JP2010271595A - Image formation control device, image forming apparatus, and image formation control method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve robustness with respect to the uncertainty of a process model, relating to image formation. <P>SOLUTION: While a constrained evaluation function related to a constraining condition for an amount of operation is minimized using an estimation equation for approximating time-series variation in the state of a toner image by repetition of feedback control, a series of amounts of operation (control input) is obtained so as to approach a reference orbit representing an ideal time change until toner images go into a desired state from a present state. As a result, since a set value for a process parameter related to image formation can be optimally set, while estimating a change in the state of a previous toner images, robustness with respect to the uncertainty of the process model related to the image formation can be improved. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to an image formation control device, an image formation device, and an image formation control method.

  A method of creating a test pattern outside the printing area on the photoreceptor or transfer belt and controlling the image forming process conditions related to the image density and image position by analogizing the density and position information from the reflectance data is widely known. ing. For example, in Patent Document 1, control test patterns for determining image forming process conditions outside the image region are created at a plurality of locations, and the image forming process conditions are determined according to the test pattern detection results at the plurality of locations. This makes it possible to reduce the influence of density deviation on the determination of image forming process conditions even when density deviation due to position occurs, while adopting an intermediate transfer method with high image overlay accuracy, and A structure for reducing the cost and space saving of a cleaning device, reducing the downtime of the device by process control for image formation using a test pattern, and obtaining stable image quality is disclosed. Yes.

  By the way, in recent years, color production printers have been developed that realize color-on-demand printing that outputs a large amount of color documents such as leaflets, catalogs, reports, and invoices at high speed. Such a color production printer is used when, for example, invoices and receipts for tens of millions of telephone charges are issued with an issue deadline of about one week. Performs continuous printing regardless of day or night (in other words, several hundreds of high-speed prints are continuously operated in units of tens of hours per minute). Under such circumstances, the high-speed type color production printer has a characteristic that the apparatus cannot be stopped during continuous operation. This is because stopping the device may cause the issue deadline for a huge number of copies to be missed. In this respect, a high-speed type color production printer is technically different from a printer (MFP: Multifunction Peripheral) installed in an office.

  On the other hand, since the control of the image forming process condition disclosed in Patent Document 1 is “offline control”, the printing operation must be stopped. Therefore, it is not possible to frequently control the image forming process conditions as disclosed in Patent Document 1. In particular, when high-speed printing of several hundred sheets per minute is performed continuously in units of several tens of hours as in the high-speed type color production printer as described above, the printing operation is performed once every few minutes. Therefore, the control of the image forming process conditions is stopped, which is contrary to the characteristics of the high-speed type color production printer in which the apparatus cannot be stopped during the continuous operation as described above. In addition, if the continuous operation is performed without executing the control of the image forming process condition, the state of the process is greatly changed, and the image quality is deteriorated. That is, for a high-speed type color production printer, a new configuration is required that can always control image forming process conditions in real time without stopping the printing operation.

  Therefore, Non-Patent Document 1 discloses a charging device and an exposure device in an image forming engine that uses an electrophotographic process in real time by measuring the toner adhesion amount on an intermediate transfer belt or an image fixed on paper. A configuration method of a feedback control system for adjusting and optimizing setting values of a developing device is disclosed.

  Since the charging device, the exposure device, the developing device, and the like in the image forming engine using the electrophotographic process interact, parameters for setting their operations cannot be determined independently. Further, since the image to be measured also has a plurality of colors or a plurality of luminance values / density values, it is necessary to perform “multi-input / multi-output control” for simultaneously determining a plurality of operation amounts. Here, the “operation amount” or “control input” in the control system is a set value of the charging device, the exposure device, and the developing device, and the “control amount” or “output” is a color measured on the fixed paper. Or density / luminance. Furthermore, in addition to "multi-input multi-output control", the input / output relationship in the electrophotographic process is generally complicated, and the same output is output for the same input depending on the operating environment (temperature, humidity, etc.) and operating time. Is not always obtained. As described above, there is a problem that an uncertain factor is included in the process model.

  In order to solve such a problem, Non-Patent Document 1 uses a method of “robust control” to bring the difference from the output target value closer to 0 and to determine the uncertain operation of the process. A controller design is described that guarantees stability under all cases.

  By the way, according to Non-Patent Document 1, the relationship between the control input and the gradation and color reproducibility of the output image is expressed as a “linear model”, and the robustness of the control system to the nonlinearity and uncertainty of the model is expressed. A feedback control system that guarantees performance is disclosed. With the method disclosed in Non-Patent Document 1, it becomes possible to frequently control processes in real time without stopping the printing operation.

  However, there are various restrictions on the set values (charging bias, exposure intensity, developing bias, etc.) of the charging device, exposure device, developing device, etc. in the image forming engine using the electrophotographic process. Each set value has a strong limit on the upper and lower limits, or the range of values that can be varied at once. Furthermore, there are mutual constraints. For example, the charging potential needs to be within a certain range with respect to the developing bias. Furthermore, the relationship between the set values of the charging device, the exposure device, the developing device, etc., and the color, density and luminance finally fixed on the paper is highly nonlinear.

  As described above, in the method disclosed in Non-Patent Document 1, restrictions on “operation amount” or “control input” such as a setting value of a charging device, an exposure device, and a developing device in an image forming engine using an electrophotographic process are used. The big problem is that the conditions (upper limit, lower limit, etc.) cannot be considered.

  Further, the relationship between the control input and the gradation and color reproducibility of the output image is non-linear. Originally, the target of “non-linear system” is approximated as “linear system” and “robust control” is applied, so there is a problem that it becomes a “conservative” control system with poor transient response. is there.

  The present invention has been made in view of the above, and provides an image formation control apparatus, an image formation apparatus, and an image formation control method capable of improving robustness against uncertainty of a process model related to image formation. For the purpose.

