these. 
     The photosensitive drum  40  is an example of the image carrier or the photosensitive member. The photosensitive drum  40  comprises a photosensitive layer of, for example, amorphous silicon, selenium, or an OPC (Organic Photoconductor) on its surface, and rotates in an arrow symbol direction. The photosensitive drum  40  charges uniformly by a primary charger  42  after an electric-charge remover  41  destaticizes uniformly. After that, exposure scanning is executed by the laser beam  81  modulated in accordance with the image signal. Thereby, an electrostatic latent image corresponding to the image signal is formed. A developing unit  44 , which is a developing mechanism, performs inverse developing of an electrostatic latent image using a two-component developer (developing material  43 ) in which the toner particles and the carrier particles are mixed, and forms a visible image (toner image). Inverse developing is a development method for causing a toner that is charged to the same polarity as the latent image to be attached at a region where the surface of the photosensitive drum  40  is exposed by the laser beam  81 , and visualizing that. A transfer charger  49  transfers the toner image to a transfer material  48  held on a carry belt  47 . The endless carry belt  47  is stretched between a roller  45  and a roller  46  and driven in an arrow symbol direction. 
     Note, only one image forming station (including the photosensitive drum  40 , the electric-charge remover  41 , the primary charger  42 , the developing unit  44 , and the like) is shown graphically in order to simplify the explanation. For a color image forming apparatus, for example, four image forming stations corresponding to each color of cyan, magenta, yellow and black are arranged sequentially on the carry belt  47  in its movement direction. Electrostatic latent images for each color, for which a color decomposition of an image of an original is performed, are formed sequentially on the photosensitive drums of each image forming station, are developed by the developing units comprising a toner of each corresponding color, and are sequentially transferred to the transfer material  48  held and conveyed by the carry belt  47 . The transfer material  48  to which the toner image is transferred is separated from the carry belt  47  and conveyed to a fixing unit (not shown), and the toner image is fixed thereon. Also, residual toner remaining on the photosensitive drum  40  after the transfer is removed by a cleaner  50 . 
     Furthermore, in addition to an oscillator  65  for generating a clock pulse for estimating a toner amount used for the image forming, an AND gate  64  and a counter  66  are illustrated in  FIG. 1 . Also, a density sensor  20  for detecting toner density in the developing unit  44 , an amplifier  21 , or the like, are also illustrated. A replenishment controller  110  comprises a CPU  67  and a storage unit  68  and controls a toner replenishment amount. 
     An example of the developing unit  44  is explained with reference to  FIG. 1  and  FIG. 2 . The developing unit  44  is arranged to face the photosensitive drum  40 , and the interior is separated into a first chamber (developing chamber)  52  and a second chamber (mixing chamber)  53  by a partition  51  extending in a vertical direction. The first chamber  52  and the second chamber  53  are examples of containers for storing toner. A non-magnetic developing sleeve  54  rotating in the arrow symbol direction is arranged in the first chamber  52 . The developing sleeve  54  functions as a conveying unit for conveying the developer to the image carrier. A magnet  55  is fixed in the developing sleeve  54 . The developing sleeve  54  carries and conveys two-component developer, supplies the developer to the photosensitive drum  40  in a developing region facing the photosensitive drum  40 , and thereby develops the electrostatic latent image. A thickness of a toner layer on the developing sleeve  54  is regulated by a blade  56 . In order to improve a developing efficiency, i.e. a rate at which toner is added to the latent image, a developing voltage in which a direct current voltage from a power supply  57  is superimposed on an alternating voltage is applied to the developing sleeve  54 . 
     In the first chamber  52 , a screw  58  is arranged. The screw  58  functions as a first circulating unit for, in addition to mixing the two-component developer existing in the first chamber  52 , causing the two-component developer to circulate between the first chamber  52  and the second chamber  53 . In the second chamber  53 , a screw  59  is arranged. The screw  59  functions as a second circulating unit for, in addition to mixing developing material  43  that was present in the second chamber  53  and toner  63  supplied by a toner replenishment basin  60 , causes developing material  43  to circulate between the first chamber  52  and the second chamber  53 . Also, the screws  58  and  59  function as mixing units for mixing a two-component developer within the developing unit  44 . A conveying screw  62  conveys toner of the toner replenishment basin  60  while rotating, and supplies toner from a toner discharging port  61  to the second chamber  53 . By the screw  59  mixing the toner  63  supplied from the toner replenishment basin  60  with the developing material  43  already present in the developing unit  44 , the density of toner particles in the developing material  43  (toner density) becomes uniform. In the partition  51 , paths (not shown) by which the first chamber  52  and the second chamber  53  communicate with each other are formed at a front side end portion and a far side end portion in  FIG. 2 . For the developing material  43  in the first chamber  52 , by developing, the toner is consumed, and the toner density decreases. The developing material  43  in the first chamber  52  moves from a path on one side to within the second chamber  53  by the screw  58 . The developing material  43 , for which the toner density is recovered in the second chamber  53 , moves into the first chamber  52  from the path on the other side by the screw  59 . 
     On a bottom wall of the first chamber (the developing chamber)  52  of the developing unit  44 , the density sensor  20  is installed. The density sensor  20  is a detection unit for detecting a toner density of the developing material  43  present in an internal region of the first developing chamber  52  of the developing unit  44 . Note that the toner density indicates a ratio of toner within the developing material  43  stored in the developing unit  44  (a ratio by weight). The density sensor  20  is an inductance sensor, or the like, for detecting a permeability of the developing material  43 . The density sensor  20  outputs a detected value corresponding to the toner density to the replenishment controller  110 . The replenishment controller  110  functions as a control unit for controlling an amount of toner to replenish the developing unit  44  with so that the toner density detected by the density sensor  20  approaches a target density. Note that the density sensor  20  is an example of an output unit for outputting an output value that changes in accordance with the toner density of a region in a container. 
     The counter  66  is a consumed toner calculation unit according to a video counting method, and counts the level of the output signal of the image processing circuit  34  for every pixel. An output signal of the pulse width modulation circuit  35  is supplied to one input of the AND gate  64 , and a clock pulse from the oscillator  65  is supplied to the other input of the AND gate  64 . Accordingly, the AND gate  64  outputs clock pulses of a number corresponding to the pulse widths of the laser driving pulse, i.e. clock pulses of a number corresponding to the density for each pixel. The counter  66  obtains a video count value by integrating a clock pulse number for each image (an original) (a maximum video count value for an A4 original is 3707×106). A pulse integration signal (the video count value) for each image from the counter  66  corresponds to a toner amount consumed in the developing unit  44  in order to form 1 toner image of the original  31 . There are various counters or the like for counting directly from image data for synchronizing the laser driving pulse other than a video counter such as the counter  66 , and any counter can be applied to the present invention. 
     The replenishment controller  110  determines the replenishment amount for the toner  63  based on the video count value and the output of the density sensor  20 , and controls a motor  70  which is a replenishment unit through a replenishment driver  69 . A driving time and a number of operations for driving of the motor  70  are proportional to the replenishment amount essentially. A driving force of the motor  70  is transmitted to the conveying screw  62  via a gear array  71 . The conveying screw  62  replenishes the developing unit  44  by conveying the toner  63  within the toner replenishment basin  60 . 
     &lt;Replenishment Control&gt; 
       FIG. 3  is a block diagram for the replenishment controller  110  of the embodiment. The replenishment controller  110  in particular comprises a bandstop filter  113  and a first determining unit  114 . The bandstop filter  113  is an example of filter unit for reducing a long period ripple that occurs in accordance with a developer circulation period in accordance with the screws  58  and  59  in the toner density detected by the density sensor  20 . The first determining unit  114  is an example of a first determining unit for determining a first replenishment amount among replenishment amounts based on the toner density for which the long period ripple is reduced by the bandstop filter  113 . For other functions illustrated by  FIG. 3 , explanation is given with reference to  FIG. 4 . A ripple period generated in accordance with a developer circulation period is, for example, 30 seconds, 60 seconds or the like. Meanwhile, a short period ripple occurs in the toner density in accordance with a rotation period (a mixing period) of the screws  58  and  59 . This ripple period is, for example, around 0.1 seconds, 0.2 seconds or the like. The short period ripple is reduced by an averaging unit  121 . 
       FIG. 4  is a flowchart for illustrating an operation of the CPU  67 . The various functions illustrated in  FIG. 3  are realized by the CPU  67  reading a control program from a ROM of the storage unit  68  and executing it when power is supplied from the external power supply to the image forming apparatus and it activates. Note that these functions may be performed by hardware by logic circuits. 
     In step S 201 , the CPU  67  enters a standby state, and determines whether or not an image formation request is received from the operation unit or an external computer. If there is no request for image formation, the CPU  67  proceeds to step S 215 . In step S 215 , the CPU  67  determines whether or not a power OFF was instructed from the operation unit. If a power OFF is not instructed, the CPU  67  returns to step S 201 . If a power OFF is instructed, the CPU  67  executes a shutdown of the image forming apparatus. If there is a request for image formation in step S 201 , the CPU  67  proceeds to step S 202 . 
     In step S 202 , the CPU  67  reads a delay calculation variable of the previous time which is stored in a RAM of the storage unit  68 , and instructs a developing controller  120  for rotation of the screws  58  and  59 . The developing controller  120  drives a motor  72  for a screw driver  122 . The motor  72  causes the screws  58  and  59  to rotate. The motor  72  is an example of a drive unit for driving a circulating unit. The drive unit drives the circulating unit so that the circulation period changes in accordance with the rotating speed of the photosensitive member. 
     In step S 203 , the CPU  67  (a difference unit  111 ) calculates to obtain a difference between an output value of the averaging unit  121  and a target value set by a target value determining unit  112 . The averaging unit  121  has a function for smoothing the output of the density sensor  20 . The averaging unit  121  functions as a calculation unit that averages detection values of the density sensor  20  to reduce short period ripple generated in toner density in accordance with the mixing period. 
     In step S 204 , the CPU  67  (the bandstop filter  113 ) obtains Yn by executing a filter calculation using the following equation with respect to a difference Xn outputted from the difference unit  111 .
 
