Patent Publication Number: US-2021179380-A1

Title: Sheet conveyor and image forming system

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The present application claims priorities from Japanese Patent Application No. 2019-226415 filed on Dec. 16, 2019 and Japanese Patent Application No. 2020-039179 filed on Mar. 6, 2020, the disclosures of which are incorporated herein by reference in their entireties. 
     BACKGROUND 
     Field of the Invention 
     The present disclosure relates to a sheet conveyor and an image forming system. 
     Description of the Related Art 
     There is conventionally known a recording apparatus that records an image on a sheet pulled out from a sheet roll (see, for example, Japanese Patent Application Laid-open No. 2013-091219). The sheet is pulled out toward a recording head by a conveyance roller. 
     In this recording apparatus, a diameter of the sheet roll is measured by an optical sensor to synchronize a sheet velocity in an outer circumference of the sheet roll with a sheet velocity in the conveyance roller. A target value of a rotation velocity of the sheet roll is calculated based on the diameter of the sheet roll measured. Further, a control input for a motor that rotates the sheet roll is corrected based on rotation acceleration of the conveyance roller in order to rotate the sheet roll according to the acceleration of the conveyance roller. 
     SUMMARY 
     In a sheet conveyor that conveys a sheet pulled out from a sheet roll, weight of the sheet roll changes depending on consumption of the sheet. The change in the weight may change a control input for a motor that is suitable for controlling acceleration motion of the sheet roll to target motion. 
     In conventional techniques, the motor is controlled without reflecting the change in the weight of the sheet roll. It has been thus difficult to appropriately perform the conveyance control of the sheet under a condition that the sheet is conveyed with an acceleration process. 
     An object of the present disclosure is to provide a sheet conveyor that is capable of appropriately executing conveyance control of a sheet with an acceleration process under an environment where weight of a sheet roll changes depending on consumption of the sheet. 
     According to a first aspect of the present disclosure, there is provided a sheet conveyor, including: a holder configured to detachably hold a sheet roll; a conveyance roller configured to convey, by rotation, a sheet pulled out from the sheet roll; a first motor configured to rotate the conveyance roller; a second motor configured to rotate the sheet roll along with conveyance of the sheet; a tension estimator configured to estimate tension of the sheet conveyed by the rotation of the conveyance roller; a measuring device configured to measure a physical quantity related to rotary motion of the conveyance roller; and a controller, wherein the controller is configured to: estimate acceleration torque of the second motor required for rotating the sheet roll depending on acceleration of the conveyance roller, based on rotation acceleration of the conveyance roller specified by the physical quantity measured by the measuring device; calculate a feedforward control input for the second motor based on the acceleration torque estimated; calculate a feedback control input for the second motor based on target tension and estimated tension as the tension estimated by the tension estimator; control the second motor based on at least one of the feedback control input calculated and the feedforward control input calculated; and control the second motor at least based on the feedforward control input from among the feedback control input and the feedforward control input under a condition that the conveyance roller is accelerated. 
     According to a second aspect of the present disclosure, there is provided a sheet conveyor, including: a holder configured to detachably hold a sheet roll; a conveyance roller configured to convey, by rotation, a sheet pulled out from the sheet roll; a first motor configured to rotate the conveyance roller; a second motor configured to rotate the sheet roll along with the conveyance of the sheet; a tension estimator configured to estimate tension of the sheet conveyed by the rotation of the conveyance roller; a measuring device configured to measure a physical quantity related to rotary motion of the conveyance roller; and a controller, wherein the controller is configured to: control the first motor, based on the physical quantity measured by the measuring device, such that the conveyance roller rotates in accordance with a velocity profile; estimate acceleration torque of the second motor required for rotating the sheet roll depending on acceleration of the conveyance roller, based on target rotation acceleration of the conveyance roller specified by the velocity profile; calculate a feedforward control input for the second motor based on the acceleration torque estimated; calculate a feedback control input for the second motor based on target tension and estimated tension as the tension estimated by the tension estimator; control the second motor based on at least one of the feedback control input calculated and the feedforward control input calculated; and control the second motor at least based on the feedforward control input from among the feedback control input and the feedforward control input, under a condition that the conveyance roller is accelerated. 
     According to a third aspect of the present disclosure, there is provided an image forming system including: the sheet conveyor as defined in the first aspect or the second aspect and a recording unit. The recording unit can form an image on the sheet conveyed by the sheet conveyor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts a configuration of an image forming system according to a first embodiment of the present disclosure. 
         FIG. 2  illustrates functions of a tensioner. 
         FIG. 3  is a block diagram of an electrical configuration of the image forming system. 
         FIG. 4  is a flowchart of a process executed by a main controller. 
         FIG. 5  is a block diagram of a velocity controller. 
         FIG. 6  is a block diagram of a configuration of a tension controller according to the first embodiment. 
         FIG. 7  is a flowchart of a process executed by a gain setter. 
         FIG. 8  is a block diagram of a configuration of a tension controller according to a second embodiment. 
         FIG. 9  is a block diagram of a configuration of a feedforward controller according to the second embodiment. 
         FIG. 10  is a flowchart partially indicating a process executed by the main controller in the second embodiment. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     First the Embodiment 
     A first embodiment of the present disclosure will be described with reference to the accompanying drawings. An image forming system  1  of this embodiment depicted in  FIG. 1  is configured so as to form an image on a sheet Q pulled out from a sheet roll Q 0  (rolled sheet). The image forming system  1  functions as a sheet conveying device for conveying the sheet Q toward the lower side of the recording head  40 . 
     The image forming system  1  includes a holder  10  (see  FIG. 3 ), a tensioner  15 , a conveying roller  20 , a nip roller  25 , a belt mechanism  30 , and a recording head  40 . In  FIG. 1 , configuration downstream of the belt mechanism  30  in a conveyance direction of the seat Q is omitted. Downstream of the belt mechanism  30 , for example, a cutter for cutting the sheet Q is provided. 
     The holder  10  removably holds the sheet roll Q 0 . The sheet roll Q 0  is formed by the sheet Q wound around a hollow core material. The holder  10  includes a rotation shaft  10 A inserted through the core material of the sheet roll Q 0 , and a holder main body (not depicted in the drawing(s)) that rotatably holds the rotation shaft  10 A. 