  In order to solve the above-described problems and achieve the object, the present invention provides an image forming control apparatus for controlling an image forming unit that forms a toner image using an electrophotographic process, and a measured value of the color of the toner image. A measurement value acquisition means for acquiring image data, and a process parameter relating to image formation according to an operation amount determined based on a difference between the measurement value fed back and the measured value fed back and a preset target value A set value determining means for determining a set value for the control value, wherein the set value determining means uses a prediction formula that approximates a time-series change in the state of the toner image due to repetition of feedback control. The toner image becomes close to a reference trajectory that represents an ideal time change from the current state to the desired state while minimizing the evaluation function with constraints on Uni obtains the operation amount of the sequence, characterized in that.

  The image forming apparatus of the present invention acquires an image forming unit that forms a toner image using an electrophotographic process, a color measuring unit that measures the color of the toner image, and a measurement value obtained by the color measuring unit. A set value for a process parameter relating to image formation according to an operation amount determined based on a difference between the measured value acquisition unit and the measured value fed back and the measured value fed back and a preset target value A set value determining means for determining the constraint on the manipulated variable using a prediction equation that approximates a time-series change in the state of the toner image due to repetition of feedback control. The operation is performed so that the toner image is close to a reference trajectory representing an ideal time change from the current state to a desired state while minimizing the attached evaluation function. Determination of the sequence, characterized in that.

  The present invention also relates to an image forming control method executed by an image forming apparatus that forms a toner image using an electrophotographic process, wherein the image forming apparatus includes a control unit and a storage unit, and the control unit The measurement value acquisition means executed in the step of acquiring the measurement value of the color of the toner image, and the set value determination means feeds back the measurement value and is preset with the measurement value fed back. Determining a set value for a process parameter relating to image formation according to an operation amount determined based on a difference from a target value, and the set value determining means includes: Using the prediction formula that approximates the time series change of the state, while minimizing the constrained evaluation function related to the constraint on the manipulated variable, the toner image is removed from the current state. Determining the amount of operation of the sequence to be close to the reference trajectory representing an ideal time variation of until Nozomu state, characterized in that.

  According to the present invention, it is possible to optimally set a process parameter setting value related to image formation after predicting a change in the state of the previous toner image, and thus robustness against the uncertainty of the process model related to image formation. The effect that it can improve property is produced.

FIG. 1 is a schematic configuration diagram partially showing a color production printer according to an embodiment of the present invention. FIG. 2 is a schematic configuration diagram illustrating the image forming unit. FIG. 3 is a block diagram showing the electrical connection of each unit provided in the printer. FIG. 4 is a block diagram showing a functional configuration related to the parameter control process. FIG. 5 is a flowchart showing the flow of parameter control processing. FIG. 6 is a plan view showing an example of a patch pattern. FIG. 7 is a schematic diagram showing the structure of a feedback control system related to image formation. FIG. 8 is a graph expressing the change of the L component as a function of the process parameter. FIG. 9 is a graph showing an example of the reference trajectory and the calculated control input. FIG. 10 is a graph showing changes in the output value due to feedback control. FIG. 11 is a graph showing changes in process parameters by feedback control.

  Exemplary embodiments of an image forming control apparatus, an image forming apparatus, and an image forming control method according to the present invention are explained in detail below with reference to the accompanying drawings.

  An embodiment of the present invention will be described with reference to FIGS. This embodiment is an example in which a color production printer that realizes color on-demand printing that outputs a large amount of color documents such as bills at high speed is applied as an image forming apparatus. Such a color production printer is used when, for example, invoices and receipts for tens of millions of telephone charges are issued in about one week. In such a situation, continuous printing is performed (in other words, several hundreds of high-speed prints are continuously operated in units of several tens of hours per minute).

  FIG. 1 is a schematic configuration diagram partially showing a color production printer 100 according to an embodiment of the present invention. FIG. 1 shows only an image forming process part (process engine part) using an electrophotographic process for performing exposure, charging, development, transfer, and fixing in a color production printer (hereinafter referred to as a printer) 100. In addition to the components shown in FIG. 1, the printer 100 includes a paper feeding device that supplies transfer paper 115 as a recording material, a manual tray for manually feeding the transfer paper 115, and an image-formed transfer. A paper discharge tray or the like (none of which is shown) for discharging the paper 115 is provided.

  As shown in FIG. 1, the printer 100 is provided with an endless belt-like intermediate transfer belt 105 as an intermediate transfer member. The intermediate transfer belt 105 is rotationally driven by a support roller 112 having a function as a drive roller while being stretched around four support rollers 112, 113, 114, and 119.

  Four image forming units 101Y, 101C, 101M, and 101K for each color of yellow (Y), cyan (C), magenta (M), and black (K) are disposed on the stretched portion of the intermediate transfer belt 105. ing. The four image forming units 101Y, 101C, 101M, and 101K for the respective colors have the same configuration and are composed of the same constituent members. In FIG. 1, the same constituent members represent the numeral portions with the same numerals, and end with a color identification code Y (yellow), C (cyan), M (magenta), and K (black) are attached. In each of the image forming units 101Y, 101C, 101M, and 101K, primary transfer as a charging device that charges the photosensitive drums 103Y, 103C, 103M, and 103K, the developing devices 102Y, 102C, 102M, and 102K, and the intermediate transfer belt 105, respectively. Devices 106Y, 106C, 106M, and 106K are arranged. The developing devices 102Y, 102C, 102M, and 102K are supplied with toner from the toner bottles 104K, 104Y, 104C, and 104M.