 Yn=b 0× Xn+Pn− 1  (1)
 
 Pn=b 1× Xn−a 1× Yn+Qn− 1  (2)
 
 Qn=b 2× Xn−a 2× Yn   (3)
 
     Here, Xn is the current output value of the difference unit  111 . Yn is this time&#39;s output value of the bandstop filter  113 . Pn and Qn are delay calculation variables for this time. Pn−1 and Qn−1 are delay calculation variables of the previous time, are read out from the storage unit  68 . The CPU  67  stores the delay calculation variables Pn and Qn obtained by the calculation this time in the storage unit  68 , and uses them in the calculation of the next time. The coefficients a1, a2, b0, b1, and b2 are filter coefficients determined in advance at the time of designing the image forming apparatus, at the time of shipment from the factory, or the like. In the present embodiment, Yn is calculated every 0.1 seconds. 
       FIG. 5A  is a Bode diagram for illustrating a relationship between frequency and gain for the bandstop filter  113 .  FIG. 5B  is a Bode diagram for illustrating a relationship between frequency and phase for the bandstop filter  113 . The solid line illustrates a characteristic of the bandstop filter  113  set such that a 30 second period ripple is reduced. The broken line illustrates a characteristic of the bandstop filter  113  set such that a 60 second period ripple is reduced. In particular, filter coefficients for configuring the bandstop filter  113  of the characteristics illustrated by the solid line are as follows.
 
 a 1=−1.97723  (4)
 
 a 2=0.977668  (5)
 
 b 0=0.990025  (6)
 
 b 1=−1.97723  (7)
 
 b 2=0.987643  (8)
 
     In this way, these filter coefficients are determined in advance in accordance with the ripple period to be reduced. Note that it is possible to change the characteristics of the bandstop filter  113  even by changing the interval (the calculation execution time interval) for executing the calculation of Yn without modifying the filter coefficients. 
     In step S 205 , the CPU  67  (the first determining unit  114 ) determines a first replenishment amount based on the output value Yn of the bandstop filter  113 . The first determining unit  114  is a PI controller (proportional integration controller), which adds the current output value Yn and the accumulated value Tn of the output values up until the previous time to determine a first replenishment amount R1n.
 