     The holder main body is fixed in a casing (not depicted in the drawing(s)) of the image forming system  1 . The core material of the sheet roll Q 0  is fixed so as not to slide with respect to the rotation shaft  10 A of the holder  10 . As a result, the sheet roll Q 0  rotates together with the rotation shaft  10 A of the holder  10 . 
     After the sheet roll Q 0  is mounted on the rotating shaft  10 A, the sheet Q is manually pulled out from the sheet roll Q 0  via the tensioner  15  to a position where the sheet Q has passed through the nip point P 2  between the conveying roller  20  and the nip roller  25 . Point P 1  in  FIG. 1  indicates the point at which the sheet Q is pulled out of the sheet roll Q 0 . 
     The conveying roller  20  conveys the sheet Q nipped between the conveying roller  20  and the nip roller  25  in the conveyance direction indicated by the thick arrow. As depicted in  FIG. 2 , the tensioner  15  is connected to the spring member  16  to be displaceable in a front-rear direction. The front side corresponds to the downstream side of the conveyance direction and the rear side corresponds to the upstream side of the conveyance direction. 
     The tensioner  15  is disposed at the rear side of the spring material  16 . The tensioner  15  applies tension to the sheet Q by backward urging force from the spring material  16 . 
     The tensioner  15  is displaced frontward by receiving pressing force from the sheet Q under a condition that the sheet Q pulled out from the sheet roll Q 0  is conveyed by the conveyance roller  20 . The pressing force from the sheet Q corresponds to tension of the sheet Q.  FIG. 2  depicts a state where the tensioner  15  and the sheet Q are displaced from a position depicted by solid lines to a position depicted by dotted lines due to the pressing force from the sheet Q. 
     A position in the front-rear direction of the tensioner  15  is stabilized at a position where the urging force of the spring material  16  and the tension of the sheet Q are balanced. The image forming system  1  is configured to estimate the tension of the sheet Q and control the tension by using the position of the tensioner  15  as an index (details are described below). 
     The belt mechanism  30  is disposed downstream of the conveyance roller  20  in the conveyance direction. The belt mechanism  30  conveys the sheet Q conveyed from the conveyance roller  20  further downstream. As depicted in  FIG. 1 , the belt mechanism  30  includes a driving roller  31 , a driven roller  32 , and a belt  33  stretched between the driving roller  31  the driven roller  32 . The driving roller  31  rotates the belt  33  by rotary motion synchronized with the conveyance roller  20 . 
     The belt mechanism  30  further includes the first facing roller  35  and the second facing roller  36 . The first facing roller  35  faces the driving roller  31  with the belt  33  interposed therebetween. The second facing roller  36  faces the driven roller  32  with the belt  33  interposed therebetween. 
     The sheet Q conveyed from the conveyance roller  20  passes between the first facing roller  35  and the belt  33  due to the rotation of the belt  33 , so that the sheet Q is conveyed downstream. The sheet Q is conveyed further downstream by passing between the second facing roller  36  and the belt  33 . A conveyance velocity of the sheet Q by the rotation of the belt  33  is the same as a conveyance velocity of the sheet Q by use of the conveyance roller  20 . 
     For example, the belt mechanism  30  can have an air absorbing function. That is, the belt  33  may have fine holes through which air passes. A suction device (not depicted) that suctions air may be provided below the belt  33 . The sheet Q may be conveyed while being sucked or absorbed to a surface of the belt  33  by the air suction performed by the suction device. 
     The recording head  40  is provided above the belt mechanism  30  to form an image on the sheet Q passing below the recording head  40 . The recording head  40 , which is a line head, simultaneously forms images for an entirety in a line direction of the sheet Q passing below the recording head  40 . The line direction is a direction along the surface of the sheet Q. The line direction is the conveyance direction of the sheet Q, in other words, a direction orthogonal to a longitudinal direction of the sheet Q. 
     The recording head  40  may be, for example, an ink-jet head that forms an image on the sheet Q in accordance with an ink-jet system. The recoding head  40  may be a thermal head that forms an image on the sheet Q in accordance with a thermosensitive system or a thermal transfer system. 
     Under a condition that the recording head  40  forms an image in accordance with the ink-jet system, a fixer  45  for drying and fixing ink may be provided downstream of the recoding head  40  in the conveyance direction. As depicted by the dotted line in  FIG. 1 , the fixer  45  may be provided above the belt mechanism  30  such that the fixer  45  is adjacent to the recording head  40 . 
     Subsequently, an electrical configuration of the image forming system  1  is explained in detail. As depicted in  FIG. 3 , the image forming system  1  includes the controller  50  that controls an entire system. The image forming system  1  further includes a supply motor  61 , a motor driver  63 , a rotary encoder  65 , and a measurement circuit  67  to control rotation of the sheet roll Q 0  installed in the holder  10 . 
     The supply motor  61  is connected to the rotation shaft  10 A of the holder  10  via a gear (not depicted). The supply motor  61  applies power to the rotation shaft  10 A. The rotation shaft  10 A of the holder  10  rotates under a condition that the rotation shaft  10 A receives power from the supply motor  61 . The sheet roll Q 0  rotates along with the rotation shaft  10 A. 
     The supply motor  61  may be a direct-current motor (DC motor). The supply motor  61  drives the rotation shaft  10 A by generating rotation torque depending on a drive current input from the motor driver  63 . The motor driver  63  inputs, to the supply motor  61 , a drive current depending on a control input U SR  input from the controller  50 . 
     The rotary encoder  65  is provided in the rotation shaft  10 A of the holder  10  or a rotation shaft of the supply motor  61 . The rotary encoder  65  outputs an encoder signal depending on rotation. The measurement circuit  67  measures a rotation position and a rotation velocity (i.e., rotation angle and angular velocity) of the sheet roll Q 0  as a physical quantity related to the rotary motion of the sheet roll Q 0 . The measurement circuit  67  inputs, to the controller  50 , the rotation position and the rotation velocity measured. The rotation position and the rotation velocity of the rotation shaft  10 A correspond to the rotation position and the rotation velocity of the sheet roll Q 0 . 
     The image forming system  1  further includes a conveyance motor  71 , a motor driver  73 , a rotary encoder  75 , and a measurement circuit  77  as the configuration for controlling the rotation of the conveyance roller  20 . 