  An exposure apparatus 200 is provided below each of the image forming units 101Y, 101C, 101M, and 101K. Based on the image information, a semiconductor laser is emitted from a laser exposure unit (not shown) provided in the exposure apparatus 200. Driven to emit writing light Lb, electrostatic latent images are formed on the photosensitive drums 103Y, 103C, 103M, and 103K as image carriers. Here, the emission of the writing light is not limited to the laser, but may be, for example, an LED (light emitting diode).

  Here, the configuration of the image forming units 101Y, 101C, 101M, and 101K will be described with reference to FIG. Hereinafter, the image forming unit 101K that forms a black toner image will be described as an example with reference to FIG. 2, but the image forming units 101Y, 101C, and 101M that form toner images of other colors also have the same configuration.

  As shown in FIG. 2, the constituent members of the image forming unit 101K for black toner are originally provided with a symbol K at the end of the symbol, but are omitted here. In the image forming unit 101, a charging device 301 for charging the photosensitive drum 103, a developing device 102, and a photosensitive member cleaning device 311 are provided around the photosensitive drum 103. A primary transfer device 106 serving as a charging device is provided at a position facing the photosensitive drum 103 via the intermediate transfer belt 105. As the primary transfer device 106, a primary transfer roller is adopted and is installed so as to be pressed against the photosensitive drum 103 with the intermediate transfer belt 105 interposed therebetween. The primary transfer device 106 is not limited to a roller shape, but may be a conductive brush shape, a non-contact corona charger, or the like.

  The charging device 301 is of a contact charging type employing a charging roller, and uniformly charges the surface of the photosensitive drum 103 by applying a voltage while contacting the photosensitive drum 103. As the charging device 301, a non-contact charging type using a non-contact scorotron charger or the like can be used.

  The developing device 102 uses a two-component developer composed of a magnetic carrier and a nonmagnetic toner. As the developer, a one-component developer may be used. The developing device 102 can be roughly divided into an agitating unit 303 and a developing unit 304 provided in the developing case. In the agitation unit 303, a two-component developer (hereinafter simply referred to as “developer”) is conveyed while being agitated and supplied onto a developing sleeve 305 as a developer carrier.

  The stirring unit 303 is provided with two parallel screws 306. A partition plate 309 is provided between the two screws 306 to partition the two screws 306 so as to communicate with each other. Further, a toner density sensor 418 for detecting the toner density of the developer in the developing device 102 is attached to the developing case 308 that houses the developing sleeve 305, the two screws 306, and the like. On the other hand, in the developing unit 304, the toner in the developer attached to the developing sleeve 305 is transferred to the photosensitive drum 103.

  The developing unit 304 is provided with a developing sleeve 305 that faces the photosensitive drum 103 through the opening of the developing case, and a magnet (not shown) is fixedly disposed in the developing sleeve 305. A doctor blade 307 is provided so that the tip approaches the developing sleeve 305. In the present embodiment, the distance at the closest portion between the doctor blade 307 and the developing sleeve 305 is set to 0.9 mm. In the developing device 102, the developer is conveyed and circulated while being stirred by two screws 306, and is supplied to the developing sleeve 305. The developer supplied to the developing sleeve 305 is drawn up and held by a magnet. The developer pumped up by the developing sleeve 305 is conveyed as the developing sleeve 305 rotates, and is regulated to an appropriate amount by the doctor blade 307. The regulated developer is returned to the stirring unit 303.

  The developer transported to the developing area facing the photosensitive drum 103 in this manner is brought into a spiked state by a magnet and forms a magnetic brush. In the developing region, a developing electric field that moves the toner in the developer to the electrostatic latent image portion on the photosensitive drum 103 is formed by the developing bias applied to the developing sleeve 305. As a result, the toner in the developer is transferred to the electrostatic latent image portion on the photosensitive drum 103, and the electrostatic latent image on the photosensitive drum 103 is visualized to form a toner image. The developer that has passed through the developing region is transported to a portion where the magnetic force of the magnet is weak, thereby leaving the developing sleeve 305 and being returned to the stirring unit 303. When the toner concentration in the stirring unit 303 becomes light by repeating such operations, the toner concentration sensor 418 detects this, and toner is supplied to the stirring unit 303 based on the detection result.

  The photoconductor cleaning device 311 includes a cleaning blade 312 made of polyurethane rubber, for example, which is arranged so that the tip of the cleaning blade 312 is pressed against the photoconductor drum 103. In this embodiment, in order to improve the cleaning performance, a conductive fur brush 310 that contacts the photosensitive drum 103 is also used. A bias is applied to the fur brush 310 from a metal electric field roller (not shown), and the tip of a scraper (not shown) is pressed against the electric field roller. The toner removed from the photosensitive drum 103 by the cleaning blade 312 and the fur brush 310 is accommodated in the photosensitive member cleaning device 311 and recovered by a waste toner recovery device (not shown).

  Here, specific settings of the image forming unit 101 will be described. The diameter of the photosensitive drum 103 is 40 mm, and the photosensitive drum 103 is driven at a linear speed of 200 mm / s. The developing sleeve 305 has a diameter of 25 mm, and the developing sleeve 305 is driven at a linear speed of 564 mm / s. The charge amount of the toner in the developer supplied to the development area is preferably in the range of about −10 to −30 μC / g. The development gap, which is the gap between the photosensitive drum 103 and the development sleeve 305, can be set in the range of 0.5 to 0.3 mm, and the development efficiency can be improved by decreasing the value. The thickness of the photosensitive layer of the photosensitive drum 103 is 30 μm, the beam spot diameter of the optical system of the exposure apparatus 200 is 50 × 60 μm, and the amount of light is about 0.47 mW. As an example, the surface of the photosensitive drum 103 is uniformly charged to −700 V by the charging device 301, and the potential of the electrostatic latent image portion irradiated with the laser by the exposure device 200 is −120 V. On the other hand, the developing bias voltage is set to -470V, and a developing potential of 350V is secured. Such process conditions are changed as appropriate according to the result of the potential control.

