Patent Publication Number: US-11390073-B2

Title: Liquid discharge apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority from prior Japanese patent application No. 2020-003725, filed on Jan. 14, 2020, the entire contents of which are incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to a liquid discharge apparatus configured to discharge liquid from nozzles. 
     BACKGROUND 
     As an example of a liquid discharge apparatus configured to discharge liquid from nozzles, JP-B-3622628 discloses an inkjet printer configured to discharge ink from nozzles for recording. In the inkjet printer disclosed in JP-B-3622628, a signal obtained by multiplying a pulse signal that is output from an encoder based on relative movement of a print head with respect to a sheet is output to the print head, so that the print head is caused to discharge ink from the nozzles. 
     SUMMARY 
     In the inkjet printer disclosed in JP-B-3622628, contaminants such as ink may be attached to the encoder. In this case, a period of the pulse signal that is output from the encoder changes when the print head passes a part of the encoder to which contaminants are attached. As a result, a period of the signal obtained by multiplying the pulse signal also changes, so that a discharge interval of ink from the nozzles may become too long or too short. In a printer configured to discharge ink from a print head while relatively moving the print head and a sheet by conveying the sheet with conveyor rollers and the like and in an inkjet printer configured to discharge ink from nozzles on the basis of a signal from an encoder corresponding to a conveying amount of a sheet, the similar problems occur. 
     An object of the present disclosure is to provide a liquid discharge apparatus that enables to discharge liquid from a nozzle at an appropriate timing. 
     A first aspect of the present disclosure is a liquid discharge apparatus including: 
     a liquid discharge head having a nozzle; 
     a carriage having the liquid discharge head mounted thereto, and configured to move in a scanning direction; 
     an encoder sensor mounted to the carriage; 
     a slit member extending in the scanning direction, and having a plurality of encoder slits aligned in the scanning direction and detected by the encoder sensor; and 
     a controller configured to:
         move the carriage in the scanning direction;   generate a plurality of multiplied signals by multiplying a detection signal obtained based on a detection result of the encoder slits by the encoder sensor, in a case where a signal change occurs in the detection signal, the signal change being either a rise or a fall of the detection signal; and   cause the liquid discharge head to discharge liquid from the nozzle, based on the plurality of multiplied signals,       

     in which in a case where the controller generates the plurality of multiplied signals as a result of occurrence of an N th  signal change in the detection signal after starting to move the carriage, where N is a natural number of 2 or greater, 
     the controller is configured to calculate a target value P N  of a number of the multiplied signals that are generated in a case where the N th  signal change occurs, based on P N =PA N +(P N−1 −PR N−1 ),
         where P N−1  is a target value of a number of the multiplied signals that are generated in a case where an [N−1] th  signal change occurs in the detection signal,   PR N−1  is a number of the multiplied signals that are actually generated during an [N−1] th  detection time period that is a period of time from the [N−1] th  signal change to the N th  signal change, and   PA N  is a standard value of a number of the multiplied signals for an N th  detection time period,       

     in a case where an actual length TR N−1  of the [N−1] th  detection time period is equal to or longer than a predetermined first time and equal to or shorter than a predetermined second time, 
     the controller is configured to generate the multiplied signals for each time calculated as [TE N /P N ] in the case where the N th  signal change occurs, where TE N  is a standard value of a length of the N th  detection time period, and 
     in a case where the actual length TR N−1  is shorter than the predetermined first time, 
     the controller is configured to generate the multiplied signals for each time calculated as [(2×TE N −TR N−1 )/P N ] in the case where the N th  signal change occurs. 
     A second aspect of the present disclosure is a liquid discharge apparatus including: 
     a liquid discharge head having a nozzle; 
     a conveyor configured to convey a medium, to which liquid is discharged from the nozzle, in a conveying direction; 
     an encoder sensor; 
     a slit member configured to relatively move in a predetermined direction with respect to the encoder sensor in a case where the medium is conveyed by the conveyor, and having a plurality of encoder slits aligned in the predetermined direction and detected by the encoder sensor; and 
     a controller configured to:
         cause the conveyor to convey the medium;   generate a plurality of multiplied signals by multiplying a detection signal obtained based on a detection result of the encoder slit by the encoder sensor, in a case where a signal change occurs in the detection signal, the signal change being either a rise or a fall of the detection signal; and   cause the liquid discharge head to discharge liquid from the nozzle, based on the plurality of multiplied signals,       