     The conveyance motor  71  may be a direct-current motor (DC motor). The conveyance motor  71  is connected to the conveyance roller  20  via a gear. The conveyance motor  71  rotates and drives the conveyance roller  20  by generating rotation torque depending on a drive current input from the motor driver  73 . The motor driver  73  inputs, to the conveyance motor  71 , a drive current depending on a control input UPF input from the controller  50 . 
     The rotary encoder  75  is provided in a rotation shaft of the conveyance roller  20  or a rotation shaft of the conveyance motor  71 . The rotary encoder  75  outputs an encoder signal depending on rotation. The measurement circuit  77  measures a rotation position and a rotation velocity (i.e., rotation angle and angular velocity) of the conveyance roller  20  as a physical quantity related to the rotary motion of the conveyance roller  20 . The measurement circuit  77  inputs, to the controller  50 , the rotation position and the rotation velocity measured. 
     The image forming system  1  further includes a position detector  80  that detects a position of the tensioner  15 . The position detector  80  detects a position X in the front-rear direction of the tensioner  15  with reference to a predefined origin position. The position detector  80  inputs the detected position X to the controller  50 . The position detector  80  may be configured, for example, by a linear encoder. 
     The image forming system  1  further includes a head driver  90 , a registration sensor  91 , a distance sensor  93 , a user interface  95 , and a communication interface  97 . The head driver  90  is configured to drive the recording head  40  in accordance with a control signal from the controller  50 . The registration sensor  91  is provided upstream of the belt mechanism  30 . The registration sensor  91  is configured to detect a leading edge of the sheet Q passing therethrough, and to input a detection signal to the controller  50 . 
     The distance sensor  93  is disposed at a position facing the sheet roll Q 0 . The distance sensor  93  is configured to measure a distance between the distance sensor  93  and the surface of the sheet roll Q 0  and to input a measurement signal to the controller  50 . For example, the distance sensor  93  is capable of measuring the distance between the distance sensor  93  and the surface of the sheet roll Q 0  by irradiating the surface of the sheet roll Q 0  with light and receiving its reflection light. The distance sensor  93  may be a sensor that measures a distance by use of ultrasonic waves. 
     The user interface  95  includes a display section for displaying a variety of information for a user and an input section for receiving instructions from the user. The display section is, for example, a liquid crystal display. The input section is, for example, a touch panel on the liquid crystal display. 
     The communication interface  97  is configured to communicate with an information device in the wired or wireless communication. The communication interface  97  may be a USB interface or a wired/wireless LAN interface. The information device may be a personal computer or a tablet terminal owned by the user. 
     The controller  50  includes a main controller  51 , a printing controller  53 , a velocity controller  55 , and a tension controller  57 . The main controller  51  includes a processor  51 A and a memory  51 B. The memory  51 B includes a Random Access Memory (RAM) and a flush memory. 
     The processor  51 A executes a variety of processes in accordance with computer programs stored in the memory  51 B. In the following, it can be understood that processes executed by the main controller  51  are executed by the processor  51 A in accordance with the computer program(s). 
     The printing controller  53 , the velocity controller  55 , and the tension controller  57  are configured, for example, by an ASIC. Image data of a printing object is input from the main controller  51  to the printing controller  53 . The printing controller  53  inputs, to the head driver  90 , a control signal for causing the recording head  40  to print an image based on the image data of the printing object. 
     The velocity controller  55  determines the control input UPF for the controller motor  71  so that the conveyance roller  20  rotates at a target rotation velocity in accordance with an instruction from the main controller  51 . The velocity controller  55  inputs, to the motor driver  73 , the control input UPF determined. In this embodiment, the control velocity of the sheet Q is controlled by controlling the rotation velocity of the conveyance roller  20 . 
     The tension controller  57  determines the control input U SR  for the supply motor  61  so that the sheet Q is conveyed while having target tension in accordance with an instruction from the main controller  51 . The tension controller  57  inputs, to the motor driver  63 , the control input U SR  determined. 
     Under a condition that the main controller  51  receives a printing instruction and image data of a printing object from an information device through the communication interface  97 , the main controller  51  executes processes indicated in  FIG. 4 . The main controller  51  controls respective sections of the image forming system  1  in cooperation with the printing controller  53 , the velocity controller  55 , and the tension controller  57  so that an image based on the image data of the printing object received is formed on the sheet Q. 
     Under a condition that the processes indicated in  FIG. 4  are started, the main controller  51  executes an initial process (S 110 ). The initial process includes a process for arranging the leading edge of the sheet Q at a predefined starting point. The starting point may be a position where the leading edge of the sheet Q is detected by the registration sensor  91 , or a position shifted downstream in the conveyance direction by a predefined distance from the position where the leading edge of the sheet Q is detected by the registration sensor  91 . 
     The starting point may be a position where the leading edge of the sheet Q enters the belt mechanism  30 . Alternatively, the starting point may be a point that is upstream in the conveyance direction from a position, where image formation is performed on the sheet Q by the recording head  40 , by a distance required for acceleration of the sheet Q. 
     After arranging the leading edge of the sheet Q at the starting point, the main controller  51  starts a conveyance process of the sheet Q (S 120 ). In the conveyance process, the main controller  51  inputs a velocity profile to the velocity controller  55 . The velocity controller  55  controls the rotation velocity of the conveyance roller  20  in accordance with the velocity profile. The velocity profile indicates a target rotation velocity of the conveyance roller  20  until the sheet Q is stopped at a target stop position. 
     Specifically, the velocity profile indicates a target rotation velocity in an acceleration section, a target rotation velocity in a constant velocity section, and a target rotation velocity in a deceleration section. The sheet Q accelerates until the sheet Q reaches a predefined velocity by controlling the rotation velocity of the conveyance roller  20  in accordance with the velocity profile. After reaching the predefined velocity, the sheet Q moves at a constant velocity, and then decelerates. 
     In the conveyance process, the main controller  51  further inputs a tension profile to the tension controller  57 . The tension controller  57  executes tension control of the sheet Q in accordance with the tension profile. The tension profile indicates target tension until the sheet Q is stopped at the target stop position. 
     After starting the conveyance process, the main controller  51  waits until the sheet Q reaches the predefined velocity (S 130 ). The main controller  51  starts the printing process under a condition that the sheet Q starts constant velocity movement (S 140 ). In the printing process, the main controller  51  causes the printing controller  53  to execute drive control of the recording head  40  for forming the image based on the image data of the printing object on the sheet Q. The recording head  40  repeatedly executes the image forming operation in the line direction in synchronization with movement in the conveyance direction of the sheet Q. 