  In the image forming unit 101 shown in FIG. 2 as described above, the surface of the photosensitive drum 101 is first uniformly charged by the charging device 301 as the photosensitive drum 103 rotates. Next, based on the image information from the print controller 410 (see FIG. 3), the exposure apparatus 200 irradiates the writing light Lb by the laser to form an electrostatic latent image on the photosensitive drum 103. Thereafter, the electrostatic latent image on the photosensitive drum 103 is visualized by the developing device 102 to form a toner image. The toner image is primarily transferred onto the intermediate transfer belt 105 by the primary transfer device 106. The transfer residual toner remaining on the surface of the photosensitive drum 103 after the primary transfer is removed by the photosensitive member cleaning device 3011 and used for the next image formation.

  Returning to FIG. 1, a secondary transfer roller 108 is provided as a secondary transfer device at a position facing the support roller 112 with the intermediate transfer belt 105 interposed therebetween. The secondary transfer roller 108 transfers the toner image formed on the intermediate transfer belt 105 to the transfer paper 115 supplied from a paper feeding device or the like by electrostatic force. When the toner image on the transfer belt 105 is secondarily transferred onto the transfer paper 115, the secondary transfer roller 108 is pressed against the portion of the intermediate transfer belt 105 wound around the support roller 112 to perform secondary transfer. The secondary transfer device may not be configured using the secondary transfer roller 108 but may be configured using, for example, a transfer belt or a non-contact transfer charger.

  As shown in FIG. 1, a fixing device 111 for fixing the toner image transferred onto the transfer paper 115 is provided downstream of the secondary transfer roller 108 in the transfer paper transport direction. The fixing device 111 has a configuration in which a pressure roller 118 is pressed against a heating roller 117. In addition, as shown in FIG. 1, the fixing device 111 measures color information from the toner image fixed on the transfer paper 115 on the downstream side in the transfer paper conveyance direction of the heating roller 117 and the pressure roller 118. A spectrometer 109 is provided.

  Further, as shown in FIG. 1, a belt cleaning device 110 is provided at a position facing the support roller 113 with the intermediate transfer belt 105 interposed therebetween. The belt cleaning device 110 is for removing residual toner remaining on the intermediate transfer belt 105 after the toner image on the intermediate transfer belt 105 is transferred to the transfer paper 115.

  Next, the electrical connection of each unit included in the printer 100 will be described. FIG. 3 is a block diagram illustrating the electrical connection of each unit included in the printer 100.

  As shown in FIG. 3, the printer 100 includes a main body control unit 406 having a computer configuration that functions as an image formation control device. The main body control unit 406 drives and controls each unit, and uses an electrophotographic process. Control the image forming operation. A main body control unit 406 includes a ROM (Read Only Memory) 405 that stores in advance fixed data such as a computer program via a bus line 409 in a CPU (Central Processing Unit) 402 that executes various calculations and drive control of each unit. A RAM (Random Access Memory) 403 that functions as a work area for storing various data in a rewritable manner is connected. The main body control unit 406 also includes an A / D conversion circuit 401 that converts information from the spectrometer 109, the toner concentration sensor 418, and the temperature / humidity sensor 417, which are color measuring means, into digital data. The circuit 401 is connected to the CPU 402 via the bus line 409.

  Connected to the main body control unit 406 is a print controller 410 that processes image data sent from a PC (Personal Computer) 411, a scanner 412, a FAX (Facsimile) 413, etc., and converts it into exposure data. The main body control unit 406 is connected to a drive circuit 414 that drives a motor and a clutch 415. The main body control unit 406 also includes a high voltage generator 416 that generates a voltage necessary for image formation in the image forming unit (the image forming unit 101, the primary transfer device 106, the exposure device 200, the secondary transfer roller 108, and the like). It is connected.

  A parameter setting unit 404 is also connected to the main body control unit 406. The parameter setting unit 404 obtains the laser intensity of the exposure apparatus 200 and the charge application of the transfer apparatus 106 based on the result calculated by the CPU 402 based on information measured by the spectrometer 109 or the like in order to obtain a stable image density. The voltage, the developing bias of the developing device 102, and the like are changed.

  Here, the operation of the printer 100 will be schematically described. For example, when printing is performed by the printer 100 according to information from the PC 411, print information including image data is transmitted from the PC 411 using a printer driver installed in the PC 411.

  The print controller 410 receives print information including image data transmitted from the PC 411, processes the image data, converts it into exposure data, and outputs a print command to the main body control unit 406. Receiving the print command, the CPU 402 of the main body control unit 406 executes image formation control processing using an electrophotographic process by following the computer program stored in the ROM 405. More specifically, the CPU 402 of the main body control unit 406 drives the motor and the clutch 415 via the drive circuit 414, the support roller 112 is driven to rotate, and the intermediate transfer belt 105 is driven to rotate. At the same time, the CPU 402 of the main body control unit 406 performs an image forming unit (image forming unit 101, primary transfer device) using an electrophotographic process via the drive circuit 414, the high voltage generator 416, and the parameter setting unit 404. 106, exposure apparatus 200, secondary transfer roller 108, etc.).