 R 1 n=g 1× Yn+g 2× Tn   (9)
 
 Tn=Tn− 1+ Yn   (10)
 
     g1 and g2 are gains, and are coefficients that are set in advance. 
     In step S 206 , the CPU  67  (a second determining unit  116 ) inputs the video count value from the counter  66 . Note that the second determining unit  116  is an example of a prediction unit for predicting a toner amount that was consumed from the developing unit based on the inputted image data. Note that the replenishment driver controls the replenishment unit based on the result of the prediction (the toner amount) by the measurement unit, and the result of the detection that is calculated and corrected by a correction unit. In step S 207 , the CPU  67  (the second determining unit  116 ) determines a second replenishment amount R2n by applying a calculation explained later to a video count value. In step S 208 , the CPU  67  (a totaling unit  117 ) totals the first replenishment amount R1n and the second replenishment amount R2n to obtain a total value Rn (Rn=R1n+R2n). In step S 209 , the CPU  67  (an arithmetic unit  118 ) adds the total value Rn to a buffer value Bn of a replenishment amount (Bn=Bn−1+Rn). Note that the initial value of the buffer value Bn is, for example, zero. 
     In step S 210 , the CPU  67  determines whether or not the elapsed time from when the replenishment driver  69  was instructed for replenishment the previous time exceeds a predetermined amount of time. The CPU  67  counts the elapsed time from when replenishment is instructed using a timer, a counter or the like. The CPU  67  resets the timer to zero when replenishment is instructed. When replenishment is instructed, the replenishment driver  69  drives the motor  70 , causing the screws  58  and  59  to rotate, and replenish the developing unit  44  with the toner  63 . If the elapsed time does not exceed the predetermined amount of time, the CPU  67  proceeds to step S 211 . In this way, the replenishment driver  69  prohibits the replenishment unit from replenishing the developing unit with toner if a predetermined amount of time has not elapsed since the previous time that replenishment was executed by the replenishment unit. If the elapsed time does exceed the predetermined amount of time, the CPU  67  proceeds to step S 213 . The predetermined amount of time is a time for allowing the toner density to become uniform in the developing unit  44 , and is determined in advance by experimentation, simulation, or the like. If the next replenishment is executed in a state in which mixing of the developing material  43  and the toner  63  in the developing unit  44  is insufficient, it will result in a localized dense portion in the toner density in the developing unit  44 . Accordingly, by continuing mixing across a predetermined amount of time from the start of replenishment, and permitting replenishment thereafter, uniformization of the toner density is achieved. 
     In step S 211 , the CPU  67  (the arithmetic unit  118 ) determines whether or not the buffer value Bn reaches a predetermined unit replenishment amount r or greater. If the buffer value Bn is the unit replenishment amount r or greater, the CPU  67  proceeds to step S 212 . If the buffer value Bn is not the unit replenishment amount r or greater, the CPU  67  proceeds to step S 213 . 
     In step S 212 , the CPU  67  (the arithmetic unit  118 ) in addition to instructing the replenishment driver  69  for replenishment, subtracts the unit replenishment amount r from the buffer value Bn. The replenishment driver  69 , in accordance with the instruction, drives the motor  70  to replenish the developing unit with the toner  63 . 
     In step S 213 , the CPU  67  determines whether or not to continue mixing by the screws  58  and  59 . For example, the CPU  67  determines that mixing should be continued if image formation by an image formation request detected in step S 201  continues. Also, the CPU  67  determines that mixing should be stopped if image formation terminates. If mixing continues, the CPU  67  returns to step S 203 , and the CPU  67  calculates the next difference. If mixing should be stopped, the CPU  67  proceeds to step S 214 . In step S 214 , the CPU  67  causes various calculated values (example: the delay calculation variables Pn and Qn, the buffer value Bn, or the like) to be stored in the storage unit  68 . Note that the buffer value Bn, the first replenishment amount R1n, the second replenishment amount R2n or the like are reset to zero. After that, the processing returns to step S 201 . In this way, the sequence of processing from step S 203  to step S 213  is something that is performed every 0.1 seconds, for example. For that reason, the unit replenishment amount r corresponds to a toner amount replenished every 0.1 seconds. 
     &lt;Second Replenishment Amount Determination Method&gt; 
     In the present embodiment, the processing for determining the replenishment amount for which the output value of the density sensor  20  is fed back is executed in intervals of 0.1 seconds during operation of the screws  58  and  59 . However, the video count value is an integrated value for 1 image. If the integrated value is converted into a replenishment amount unchanged, the replenishment amount for every 0.1 seconds will be excessive. This is because the first replenishment amount R1n is determined based on an output value of the density sensor  20  which is output every 0.1 seconds. Accordingly, the second replenishment amount R2n determined based on the video count value is made to be a replenishment amount distributed every 0.1 seconds. Accordingly, the second determining unit  116  outputs a replenishment amount based on the video count value divided over a predetermined number of times. 
       FIG. 6  is a flowchart for illustrating an operation of the CPU  67  (the second determining unit  116 ). The second determining unit  116  starts a calculation for determining the replenishment amount at the same time as starting rotation of the screws  58  and  59 . 
     In step S 301 , the second determining unit  116  reads out a calculated value of the previous time from the storage unit  68 . In step S 302 , the second determining unit  116  inputs the video count value (the integrated value) from the counter  66 . Step S 302  is performed every 0.1 seconds across a period in which the screws  58  and  59  are rotating, but until an integration of the video count value for 1 image ends, 0 is input as the video count value. At the point in time when the integration ends, the integrated value is inputted one time. 
     In step S 303 , it is determined whether or not the video count value that the second determining unit  116  inputted is 0. If the video count value is 0, the second determining unit  116  proceeds to step S 307  without modifying the current second replenishment amount. If the video count value is not 0, the second determining unit  116  proceeds to step S 305 . 
     In step S 305 , the second determining unit  116  determines a second replenishment amount U2k. The second replenishment amount U2k is determined by the following formula, for example.
 
 U 2 k=g 2×( U 2 k− 1× C+V )÷ D   (11)
 
     Here, U2k is the second replenishment amount determined this time. Here, U2k−1 is the second replenishment amount determined the previous time. V is the inputted video count value (the integrated value). D is the number of divisions. C is a current value of the division counter. The division counter C is an integer greater than or equal to 0, and an initial value is the number of divisions D. Until the division counter C becomes 0, it is decremented by 1 every 0.1 seconds in step S 308 . 
     Note that the second replenishment amount U2k is updated every execution of step S 305 . In other words, the second replenishment amount U2k is used as R2n without being updated until step S 305  is executed or the count value C becomes zero. Incidentally, before the first video count value is input, and replenishment of toner of a replenishment amount corresponding thereto finishes, the next video count value is input. In other words, it is necessary to carry over the remaining amount in the total replenishment amount for the first video count value to the replenishment amount for the next video count value. U2k−1×C has the meaning of this carried over replenishment amount. For example, when the next video count value is input immediately for the first video count value, C is still a large value, and a large portion of the replenishment amount corresponding to the first video count value is carried over. If C is zero, the replenishment amount corresponding to the first video count value is not carried over. 
     In this way, if the division counter C is not 0, the output of the division replenishment amount for the video count value of the previous time is not terminated. For this reason, as is illustrated in formula (11), the second determining unit  116  obtains the second replenishment amount U2k by totaling the remaining replenishment amount (U2k−1×C) and the video count value V input newly. If the division counter C is 0, the second determining unit  116  determines the second replenishment amount U2k from the video count value V of this time. The second replenishment amount determined here is subsequently used as the second replenishment amount R2n (R2n=U2k). 
     In step S 306 , the second determining unit  116  sets the number of divisions D to the division counter C.
 