     The main controller  51  executes an ending process (S 160 ) under a condition that the printing process and the conveyance process are completed (S 150 : Yes). The ending process includes a process in which the user is informed of the completion of printing through the user interface  95 . Then, the main controller  51  ends the processes indicated in  FIG. 4 . 
     Referring to  FIG. 5 , a detailed configuration of the velocity controller  55  is explained below. The velocity controller  55  calculates the control input UPF for the conveyance motor  71  based on a deviation between the rotation velocity of the conveyance roller  20  measured by the measurement circuit  77  and the target rotation velocity. The velocity controller  55  is configured to execute feedback control for the conveyance roller  20  based on the control input UPF calculated. In the following, the actual rotation velocity means a measured value of the rotation velocity. 
     The velocity controller  55  includes a velocity instruction device  101 , a deviation calculator  103 , a PID controller  105 , a static friction compensation device  107 , and an adder  109 . The velocity instruction device  101  outputs a target rotation velocity (or at each point of time from the start of control in accordance with the velocity profile input from the main controller  51 . 
     The deviation calculator  103  calculates a deviation E V =(ω r −ω) between the target rotation velocity ω r  output from the velocity instruction device  101  and an actual rotation velocity w input from the measurement circuit  77 . The PID controller  105  calculates a control input Uv for the conveyance motor  71  based on the deviation E V  input from the deviation calculator  103 . 
     The PID controller  105  includes: a proportional element that amplifies the deviation E V  with a gain G p  and outputs it; an integral element that amplifies an integral value INT(E V ) of the deviation E V  with a gain G and outputs it; and a differential element that amplifies an integral value DIF(E V ) of the deviation E V  with a gain G d  and outputs it. The PID controller  105  calculates a total of the output from the proportional element, the integral element, and the differential element as the control input Uv for the conveyance motor  71 . 
     The static friction compensation device  107  outputs a compensation amount C for compensating for the shortage of control input Uv caused by static friction. The compensation amount C is a fixed value under a condition that the actual rotation velocity w is zero, that is, in a static state. The compensation amount C is zero under a condition that the actual rotation velocity w is not zero, that is, in a non-static state. 
     The adder  109  corrects the control input Uv output from the PID controller  105  by the compensation amount C, and inputs, to the motor driver  73 , a control input UPF=Uv C after correction. The motor driver  73  inputs, to the conveyance motor  71 , a drive current corresponding to the control input UPF input from the velocity controller  55 , and drives the conveyance motor  71  so that rotation torque corresponding to the control input UPF is generated. The rotation velocity of the conveyance roller  20  and the conveyance velocity of the sheet Q corresponding to the rotation velocity of the conveyance roller  20  are subjected to the feedback control by the velocity controller  55 . 
     The tension control is executed by the tension controller  57  depicted in  FIG. 6 . The tension controller  57  calculates the control input U SR  for the supply motor  61  based on a deviation between tension of the sheet Q estimated from the position X of the tensioner  15  detected by the position detector  80  (hereinafter referred to as estimated tension) and the target tension. The tension controller  57  thus executes the feedback control for the tension of the sheet Q based on the control input U SR  calculated. 
     As depicted in  FIG. 6 , the tension controller  57  includes a tension instruction device  110 , a tension estimator  120 , a deviation calculator  130 , a PID controller  140 , a roll diameter estimator  150 , a feedforward controller  160 , an adder  170 , and a gain setter (gain setting device)  180 . 
     The tension instruction device  110  outputs target tension T r  at each point of time from the start of control in accordance with the tension profile input from the main controller  51 . The tension estimator  120  estimates tension T acting on the sheet Q based on the position X of the tensioner  15  input from the position detector  80 . Specifically, the tension estimator  120  can calculate, as estimated tension T, a value k·X obtained by multiplying the position X of the tensioner  15  by a certain proportional efficient k. 
     The deviation calculator  130  calculates a deviation E T =T r −T between the target tension T r  and the estimated tension T. The PID controller  140  calculates a feed back control input U B  for the supply motor  61  based on the deviation E T  input from the deviation calculator  130 . 
     As depicted in  FIG. 6 , the PID controller  140  includes a proportional gain amplifier  141 , an integral gain amplifier  142 , a differential gain amplifier  143 , an integrator  145 , a differentiator  146 , and an adder  148 . The deviation E T  calculated by the deviation calculator  130  is input to the proportional gain amplifier  141 , the integrator  145 , and the differentiator  146 . The proportional gain amplifier  141  amplifies the deviation E T  input from the deviation calculator  130  with the gain K p  and outputs it. 
     The integrator  145  executes integral calculation for the deviation E T  and inputs an integral value INT(E T ) of the deviation E T  to the integral gain amplifier  142 . The integral gain amplifier  142  amplifies the integral value INT(E T ) of the deviation E T  input from the integrator  145  with a gain K i  and outputs it. 
     The differentiator  146  executes differential calculation for the deviation E T , and inputs a differential value DIF(E T ) of the deviation E T  to the differential gain amplifier  143 . The differential gain amplifier  143  amplifies the differential value DIF(E T ) of the deviation E T  input from the differentiator  146  with a gain K d  and outputs it. 
     The adder  148  adds K p ·E T  output from the proportional gain amplifier  141 , K i ·INT(E T ) output from the integral gain amplifier  142 , and K d ·DIF(E T ) output from the differential gain amplifier  143 . The adder  148  outputs an addition value K p ·E T  Ki·INT(E T )+K d ·DIF(E T ) as the feedback control input U B  for the supply motor  61 . 
     The adder  170  outputs an addition value U B +U F  obtained by adding the feedback control input U B  input from the PID controller  140  and a feedforward control input U F  input from the feedforward controller  160  as the control input U SR  for the supply motor  61 . 
     The feedforward controller  160  includes a differentiator  161 , an acceleration torque estimator  163 , and an FF gain amplifier  165 . The differentiator  161  differentiates the rotation velocity ω of the conveyance roller  20  input from the measurement circuit  77  to calculate rotation acceleration α of the conveyance roller  20 . The rotation acceleration corresponds to angle acceleration. In the following, the rotation acceleration α calculated from the differentiator  161  is expressed as an actual rotation acceleration α. 