  The operation of the image forming unit (image forming unit 101, primary transfer device 106, exposure device 200, secondary transfer roller 108, etc.) using an electrophotographic process will be described below. The exposure apparatus 200 irradiates the writing light Lb on the photosensitive drums 103Y, 103C, 103M, and 103K of the image forming units 101Y, 101C, 101M, and 101K based on the image data transmitted from the print controller 410, respectively. . As a result, electrostatic latent images are formed on the photosensitive drums 103Y, 103C, 103M, and 103K, and are visualized by the developing devices 102Y, 102C, 102M, and 102K. Then, yellow, cyan, magenta, and black toner images are formed on the photosensitive drums 103Y, 103C, 103M, and 103K, respectively. The respective color toner images formed in this way are primarily transferred by the primary transfer devices 106Y, 106C, 106M, and 106K so as to sequentially overlap the intermediate transfer belt 105. As a result, a composite toner image in which the toner images of the respective colors overlap is formed on the intermediate transfer belt 105. In addition, the main body control unit 406 controls the drive circuit 414 in accordance with the timing at which the composite toner image formed on the intermediate transfer belt 105 as described above is conveyed to the secondary transfer unit facing the secondary transfer roller 108. The transfer paper 115 is supplied by driving the motor and the clutch 415 via the control to control the paper feeding device (not shown). The transfer paper 115 supplied from the paper feeding device is fed between the intermediate transfer belt 105 and the secondary transfer roller 108, and the secondary transfer roller 108 causes the composite toner image on the intermediate transfer belt 105 to be transferred onto the transfer paper 115. Secondary transfer is performed. Thereafter, the transfer paper 115 is conveyed to the fixing device 111 while being attracted to the secondary transfer roller 108, and heat and pressure are applied by the fixing device 111 to perform a toner image fixing process. The transfer paper 115 that has passed through the fixing device 111 is discharged and stacked on a paper discharge tray (not shown). The transfer residual toner remaining on the intermediate transfer belt 105 after the secondary transfer is removed by the belt cleaning device 110.

  Next, parameter control processing in image formation control processing using an electrophotographic process executed by the CPU 402 of the main body control unit 406 according to a computer program will be described in detail. Here, FIG. 4 is a block diagram showing a functional configuration related to the parameter control process, and FIG. 5 is a flowchart showing a flow of the parameter control process.

  As shown in FIG. 4, the CPU 402 of the main body control unit 406 implements the measurement value acquisition unit 10 and the set value determination unit 20 by following the computer program.

  The measurement value acquisition means 10 acquires a measurement value by a spectrometer 109 that measures the color of the toner image fixed on the transfer paper 115 as a recording material.

  The set value determination unit 20 feeds back the measurement value acquired by the measurement value acquisition unit 10 and forms an image according to the operation amount determined based on the difference between the fed back measurement value and a preset target value. A setting value for the process parameter is determined. More specifically, the set value determining means 20 uses the prediction formula that approximates the time-series change in the state of the toner image due to the repetition of feedback control, while minimizing the evaluation function with constraints on the constraint on the operation amount, A sequence of manipulated variables is obtained so that the image is close to a reference trajectory representing an ideal time change from the current state to the desired state.

  As shown in FIG. 5, when a print job is started (Yes in step S1), the CPU 402 of the main body control unit 406 detects color information (measurement) from the toner image fixed on the transfer paper 115 from the spectrometer 109. Color data) is acquired (step S2: measurement value acquisition means 10).

  Here, for example, digital image data input to the print controller 410 by the PC 411, the scanner 412, and the FAX 413 is processed to sample several colors. As the digital image processing, a color palette extraction method as described in JP-A-2005-275854 is applied. A color palette is a collection of color clusters obtained by clustering the colors of all the pixels of a digital image and having the highest number of constituent pixels. Colorimetric data is obtained by measuring the color after fixing at the pixel position corresponding to the color in the color palette with the spectrometer 109 and inputting it to the CPU 402.

  Alternatively, an image obtained by periodically outputting an image in which a patch pattern as shown in FIG. 6 is printed on the transfer paper 115, measuring with the spectrometer 109, and inputting to the CPU 402 may be used as the colorimetric data.

  In the subsequent step S3, the CPU 402 determines the operation amount for the process parameter by comparing the colorimetric data acquired in step S2 with the color of the corresponding digital image data by a method described later. Here, the operation amount with respect to the process parameter is the setting of the process parameter relating to image formation such as the laser intensity (LDP) of the exposure apparatus 200, the charge application voltage (Cdc) of the transfer apparatus 106, the development bias (Vb) of the development apparatus 102, etc. Value.

  Thereafter, the process parameter is determined using the operation amount for the process parameter determined in step S3 (step S4), and the process parameter determined in step S4 (laser intensity of the exposure apparatus 200, charging applied voltage of the transfer apparatus 106, The developing bias of the developing device 102 is set in the parameter setting unit 404 (step S5). Steps S3 to S4 are executed by the set value determining means 20. The process parameters (laser intensity of the exposure apparatus 200, charging application voltage of the transfer apparatus 106, development bias of the developing apparatus 102) set in the parameter setting unit 404 in this way are the image forming units 101 (transfer apparatus 106, developing apparatus). 102) and output to the exposure apparatus 200 or the like and reflected in the processing.

  The processes in steps S2 to S5 as described above are repeated until the print job ends, that is, until the output of the designated number of sheets is completed (Yes in step S6). That is, when the output of the designated number of sheets is not completed (No in step S6), the processes in steps S2 to S5 are repeated for the toner image fixed on the next transfer sheet 115.

  When the output of the designated number of sheets is completed (Yes in step S6), the series of flow ends here.

  Next, the method for determining the operation amount for the process parameter in step S3 will be described in detail.

  When determining the operation amount for the process parameter, the CPU 402 receives the colorimetric data and the color on the corresponding digital image data as an input, for example, as a vector value in the color space of L * a * b *. For example, for eight colors such as the patch pattern shown in FIG. 6, the color vector on the digital image data corresponding to the color measurement data vector is fixed to the kth sheet of paper for each of the eight colors. A 24-dimensional vector y (k) in which the averages of L * a * b * measured in the image are arranged, and a 24-dimensional vector r0 in which L * a * b * components on the digital image data are arranged.

