JP2019074574A - Image forming apparatus and image forming system - Google Patents

Abstract

To provide a control system and an image forming apparatus that, in density prediction control, can accurately predict density even in the vicinity of a conditional branch point where a density prediction model changes, without significantly reducing accuracy in density prediction.SOLUTION: An image forming apparatus comprises: image forming means that forms toner images on image carriers; a density prediction unit that predicts the density of a predetermined patch image without performing image formation in the image forming means; and an input signal output unit for outputting an input signal for performing density prediction in the density prediction unit. The density prediction unit has a plurality of density prediction functions in advance, has a determination criterion value set thereto for selecting the density prediction function in calculating a predicted density, and selects the density prediction function according to the signal from the input signal output unit. When the signal from the input signal output unit is the determination criterion value or within a certain range including the determination criterion value, the image forming apparatus calculates the predicted density by using the plurality of density prediction functions.SELECTED DRAWING: Figure 24

Description

  The present invention relates to an image forming apparatus and an image forming system.

  The image forming apparatus is affected by short-term fluctuations due to fluctuations in the environment in which the apparatus is installed or in the apparatus, and long-term fluctuations due to temporal changes (aging deterioration) of the photosensitive member and developer. In some cases, the density and density tonality of the output image may differ from the desired density and tonality.

  Therefore, in order to match the density and tonality of the output image to the desired density and tonality in the image forming apparatus, it is necessary to correct the image forming conditions as needed in consideration of various variations thereof.

  As described above, the process of appropriately correcting changes in density and color is generally referred to as calibration, and, for example, forms several pattern images with uniform density on a sheet of paper, a photosensitive member, an intermediate transfer member, etc. The density of the formed pattern is measured and compared with the target value, and various conditions for forming an image are appropriately adjusted based on the comparison result.

  Conventionally, in order to stabilize the density and tonality of the output image described above, as described in Patent Document 1, a specific pattern such as a gradation pattern is formed on a sheet of paper and gradation pattern information read by an image reading unit The image quality stability is improved by feeding back to the image forming conditions such as γ correction.

  In addition, as described above, calibration is required when there are environmental changes or long standing, especially when the power is turned on the first time when environmental changes are likely to occur, or when returning from the power saving mode. Correction of tonality is required. As a technique for performing such calibration when turning on the power, a technique as disclosed in Patent Document 2 has been proposed.

  On the other hand, in recent years, there has been an increasing demand for improvement in usability as well as stability in image quality, particularly productivity improvement by reduction of standby time and downtime, and as described above, for calibration control for image quality stabilization. However, there is a strong demand for control in a shorter time. As a countermeasure technology for shortening the control time, calibration for environment fluctuation and density adjustment after being left for a long time, and control time arising from color measurement of patch imaging and imaging patch are shortened. In addition, concentration prediction control that predicts instantaneously is proposed by modeling the correlation between the fluctuation of the external environment and the fluctuation of the patch, using the fluctuation of the external environment as an input value.

JP, 2000-238341, A Unexamined-Japanese-Patent No. 2003-167394

  However, in the above-described concentration prediction control, when environmental fluctuations, leaving times, and the like are used as input values, the correlation between the input values and the density fluctuations of the patch with respect to the input values is not always the same.

  For example, when changing from a low humidity environment (for example, 10% humidity) to a low humidity environment (for example, 15% humidity) or from a low humidity environment (for example, 10% humidity) to a high humidity environment (for example, 70% humidity) , The correlation will be different. That is, a correlation according to the amount of fluctuation is required.

  At this time, it is conceivable to appropriately select a correlation or correlation model (hereinafter referred to as a concentration prediction model) to be used according to the amount of fluctuation, but the following problems occur.

  That is, since the model structure itself changes before and after the conditional branch point at which the selected concentration prediction model changes, the calculated concentration prediction variation amount is different. At this time, if the model used near the conditional branch point is not accurate, the accuracy of concentration prediction may be significantly reduced.

  The present invention has been made in view of the above-described circumstances, and an object thereof is to use calibration for color and density gradation stabilization control as input values of fluctuations in the external environment. In the concentration prediction control performed by calculating the predicted concentration value, when the concentration prediction model selected according to the variation changes, the accuracy of concentration prediction is not significantly reduced even in the vicinity of the conditional branch point. It is an object of the present invention to provide a control system capable of predicting accuracy and an image forming apparatus equipped with the control system.

In order to achieve the above object, an image forming apparatus according to the present invention is
An electrophotographic image forming apparatus that forms an image on an image carrier based on image data and transfers and fixes the formed image on a recording medium,
An image forming unit that forms a toner image on an image carrier;
A density prediction unit which predicts the density of a predetermined patch image without performing image formation in the image forming means;
And an input signal output unit for outputting an input signal for performing concentration prediction in the concentration prediction unit,
The concentration prediction unit has a plurality of concentration prediction functions in advance.
When calculating the predicted concentration, a judgment reference value for selecting the concentration prediction function is set,
In the image forming apparatus, the density prediction function is selected according to a signal from the input signal output unit.
When the signal from the input signal output unit is within a predetermined range including the determination reference value and the determination reference value, a plurality of concentration prediction functions are used to calculate a predicted concentration.

  According to the image forming apparatus according to the present invention, it is possible to achieve calibration in a short time and with high accuracy for the control of color and density gradation stabilization.

Overall schematic view of the image forming apparatus in the embodiment Print system configuration Concentration prediction block block diagram according to the present invention The figure which shows the flow at the time of automatic gradation correction execution in this execution example The figure which shows the gradation correction table at the time of the automatic gradation correction in a present Example The figure which shows the flow which forms revision LUT from the density forecast value in this execution example The figure which shows the relationship of the initial stage correction | amendment LUT, a basic concentration curve, and a prediction concentration curve in a present Example A diagram showing a prediction LUT created from a predicted density curve in the present embodiment Diagram showing the relationship between the initial correction LUT, the prediction LUT, and the combined correction LUT in this embodiment The figure which shows the flow which calculates predicted density from the picture density prediction model in this execution example Diagram showing the flow of creating a prediction function model in the present embodiment The figure which shows an example of the measurement data for prediction function model creation which concerns on the present Example 1 The figure which shows the prediction function model according to the conditions concerning the present Example 1 The figure which shows the prediction accuracy of the prediction function model classified by condition used in the present Example 1 The figure which shows an example of the measurement data for conditional branch verification in a present Example 1 The figure which shows the fluctuation amount of the measurement data for conditional branch verification in a present Example 1, and the model kind selected. The figure which shows the fluctuation amount of the measurement data for conditional branch verification in the present Example 1. The figure which shows the predicted concentration fluctuation amount and the predicted concentration value which were calculated at the time of conditional branch verification in the present Example 1 FIG. 6 is a view showing an example of measurement values and measurement value variations of the toner concentration sensor in the developing device in the first embodiment. The figure which shows the measurement value with respect to the measurement value of measurement value and measurement value in the developing device in a present Example 1 with respect to a measurement value FIG. 6 is a diagram showing the amount of fluctuation with respect to the measurement value of the toner concentration sensor in the developing device and the model type selected A diagram showing the predicted density fluctuation amount, the predicted density value, and ΔE when the model type is changed with respect to the measurement value of the toner density sensor in the developing device in the present embodiment 1. The figure which shows (DELTA) E at the time of performing the averaging process in the conditional branch point which concerns on a present Example 1 The figure which shows the flow in the case of model type selection with respect to the sensor value fluctuation amount based on a present Example 1 Schematic which shows the relationship between the sensor value fluctuation amount which concerns on a present Example 2, and FB rate of the model to be used Schematic diagram showing the distance from a conditional branch point when calculating the sensor value fluctuation amount according to the third embodiment and the FB ratio of a model to be used