     The acceleration torque estimator  163  estimates acceleration torque τ of the supply motor  61  required for acceleration of the conveyance roller  20  based on the actual rotation acceleration α, in other words, required for rotation of the sheet roll Q 0  depending on the acceleration of the sheet Q. Specifically, the acceleration torque τ is calculated in accordance with an equation τ=J(R)·(R P /R)·α based on the actual rotation acceleration α, the roll diameter R that is a radius of the sheet roll Q 0 , a radius R P  of the conveyance roller  20 , and an inertia J(R) of the sheet Q 0  estimated from the roll diameter R. 
     Under a condition that the rotation acceleration of the conveyance roller  20  is a, the acceleration of the sheet Q conveyed by the rotation of the conveyance roller  20  is R P ·α. The sheet roll Q 0  is required to rotate at rotation acceleration (R P /R)·α to pull out the sheet Q from the sheet roll Q 0  at the same acceleration. Under a condition that the inertia is J, the acceleration torque required for achieving this rotation is J·(R P /R)·α. 
     A function J(R) for calculating the inertia J(R) of the sheet roll Q 0  with the roll diameter being R is prepared in advance. The radius R P  of the conveyance roller  20  is a fixed value of the image forming system  1 . 
     The roll diameter R of the sheet roll Q 0  is estimated by the roll diameter estimator  150  based on the measurement signal output from the distance sensor  93 . The measurement signal output from the distance sensor  93  indicates a distance Z between the surface of the sheet roll Q 0  and the distance sensor  93 . The distance from the center of the sheet roll Q 0  to the distance sensor  93  is a fixed value Z 0 . The roll diameter estimator  150  can estimate the roll diameter R of the sheet roll Q 0  by subtracting the distance Z from the fixed value Z 0  (R=Z 0 −Z). 
     The acceleration torque estimator  163  calculates the acceleration torque τ based on the above equation and information of the roll diameter R input from the roll diameter estimator  150 . The FF gain amplifier  165  adjusts the acceleration torque τ calculated so that the acceleration torque τ calculated is amplified by a gain K FF , and outputs acceleration torque K FF ·τ after adjustment as the feedforward control input U F . The gain K FF  is normally a value 1, and the gain K FF  may be finely adjusted from the value 1 depending on machine characteristics of a rotation system. 
     The motor driver  63  inputs a drive current corresponding to the control input U SR =U F  U B  to the supply motor  61 , and drives the supply motor  61  so that rotation torque corresponding to the control input U SR  is generated. The tension of the sheet Q is controlled to the target tension by executing the feedforward control and the feedback control for the supply motor  61 . 
     In this embodiment, the gain setter  180  is configured to adjust the gains K p , Kc, and K d  in the PID controller  140  based on the roll diameter R estimated by the roll diameter estimator  150 . The gains K p , K i , and K d  are set to K p =K p (R), =K i (R), K d =K d (R) in accordance with the functions K p (R), K i (R), and K d (R) of which variables are the roll diameter R. The functions K p (R), K i (R), and K d (R) are determined in advance through an examination. 
     Specifically, the gain setter  180  adjusts the gains K p , K i , and K d  by repeatedly executing the processes in  FIG. 7 . Under a condition that the processes in  FIG. 7  are started, the gain setter  180  calculates gains K p =K p (R), =K i (R), K d =K d (R) to be set in the PID setter  140  based on the latest roll diameter R estimated by the roll dimeter estimator  150  (S 210 ). 
     Further, the gain setter  180  determines whether the velocity profile is the constant velocity section (S 220 ). Under a condition that the gain setter  180  has determined that the velocity profile is the constant velocity section, the gain setter  180  updates the gains K p , K i , K d  to values depending on the roll diameter R by setting the gains K p =K p (R), K i =K i (R), K d =K d (R) calculated in S 210  in the PID setter  140  (S 240 ). Then, the gain setter  180  ends the processes in  FIG. 7 . 
     Under a condition that the gain setter  180  has determined in S 220  that the velocity profile is not the constant velocity section, the gain setter  180  corrects the gains K p =K p (R), =K i (R), K d =K d (R) calculated in S 210  to small values (S 230 ). For example, the gain setter  180  corrects the gains K p =K p (R), =K i (R), K d =K d (R) calculated in S 210  to values K p =h·K p (R), K i =h·K i (R), K d =h·K d (R) obtained by multiplying the gains K p =K p (R), =K i (R), K d =K d (R) by a coefficient h less than one. 
     After that, the gain setter  180  sets the gains corrected in S 230  in the PID controller  140  (S 240 ). After executing the process of S 240 , the gain setter  180  ends the processes in  FIG. 7 . The gain setter  180  repeats such processes. 
     The image forming system  1  of this embodiment described above differentiates the rotation velocity w of the conveyance roller  20  measured by the rotary encoder  75  and the measurement circuit  77  to specify the rotation acceleration α of the conveyance roller  20 . Based on the rotation acceleration α of the conveyance roller  20  specified, the image forming system  1  calculates the acceleration torque τ of the supply motor  61  required for rotating the sheet roll Q 0  depending on the acceleration of the conveyance roller  20 . 
     Based on the acceleration torque τ calculated, the controller  50  calculates the feedforward control input U F  for the supply motor  61 . Further, the controller  50  estimates the tension of the sheet Q based on the position X of the tensioner  15 . The controller  50  calculates the feedback control input U B  for the supply motor  61  based on the deviation between the target tension T r  and the estimated tension T. 
     The controller  50  calculates the control input U SR  for the supply motor  61  based on the feedback control input U B  and the feedforward control input U F . Then, the controller  50  controls the supply motor  61  so that the drive current corresponding to the calculated control input U SR  is input to the supply motor  61 . 
     In the image forming system  1 , a component of the feedforward control input U F  included in the control input U SR  functions significantly during a process in which the sheet Q is conveyed with acceleration by rotation of the conveyance roller  20 . 
     That is, the sheet roller Q 0  rotates so that the sheet Q is pulled out from the sheet roll Q 0  depending on the acceleration of the sheet Q by rotation of the conveyance roller  20 . The acceleration torque depending on the inertia of the sheet roll Q 0  is compensated by the feedforward control input U F . 