When determining the operation amount with respect to the process parameter, the CPU 402 functions as a feedback control system related to image formation as shown in FIG. 7, and the controller K is a k-th (step k) paper-fixed image. From the difference between the measured output value y (k) and the target value r0, the control input v (k) and the parameter setting value u (k) of the image forming unit 101 and the like are determined. The relationship between u and y in the steady state is stored in the ROM 405 using the following expression represented by a multivariable function G that does not include time.
y = G (u)

Here, the graph shown in FIG. 8 shows the L component of “K1” in the patch pattern shown in FIG. 6, the laser intensity (LDP) of the exposure apparatus 200, the charging application voltage (Cdc) of the transfer apparatus 106, and the developing apparatus 102. 5 is a graph plotting changes in L component with respect to Vb when Cdc and LDP are fixed to some values when expressed as a polynomial function of development bias (Vb). This graph
L = 0.00007 · Cdc ² + 0.00033 · LDP ² −0.00014 · Vb ²
+0.00011 · Cdc · LDP-0.00005 · LDP · Vb + 0.00039 · Vb · Cdc
+ 0.173 · Cdc ² −0.315 · LDP ² + 0.172 · Vb ² +151.12
It is expressed by a two-dimensional expression.

ここで、コントローラＫは、プロセスパラメータｕ（ｋ）そのものではなく、その差分ｖ（ｋ）を決めるものとすると、次の式（２）のように記述できる。

また、下記式（３）に示すように、プロセスパラメータｕ（ｋ）の変化に対する出力の変化を表す行列を、各ステップｋにおけるヤコビアン行列と定義する。

ただし、多変数関数Ｇは一般に非線形であるので、行列Ｂ（ｋ）はステップごとに変化する。したがって、上述した式（１）で表される系は、線形時変系として、状態変数ｘ、外乱ｄによって、次に示す状態方程式（４）で記述できる。

特に、行列Ｂ（ｋ）は、時刻ｋ−１におけるプロセスパラメータｕに依存するので、下記式のように記述することができる。
Ｂ（ｋ）＝Ｂ（ｕ（ｋ−１））
これは、ＬＰＶ（Linear Parameter Varying）と呼ばれるシステムである。各ステップｋにおいて、行列Ｂ（ｋ）は、直前のパラメータ設定値ｕ（ｋ−１）に応じて毎回変更する。このようにすることによって、画像形成プロセスの非線形性が大きい系における制御を効果的に行うことが可能になる。 From the Taylor expansion of the multivariable function G, the relationship between the process parameter u (k) and the image factor y (k) related to image formation in step k (kth paper) is the nominal output initial value y (1). Assuming that the output is for the set value u (0), the following expression (1) can be used.

Here, if the controller K determines not the process parameter u (k) itself but the difference v (k), it can be described as the following equation (2).

Further, as shown in the following equation (3), a matrix representing an output change with respect to a change in the process parameter u (k) is defined as a Jacobian matrix at each step k.

However, since the multivariable function G is generally non-linear, the matrix B (k) changes at each step. Therefore, the system represented by the above equation (1) can be described as a linear time-varying system by the state equation (4) shown below by the state variable x and the disturbance d.

In particular, since the matrix B (k) depends on the process parameter u at time k−1, it can be described as the following equation.
B (k) = B (u (k-1))
This is a system called LPV (Linear Parameter Varying). In each step k, the matrix B (k) is changed every time according to the immediately preceding parameter setting value u (k−1). By doing so, it is possible to effectively perform control in a system in which the nonlinearity of the image forming process is large.

  As shown in FIG. 7, in step k, the controller K determines the control input v (k) from the output value y (k) and the target value r0. The control input v (k) is added to u (k-1) by the equation (2), and the process parameter is set to u (k). The output of step k + 1 is obtained by adding disturbance d to the output from the process.

したがって、下記に示すように、ＣＭＹＫのそれぞれのシステムを独立に考えることができる。

Ｌ，ａ，ｂの値は、図８に示すＬのように、露光装置２００のレーザ強度（ＬＤＰ）、転写装置１０６の帯電印加電圧（Ｃｄｃ）、現像装置１０２の現像バイアス（Ｖｂ）の関数として、下記式（６）に示すように与えられる。

このようにＬ，ａ，ｂが、Ｃｄｃ，ＬＤＰ，Ｖｂの多項式で表現される場合、Ｂ＊（ｋ）は３×３行列で、下記式（７）に示すように記述できる。

ただし、一般の混色から構成されるパレット（ＣＭＹの３色のグレイ，赤・青・緑色など）の場合には、下記式（８）に示すような表現になるため，ブロック対角構造にはならない。

The modeling of the system is to determine the change of the output with respect to the change of the matrix B (k), ie the process parameter. For example, when each is composed of a single color as in the patch pattern shown in FIG. 6, the matrix B (k) has a block diagonal structure as shown in the following equation (5).

Therefore, as shown below, each system of CMYK can be considered independently.

The values of L, a, and b are functions of the laser intensity (LDP) of the exposure apparatus 200, the charging application voltage (Cdc) of the transfer apparatus 106, and the developing bias (Vb) of the developing apparatus 102, as indicated by L in FIG. As shown in the following formula (6).

Thus, when L, a, and b are expressed by Cdc, LDP, and Vb polynomials, B * (k) is a 3 × 3 matrix, which can be described as shown in the following equation (7).

However, in the case of a palette composed of general mixed colors (CMY three colors gray, red, blue, green, etc.), the expression is as shown in the following formula (8). Don't be.