 C=D   (12)
 
     In step S 307 , the second determining unit  116  determines whether or not the division counter C is 0. Because the division replenishment based on the video count value V is not completed if the division counter C is not 0, the second determining unit  116  proceeds to step S 308 . In step S 308 , the second determining unit  116  subtracts 1 from the division counter C. Meanwhile, because if the division counter C is 0, the division replenishment is completed, the second determining unit  116  proceeds to step S 309 . In step S 309 , the second determining unit  116  sets the second replenishment amount R2n to 0. 
     In step S 310 , the second determining unit  116  outputs the second replenishment amount R2n to the totaling unit  117 . In step S 311 , the second determining unit  116  determines whether or not mixing should be continued. The method of the determination of step S 311  is similar to that of step S 213 . If mixing should be continued, the second determining unit  116  returns to step S 302 . If mixing should be stopped, the second determining unit  116  proceeds to step S 312 . In step S 312 , the second determining unit  116  causes the division counter C and the second replenishment amount R2n to be stored in the storage unit  68 . 
     &lt;Processing Accompanying Introduction of Bandstop Filter&gt; 
     While the screw  58  is rotating, a ripple of a particular frequency occurs in the detected values of the density sensor  20 . A long period ripple frequency is the reciprocal of the toner circulation period. The bandstop filter  113  is arranged in order to reduce this long period ripple in the detected value of the density sensor  20 . Furthermore, a short period ripple occurs in accordance with the mixing period (rotation period) of the screw  58 . While the ripple period accompanying toner circulation is around 30 seconds, the ripple period accompanying the rotation period is around 0.1 seconds. The numerical values of these periods are merely examples. Accordingly, a unit for reducing a short period ripple is necessary. Note that while the screw  58  is rotating, detected values of the density sensor  20  are acquired at predetermined intervals. 
       FIG. 7A  exemplifies detected values D1 o the density sensor  20 , a moving average D2 of the detected values, and average values D3 accompanying an initial mask.  FIG. 7B  is a view for magnifying a portion of an interval in which the initial mask is applied in  FIG. 7A . In  FIG. 7A  and  FIG. 7B , a solid line illustrates the detected values D1 of the density sensor  20 . The broken line illustrates the moving average D2 of the detected values. The dashed-dotted line illustrates the average values D3 accompanying the initial mask. 
     As is illustrated by the solid line of  FIG. 7A  and  FIG. 7B , the detected values D1 of the density sensor  20  pulsate accompanying the rotation of the screw  58 . This is because the toner density of the developing material  43  detected by the density sensor  20  varies in accordance with the rotation period of the screw  58 . Accordingly, the averaging unit  121  averages the detected values D1 in accordance with the rotation period of the screw  58 , and outputs the average values to the difference unit  111 . 
     In a case where a replenishment amount is calculated for each page, if averaging is executed with a sufficient margin from when the screw  58  starts rotating, the short period ripple will become smaller. However, for the bandstop filter  113 , detected values of the density sensor  20  in a predetermined interval when the screw  58  is rotating are necessary. In other words, average values are necessary immediately when the screw  58  starts rotating. 
     As the broken lines of  FIG. 7A  and  FIG. 7B  illustrate, when the moving average D2 is obtained for the detected values D1 of the density sensor  20  simply, the moving average D2 does not converge at the point where rotation of the screw  58  starts. Accordingly, the averaging unit  121  performs averaging processing by a flow illustrated in  FIG. 8 . In particular, the averaging unit  121  executes averaging by masking an unstable region generated across a predetermined period immediately after the rotation of the screw  58  starts. This brings about an effect that the memory capacity required for the calculation can be reduced. In this way, the averaging unit  121  is an example of a masking unit that masks the toner density output from the density sensor  20  across a predetermined period from when the screws  58  and  59  start operation so that it is not reflected in the first replenishment amount R1n. 
     Using  FIG. 8 , explanation will be given for an averaging calculation that the averaging unit  121  executes. The averaging unit  121  starts a calculation for averaging when the screws  58  and  59  start rotating. 
     In step S 401 , the averaging unit  121  reads from the storage unit  68  the last averaging output value (an average value) saved when the screws  58  and  59  stopped the previous time. In step S 402 , the averaging unit  121  sets the mask counter Cm and the accumulation counter Ca to 0. The mask counter Cm is a counter for managing the target of masking in the detected values D1 of the density sensor  20 . The accumulation counter Ca is a counter for counting how many times the detected values D1 are accumulated. In step S 403 , the averaging unit  121  adds 1 to the accumulation counter Ca. In step S 404 , the averaging unit  121  determines whether or not the mask counter Cm reaches a predetermined value Cmx. The predetermined value Cmx indicates a total number of the masked average value. If the mask counter Cm is the predetermined value Cmx, the averaging unit  121  proceeds to step S 406 . If the mask counter Cm is not the predetermined value, the averaging unit  121  proceeds to step S 405 . In step S 405 , the averaging unit  121  adds 1 to the mask counter Cm. 
     In step S 406 , the averaging unit  121  adds (an accumulation calculation) the current detected value D1 of the density sensor  20  to the accumulated value Da of the detected value D1. In step S 407 , the averaging unit  121  determines whether or not the accumulation counter Ca reaches the predetermined value Cax. If the accumulation counter Ca does not reach the predetermined value Cax, the averaging unit  121  skips step S 408  and step S 409  and proceeds to step S 410 . The predetermined value Cax is the accumulated total number of the detected values D1, and is predetermined. If the accumulation counter Ca the predetermined value Cax reaches the predetermined value Cax, the averaging unit  121  proceeds to step S 408 . 
     In step S 408 , the averaging unit  121  sets the accumulation counter Ca to 0. In step S 409 , the averaging unit  121  determines whether or not the mask counter Cm reaches a predetermined value Cmx. The value of the predetermined value Cmx, as  FIG. 7B  illustrates, corresponds to the time from the time at which the screw  58  starts rotating to the time at which the moving average D2 finally converges with the average values D3. If the mask counter Cm does not reach the predetermined value Cmx, the initial change component remains in the detected value D1, and so it should be masked. Accordingly, the averaging unit  121  proceeds to step S 410 . Note that, if the mask counter Cm reaches the predetermined value Cmx, the initial change component does not remain in the detected values D1, and so masking is not necessary. Accordingly, the averaging unit  121  proceeds to step S 411 . 
     In step S 410 , the averaging unit  121  sets an average value D3′ of the previous time stored in the storage unit  68  as the average value D3 output to the difference unit  111 . In step S 411 , the averaging unit  121  obtains the average value D3 by dividing the accumulated value Da by the predetermined value Cax which is the accumulation number. In step S 412 , the averaging unit  121  outputs the average value D3 to the difference unit  111 . In step S 413 , the averaging unit  121  determines whether or not mixing should be continued. This is determination processing similar to that of step S 213  and step S 311 . If mixing should be continued, the averaging unit  121  returns to step S 403 . If mixing should be stopped, the averaging unit  121  proceeds to step S 414 . In step S 414 , the averaging unit  121  causes the last average value D3 to be stored in the storage unit  68 . 
     In this way, in accordance with this embodiment, by using the bandstop filter  113 , a long period ripple that occurs in the toner density depending on the toner circulation period can be reduced. Furthermore, by using the averaging unit  121 , a short period ripple that occurs in the toner density depending on the mixing period of the screws  58  and  59  can be reduced. Furthermore, by masking the toner density acquired in a predetermined period from when rotation of the screws  58  and  59  starts among the detected values of the toner density, an influence of an initial rotation change component can be reduced. Note that, by using the average value D3′ of detected values in the past in the predetermined period, it is possible to prepare data necessary for the bandstop filter  113 . 
     Comparative Example 1 
     Explanation will be given comparative example 1 to explain the effect of the embodiment. Comparative example 1 is something that omits the bandstop filter  113  and the averaging unit  121  from the embodiment. Note that comparative example 1 is not prior art. 
       FIG. 9  is a block diagram for the replenishment controller of comparative example 1. Because the averaging unit  121  is omitted, the difference unit  111  calculates the difference Xn between a detected value D1n from the density sensor  20  and a target value Dt determined by the target value determining unit  112 . Also, because the bandstop filter  113  is omitted, the first determining unit  114  determines as the first replenishment amount R1n a sum of something for which a predetermined gain g1 is multiplied with the difference Xn of this time, and something for which a predetermined gain g2 is multiplied with the accumulated value Tn of the difference up until the previous time.
 