     In this embodiment, the gains K p , and K d  of the PID controller  140  at the time of acceleration are adjusted to be smaller than those at the time of the constant velocity so that the feedforward control functions significantly. This reduces the feedback control input U B . The rotation acceleration α is substantially zero in the constant velocity section. The feedforward control thus hardly functions, and the feedback control functions significantly. 
     In this embodiment, the sheet Q forming the sheet roll Q 0  is reduced by use, which changes the radius R of the sheet roll Q 0 , the weight of the sheet roll Q 0 , and the inertia J(R). The controller  50  estimates the inertia J(R) of the sheet roll Q 0  based on the radius R of the sheet roll Q 0  estimated. Based on the inertia J(R) and the rotation acceleration α of the conveyance roller  20 , the controller  50  estimates the acceleration torque τ depending on the inertia J(R). 
     According to this embodiment, the deviation E T  between the target tension T r  and the estimated tension T, the integral value of the deviation E T , and the differential value of the deviation E T  are amplified by amounts corresponding to the gains K p , K i , and K d , and the feedback control input U B  corresponding to the amplified values is calculated. The gains K p , and K d  are adjusted to values corresponding to the diameter R of the sheet roll Q 0  as described above. 
     Thus, in this embodiment, the supply motor  61  is controlled appropriately immediately after a new sheet roll Q 0  is installed in the holder  10 , immediately before the sheet Q in the sheet roll Q finishes up, at the time of acceleration, and at the time of the constant velocity. 
     That is, the controller  50  inhibits the effect from a remaining amount and a motional state of the sheet roll Q 0 , and is capable of appropriately executing the conveyance velocity control and the tension control of the sheet Q so that they are linked with each other. Further, the controller  50  controls the conveyance velocity and the tension of the sheet Q with high accuracy to convey the sheet Q appropriately. Thus, it is possible to inhibit a skew of the sheet Q and errors in the conveyance velocity and the stop position of the sheet Q due to an excess or shortage of tension. 
     According to the technique of the present disclosure, it is possible to appropriately execute the conveyance control of the sheet Q with an acceleration process under the environment where the weight of the sheet roll Q 0  changes depending on the consumption of the sheet Q. 
     In the above embodiment, the control input U SR  including the feedforward control input U F  and the feedback control input U B  is calculated for the supply motor  61  irrespective of whether the section is the acceleration section. However, the tension controller  57  may calculate the control input U SR  only including the feedback control input U B  in the constant velocity section. That is, the tension controller  57  may calculate the control input U SR  not to include the feedforward control input U F . 
     The tension controller  57  may calculate the control input U SR  only including the feedforward control input U F  in a non-constant velocity section, especially in the acceleration section. That is, the tension controller  57  may calculate the control input U SR  not to include the feedback control input U B . 
     The controller  50  can control the supply motor  61  based on at least one of the feedback control input U B  and the feedforward control input U F . During the acceleration of the conveyance roller  20 , the controller  50  can control the supply motor  61  at least based on the feedforward control input U F  from among the feedback control input U B  and the feedforward control input U F . The controller  50  can control the supply motor  61  at least based on the feedback control input U B  during the rotation of the conveyance roller  20  at the constant velocity. 
     The holding structure of the sheet roll Q 0  by the holder  10  and the driving system of the sheet roll Q 0  are not limited to the above embodiment. In the image forming system  1  described above, the core material of the sheet roll Q 0  is inserted into the rotation shaft  10 A of the holder  10 . 
     However, the holder may be formed from a hollow cylindrical material of which inside has an accommodation space for the sheet roll Q 0 . The holder may be configured so that an inner surface defining the accommodation space for the sheet roll Q 0  rotates. The sheet roll Q 0  may rotate depending on the rotation of the inner surface of the holder in a state of being accommodated in the holder. Further, a roller brought into contact with an outer circumferential surface of the sheet roll Q 0  may be provided. The sheet roll Q 0  may rotate by rotation of this roller. 
     Second Embodiment 
     Subsequently, the image forming system  1  of the second embodiment is explained. The image forming system  1  of the second embodiment is an image forming system partially different from the first embodiment. In the image forming system  1  of the second embodiment, the constitutive parts or components, which are the same as or equivalent to those of the first embodiment, are designated by the same reference numerals, and any explanation thereof is omitted as appropriate. Configurations of the image forming system  1  of the second embodiment that are different from the first embodiment are explained selectively. 
     In the second embodiment, the controller  50  includes a tension controller  200  depicted in  FIG. 8  instead of the tension controller  57  depicted in  FIG. 6 . The tension controller  200  includes the tension instruction device  110 , the tension estimator  120 , the deviation calculator  130 , the PID controller  140 , the roll diameter estimator  150 , the gain setter (gain setting device)  180 , a primary delay filter  210 , a target velocity generator  220 , a deviation calculator  230 , an adder  240 , a supply velocity controller  250 , a feedforward controller  260 , and an adder  270 . 
     The deviation calculator  130  calculates a deviation E T =T r −T between the target tension T r  output from the tension instruction device  110  and the estimated tension T output from the tension estimator  120  similar to the first embodiment. The PID controller  140  calculates a tension control input U T =K p ·E T +K i ·INT(E T )+K d ·DIF(E T ) based on the deviation E T  input from the deviation calculator  130 . 
     The tension control input U T  corresponds to the feedback control input U B  of the first embodiment. The gain setter  180  is configured to adjust the gains K p , K i , and K d  in the PID controller  140  based on the roll diameter R estimated by the roll diameter estimator  150 . 
     The target velocity generator  220  calculates a target rotation velocity ω sr  of the sheet roll Q 0  based on the target rotation velocity ω r  of the conveyance roller  20  input from the velocity instruction device  101  of the velocity controller  55  via the primary delay filter  210  and the roll diameter R estimated by the roll diameter estimator  150 . 
     The target velocity generator  220  calculates the target rotation velocity ω sr  in accordance with an equation ω sr =(R P /R)·ω r  so that the conveyance roller  20  and the sheet roll Q 0  rotate at the same circumferential velocity. R p  is a radius of the conveyance roller  20  as described above. The target rotation velocity ω sr  of the sheet roll Q 0  corresponds to the target rotation velocity ω sr  of the rotation shaft  10 A. 
     The deviation calculator  230  calculates a deviation E W =(ω sr −ω s ) between the target rotation velocity ω sr  output from the target velocity generator  220  and the rotation velocity ω s  of the sheet roll Q 0  measured by the measurement circuit  67 . The rotation velocity ω s  of the sheet roll Q 0  corresponds to an angular velocity of the sheet roll Q 0  or the rotation shaft  10 A. 