ここで、ＲとＱは正定値対称行列であって、Ｒは各要素の誤差への重み付け、Ｑは上記条件（２）に対応して各因子に重み付けする。言い換えれば、Ｒは制御量のスケール因子、Ｑは制御入力（操作量）のスケール因子である。また、行列Ａとベクトルｂは、（３）の制約条件に対応する。 Here, the design method of the controller K in step k as shown in FIG. 7 will be examined. The controller K needs to determine the control input v from the output value y and the target value r0 so as to satisfy the following conditions.
(1) Difference between output and target value in next step k + 1 ‖y (k + 1) −r0‖ = ‖y (k) + B (k) v (k) −r0‖
Be smaller.
(2) The method of changing the control input v can be adjusted. That is, the scale factor of each element, the mobility of a target value that differs for each process / module, etc. must be considered. Furthermore, since the process model G includes uncertain factors, excessive fluctuations in the control input v are undesirable, and it is necessary to be able to adjust maintainability and operability.
(3) A constraint condition for the control input v can be considered. It is necessary to consider the upper and lower limits.
By combining these three conditions, a term representing “fitness” like the condition in (1), a term representing “fine” for inappropriate variation like the condition in (2), and (3) The control input v is determined by solving a quadratic programming problem that minimizes the following equation (9) that also incorporates the constraint conditions such as:

Here, R and Q are positive definite symmetric matrices, where R is a weight for each element error, and Q is a weight for each factor corresponding to the condition (2). In other words, R is a scale factor of the control amount, and Q is a scale factor of the control input (operation amount). The matrix A and the vector b correspond to the constraint condition (3).

  In the present embodiment, the above-described concept is extended to determine the control input v so as to optimize the behavior of the control system in a longer period, not just the step k + 1 immediately after. Such control by the CPU 402 is referred to as “model prediction control”. In the following, “model predictive control” will be described in detail.

  As shown in FIG. 9, the CPU 402, as shown in FIG. 9, “reference trajectories” (r [k + 1 | k], r [k + 2 | k], r (k + 1, k + 2,... .., R [k + p | k]), and an output sequence (y [k + 1 | k], y [k + 2 | k],..., Y [k + p | k]) is determined using the equation (4). Is a sequence of control inputs (v [k | k], v [k + 1 | k],..., V [k + p−1 | k]) so that is close to the “reference trajectory”. At that time, the “fine” for excessive change of the control input v and the optimum determination in consideration of the constraint conditions are performed. Specifically, steps k + 1, k + 2,. . . A prediction formula for the future output y and a constraint evaluation function for determining the control input v are required. FIG. 9 shows one patch, that is, one color among the patch patterns shown in FIG.

  First, steps k + 1, k + 2,. . . A prediction formula for the future output y in FIG.

ここで、外乱ｄに対して、一定値の出力外乱が存在する。すなわち、

と仮定すると、予測値は、時刻ｋでの測定出力と予測出力の差

と表せる。したがって、予測式は、下記式（１１）と記述することができる。

The predicted value of the j step ahead in step k is represented as [k + j | k], and the actual value is represented by (k) (y (k), v (k), etc.). Given.

Here, there is a constant output disturbance with respect to the disturbance d. That is,

Assuming that the predicted value is the difference between the measured output at time k and the predicted output

It can be expressed. Therefore, the prediction formula can be described as the following formula (11).

  Next, a restricted evaluation function for determining the control input v will be described.

式（１２）におけるｖ＿ｍｉｎ，ｖ＿ｍａｘ，ｕ＿ｍｉｎ，ｕ＿ｍａｘは、図７におけるｖとｕの範囲である。また、参照軌道ｒは、例えば下記式（１３）のように与えることができる。

The constrained evaluation function at step k can be described by the following equation (12) by the predicted horizon length p, the reference trajectory r, and the weight matrices (positive definite symmetry) Q and R.

In Expression (12), v_min, v_max, u_min, and u_max are ranges of v and u in FIG. Further, the reference trajectory r can be given by, for example, the following formula (13).

The controller K has an optimal control input sequence (v [k | k], v [k + 1 | k],..., V [k + p-1 | k]) that minimizes the constraint evaluation function as described above. Is calculated using a prediction formula. Using the first element v [k | k] as v (k), the process parameter at step k is updated as in the following equation.
u (k) = u (k-1) + v (k)

  The calculation of the optimal control input sequence can be solved as a “secondary programming problem”. The formulation as a secondary planning problem is described below.

ここで、

とおくと、

のように、表すことができる。また、各操作量のスケール因子を考慮して、

とおくと、制約付評価関数は、下記式（１５）のようにまとめられる。

さらに、下記に示す制約条件

を適当な行列Ｃ_ｋとｂにより下記のように表すと、

モデル予測制御は、下記式（１６）に示すように、各ステップｋにおいて最適な操作量系列Ｖ_ｋについての２次計画問題を解く問題として定式化できるので、効率的に画像形成プロセス条件を決定することが可能になる。

なお、式（１６）の問題の解法には、内点法などの効率的アルゴリズムを使うことができる。 The prediction formula expressed as formula (11) can be rewritten as the following formula (14).

here,

After all,

Can be expressed as: In addition, considering the scale factor of each manipulated variable,

In other words, the restricted evaluation function can be summarized as the following equation (15).

In addition, the constraints shown below

Is represented by an appropriate matrix C _k and b as follows:

Since the model predictive control can be formulated as a problem for solving the quadratic programming problem for the optimum manipulated variable series V _{k at} each step k, as shown in the following equation (16), the image forming process conditions are efficiently determined. It becomes possible to do.

An efficient algorithm such as an interior point method can be used to solve the problem of equation (16).

  The above is the description of the method for determining the operation amount for the process parameter in step S3.

ｖ［ｋ｜ｋ］をｖ（ｋ）として用いて、ステップｋにおけるプロセスパラメータを下記式のように更新する。
ｕ（ｋ）＝ｕ（ｋ−１）＋ｖ（ｋ）
ｕ（ｋ）をプロセスパラメータの設定値として入力した後の出力の測定値がｙ（ｋ＋１）である。 In the determination of the process parameter using the operation amount for the process parameter determined in step S3 in step S4, in the vector obtained as a solution as shown below,

Using v [k | k] as v (k), the process parameter at step k is updated as in the following equation.
u (k) = u (k-1) + v (k)
The measured value of the output after u (k) is input as the process parameter setting value is y (k + 1).