 R 1 n=g 1× Xn+g 2× Tn   (13)
 
 Tn=Tn− 1+ Xn   (14)
 
     Note that the second replenishment amount R2n of comparative example 1 is the same as that of the embodiment. The flowchart of comparative example 1 is something that omits steps related to the bandstop filter  113  and the averaging unit  121  from the flowchart of the embodiment. Specifically, steps that are omitted are the variable read out of step S 202  and the filter calculation of step S 204 , or the like. 
     Comparative Example 2 
     The comparative example 2, is something in which in step S 207  of the first embodiment, processing for dividing the replenishment amount based on the video count value illustrated in  FIG. 6  over a predetermined number of times and outputting is omitted. In other words, the replenishment amount converted from the video count value (the integrated value for 1 image) is reflected in the total value in one go. Note that comparative example 2 is not prior art. In the comparative example 2, processing other than the processing illustrated in  FIG. 6  and that of step S 207  of the embodiment is the same as in the embodiment. In other words, the block diagram of the comparative example 2 is the same as in  FIG. 3 . Also, the mask processing illustrated in  FIG. 8  is used. For the second replenishment amount R2n, when V that is not zero is input, calculation is performed by the formula (15). When V is zero, the second replenishment amount R2n becomes zero.
 
 R 2 n=g 2× V   (15)
 