     in which in a case where the controller generates the plurality of multiplied signals as a result of occurrence of an N th  signal change in the detection signal after starting to convey the medium, where N is a natural number of 2 or greater, 
     the controller is configured to calculate a target value P N  of a number of the multiplied signals that are generated in a case where the N th  signal change occurs, based on P N =PA N +(P N−1 −PR N−1 ),
         where P N−1  is a target value of a number of the multiplied signals that are generated in a case where an [N−1] th  signal change occurs in the detection signal,   PR N−1  is a number of the multiplied signals that are actually generated during an [N−1] th  detection time period that is a period of time from the [N−1] th  signal change to the N th  signal change, and   PA N  is a standard value of a number of the multiplied signals for an N th  detection time period,       

     in a case where an actual length TR N−1  of the [N−1] th  detection time period is equal to or longer than a predetermined first time and equal to or shorter than a predetermined second time, 
     the controller generates the multiplied signals for each time calculated as [TE N /P N ] in the case where the N th  signal change occurs, where TE N  is a standard value of a length of the N th  detection time period, and 
     in a case where the actual length TR N−1  is shorter than the predetermined first time, 
     the controller is configured to generate the multiplied signals for each time calculated as [(2×TE N −TR N−1 )/P N ] in a case where the N th  signal change occurs. 
     A third aspect of the present disclosure is a liquid discharge apparatus including: 
     a liquid discharge head having a nozzle; 
     a carriage having the liquid discharge head mounted thereto, and configured to move in a scanning direction; 
     an encoder sensor mounted to the carriage; 
     a slit member extending in the scanning direction, and having a plurality of encoder slits aligned in the scanning direction and detected by the encoder sensor; and 
     a controller configured to:
         move the carriage in the scanning direction;   generate a plurality of multiplied signals by multiplying a detection signal obtained based on a detection result of the encoder slits by the encoder sensor, in a case where a signal change occurs in the detection signal, the signal change being either a rise or a fall of the detection signal; and   cause the liquid discharge head to discharge liquid from the nozzle, based on the plurality of multiplied signals,       

     in which in a case where the controller generates the plurality of multiplied signals as a result of occurrence of an N th  signal change in the detection signal after starting to move the carriage, where N is a natural number of 2 or greater, 
     in a case where an actual length TR N−1  of an [N−1] th  detection time period that is a period of time from an [N−1] th  signal change to an N th  signal change is equal to or longer than a predetermined first time and equal to or shorter than a predetermined second time, 
     the controller is configured to:
         calculate a target value P N  of a number of the multiplied signals that are generated in a case where the N th  signal change occurs, based on P N =PA N +(P N−1 −PR N−1 ),
           where PR N−1  is a number of the multiplied signals that are actually generated during the [N−1] th  detection time period, and   PA N  is a standard value of a number of the multiplied signals for an N th  detection time period, and   
           generate the multiplied signals for each time calculated as [TE N /P N ] in a case where the N th  signal change occurs, where TE N  is a standard value of a length of the N th  detection time period, and       

     in a case where the actual length TR N−1  is longer than the predetermined second time, 
     the controller is configured to:
         calculate the target value P N  of the number of the multiplied signals that are generated in the case where the N th  signal change occurs, based on P N =(M N−1 +1)×PA N +(P N−1 −PR N−1 ),
           where M N−1  is a number of the encoder slits that are not detected during the [N−1] detection time period, and   
           generate the multiplied signals for each time calculated as [(2×TE N −TR N−1 +M N−1 ×C N−1 )/P N ] in the case where the N th  signal change occurs,
           where C N−1  is a standard value of a length of the [N−1] th  detection time period.   
               