     The adder  240  calculates a control input U C =(U T +E W ) by adding the deviation E W  to the tension control input U T  output from the PID controller  140 . The supply velocity controller  250  is configured as the PID controller to calculate a feedback control input U B * by adding a velocity control component to the control input U C  output from the adder  240 . Instead of the feedback control input U B  in the first embodiment, the feedback control input U B * is input to the adder  270  in this embodiment. 
     The supply velocity controller  250  includes a proportional gain amplifier  251 , an integral gain amplifier  252 , a differential gain amplifier  253 , an integrator  255 , a differentiator  256 , and an adder  258 . The control input U C  output from the adder  240  is input to the proportional gain amplifier  251 , the integrator  255 , and the differentiator  256 . The proportional gain amplifier  251  amplifies the control input U C  input with a gain K wp  and outputs it. 
     The integrator  255  inputs an integral value INT(U C ) of the control input U C  to the integral gain amplifier  252 . The integral gain amplifier  252  amplifies the integral value INT(U C ) input with a gain K wi  and outputs it. The differentiator  256  inputs a differential value DIF(U C ) of the control input U C  to the differential gain amplifier  253 . The differential gain amplifier  253  amplifies the differential value DIF(U C ) input with a gain K wd  and outputs it. 
     The adder  258  adds K wp ·U C  output from the proportional gain amplifier  251 , K wi ·INT(U C ) output from the integral gain amplifier  252 , and K wd ·DIF(U C ) output from the differential gain amplifier  253 . Then, the adder  258  outputs an addition value K wp ·U C +K wi ·INT(U c )+K wd ·DIF(U c ) as the feedback control input U B *. 
     As depicted in  FIG. 9 , the feedforward controller  260  includes a differentiator  261 , an acceleration torque estimator  263 , a viscous friction estimator  265 , a dynamic friction estimator  267 , and adders  268 ,  269 . The differentiator  261  differentiates the target rotation velocity ω r  of the conveyance roller  20  input from the primary delay filter  210  to calculate target rotation acceleration α r  of the conveyance roller  20 . 
     The acceleration torque estimator  263  estimates, based on the target rotation acceleration α r , the acceleration torque τ of the supply motor  61  required for rotating the sheet roll Q 0  depending on the acceleration of the conveyance roller  20 . Specifically, the acceleration torque τ is calculated in accordance with an equation τ=J(R)·(R P /R)·α r  based on the target rotation acceleration α r , the roll diameter R estimated by the roll diameter estimator  150 , the radius R P  of the conveyance roller  20 , and the inertia J(R) of the sheet Q 0  estimated from the roll diameter R. 
     The viscous friction estimator  265  estimates viscous friction torque τ vf  in a rotary coordinate system of the sheet roll Q 0  based on the target rotation velocity ω r  of the conveyance roller  20  input from the primary delay filter  210 . The viscous friction torque τ vf  may be calculated in accordance with an equation τ vf =C vf ·(R p /R)·ω r . C vf  corresponds to a viscous friction coefficient. (R p /R)·ω r  is the target rotation velocity ω sr  of the sheet roll Q 0  or the rotation shaft  10 A. 
     The dynamic friction estimator  267  estimates dynamic friction torque τ df  in the rotary coordinate system of the sheet roll Q 0  based on the target rotation velocity for of the conveyance roller  20  input from the primary delay filter  210 . Specifically, under a condition that the target rotation velocity for is not zero, the dynamic friction estimator  267  calculates, based on a dynamic friction coefficient C df , dynamic friction torque τ df =C dr ·N(R) in the rotary coordinate system of the sheet roll Q 0 . N(R) is drag N depending on the roll diameter R. 
     Under a condition that the target rotation velocity for is zero, the dynamic friction estimator  267  calculates dynamic friction torque τ df =0. Or, under the condition that the target rotation velocity for is zero, the dynamic friction estimator  267  may calculate, based on a static friction coefficient C sf , static friction torque τ sf =C sf ·N(R) in the rotary coordinate system of the sheet roll Q 0  as the dynamic friction torque τ df . 
     The adder  268  calculates friction torque τ f =τ vf +τ df  by adding the dynamic friction torque τ df  input from the dynamic friction estimator  267  and the viscous friction torque τ vf  input from the viscous friction estimator  265 . 
     The adder  269  adds the friction torque τ f  input from the adder  268  to the acceleration torque τ input from the acceleration torque estimator  263  to calculate feedforward control input U F *=τ f +τ f . The adder  269  inputs the feedforward control input U F * calculated to the adder  270 . The feedforward control input U F * corresponds to a control input obtained by adding a friction compensating component to the feedforward control input U F  calculated from the feedforward controller  160  of the first embodiment. 
     The adder  270  outputs an addition value U B *+U F * obtained by adding the feedback control input U B * input from the supply velocity controller  250  and the feedforward control input U F * input from the feedforward controller  260 , as the control input U SR  for the supply motor  61 . 
     According to the tension controller  200  of the second embodiment described above, it is possible to control the rotation of the sheet roll Q 0  with high accuracy while including the friction torque caused by the rotary coordinate system of the sheet roll Q 0 . 
     The feedforward controller  260  of the second embodiment is different from that of the first embodiment and beneficial in that the feedforward control input U F * is calculated not based on the actual rotation velocity w of the conveyance roller  20  but based on the target rotation velocity ω r . 
     A power transmission system such as a gear is provided between the supply motor  61  and the rotation shaft  10 A of the holder  10 . Thus, there is a time lag until driving of the supply motor  61  is reflected in the rotary motion of the sheet roll Q 0 . The time lag may cause a control error if the feedforward control input U F  is calculated based on the actual rotation velocity ω of the conveyance roller  20  to control the supply motor  61 . 
     In the second embodiment, the feedforward control input U F * is calculated based on the target rotation velocity ω r  of the conveyance roller  20 . In this case, the rotary motion of the sheet roll Q 0  can be controlled by controlling the supply motor  61  while inhibiting the effect of the time lug. 
     Under the condition that the feedforward control input U F * is calculated based on the target rotation velocity ω r , tensioning for the sheet Q is preferably performed before the conveyance process of the sheet Q is started so that the target rotation velocity (Dr indicates movement or motion of the sheet Q well. 