     &lt;Explanation of Effect of Replenishment Control of Embodiment&gt; 
     Explanation is given for an effect of the embodiment by comparing the embodiment with comparative example 1 and the comparative example 2.  FIG. 10A  illustrates output values of the density sensor  20  in the embodiment.  FIG. 10B  illustrates output values of the density sensor  20  in comparative example 1. Note that equivalent feedback gains are set for the output values of the embodiment and the output values of comparative example 1 respectively.  FIG. 10C  illustrates an output value for when the gain of comparative example 1 caused to be lower than in the embodiment. 
     It can be seen by comparing  FIG. 10A  and  FIG. 10B  that the embodiment can reduce a plurality of ripples for which the periods differ sufficiently by the averaging processing and the filter. In other words, in the embodiment, the output values converge quickly to the target value. In comparative example 1, because a feedback gain that is equivalent to that of the embodiment is set, large ripples occur in the output values. This is because the toner cannot be mixed sufficiently due to the miniaturization of the developing unit  44 . In other words, in comparative example 1, developer for which the toner density is not uniform in the detection unit of the density sensor  20  pours in. Its influence is fed back for the toner replenishment amount, and control oscillation occurs. In order to prevent this oscillation, lowering of the feedback gain can be considered. However, when the feedback gain is lowered, the capability of the output value to return to the target value is degraded, as is illustrated in  FIG. 10C . Accordingly, once the output values deviate from the target value due to an external disturbance, the state of deviation continues for a long time. 
     In contrast to this, in the embodiment, the change in the output values of the density sensor  20  depending of the toner circulation period can be reduced by the bandstop filter  113 . Also, the change in the output values of the density sensor  20  in accordance with the mixing period can be reduced by the averaging unit  121 . Accordingly, in the embodiment, the influence of change on the feedback control decreases, and good trackability with respect to the target value, and good convergence can be realized. 
     Also, in the embodiment, the calculation period of the bandstop filter  113  may be synchronized to the operation of the screws. This means that the calculation period of the bandstop filter  113  is not influenced by the size of the image. 
       FIG. 10D  illustrates output values of the density sensor in comparative example 2. Comparing  FIG. 10D  and  FIG. 10A , in  FIG. 10D , in several places ripples of the waveform becomes large.  FIG. 11A  illustrates a total value that the totaling unit  117  of the embodiment outputs.  FIG. 11B  illustrates a replenishment buffer value in the arithmetic unit  118  of the embodiment.  FIG. 11C  illustrates a total value that the totaling unit  117  of the comparative example 2 outputs.  FIG. 11D  illustrates a replenishment buffer value in the arithmetic unit  118  of the comparative example 2. 
     In the comparative example 2, the calculation of the replenishment amount is executed in fine steps in synchronization with the operation of the screw as in the embodiment. For this reason, as  FIG. 11C  illustrates, there are cases where the video count value inputted discretely becomes a relatively large value. In other words, in the comparative example 2, there are cases of excessive replenishment amounts. This is the cause of the ripples illustrated in  FIG. 10D . 
     In contrast to this, in the embodiment, the video count value is distributed with good balance and reflected in the replenishment amount as  FIG. 11A  illustrates. For this reason, in the embodiment, as  FIG. 10A  illustrates, the output values of the density sensor  20  transition well. 
     &lt;Adjustment of Stopband in Accordance with Process Speed&gt; 
     The image forming apparatus has multiple process speeds (also referred to as an image forming speed, a conveying speed or the like), and the process speed is switched in accordance with the characteristics (the thickness, material, or the like) of a recording medium such as the transfer material  48 , or the like. For example, when forming an image on thick paper, the process speed is slower than the process speed for a normal paper. This is because in order to fix toner on a thick paper, it is necessary to apply more heat to the thick paper in the fixing unit. For this reason, by making the process speed slower, the time over which the thick paper passes through the fixing unit is made to be longer, and an amount of heat applied to the thick paper is increased. 
     As described above, the screws  58  and  59  are driven by the motor  72 , but the rotating speed of the screws  58  and  59  is proportional to the process speed (the image forming speed). This is because the speed at which the toner is consumed is proportional to the process speed, and therefore it is necessary to make the speed at which the toner is caused to circulate also be proportional to the process speed. 
     In this way, when the type of the recording medium is designated, the CPU  67  modifies the process speed in accordance with that type. In other words, the CPU  67  modifies the rotating speeds of the screws  58  and  59 , and the circulation period of the developer also changes. As described above, because a long period ripple corresponds to the developer circulation period, when the circulation period is modified, the ripple period (frequency) also changes. Accordingly, if the CPU  67  adjusts the stopband of the bandstop filter  113  in accordance with the process speed and the type of the recording medium, it can control with higher precision replenishment of the developing unit with toner in an image forming apparatus having a plurality of process speeds. 
     Here, in general, the stopband of the bandstop filter  113  is adjustable by modifying the filter coefficients. However, if the bandstop filter  113  is realized by a digital filter, it is possible to modify the stopband even by modifying the calculation execution time interval of the filter calculation described above. For example, assume that the ripple period for the process speed for a normal paper is 30 seconds, and the calculation execution time interval for the process speed for normal paper is 0.1 seconds. When it is assumed that the ripple period for the process speed for thick paper is 60 seconds, if the calculation execution time interval for the process speed for thick paper is modified to 0.2 seconds, ripples can be reduced. Note that the calculation execution time interval is a temporal interval for execution of 1 calculation loop comprised of step S 203  through step S 213 . This means that if the calculation execution time interval is 0.1 seconds, the calculation loop is executed one time every 0.1 seconds. 
       FIG. 12  is a block diagram for illustrating an example of functions added as functions that the CPU  67  executes. A type specifying unit  151  specifies a type of a recording medium based on information input from an operation unit, a host computer, a sensor or the like. As the sensor, for example, there is an optical sensor for detecting a grammage based on a transmitted light amount of a recording medium, an ultrasonic sensor for detecting a grammage based on an ultrasonic wave transparency amount, or the like. The type specifying unit  151  outputs information indicating the recording medium type to a speed determining unit  152 . In other words, the type specifying unit  151  is an example of a type acquisition unit for acquiring information related to the type of the sheet on which the image is formed by the image forming apparatus. The drive unit drives the circulating unit based on information related to the type of the sheet acquired by the type acquisition unit. The drive unit adjusts the conveying speed at which toner is conveyed by the circulating unit based on information related to the type of the sheet. The speed determining unit  152  determines the process speed based on information indicating the type of the recording medium (examples: normal paper, thick paper, etc.), and outputs the process speed to a band adjustment unit  153 . Also, the speed determining unit  152  determines the rotating speed of the screws  58  and  59  based on the process speed, and sets the developing controller  120 . Note that the storage unit  68  may hold information such as a database or a table indicating a correspondence relationship with process speeds and information indicating types of the recording medium. Also, the storage unit  68  may hold a conversion function, a database, or a table or the like indicating a correspondence relationship between process speeds and rotating speeds of the screws  58  and  59 . With this, the speed determining unit  152  may determine the rotating speed and the process speed with reference to the information stored in the storage unit  68 . The band adjustment unit  153  adjusts the stopband of the bandstop filter  113  in accordance with the process speed. The band adjustment unit  153  adjusts the stopband to reduce a 30 second period ripple if, for example, the process speed is a first process speed V1. Also, the band adjustment unit  153  adjusts the stopband to reduce a 60 second period ripple if, for example, the process speed is a second process speed V2. The first process speed V1 is a process speed for a normal paper and the second process speed V2 is a process speed for a thick paper. Note that if the above described filter calculation is executed, the band adjustment unit  153  may adjust the stopband by setting the calculation execution time interval. The bandstop filter  113  operates in accordance with the stopband set by the band adjustment unit  153 , and reduces a long period ripple. The storage unit  68  may store a conversion function, a database, or a table or the like indicating a correspondence relationship between process speeds and the stopband. The band adjustment unit  153  may also acquire the stopband with reference to information stored in the storage unit  68  based on the process speed. A timer  154  is a timer for managing the interval at which to execute the sequence of filter calculations from the sampling of the toner density to the replenishment amount calculation. By modifying the calculation execution time interval, the band adjustment unit  153  sets to the timer  154  a calculation execution time interval in accordance with the process speed in a case where the stopband is adjusted. The storage unit  68  may store a conversion function, a database, or a table or the like indicating a correspondence relationship between process speeds and calculation execution time intervals. The band adjustment unit  153  may also acquire the calculation execution time interval with reference to information stored in the storage unit  68  based on the process speed. Note that the band adjustment unit  153  may acquire a filter coefficient corresponding to the process speed from the storage unit  68  and set it to the bandstop filter  113 . 