     A fourth aspect of the present disclosure is a liquid discharge apparatus including: 
     a liquid discharge head having a nozzle; 
     a conveyor configured to convey a medium, to which liquid is discharged from the nozzle, in a conveying direction; 
     an encoder sensor; 
     a slit member configured to relatively move in a predetermined direction with respect to the encoder sensor in a case where the medium is conveyed by the conveyor, and having a plurality of encoder slits aligned in the predetermined direction and detected by the encoder sensor; and 
     a controller configured to:
         cause the conveyor to convey the medium;   generate a plurality of multiplied signals by multiplying a detection signal obtained based on a detection result of the encoder slit by the encoder sensor, in a case where a signal change occurs in the detection signal, the signal change being either a rise or a fall of the detection signal; and   cause the liquid discharge head to discharge liquid from the nozzles, based on the plurality of multiplied signals,       

     in which in a case where the controller generates the plurality of multiplied signals as a result of occurrence of an N th  signal change in the detection signal after starting to convey the medium, where N is a natural number of 2 or greater, 
     in a case where an actual length TR N−1  of an [N−1] th  detection time period that is a period of time from an [N−1] th  signal change to an N th  signal change is equal to or longer than a predetermined first time and equal to or shorter than a predetermined second time, 
     the controller is configured to:
         calculate a target value P N  of a number of the multiplied signals that are generated in a case where the N th  signal change occurs, based on P N =PA N +(P N−1 −PR N−1 ),
           where PR N−1  is a number of the multiplied signals that are actually generated during the [N−1] th  detection time period, and   PA N  is a standard value of a number of the multiplied signals for an N th  detection time period, and   
           generate the multiplied signals for each time calculated as [TE N /P N ] in a case where the N th  signal change occurs, where TE N  is a standard value of a length of the N th  detection time period, and       

     in a case where the actual length TR N−1  is longer than the predetermined second time, 
     the controller is configured to:
         calculate the target value P N  of the number of the multiplied signals that are generated in the case where the N th  signal change occurs, based on P N =(M N−1 +1)×PA N +(P N−1 −PR N−1 ),
           where M N−1  is a number of the encoder slits that are not detected during the [N−1] detection time period, and   
           generate the multiplied signals for each time calculated as [(2×TE N −TR N−1 +M N−1 ×C N−1 )/P N ] in a case where the N th  signal change occurs,
           where C N−1  is a standard value of a length of the [N−1] th  detection time period.   
               