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

Example 1
First, a first embodiment of the present invention will be described.

  In the present embodiment, a method of solving the above-mentioned problems will be described using an electrophotographic image forming apparatus. Although the description will be made by the electrophotographic method, the characteristic points of the control, particularly the matters described in the claims, have the same problem with an ink jet printer, a sublimation printer, etc. and solve the problem using a method described below. Can. Therefore, the claims in each image forming apparatus are claimed to be within the scope of the claims of the patent.

(Image forming device)
(Leader department)
As shown in FIG. 1, the image forming apparatus 100 has a reader unit A. An original placed on the original table glass 102 of the reader unit A is illuminated by a light source 103, and light reflected from the original 101 forms an image on a CCD sensor 105 via an optical system 104. The CCD sensor 105 is composed of red, green and blue CCD line sensors arranged in three rows, and generates red, green and blue color component signals for each line sensor. The reading optical system unit is moved in the direction of the arrow shown in FIG. 1 to convert the image of the original 101 into an electrical signal for each line.

  To determine the white level of the positioning member 107 and the CCD sensor 105 which abuts one side of the original 101 on the original table glass 102 to prevent the oblique placement of the original 101, and performs shading correction in the thrust direction of the CCD sensor 105 The reference white plate 106 of The image signal obtained by the CCD sensor 105 is subjected to A / D conversion by the reader control unit 108, shading correction using a read signal of the reference white plate 106, and color conversion, sent to the printer unit, and processed by the printer control unit. Ru. Further, the reader unit A is connected with an operation unit 20 and a display 218 for the operator to operate copying start and various settings.

(Printer section)
As shown in FIG. 1, the image forming apparatus 100 is a full-color printer of a tandem type intermediate transfer system in which yellow, magenta, cyan and black image forming portions PY, PM, PC and PK are arranged along the intermediate transfer belt 6. is there.

  In the image forming portion PY, a yellow toner image is formed on the photosensitive drum 1Y and is primarily transferred to the intermediate transfer belt 6. In the image forming unit PM, a magenta toner image is formed on the photosensitive drum 1M, and is superimposed on the yellow toner image of the intermediate transfer belt 6 to be primarily transferred. In the image forming units PC and PK, cyan toner images and black toner images are formed on the photosensitive drums 1C and 1K, respectively, and are similarly sequentially superimposed on the intermediate transfer belt 6 and primarily transferred.

  The four color toner images primarily transferred to the intermediate transfer belt 6 are conveyed to the secondary transfer portion T 2 and collectively secondarily transferred to the recording material P. The recording material P on which the four color toner images are secondarily transferred is subjected to heat and pressure by the fixing device 11 to be fixed to the surface, and then discharged to the outside of the machine body.

  The intermediate transfer belt 6 is stretched around and supported by the tension roller 61, the drive roller 62, and the opposite roller 63, and is driven by the drive roller 62 to rotate in the direction of arrow R2 at a predetermined process speed.

  The recording material P pulled out of the recording material cassette 65 is separated one by one by the separation roller 66 and fed to the registration roller 67. The registration roller 67 receives the recording material P in a stopped state and causes the recording material P to stand by, and feeds the recording material P to the secondary transfer portion T2 in timing with the toner image of the intermediate transfer belt 6.

  The secondary transfer roller 64 contacts the intermediate transfer belt 6 supported by the opposing roller 63 to form a secondary transfer portion T2. By applying a positive DC voltage to the secondary transfer roller 64, the toner image charged to the negative polarity and carried on the intermediate transfer belt 6 is secondarily transferred onto the recording material P.

  The image forming portions PY, PM, PC, and PK have substantially the same configuration as that of the developing devices 4Y, 4M, 4C, and 4K except that the colors of the toners are different from yellow, magenta, cyan, and black. In the following, suffixes Y, M, C, and K added to reference numerals to indicate that they are for one of the colors will be collectively described in a case where distinction is not particularly required.

  As shown in FIG. 1, the image forming unit has a charging device 2, an exposure device 3, a developing device 4, a primary transfer roller 7, and a cleaning device 8 arranged around the photosensitive drum 1.

  The photosensitive drum 1 has a photosensitive layer having a negative charge polarity formed on the outer peripheral surface of an aluminum cylinder, and rotates in the direction of arrow R1 at a predetermined process speed. The photosensitive drum 1 is an OPC photosensitive member having a near infrared light (960 nm) reflectance of about 40%. However, it may be an amorphous silicon photosensitive member having a similar reflectance.

  The charging device 2 uses a scorotron charger and irradiates the photosensitive drum 1 with charged particles associated with corona discharge to charge the surface of the photosensitive drum 1 to a uniform negative potential. The scorotron charger has a wire to which a high voltage is applied, a shield unit connected to ground, and a grid unit to which a desired voltage is applied. A predetermined charging bias is applied to the wire of the charging device 2 from a charging bias power supply (not shown). A predetermined grid bias is applied to the grid portion of the charging device 2 from a grid bias power supply (not shown). Although depending on the voltage applied to the wire, the photosensitive drum 1 is charged substantially to the voltage applied to the grid portion.

  The exposure device 3 scans a laser beam with a rotating mirror and writes an electrostatic image of an image on the charged surface of the photosensitive drum 1. A potential sensor (not shown), which is an example of the potential detection means, can detect the potential of the electrostatic image formed on the photosensitive drum 1 by the exposure device 3. The developing device 4 causes toner to adhere to the electrostatic image on the photosensitive drum 1 and develops the toner image.