       FIG. 13  is a flowchart illustrating steps added to the filter operation processing illustrated in  FIG. 4 . Step S 501  through step S 503  are added between step S 202  and step S 203  illustrated in  FIG. 4 . In step S 501 , the CPU  67  (the type specifying unit  151 ) specifies a type of a recording medium based on information input from an operation unit, a host computer, a sensor or the like. In step S 502 , the CPU (the speed determining unit  152 ) determines the process speed in accordance with the recording medium type. Note that the process speed is information relating to a circulation period at which the circulating unit causes toner to circulate. The speed determining unit  152  is an example of an acquisition unit for acquiring information related to the circulation period at which the circulating unit causes toner to circulate. The circulation period changes in accordance with the conveying speed at which toner is conveyed by the circulating unit. In step S 503 , the CPU  67  (the band adjustment unit  153 ) adjusts the stopband of the bandstop filter  113  in accordance with the process speed. In this way, the band adjustment unit  153  is an example of a determining unit for determining a correction condition &lt;a filter coefficient&gt; based on information acquired by the acquisition unit. Also, the band adjustment unit  153  is an example of a determining unit for determining a calculation condition &lt;a calculation execution time interval&gt; based on information acquired by the acquisition unit. For a method of adjusting the stopband, there is a method of adjusting a filter coefficient, and a method of adjusting a calculation execution time interval. 
       FIG. 14  is a flowchart illustrating steps added to the filter operation processing illustrated. Here, a step of adjusting the stopband in step S 503  is comprised by step S 601  through step S 603 . In step S 601 , the CPU  67  (the band adjustment unit  153 ) determines the calculation execution time interval in accordance with the process speed. In step S 602 , the CPU  67  resets the timer  154  to zero. In step S 603 , the CPU  67  determines whether or not the calculation time has arrived based on time measured by the timer  154  and the calculation execution time interval. The calculation time arrives periodically every calculation execution time interval. For example, if the calculation execution time interval is 0.2 seconds, the calculation time arrives every 0.2 seconds. When the calculation time arrives, the CPU  67  executes the above described step S 203  through step S 213 . However, when it is determined that mixing should be continued in step S 213 , the CPU  67  returns to step S 602 , resets the timer  154 , and waits for the next calculation time. 
     In this way, by adjusting the stopband of the bandstop filter  113  in accordance with the process speed, a long period ripple whose period changes in accordance with the process speed can be reduced. With this, even in an image forming apparatus with a plurality of process speeds, it is possible to control at a high precision replenishment of the developing unit with toner. Note that the bandstop filter  113  is an example of a correction unit for correcting a detection result of the detection unit based on a correction condition determined by the determining unit. Also, the replenishment driver  69  is an example of a controller for controlling the replenishment unit based on the detection result corrected by the correction unit. The bandstop filter  113  is an example of a calculation unit for calculating the amount of toner with which to replenish the developing unit from the output value outputted from the output unit based on the calculation condition determined by the determining unit. The replenishment driver  69  is an example of a controller for controlling the replenishment unit based on an amount calculated by the calculation unit. 
     Incidentally, the fixing unit, the photosensitive drum  40 , the carry belt  47  and the conveyance roller arranged for a conveyance path rotate at a circumferential speed matching the process speed. As described above, the screws  58  and  59  rotate at a rotating speed proportional to the process speed. In other words, the motor  72  drives not just the screws  58  and  59  but also other rotating members. Also, other rotating members may be driven by other motors. In any case, the screws  58  and  59  rotate at a rotating speed proportional to the process speed. For this reason, the frequency of the long period ripple changes in accordance with the process speed. 
     CONCLUSION 
     In accordance with this embodiment, the replenishment controller  110  is provided with the bandstop filter  113  and the first determining unit  114 . The bandstop filter  113  reduces a long period ripple that occurs in accordance with a toner circulation period in accordance with the screws  58  and  59  in the toner density detected by the density sensor  20 . The first determining unit  114  determines the first replenishment amount R1n based on the toner density for which the long period ripple is reduced by the bandstop filter  113 . With this, it becomes possible to control at a high precision the replenishment of the developing unit  44  with toner. In particular, when aiming for a reduction in capacity or a miniaturization of the developing unit  44 , a long period ripple becomes noticeable. Accordingly, by reducing this long period ripple, replenishment of the developing unit  44  with toner is of a higher precision. In other words, a reduction in capacity and a miniaturization of the developing unit  44  and a precision improvement for replenishment are both achieved where it was difficult to achieve both up until now. 
     As is explained using  FIG. 4 , the bandstop filter  113  is configured so as to execute a filter calculation at predetermined intervals during operation of the screws  58  and  59 , for example. As is explained regarding step S 214 , or the like, the replenishment controller  110  comprises the storage unit  68  for storing a calculation variable used by the bandstop filter  113  when the screws  58  and  59  are stopped. As explained regarding step S 202 , step S 204  or the like, the bandstop filter  113  is configured to execute a filter calculation using the calculation variables Pn and Qn read from the storage unit  68  when the screws  58  and  59  start operation. With this, a ripple is reduced precisely by continuing to use the calculation variables Pn and Qn of the previous time. 
     The replenishment controller  110  may further comprise the averaging unit  121  which masks the toner density output from the density sensor  20  across a predetermined period from when the screws  58  and  59  start operation so that it is not reflected in the first replenishment amount R1n. The averaging unit  121  is an example of a calculation unit for averaging a detection result of the detection unit. Note that the correction unit corrects the calculation result of the calculation unit based on a correction condition (a filter coefficient) determined by the determining unit. Also, the calculation unit averages the output values outputted from the output unit, and calculates an amount from the average value of output values based on the calculation condition determined by the determining unit. As is explained regarding  FIG. 7A  or the like, even if the moving average D2 is obtained for the detected values D1 of the density sensor  20 , the moving average D2 does not converge to an actual value in a predetermined period from when the screws  58  and  59  start operation. Accordingly, it becomes possible to further control replenishment of the developing unit  44  with toner at a higher precision by masking the moving average D2 for the detected values D1 for a predetermined period from when the screws  58  and  59  start operation. 
     Also, the averaging unit  121  may also function as a reduction unit for reducing a short period ripple that occurs in the toner density in accordance with a mixing period of the screws  58  and  59 . As described above, the screws  58  and  59  are driven by a motor and rotate, conveying toner while mixing. Accordingly, a short period ripple occurs in accordance with the rotation period of the screws  58  and  59 . Accordingly, by the averaging unit  121  reducing the short period ripple, it becomes possible to control at a high precision replenishment of the developing unit  44  with toner. Note that the calculation unit averages the output values outputted from the output unit, and calculates an amount of toner with which to replenish the developing unit from the average value of the output values based on a calculation condition determined by the determining unit. 