     In the second embodiment, before the conveyance process of the sheet Q is started in S 120 , the main controller  51  executes a tensioning process (S 115 ) indicated in  FIG. 10 . In S 115 , in a state of stopping the conveyance roller  20 , the main controller  51  controls the tension controller  57  to rotate the supply motor  61  in a reverse direction until the estimated tension T reaches reference tension TO. 
     Under a condition that the supply motor  61  rotates in a normal direction, the sheet Q is conveyed or sent in the conveyance direction. In S 115 , rotating the supply motor  61  in the reverse direction in the state of stopping the conveyance roller  20  rewinds part of the sheet Q to the sheet roll Q 0 , and thus tension is applied to the sheet Q. 
     The reference tension TO is the target tension T r  under the condition that the conveyance process of the sheet Q is started in S 120  or tension in the vicinity thereof. In the conveyance process (S 120 ) of the sheet Q after the tensioning process (S 115 ) is executed, the tension of the sheet Q at the beginning of the conveyance process is substantially the same as the target tension T r , and the conveyance roller  20  and the sheet roll Q 0  rotate at substantially the same circumferential velocity. 
     In the conveyance process (S 120 ) executed after the tensioning process (S 115 ), the target rotation velocity (Dr indicates actual motion or movement of the sheet Q well and it is possible to appropriately execute the conveyance control of the sheet Q. 
     The exemplary embodiments of the present disclosure including the first embodiment and the second embedment are explained above. The present disclosure, however, is not limited to the exemplary embodiments described above and can adopt various aspects. 
     For example, the tensioning process (S 115 ) may be executed in the first embodiment. Similar to the feedforward controller  260  in the second embodiment, the feedforward controller  160  in the first embodiment may estimate the viscous friction torque and/or the dynamic friction torque and may calculate the feedforward control input U F  by adding the viscous friction torque and/or the dynamic friction torque to the acceleration torque τ. In that case, the feedforward controller  160  may estimate the viscous friction torque and/or the dynamic friction torque not based on the target rotation velocity ω r  but based on the actual rotation velocity ω. Similarly, instead of the target rotation velocity ω r , the actual rotation velocity ω may be input to the feedforward controller  260  of the second embodiment. 
     The technique of the present disclosure may be applied to various image forming systems. The technique of the present disclosure may be applied to an image forming system not including the belt mechanism  30 . In this case, the image forming system may include a platen for supporting the sheet Q, instead of the belt mechanism  30 . 
     The technique of the present disclosure may be applied to an image forming system in which a recording head of a serial driving system is provided as the recording head  40  instead of the line head. In this case, the recording head forms an image on the sheet Q by reciprocatingly moving in the line direction. The technique of the present disclosure may be applied to an image forming system of an electrophotographic system. 
     The technique of the present disclosure may be applied to a system for forming an image on a surface of the sheet Q that faces the outside in a radial direction of the sheet roll Q 0 . Or, the technique of the present disclosure may be applied to a system for forming an image on a back surface of the sheet Q that faces the inside in the radial direction of the sheet roll Q 0 . The technique of the present disclosure may be applied to a system for forming an image on both surfaces of the sheet Q. 
     The technique of the present disclosure can be applied not only to the system for forming an image on the sheet Q by use of a color material but also to a variety of systems. For example, the technique of the present disclosure may be applied to a system for making a mark in the sheet Q through perforation or to a system for irradiating a surface of the sheet Q with light to sterilize the surface. The technique of the present disclosure may be applied to a system for forming a trace pattern on a sheet-like substrate. The sheet roll Q 0  and the sheet Q may be paper, vinyl, or a flexible printed board (FPC). 
     The configuration(s) of the tensioner  15  and the tension estimator  120  is/are not limited to the above embodiments. The tensioner may be configured as an arm in which the first end is pivotally supported and the second end has a roller, like a pendulum arm. The tensioner may include an actuator to apply tension to the sheet Q, and tension may be estimated from a change amount of the actuator. A dedicated sensor may be provided to estimate tension. The sensor may act on the tensioner  15  or the sheet Q to detect tension. The configuration(s) of the rotary encoders  65  and  75  are not limited to the above embodiments. The rotary encoders  65  and  75  may not be optical rotary encoders, but magnetic rotary encoders. 
     In the above embodiment(s), the roll diameter R is measured by using the distance sensor  93 . The roll diameter R may be estimated without using the distance sensor  93 . For example, the roll diameter R may be estimated from the conveyance amount of the sheet Q of the conveyance roller  20  and the rotation amount of the sheet roll Q 0  corresponding thereto. The conveyance amount of the sheet Q can be specified by the rotation amount of the conveyance roller  20 . The rotation amounts (i.e., rotation angles) of the conveyance roller  20  and the sheet roll Q 0  can be measured based on the outputs from the rotary encoders  65  and  75 . 
     The printing controller  53 , the velocity controller  55 , and the tension controllers  57 ,  200  may be configured by combining the CPU and the ASIC. In each of the controller  50 , the main controller  51 , the printing controller  53 , the velocity controller  55 , and the tension controllers  57 ,  200 , the number of the CPU(s) and the ASIC(s) and whether or not the CPU and/or the ASIC is/are provided therein is not limited to the above specific examples. 
     The PID controllers  105 ,  140  used for feedback control may be replaced by any other controller such as a PI controller. Part of the gains K p , K i , and K d  may not be updated based on the roll diameter R. In the second embodiment, the gains K wp , K wi , and K wd  may be updated based on the roll diameter R similarly to the gains K p , K i , and K d . 
     The function provided in one component in each of the above exemplary embodiments may be distributed in components. The function provided in components may be integrated in one component. Part of the configuration according to each of the above exemplary embodiments may be omitted. The embodiments of the present disclosure include various embodiments or aspects that are included in the technical ideas specified by the following claims. 
     There is a correspondence relationship between the words and terms as follows. The conveyance motor  71  corresponds to an exemplary first motor. The supply motor  61  corresponds to an exemplary second motor. The rotary encoder  75  and the measurement circuit  77  correspond to an exemplary measuring device. The distance sensor  93  and the roll diameter estimator  150  correspond to an exemplary roll diameter measuring device. The rotary encoder  65  and the measurement circuit  67  correspond to an exemplary roll measuring device.