  Here, FIG. 10 shows an example of a change in the output value y (k) when the process shown in FIG. 5 is applied. Here, the horizontal axis of the graph of FIG. 10 indicates the number of the output paper, or the number of times of feedback when the feedback control is performed every several sheets instead of all the sheets. The vertical axis of the graph of FIG. 10 is each coordinate value in the L * a * b * color space, and the dotted line is the target value at each coordinate. As described above, in the first sheet, there is a difference of ΔE = 8.1 between the target value and the output color, but the output y is set to the target by real-time feedback control without stopping the printing operation. Follow the value.

  Further, FIG. 11 shows an example of a change in the process parameter u (k) when the process as shown in FIG. 5 is applied. Here, the horizontal axis of the graph of FIG. 11 is the same as that of FIG. 10, and when the feedback control is performed for each of the output paper numbers or every several sheets, the number of times the feedback is applied. It is. The vertical axis of the graph in FIG. 11 represents the laser intensity (LDP) of the exposure apparatus 200, the charging applied voltage (Cdc) of the transfer apparatus 106, and the developing bias (Vb) of the developing apparatus 102. In this way, the process parameters converge to the optimum values by real-time feedback control without stopping the printing operation.

  As described above, according to the present exemplary embodiment, the toner image can be minimized while minimizing the evaluation function with constraints related to the constraint on the operation amount using a prediction formula that approximates the time-series change of the state of the toner image due to repetition of feedback control. By predicting the change in the state of the previous toner image by obtaining a sequence of manipulated variables so as to approximate the reference trajectory representing the ideal time change from the current state to the desired state. Thus, it is possible to optimally set the process parameter setting values related to image formation, so that it is possible to improve the robustness against the uncertainty of the process model related to image formation.

  In the present embodiment, the color information is measured from the toner image after being fixed on the transfer paper 115 by the spectrometer 109. However, the present invention is not limited to this, and the color information is measured from the toner image on the intermediate transfer belt 105. Color information may be measured.

DESCRIPTION OF SYMBOLS 10 Measurement value acquisition means 20 Set value determination means 100 Image forming apparatus 109 Color measurement means 406 Image formation control apparatus

JP 2008-40441 A

Perry Y Li and Sohail A Dianat “Robust Stabilization of Tone Reproduction Curves for the Xerographic Printing Process” IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 9, NO.2, MARCH 2001

Claims (9)

In an image formation control apparatus that controls an image forming unit that forms a toner image using an electrophotographic process,
Measurement value acquisition means for acquiring a measurement value of the color of the toner image;
Setting value determination that feeds back the measured value and determines a setting value for a process parameter related to image formation according to an operation amount determined based on a difference between the fed back measured value and a preset target value Means,
With
The set value determining means minimizes a constrained evaluation function related to a constraint condition for the operation amount by using a prediction formula that approximates a time-series change in the state of the toner image due to repetition of feedback control. Obtaining a sequence of the manipulated variables so as to be close to a reference trajectory representing an ideal time change from the current state to a desired state;
An image formation control apparatus characterized by that. The prediction formula includes a matrix representing an output change with respect to a change in the process parameter, and the matrix is changed according to a setting value for the immediately preceding process parameter.
The image formation control apparatus according to claim 1. The set value determining means applies a solution of a quadratic programming problem when obtaining the optimum sequence of manipulated variables that minimizes the constrained evaluation function;
The image formation control apparatus according to claim 1. An image forming unit that forms a toner image using an electrophotographic process;
Color measuring means for measuring the color of the toner image;
Measurement value acquisition means for acquiring a measurement value by the color measurement means;
Setting value determination that feeds back the measured value and determines a setting value for a process parameter related to image formation according to an operation amount determined based on a difference between the fed back measured value and a preset target value Means,
With
The set value determining means minimizes a constrained evaluation function related to a constraint condition for the operation amount by using a prediction formula that approximates a time-series change in the state of the toner image due to repetition of feedback control. Obtaining a sequence of the manipulated variables so as to be close to a reference trajectory representing an ideal time change from the current state to a desired state;
An image forming apparatus. The prediction formula includes a matrix representing an output change with respect to a change in the process parameter, and the matrix is changed according to a setting value for the immediately preceding process parameter.
The image forming apparatus according to claim 4. The set value determining means applies a solution of a quadratic programming problem when obtaining the optimum sequence of manipulated variables that minimizes the constrained evaluation function;
The image forming apparatus according to claim 4. An image formation control method executed in an image forming apparatus for forming a toner image using an electrophotographic process,
The image forming apparatus includes a control unit and a storage unit, and is executed in the control unit.
A measurement value acquisition means for acquiring a measurement value of the color of the toner image;
A set value determining means feeds back the measured value, and a set value for a process parameter relating to image formation according to an operation amount determined based on a difference between the fed back measured value and a preset target value A step of determining
Including
The set value determining means minimizes a constrained evaluation function related to a constraint condition for the operation amount by using a prediction formula that approximates a time-series change in the state of the toner image due to repetition of feedback control. Obtaining a sequence of the manipulated variables so as to be close to a reference trajectory representing an ideal time change from the current state to a desired state;
An image formation control method characterized by the above. The prediction formula includes a matrix representing an output change with respect to a change in the process parameter, and the matrix is changed according to a setting value for the immediately preceding process parameter.
The image forming control method according to claim 7. The set value determining means applies a solution of a quadratic programming problem when obtaining the optimum sequence of manipulated variables that minimizes the constrained evaluation function;
The image forming control method according to claim 7.

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