  The primary transfer roller 7 presses the inner side surface of the intermediate transfer belt 6 to form a primary transfer portion T 1 between the photosensitive drum 1 and the intermediate transfer belt 6. By applying a positive DC voltage to the primary transfer roller 7, the negative toner image carried on the photosensitive drum 1 is primarily transferred to the intermediate transfer belt 6 passing through the primary transfer portion T1.

  An image density sensor (patch detection sensor) 400 is disposed to face the intermediate transfer belt, and measures the image density of unfixed toner. In the present embodiment, although the configuration is such that it is disposed to face the intermediate transfer belt, it is possible to appropriately dispose it including the configuration that is disposed to face the photosensitive drum. An image density sensor disposed on a photosensitive drum or an intermediate transfer belt is a sensor for measuring an image density of unfixed toner, but an image density sensor for measuring a pattern image after fixing is located downstream of the fixing device. It is also possible to arrange, and it is not limited to the image density sensor described in the present embodiment.

  The cleaning device 8 causes the photosensitive drum 1 to rub the cleaning blade, escapes the transfer to the intermediate transfer belt 6, and collects the transfer residual toner remaining on the photosensitive drum 1.

  The belt cleaning device 68 causes the intermediate transfer belt 6 to rub the cleaning blade, escapes the transfer to the recording material P, and collects the transfer residual toner remaining on the intermediate transfer belt 6 after passing through the secondary transfer portion T2. .

(Image processing unit)
FIG. 2 is a diagram showing a print system configuration in the present invention.

  In the figure, reference numeral 301 denotes a host computer, and 100 denotes an image forming apparatus. The host computer 301 and the image forming apparatus 100 are connected by a communication line such as USB 2.0 High-Speed or 1000Base-T / 100Base-TX / 10Base-T (IEEE 802.3 compliant).

  In the image forming apparatus 100, a printer controller 300 controls the overall operation of the printer. The printer controller 300 also has a host I / F unit 302 that controls input and output with the host computer 301, and an input / output buffer 303 for transmitting and receiving data from the control code from the host I / F unit 302 and each communication unit. The printer controller CPU 313 which controls the overall operation of the controller 300, a program ROM 304 in which the control program and control data of the printer controller CPU 313 are built, the control code, the calculations necessary for interpretation and printing of data, or processing of print data RAM 309 used as a work memory for image processing, an image information generation unit 305 that generates various image objects from settings of data received from the host computer 301, and RIP (Raster Im) that expands the image objects into a bitmap image ge Processor) 314, a color processing unit 315 that performs color conversion processing of multiple colors, a tone correction unit 316 that performs tone correction of a single color, and a pseudo that performs pseudo halftone processing such as a dither matrix or error diffusion method. The halftone processing unit 317 has an engine I / F unit 318 that transfers the converted image to the image forming engine unit, and the image is transferred to the image forming engine unit to form an image.

  The above is the flow of image processing of the printer controller at the time of basic image formation, and is indicated by a thick solid line.

  The printer controller 300 manages not only the image formation but also various control operations. A control program for this purpose is provided in the program ROM 304, and a maximum density condition determination unit (Vcont: called development contrast) 306 that performs maximum density adjustment, a predicted density calculation unit 307 that predicts density by the output value from the sensor, etc. A tone correction table generation unit (γLUT) 308 that performs tone correction is included. A detailed description of various control operations in the printer controller will be described later.

  A table storage unit 310 for temporarily storing the adjustment results of the maximum density condition determination unit 306 to the gradation correction table generation unit 308, an operation panel 218 for instructing the operation of the printing apparatus and the execution of the correction process, the printer controller 300 and the operation A panel I / F unit 311 connecting the panel 218, an external memory unit 181 used for storing print data and information of various printing apparatuses, a memory I / F unit 312 connecting the controller 300 and the external memory unit 181; And it is comprised from the system bus 319 which connects each unit.

(Concentration prediction unit)
Next, the predicted density calculation unit in the printer controller will be described with reference to FIG.

  Various signal values from the sensor 200, the timer 201, and the counter 202 provided in the image forming apparatus are input to the predicted density calculation unit 307 in the printer controller. At this time, first, the signal value is input to the input signal value processing unit 320 in the predicted concentration calculation unit. The input signal value processing unit calculates a difference between a signal value storage unit 321 storing basic signal values and a signal value stored in the input signal value and the signal value storage unit 321. And a difference calculation unit 322.

  The signal value processed from the input signal value processing unit is input to the concentration prediction unit 330. The concentration prediction unit includes a concentration storage unit 331 which stores a basic concentration, and a prediction function unit 332 which predicts the concentration from the input value from the input signal processing unit. The prediction function unit has an image density prediction model for calculating the density change amount from the basic density from the input value, and calculates the density change amount calculated here and the basic density stored in the density storage unit. Add together to calculate the current predicted concentration. The image density prediction model will be described later. In addition, acquisition of basic signal values and acquisition of basic concentrations will be described later.

  The calculated predicted density is input to the tone correction table generation unit 308, and a γLUT to be input to the tone correction unit 316 is created. The tone correction method will be described later.

(Basic signal value, basic concentration acquisition)
Next, the method of acquiring the basic signal value stored in the signal value storage unit 321 and the basic concentration stored in the density storage unit 331 described in the above-described density prediction unit will be described.

  The basic density used in the present embodiment is acquired at the time of automatic gradation correction control using an output image (toner image after fixing) formed on a sheet regularly performed as shown in FIG.

  First, when automatic tone correction is executed by the user, an image pattern of 64 tones of each color is formed and output onto paper (S201). The number of gradations is not limited to this.

  The output image is set in the reader unit by the user, and the density of the image pattern is automatically detected (S202).

  Interpolation processing and smoothing processing are performed from the density obtained from the image pattern to obtain the engine γ characteristic of the entire density region. Next, a tone correction table for converting an input image signal into an output image signal is created using the obtained engine γ characteristic and a preset tone target (S203).

  In this embodiment, as shown in FIG. 5, inverse conversion processing is performed so as to match the gradation target.

  When this operation is completed, the density on the paper matches the gray level target in the entire density area.

  Therefore, if a plurality of toner image patterns are formed under the above conditions (S204) and the density is detected using the image density sensor 400 on the intermediate transfer body (S205), the density value becomes the target density on the intermediate transfer body The basic concentration is stored in the concentration storage unit 331 (S206). In this embodiment, after the tone correction table is created, an image pattern of 10 tones of each color is formed, the density value is detected using the image density sensor 400, and the result is stored as the basic density in the density storage unit 331. Do.