     As is explained regarding  FIG. 8 , the averaging unit  121  may also hold in the storage unit  68  a toner density (example: a detected value D1, the average value D3, or the like) for when the screws  58  and  59  are stopped. The averaging unit  121  may cause the toner density held in the storage unit  68  to be reflected in the first replenishment amount R1n in place of the masked toner density for the predetermined period when the screws  58  and  59  resume operation. In the bandstop filter  113 , data for the toner density becomes necessary immediately when the screws  58  and  59  resume operation. However, the toner density is not provided in the masking interval. Accordingly, the storage unit  68  stores the toner density when the screws  58  and  59  are stopped, and the averaging unit  121  reads that out and uses it when the rotation of the screws  58  and  59  resumes. With this, when the screws  58  and  59  resume operation, the toner density (average value) is supplied to the bandstop filter  113  immediately. Because the toner  63  is not replenished while the screws  58  and  59  are stopped, the toner density of the developing material  43  does not change. Accordingly, even if the toner density for when replenishing the previous time is used as the toner density for when replenishing this time, a replenishment amount calculation precision is not degraded much. 
     The averaging unit  121  may also function as an averaging unit for obtaining an average value of the toner densities that the density sensor  20  outputs. In such a case, the replenishment controller  110  controls the replenishment amount using the average value of the toner densities. The averaging unit  121  may obtain a moving average value of toner densities that the density sensor  20  outputs. Because not so many detected values of toner density are required to obtain the moving average value, the storage capacity for holding the detected values of toner density is reduced. Additionally, the sample number used in calculating the moving average value (the number of detected values of toner density) is set to a number of an extent to which the short period ripple can be reduced. 
     As is explained using  FIG. 3 , the difference unit  111  may calculate the difference Xn between the toner density (average value) and a target density. In such a case, the bandstop filter  113  reduces the frequency component of a ripple in the frequency components included in the difference by applying a filter calculation to the difference Xn for toner density. Such a frequency passage characteristic of the bandstop filter  113  is a frequency passage characteristic for which the frequency component of the ripple is reduced as is illustrated in  FIG. 5A . In this way, a coefficient necessary for the filter calculation is determined depending on the frequency of the ripple. 
     As is explained using  FIG. 3 , by determining the replenishment amount considering not only the toner density but also the toner consumption amount obtained from the image signal, the toner replenishment amount is controlled stably. In such a case, the counter  66  counts the toner amount consumed in developing an electrostatic latent image based on the image signal. The second determining unit  116  determines the second replenishment amount R2n based on the count value of the counter  66 . The totaling unit  117  totals the first replenishment amount R1n that the first determining unit  114  determines and the second replenishment amount R2n that the second determining unit  116  determines. The CPU  67 , the developing controller  120 , and the toner replenishment basin  60  replenish the developing unit  44  with toner based on the total value of the totaling unit  117 . With this, the toner replenishment amount is controlled stably. Note that, the second determining unit  116  may determine the second replenishment amount R2n by plurally dividing the replenishment amount obtained by converting the count value. The toner consumption amount for 1 image is not ascertained until the count ends. When the toner consumption amount is reflected in the replenishment amount all at once, the replenishment amount is not stable as explained using  FIG. 11C  and  FIG. 11D . This leads to an increase in ripples. Accordingly, by distributing the toner consumption amount for 1 image temporally, and causing it to be reflected in the replenishment amount, the replenishment amount is stable, as is explained using  FIG. 11A ,  FIG. 11B  or the like. In other words, a ripple in the toner density is reduced. 
     There are cases in which a ripple occurs in the developing unit  44 , which is divided into the developing chamber and the mixing chamber. Accordingly, by applying the present embodiment, it becomes possible to control at a high precision replenishment of the developing unit  44  with toner. 
     As is explained using  FIG. 12  through  FIG. 14 , the bandstop filter  113 , the band adjustment unit  153 , or the like adjust a stopband of a long period ripple in accordance with the modified circulation period when the circulation period of the developer is modified. In this way, by adjusting the stopband of the bandstop filter  113  in accordance with the circulation period, a long period ripple whose period changes in accordance with the circulation period is reduced. As described above, because the circulation period and the process speed are correlated, adjusting the stopband in accordance with the process speed is equivalent to adjusting a stopband in accordance with the parameters correlated with the process speed such as the conveying speed, the circulation period, or the like. With this, even in an image forming apparatus with a plurality of process speeds, it is possible to control at a high precision the replenishment of the developing unit with toner. 
     When the process speed is modified, the rotating speed of the conveyance rollers arranged for a conveyance path, the rotating speed of the photosensitive drum  40 , and the rotating speed of a pressure roller of the fixing unit are modified. In other words, the circulation period of developer is linked to the conveying speed of the conveyance rollers arranged for a conveyance path. Similarly, the circulation period of developer is linked to the rotating speed of the photosensitive drum  40 . Similarly, the circulation period of developer is linked to the rotating speed of the pressure roller. Because the long period ripple period (frequency) changes when the circulation period is modified, it is necessary that the stopband of the bandstop filter  113  be adjusted. In the present embodiment, by adjusting the stopband of the bandstop filter  113  the process speed is modified, a long period ripple whose period changes in accordance with the process speed is reduced precisely. 
     The bandstop filter  113 , the band adjustment unit  153 , or the like, modify an execution time interval for the filter calculation for the bandstop filter  113  in accordance with the circulation period when the circulation period is modified. In this way, because the circulation period is correlated with the process speed, as is explained using  FIG. 14 , the stopband of the bandstop filter  113  is adjusted by the execution time interval of the filter calculation being adjusted in accordance with the circulation period. In other words, the bandstop filter  113  reduces the long period ripple having a frequency component in accordance with the circulation period. 
     The conveying speed of the recording medium (the process speed) may be selected from among a first conveying speed and a second conveying speed that is slower than the first conveying speed in accordance with the type of the recording medium. For example, the first conveying speed is a process speed V1 for normal paper and the second conveying speed is a process speed V2 for thick paper. The bandstop filter  113  may execute a filter calculation using a first filter coefficient determined in advance to reduce a ripple of a frequency component in accordance with the circulation period corresponding to the first conveying speed when the first conveying speed is selected for the carry belt  47 . Also, the bandstop filter  113  may execute a filter calculation using a second filter coefficient determined in advance to reduce a ripple of a frequency component in accordance with the circulation period corresponding to the second conveying speed when the second conveying speed is selected for the carry belt  47 . In this way, the stopband of the bandstop filter  113  is adjustable by modifying a filter coefficient without modifying the calculation execution time interval. Also, the stopband of the bandstop filter  113  is adjustable by modifying a filter coefficient without modifying the calculation execution time interval. 
     Because the long period ripple is correlated with the circulation period of the developer, explanation was given for the band adjustment unit  153  adjusting the stopband of the bandstop filter  113  in accordance with the circulation period. As described above, the process speed (the conveying speed of the recording medium) or the like is a parameter that is correlated to the circulation period. Accordingly, the band adjustment unit  153  adjusts the stopband of the bandstop filter  113  in accordance with the process speed. Also, there is a correlation between the process speed and the type of the recording medium. Accordingly, the band adjustment unit  153  may adjust the stopband in accordance with the type of the recording medium. In any case, the stopband is adjusted as appropriate in accordance with frequency and period of the ripple. 
     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. 2015-002596, filed Jan. 8, 2015, which is hereby incorporated by reference herein in its entirety.