  Further, this automatic gradation correction is performed, and the sensor, counter, and timer values at the time of acquiring the basic density are stored in the signal value storage unit 321 as basic signal values (S207).

  In the present embodiment, since the image density prediction model is a model for predicting patch density on the intermediate transfer body, the basic density value is the density value measured on the intermediate transfer body, but, for example, on the recording medium In the case of using a model for predicting the patch density of the image, the basic density value is stored as the patch density on the recording medium. The basic density may be appropriately selected depending on which position the patch density of the image density prediction model is to be handled, and is not limited to the above.

(How to create LUT)
Next, in the present embodiment, a method of reflecting the predicted density value in the LUT will be described.

  First, a tone correction table (hereinafter referred to as a basic correction LUT) is formed according to the engine γ characteristic so as to become a preset gradation target (hereinafter referred to as a gradation LUT) at the time of automatic gradation correction performed by the user. After that, the basic density values of 10 tones of each color described above are obtained. After the automatic tone correction, the input image data is multiplied by the initial correction LUT, and input to the engine. The engine γ characteristic is combined and output, and the output is performed so as to become the target tone LUT.

  After that, for example, when the power is turned on, when returning from sleep, when the environment changes, the predicted density value is acquired at an arbitrary preset timing, and the LUT (hereinafter, composite correction LUT) at the time of image output is obtained using the acquired predicted density value. create.

  A method of creating a combined correction LUT will be described using FIGS. 6, 7, 8 and 9. FIG.

  First, predicted density values are obtained (S301). Next, the obtained predicted density value is plotted for each tone, and a density curve (broken line) corresponding to the predicted density value indicated by the ○ point in FIG. 7 is created (S302).

  In order to correct the density curve of the predicted density value to an initial density curve, inverse conversion is performed, and a prediction LUT as shown by the long broken line in FIG. 8 is created (S303).

  Finally, a composite correction LUT as shown by the long two-dot chain line in FIG. 9 obtained by multiplying the prediction LUT and the initial correction LUT is created (S304), reflected on the output image, and output.

  Note that the concentration curve may be created by a generally used approximation method such as using an approximation formula connecting 10 points.

(Predicted concentration calculation)
The flow for calculating the predicted concentration value is as shown in FIG. Here, in the method described above, a flow for predicting the concentration when the main body is activated in a state where the basic signal value and the basic concentration are obtained in advance will be described.

  First, when the main body is activated, input signal values at the time of activation of the main body are acquired from sensors, timers, and counters provided in the image forming apparatus (S401).

  The difference between the acquired signal value and the basic signal value stored in advance is extracted (S402).

  Next, the extracted difference value is substituted into an image density prediction model formula created based on examination in advance (S403), and a difference value from the basic density of the current density is calculated as a predicted value (S404) ).

  The predicted concentration value at the present time is calculated from the sum of the difference prediction value and the basic concentration value (S405).

(Creating a concentration prediction model)
The image density prediction model can be obtained by formulating information having correlation with the density fluctuation of the image as input information, and using the image density information as output information, based on experimental results. The input information may be environmental information that can be obtained from the sensor 200 immediately after the image forming apparatus is turned on, time information such as an idle time from printing before it can be obtained from the timer 201, the number of toner replenishments that can be obtained from the counter 202, It is the number information such as the idle rotation number.

  The image density prediction model does not necessarily consist of information with the highest correlation to the image density. For example, in the case where environmental information obtained from the sensor 200 has the highest correlation with past information from printing, in printing immediately after power on, the past information can not be obtained because the sensor is not energized. In an image forming apparatus having density fluctuation characteristics highly correlated with past environmental information, in order to perform density correction using an image density prediction model, prediction using current information at the time of printing instead of past environmental information You need to build a model.

  Hereinafter, the procedure of creating in advance an image density prediction model used in the present invention will be described with reference to the flowchart of FIG.

  First, a large number of variation patterns of environmental conditions are prepared, and printing is performed under the conditions to measure environmental conditions and image density (S101).

  The environmental conditions include toner concentration in the developing unit at printing, temperature / humidity at various locations, toner concentration in the developing unit at the time of previous printing, and a leaving time from the previous printing. These are environmental information that can be obtained immediately after the power is turned on. Further, the image density is any of the density of the toner patch on the photosensitive member, the density on the intermediate transfer member, and the density on the print medium.

  Next, the measurement data is divided into identification data and verification data (S102).

  Next, the measurement data is used as environmental fluctuation and image density fluctuation data based on the first data of each experiment day (S103).

  Next, a curve fit is performed on the identification data by using a linear functional expression with each environmental condition as an input variable and the image density of each gradation as an output variable (S104).

  For example, in the following description, the toner concentration in the developing unit, the temperature in the developing unit, the humidity outside the developing unit, and the leaving time from the previous printing are described as input values from the sensor, but are limited thereto is not. In addition, although the description up to the 4-input linear function model is described for the sensor input values described above, the model creation can be performed by performing the same processing even when using the 5-input or more sensor input. It is possible and not limited to this.

  Finally, the prediction errors for the combinations of input variables are compared to obtain an optimum combination of input variables and a linear function model, which is used as an image density prediction model (S106).

  In this embodiment, the sum of the square sum of the prediction error calculated using the identification data and the square sum of the prediction error calculated using the verification data is evaluated, and both identification and verification are considered. A linear function model that provides an optimal combination of input variables is used as an image density prediction model. The sum of squares of prediction errors calculated using the verification data may be compared, and a linear function model having this value may be used.

In this embodiment, the input variables was as simple as a x _{1 (t),} by providing a product or quotient of environmental conditions as _{x 1 (t) × x 2} (t), complex Models can also be considered. For example, it is possible to create an input variable that can express the change in the toner charge amount in consideration of the toner concentration in the developing device and the leaving time, and to study the prediction model.

  In this case, for the sake of simplicity, only the curve fit based on the first data of each experiment day was explained, but by performing the curve fit based on each measured data and evaluating the prediction accuracy with the sum of all prediction errors Furthermore, a prediction model with a smaller error can be obtained.

(Creation model and prediction accuracy)
In this embodiment, one or more of toner concentration in developing unit, developing unit internal temperature, developing unit internal humidity, developing unit internal moisture amount, external environment temperature, external environment humidity, and external environment water content A predicted density model showing the correlation between each input value and the density detected on the intermediate transfer member of the 10 gradation toner patch was created by the method described above. The input value is not limited to this, and the detected density value is not limited to that on the intermediate transfer member.

  In the present embodiment, a case is described in which a plurality of models for density prediction are held in advance in accordance with the environmental fluctuation state and the state of the image forming apparatus before leaving.

In the present embodiment, as an index indicating the difference (prediction error) between the predicted density and the actual density, the difference is calculated as ΔE, which is the difference in chromaticity. ΔE can be represented by a three-dimensional distance (formula 1) in the L * a * b * color space defined by CIE.
ΔE = √ ((L1-L2) ^ 2 + (a1-a2) ^ 2 + (b1-b2) ^ 2)
... (Equation 1)
For example, even in the same density shift amount, in the high density region and the low density region, the distance of the chromaticity point in the L * a * b * color space to the shift amount is different, so ΔE is actually It is effective when evaluating the gap part which feels.

  In this example, in order to evaluate the deviation between the actual measurement value of the patch density of 10 gradations and the prediction value, the evaluation was performed by ΔE.

  Note that Equation 2 was used to convert the deviation ΔD between the actual measurement value and the predicted concentration value into ΔE.

ΔE = ((− 47.03 * (evaluation concentration range) +71.64)) × ΔD
... (Equation 2)
Equation 2 can be calculated by acquiring in advance the relationship between the density and chromaticity of the image forming apparatus to be used and ΔE. Equation 2 changes depending on the type of image forming apparatus and toner used, and is not limited to this.

  FIG. 12 shows an example of measurement data used in the present embodiment. FIG. 12A shows data under environmental conditions. FIG. 12 (b) is data of image density. In the present embodiment, (1) there is no change in temperature and humidity environment, and there is a history change, (2) there is no change in history and there is a change in temperature and humidity environment, (3) history change and temperature and humidity In the case where there is both a change in the environment, and (4) in the absence of both a history change and a change in temperature and humidity environment, the data of were used to create a predicted concentration model based on the flow of FIG. The predicted concentration model created is shown in FIG.

  In the present embodiment, the temperature / humidity environment does not change if the absolute value of the fluctuation amount of the environment humidity is smaller than 5%, if there is no change in the temperature / humidity environment, if it is 5% or more, the temperature / humidity environment changes. It classified as there. Further, as to the presence or absence of the history change before leaving, when the absolute value of the fluctuation amount of the toner density sensor from the previous sampling time point is smaller than 0.1 when sampled, there is no history change before leaving 0.1 The above cases were classified as having a history change before leaving.

  The temperature and humidity environment fluctuation and the threshold value of the history fluctuation before leaving may vary depending on the type of the image forming apparatus and the type of toner, and are not limited to the above.

  Under the conditions as described above, the concentration prediction function was created based on the flow of FIG. 11, and the created concentration prediction function was evaluated. The accuracy evaluation of the concentration prediction function was performed by performing the above-described ΔE calculation in the calculation of the prediction error in the flow of FIG. 11 (S105). That is, the difference between the measured concentration and the predicted concentration was evaluated using ΔE.

  An evaluation result is shown in FIG.

  FIG. 14 shows the case where verification is performed using measurement data according to each variation pattern when the predicted concentration model is individually created according to each variation pattern (1) (2) (3) (4) From the prediction accuracy, it can be seen that the prediction and measurement errors can be predicted with a maximum accuracy of 1.46 and 1.04 on average.

(Predictive accuracy near conditional branch point)
Next, a method of calculating a predicted concentration at a conditional branch point, which is a feature of this embodiment, will be described. As described above, the conditional branching point is a condition under which the created model is switched according to the history fluctuation or the fluctuation amount of the change of the temperature and humidity environment, and in the present embodiment, the condition branch point is a change of the temperature and humidity environment. The absolute value of the fluctuation amount of environmental humidity is 5% at the point of judging presence or absence, and the absolute value of fluctuation amount of the toner density sensor is 0.1 at the point of judging the existence of history change before leaving It is.

  First, a problem that occurs when the model is switched at the conditional branch point will be described. Here, although the case where the absolute value of the variation amount of the history variation is 0.1 will be described, the same applies to the conditional branch point of the temperature and humidity variation.

  As an example, the case where there are environmental humidity and toner concentration in the developing device as shown in FIG. 15 will be described. Further, at this time, numerical values as shown in FIG. When there is a fluctuation as shown in FIG. 15, the fluctuation amount of each sensor value is as shown in FIG. 16 and FIG. In accordance with the absolute value of the fluctuation amount, an individual model corresponding to the above-described four types of fluctuation patterns is selected. In this embodiment, since the absolute value of the variation of the environmental humidity is 5% and the absolute value of the variation of the toner concentration in the developing device is 0.1, the environmental humidity changes up to 23880 seconds. Yes, no change in toner concentration in developing unit, ie no change in temperature / humidity environment, there is a fluctuation in model with fluctuation pattern (1), no change in environmental humidity thereafter, no change in toner concentration in developing unit, ie, It becomes fluctuation pattern (4) with the model which has neither change of the history fluctuation and the change of temperature and humidity environmental fluctuation.

  At this time, for example, the density predicted value when the image DUTY is 60% will be described. The same applies to the other images DUTY, and the present invention is not limited to this.

  The density fluctuation amount when the image DUTY is 60% can be calculated using the model shown in FIG. In addition, the initial density of the image DUTY 60% was 0.572. Therefore, using the models of fluctuation patterns (1) and (4), the predicted density fluctuation amount for each elapsed time and the predicted density value become values as shown in FIG.

  By the way, there is always a variation of several percent in the sensor used. Therefore, even in the case shown in FIG. 16, the sensor values do not necessarily show the same value. The variation in the measured values does not pose a major problem when the concentration prediction model used is the same.

  For example, assuming that the toner concentration sensor value in the developing device shown in FIG. 15 is the central value (pattern A), if the toner concentration sensor in the developing device used has a measurement variation of ± 1%, There is variation in measured values as shown in FIG. At this time, when the concentration prediction model does not change, the upper and lower limits of each measurement variation are alternately measured (pattern B), and the concentration prediction value as shown in FIG. It turns out that it does not change with about .004.

  However, in this case, the concentration prediction model actually changes. FIG. 21 shows the toner concentration value in the developing device, the variation amount, and the density prediction model to be selected in the pattern A and the pattern B.

  As can be seen from FIG. 21, in the pattern A, the selected model at the elapsed time of 16520 sec is the fluctuation pattern (1), while in the pattern B, the density prediction model is changed by being selected as the fluctuation pattern (4) I understand that.

  The predicted density fluctuation amount and the predicted density value at this time, and ΔE of the predicted density values in pattern A and pattern B are shown in FIG.

  As can be seen from this, when the model to be used changes, it is understood that the concentration prediction fluctuation amount largely changes at that point, and the ΔE of the prediction concentration value becomes large.

  Therefore, in the present embodiment, the concentration prediction fluctuation amount is calculated from both models before and after the conditional branching point so that the concentration prediction value is calculated in the vicinity of the conditional branching point so as not to significantly degrade the accuracy of concentration prediction before and after the conditional branching point. calculate.

  In the present embodiment, when the elapsed time is 16520 seconds, the selection model uses both the fluctuation pattern (1) and the fluctuation pattern (4) and calculates the average value of the predicted density fluctuation amount calculated from each of them at that point. Assumed as the predicted concentration fluctuation amount.

  In FIG. 23, the change in toner concentration in the developing device is the density prediction model selected for each of the case of pattern A and the case of pattern B described above, and the predicted density fluctuation amount calculated from the selected model, predicted density Indicates a value.

  As shown in FIG. 23, in the model selected when the change in toner density in the developing device is output as shown in pattern A, the conditional branch point 0.1 of the toner density sensor is obtained when the elapsed time is 16520 sec. Therefore, both models of fluctuation pattern (1) and fluctuation pattern (4) are selected, and the predicted density fluctuation amount is calculated by each model, and the averaged density fluctuation is the predicted density fluctuation amount with an elapsed time of 16520 sec. And On the other hand, the model selected when the pattern B is output is smaller than the conditional branch point 0.1 of the toner density sensor when the elapsed time is 16520 sec, so the model of the fluctuation pattern (4) is used. The predicted concentration value is calculated using the model of the variation pattern (4).

  Further, in FIG. 23, the difference between predicted density values when sensor values are output as in pattern A and pattern B is indicated by ΔE. As can be seen from this, it is possible to prevent a significant decrease in the prediction accuracy by calculating the predicted concentration value using both models crossing the branch point in the vicinity of the conditional branch point as in this embodiment. I understand that

  In this embodiment, although the case where the toner concentration sensor value in the developing device is in the vicinity of the conditional branch point is described, the same applies to the sensor value of the temperature and humidity environment. Further, when both the toner concentration sensor value in the developing device and the temperature / humidity environment sensor value are near the conditional branch point, that is, the absolute value of the fluctuation amount of the environmental humidity is 5%, the absolute value of the fluctuation amount of the toner concentration in the developing device In the case where is 0.1, the amount of concentration fluctuation is calculated with each of the four models (1) (2) (3) (4) according to the fluctuation pattern of the concentration prediction model described above, and then averaged. If the concentration predicted value is calculated, it is possible to prevent the decrease in prediction accuracy near the conditional branch point.

  Further, with regard to the value of the conditional branch point, in the present embodiment, the absolute value of the environmental humidity fluctuation amount is 5%, and the absolute value of the toner concentration fluctuation amount in the developing device is 0.1. It is not a thing. Furthermore, the method of calculating the predicted concentration fluctuation amount from the model across the branch point as described in this embodiment and calculating the predicted density value from the average value is not the value of the branch point alone, but before and after the branch point. It is desirable to set a certain width. It is desirable that the width before and after the branch point be appropriately determined according to the detection accuracy and the fluctuation width of the sensor to be used, or the fluctuation of the environment used when creating the predicted density model.

  For example, the sensor used in this embodiment has a detection fluctuation of about 0.4% for the environmental humidity sensor, while the toner concentration sensor has a detection fluctuation of about 0.04. If the absolute value of the environmental humidity fluctuation amount is 5%, the range of 4.8% to 5.2%, and if the toner concentration sensor 0.1, the range of 0.08 to 0.12 The predicted concentration value is calculated as an average value using both models. The detection fluctuation is not limited to this.

  FIG. 24 illustrates a flow of selecting a model used to calculate the predicted concentration under the conditions as described above.

  First, each sensor input value immediately before the image forming apparatus is left or immediately after the image formation in the image forming apparatus is stored (S501).

  Next, each sensor input value at the instant when the image forming apparatus has risen due to job acceptance or the like is acquired (S502).

  Next, the sensor input value difference acquired in S501 and S502 is calculated (S503), and the difference between the toner density sensors is compared (S504). If the difference between the toner density sensors is 0.08 or more and 0.12 or less, the process proceeds to step S505. If not, the process proceeds to step S510. In S505, the differences of the environmental humidity sensors are compared. If the difference between the environmental humidity sensor is 4.8% or more and 5.2% or less, in S506, the predicted concentration fluctuation amount is calculated in each of (1) (2) (3) (4) of the concentration prediction model. By averaging these, the predicted density fluctuation amount is calculated. If not, the process proceeds to S507.

  In S507, the differences of the environmental humidity sensors are compared again. If the difference of the environmental humidity sensor is smaller than 4.8%, the predicted concentration fluctuation amount is calculated in each of (1) and (3) of the concentration prediction model in S508, and the prediction is performed by averaging them. Calculate the concentration fluctuation amount. If not, in S 509, the predicted density fluctuation is calculated by calculating the predicted density fluctuation in each of (2) and (4) of the density prediction model and averaging the same. If it is determined in S504 that the difference between the toner concentration sensors is not less than 0.08 and not less than 0.12, the process proceeds to S510, and the difference of the toner concentration sensors is compared in S510. If the difference between the toner density sensors is smaller than 0.08, the process proceeds to step S511. If not, the process proceeds to step S516.

In S511, the differences of the environmental humidity sensors are compared. If the difference between the environmental humidity sensor is 4.8% or more and 5.2% or less, in S512, the predicted concentration fluctuation amount is calculated in each of (1) and (2) of the concentration prediction model, and is averaged. Thus, the predicted concentration fluctuation amount is calculated. If not, the process proceeds to S513. In S513, the differences of the environmental humidity sensors are compared again. If the difference of the environmental humidity sensor is smaller than 4.8%, the predicted concentration fluctuation amount is calculated from (1) of the concentration prediction model in S514. If not, in S515, the predicted concentration fluctuation amount is calculated from (2) of the concentration prediction model. If the difference between the toner density sensors is not smaller than 0.08 in S510, the process proceeds to S516.
In S516, the differences of the environmental humidity sensors are compared. If the difference between the environmental humidity sensor is 4.8% or more and 5.2% or less, in S517, the predicted density fluctuation amount is calculated in each of (3) and (4) of the density prediction model, and is averaged. Thus, the predicted concentration fluctuation amount is calculated. If not, the process proceeds to S518. In S518, the differences of the environmental humidity sensors are compared again. If the difference of the environmental humidity sensor is smaller than 4.8%, the predicted concentration fluctuation amount is calculated from (3) of the concentration prediction model in S519. If not, in S520, the predicted concentration fluctuation amount is calculated from (4) of the concentration prediction model.

  As described above, the amount of fluctuation in density prediction control in which calibration for color tone / density gradation stabilization control is performed by calculating the predicted density value by using the fluctuation of the external environment as the input value. When the concentration prediction model selected in accordance with changes in the condition, the prediction concentration is calculated using the model before and after the branch point also near the conditional branch point, without significantly reducing the accuracy of concentration prediction. It is possible to predict to the accuracy.

Example 2
In the first embodiment, when the fluctuation amount of the sensor output value is within the set condition branch point or a certain range provided before and after the condition branch point, both models crossing the branch point or The method of calculating the predicted concentration fluctuation amount and the predicted concentration value under the conditions by calculating the predicted concentration fluctuation amounts respectively using a plurality of models and averaging the calculated predicted concentration fluctuation amounts has been described.

  In the second embodiment, when calculating the predicted density fluctuation, a method of changing the feedback rate (FB ratio) of the predicted density fluctuation calculated from the model to be used according to the sensor output value fluctuation is described. Do.

  The configuration of the image forming apparatus, the method of acquiring the concentration, the model creation flow for performing concentration prediction, and the concentration prediction model created for each fluctuation pattern are the same as in the first embodiment.

  The description in the present embodiment describes, as an example, a method of calculating the predicted density fluctuation amount using a density prediction model with respect to the fluctuation amount of the toner density sensor, but is not limited thereto. Also, similar effects can be obtained with respect to the amount of fluctuation of other sensors.

  In the first embodiment, the branch point of the absolute value of the fluctuation amount of the toner concentration sensor is 0.1 and the swing width before and after the branch point is 0.04. However, in the second embodiment, the branch is performed. Although the case where the point is 0.1 and the swing width before and after the branch point is 0.08 will be described, the present invention is not limited to this.

  This will be described with reference to FIG.

  In FIG. 25, the horizontal axis represents the fluctuation amount of the toner concentration sensor, and the vertical axis represents the FB ratio of the predicted concentration fluctuation amount calculated from the model.

  The model (1) and the model (4) in FIG. 25 are the same as in Example 1 and the concentration prediction models (1) and (4) in FIG. For the density prediction model, model (4), when it is determined that there is no change, and there is a change in toner density sensor, it is determined that there is no change in environmental humidity and no change in toner density sensor. It is a concentration prediction model.

  As can be seen from FIG. 25, in the model (1), the FB ratio is 0% for the absolute value of the fluctuation amount of the toner concentration sensor from 0 to 0.06, and gradually to 0.14 at the border of 0.06 In the case of 0.14, the FB ratio is 100%, and the FB ratio is set to 100% even in the case of 0.14.

  On the other hand, in the model (4), the FB ratio is 100% when the absolute value of the fluctuation amount of the toner concentration sensor is 0 to 0.06, and gradually decreases to 0.14 after 0.06. When it becomes 14, the FB rate is 0%, and the FB rate is set to be 0% even in the case of more than that.

  That is, the FB ratio of each model is expressed by the following equation, where X (−) is the fluctuation value of the toner concentration sensor and Y (%) is the FB ratio.

Model (1)
When X <0.06 Y = 0
When 0.06 ≦ X ≦ 0.14 Y = 100 * (X−0.06) /0.08
When X> 0.14 Y = 100
Model (4)
When X <0.06 Y = 100
When 0.06 ≦ X ≦ 0.14 Y = 100 * (0.14-X) /0.08
When X> 0.14 Y = 0
As an example, the predicted density fluctuation amount of the image DUTY 50% patch in the case of the environmental humidity fluctuation amount 0.6, the environmental water amount fluctuation amount 131.2, and the toner concentration fluctuation amount in the developing device 0.12 is calculated. At this time, consider a model that determines that there is no change in environmental humidity. In this case, since the fluctuation value of the toner concentration sensor is 0.12,
FB ratio of model (1) = 100 * (0.12-0.06) / 0.08 = 75%
FB ratio of model (4) = 100 * (0.14-0.12) / 0.08 = 25%
It becomes.

Referring to the model at the image duty of 50% in FIG. 13, the density fluctuation amount calculated in each model is
Concentration fluctuation amount of model (1) = (-8.07E-02) * 0.1 2 + (-6.63E-03) * 0.6
= -0.00137
Concentration fluctuation amount of model (4) = (-9.97E-02) * 0.12+ (-4.09E-05) * 131.2
= -0.00173
It becomes. Therefore, the predicted concentration fluctuation under the conditions described above is
(Estimated concentration fluctuation)
= (Model (1) predicted concentration fluctuation amount) * (Model (1) FB rate)
+ (Model (4) predicted concentration fluctuation amount) * (Model (4) FB rate)
= (-0.00137) * 0.75 + (-0.00173) * 0.25
= 0.146
It becomes.

  In the above description, although the increase or decrease of the FB rate is calculated by a linear function equation, it is not limited to this, for example, a quadratic function equation, an exponential function equation, etc. may be appropriately used May be

  As described above, when calculating the predicted concentration using the models before and after the conditional branch point, it is possible to predict the concentration from the instantaneous sensor input value by changing the FB ratio of each model. By using the method, it is possible to predict with high accuracy without significantly reducing the accuracy of concentration prediction.

[Example 3]
In the second embodiment, when the fluctuation amount of the sensor output value is within the set condition branch point or a certain range provided before and after the condition branch point, both models crossing the branch point or In the method of calculating the predicted concentration fluctuation amount using a plurality of models, multiplying each calculated predicted concentration fluctuation amount by the FB rate, and calculating the concentration predicted fluctuation amount and concentration predicted value under the conditions, the branch point is crossed. The two models were described.

  In the third embodiment, the case where there are four models crossing the branch point will be described. Note that the method of the FB ratio of the predicted density fluctuation amount calculated from each of the plurality of predicted density models described in the third embodiment is an example, and the present invention is not limited to this.

  The configuration of the image forming apparatus, the method of acquiring the concentration, the model creation flow for performing concentration prediction, and the concentration prediction model created for each fluctuation pattern are the same as in the first embodiment.

  The description in the present embodiment will explain, as an example, a method of calculating a predicted density fluctuation amount using a density prediction model with respect to the absolute value of the fluctuation amount of the environmental humidity and the absolute value of the fluctuation amount of the toner concentration in the developing device. However, it is not limited to this.

  In this embodiment, the branch point of the absolute value of the fluctuation amount of the toner concentration sensor is 0.1, the fluctuation width of around the branch point is 0.08, and the branch point of the absolute value of the fluctuation amount of the environmental humidity sensor is 5.0. Although the case where the swing width before and after the branch point is 0.4 is described, it is not limited to this.

  This will be described with reference to FIG.

In FIG. 26, the vertical axis (Y axis) represents the absolute value of the environmental humidity fluctuation amount, and the horizontal axis (X axis) represents the absolute value of the toner concentration fluctuation amount in the developing device. Each point from A to D in the figure is (X, Y) = (absolute value of toner concentration fluctuation amount in developing unit, absolute value of environmental humidity fluctuation amount), respectively.
A point: (0.06, 0.52)
Point B: (0.06, 0.48)
Point C: (0.14, 0.52)
Point D: (0.14, 0.48)
As described above, the above-mentioned conditional branch points are intersection points.

  The model number shown outside the intersection is the concentration prediction model used in that area, and there is no history variation in the area of X <0.06 and Y> 0.52 which is outside the point A, for example. This means that the predicted concentration fluctuation amount is calculated using the model (2) in the case where there is a change in temperature and humidity environment.

  Here, as an example, the absolute value of the variation of the environmental humidity sensor and the absolute value of the variation of the toner concentration sensor are indicated by x marks (point E) near the center, that is, (X, Y) = (0.08, 0) A method of calculating the predicted density fluctuation amount when it is detected as .49) will be described.

  At point E, the absolute value of the fluctuation amount of the toner concentration sensor is in the range of 0.06 or more and 0.14 or less, and the absolute value of the fluctuation amount of the environmental humidity sensor is in the range of 4.8 or more and 5.2 or less. Models used for prediction span four types.

  When these four types of models are used, the FB ratio of the predicted density variation calculated by each model is changed according to the distance to the intersection between point E and points A to D as an example.

Assuming that the distances from point E to points A to D are a to d,
Distance between two points = ((X1-X2) ^ 2 + (Y1-Y2) ^ 2) ^ 0.5
Because
a = 0.0361
b = 0.0224
c = 0.0671
d = 0.0608
It becomes. If we calculate the reciprocal of this distance respectively,
(1 / a) = 27.7
(1 / b) = 44.7
(1 / c) = 14.9
(1 / d) = 16.4
It becomes.
The FB ratio is determined by the following equation according to the reciprocal of each of the distances.

Model (1) FB ratio (%) = 100 * (1 / c) / ((1 / a) + (1 / b) + (1 / c) + (1 / d)) = 14.4
Model (2) FB ratio (%) = 100 * (1 / a) / ((1 / a) + (1 / b) + (1 / c) + (1 / d)) = 26.7
Model (3) FB ratio (%) = 100 * (1 / d) / ((1 / a) + (1 / b) + (1 / c) + (1 / d)) = 15.8
Model (4) FB ratio (%) = 100 * (1 / b) / ((1 / a) + (1 / b) + (1 / c) + (1 / d)) = 43.1
It becomes.

  That is, although the predicted concentration fluctuation amount at point E is calculated using all of the models (1) to (4), the FB ratio of each model takes into consideration the distance to each intersection of A to D, and in this case Since the closest to the point B, the FB rate of the model (4) is the highest, and the farthest to the point C, the FB rates of the model (1) are the lowest. decide.

  As described above, when calculating the predicted concentration using the models before and after the conditional branch point, the FB ratio of each model is changed according to the distance from each conditional branch point, from the instantaneous sensor input value It is possible to predict the concentration, and by using this method, it is possible to predict with high accuracy without significantly reducing the accuracy of concentration prediction.

1 photosensitive drum, 2 charging device, 3 exposure device, 4 developing device, 6 transfer device,
200 Intermediate Transfer Over Image Density Sensor, 300 Printer Controller

Claims (7)

An electrophotographic image forming apparatus that forms an image on an image carrier based on image data and transfers and fixes the formed image on a recording medium,
An image forming unit that forms a toner image on an image carrier;
A density prediction unit which predicts the density of a predetermined patch image without performing image formation in the image forming means;
And an input signal output unit for outputting an input signal for performing concentration prediction in the concentration prediction unit,
The concentration prediction unit has a plurality of concentration prediction functions in advance.
When calculating the predicted concentration, a judgment reference value for selecting the concentration prediction function is set,
In the image forming apparatus, the density prediction function is selected according to a signal from the input signal output unit.
When the signal from the input signal output unit is within a certain range including the determination reference value and the determination reference value, a plurality of density prediction functions are used to calculate a predicted density. apparatus. The image forming apparatus according to claim 1, wherein a plurality of determination reference values for selecting the density prediction function are set. The plurality of concentration prediction functions selected when the signal from the input signal output unit is within a certain range including the determination reference value and the determination reference value are:
A density prediction function which is selected when it is larger than the judgment reference value and not within a fixed range including the judgment reference value;
The image forming apparatus according to claim 1 or 2, wherein the density prediction function is selected when the density is smaller than the judgment reference value and not within a predetermined range including the judgment reference value. The predicted concentration value predicted by the concentration prediction unit is a combination of a reference concentration value and a difference value from the reference concentration value,
The prediction function used in the concentration prediction unit is a prediction function determined from the correlation between the difference value from the reference concentration and the difference value from the input signal value serving as the reference,
(Predicted concentration) = (reference concentration) + (difference predicted concentration value from reference concentration)
(Difference predicted density value from reference density) = α * (difference value from reference input signal value)
The image forming apparatus according to any one of claims 1 to 3, wherein α is represented by an arbitrary coefficient. When the signal from the input signal output unit is within a certain range including the determination reference value and the determination reference value, the predicted concentration value predicted by the concentration prediction unit is:
The method according to any one of claims 1 to 4, characterized in that it is calculated using difference predicted concentration values from a plurality of reference concentrations calculated using a plurality of selected concentration prediction functions. Image forming device. The difference predicted concentration value from the reference concentration is calculated by averaging the difference predicted concentration values from the plurality of reference concentrations calculated using the plurality of selected concentration prediction functions. An image forming apparatus according to any one of claims 1 to 5. The difference predicted concentration value from the reference concentration is calculated using a difference predicted concentration value from a plurality of reference concentrations calculated using a plurality of selected concentration prediction functions.
6. The method according to any one of claims 1 to 5, wherein the difference predicted concentration value calculated in each concentration prediction function is calculated by weighting in accordance with the signal from the input signal output unit. An image forming apparatus according to claim 1.