     According to the liquid discharge apparatus of the present disclosure, it is possible to generate the multiplied signals at an appropriate time interval even in a case where contaminants are attached to the encoder slits, for example. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic configuration view of a printer in accordance with a first embodiment of the present disclosure. 
         FIG. 2A  depicts an encoder scale shown in  FIG. 1 , as seen from a downstream side with respect to a conveying direction,  FIG. 2B  depicts the encoder scale and an encoder sensor in a state where the encoder sensor faces an encoder slit of the encoder scale, as seen from a left side in a scanning direction, and  FIG. 2C  depicts the encoder scale and the encoder sensor in a state where the encoder sensor does not face the encoder slit of the encoder scale, as seen from the left side in the scanning direction. 
         FIG. 3  is a block diagram depicting an electric configuration of the printer in accordance with the first embodiment. 
         FIG. 4  is a flowchart depicting a processing flow for generating multiplied signals in the first embodiment. 
         FIG. 5  is a flowchart depicting first multiplied signal generation processing of  FIG. 4 . 
         FIG. 6  is a flowchart depicting second multiplied signal generation processing of  FIG. 4 . 
         FIG. 7  is a flowchart depicting third multiplied signal generation processing of  FIG. 4 . 
         FIG. 8  is a flowchart depicting a processing flow for updating a value of a position parameter. 
         FIG. 9A  illustrates generation of multiplied signals when a rise occurs in an encoder signal in a case where contaminants are attached to the encoder scale, and  FIG. 9B  illustrates generation of multiplied signals when a rise occurs in the encoder signal after  FIG. 9A . 
         FIG. 10A  is a view corresponding to  FIG. 9A  in a case where contaminants are attached to the encoder scale in an aspect different from  FIGS. 9A and 9B , and  FIG. 10B  is a view corresponding to  FIG. 9B , in a case of  FIG. 10A . 
         FIG. 11A  is a view corresponding to  FIG. 9A  in a case where contaminants are attached to the encoder scale in an aspect different from  FIGS. 9A to 10B , and  FIG. 11B  is a view corresponding to  FIG. 9B , in a case of  FIG. 11A . 
         FIG. 12A  is a view corresponding to  FIG. 9A  in a case where contaminants are attached to the encoder scale in an aspect different from  FIGS. 9A to 11B , and  FIG. 12B  is a view corresponding to  FIG. 9B , in a case of  FIG. 12A . 
         FIG. 13A  is a view corresponding to  FIG. 9A  in a case where contaminants are attached to the encoder scale in an aspect different from  FIGS. 9A to 12B , and  FIG. 13B  is a view corresponding to  FIG. 9B , in a case of  FIG. 13A . 
         FIG. 14A  is a view corresponding to  FIG. 9A  in a case where contaminants are attached to the encoder scale in an aspect different from  FIGS. 9A to 13B , and  FIG. 14B  is a view corresponding to  FIG. 9B , in a case of  FIG. 14A . 
         FIG. 15  is a schematic configuration view of a printer in accordance with a second embodiment. 
         FIG. 16A  depicts an encoder disk shown in  FIG. 1 , as seen from the scanning direction,  FIG. 16B  depicts the encoder disk and the encoder sensor in a state where the encoder sensor faces an encoder slit of the encoder disk, as seen from a downstream side with respect to the conveying direction, and  FIG. 16C  depicts the encoder disk and the encoder sensor in a state where the encoder sensor does not face the encoder slit of the encoder disk, as seen from the downstream side with respect to the conveying direction. 
         FIG. 17  is a block diagram depicting an electric configuration of the printer in accordance with the second embodiment. 
         FIG. 18  is a flowchart depicting a processing flow for generating multiplied signals in the second embodiment. 
         FIG. 19A  is a block diagram depicting an electric configuration of a printer in accordance with a modified embodiment 1, and  FIG. 19B  is a flowchart depicting a flow of third multiplied signal generation processing in the modified embodiment 1. 
         FIG. 20  is a flowchart depicting a flow of third multiplied signal generation processing in a modified embodiment 2. 
         FIG. 21  is a flowchart depicting a processing flow for generating multiplied signals in a modified embodiment 3. 
         FIG. 22  is a flowchart depicting a processing flow for generating multiplied signals in a modified embodiment 4. 
         FIG. 23  is a flowchart depicting a processing flow for generating multiplied signals in a modified embodiment 5. 
         FIG. 24  is a flowchart depicting a processing flow for generating multiplied signals in a modified embodiment 6. 
     
    
    
     DETAILED DESCRIPTION 
     First Embodiment 
     A first embodiment of the present disclosure is described. 
     As shown in  FIG. 1 , a printer  1  in accordance with the first embodiment (“liquid discharge apparatus” of the present disclosure) includes a carriage  2 , a sub-tank  3 , an inkjet head  4  (“liquid discharge head” of the present disclosure), a platen  5 , conveyor rollers  6  and  7 , a linear encoder  8 , and the like. 
     The carriage  2  is supported to two guide rails  11  and  12  extending in a scanning direction. The carriage  2  is connected to a carriage motor  56  (refer to  FIG. 3 ) via a belt and the like (not shown), and when the carriage motor  56  is driven, the carriage  2  moves in the scanning direction along the guide rails  11  and  12 . In the below, the right side and the left side in the scanning direction are defined and described, as shown in  FIG. 1 . 
     The sub-tank  3  is mounted to the carriage  2 . Herein, the printer  1  is provided with a cartridge holder  14  at an end portion on the right side in the scanning direction and on a downstream side with respect to a conveying direction of a recording sheet P (“medium” of the present disclosure) orthogonal to the scanning direction. Four ink cartridges  15  aligned side by side in the scanning direction are removably mounted to the cartridge holder  14 . Black, yellow, cyan and magenta inks (“liquid” of the present disclosure) are stored in the four ink cartridges  15  from those arranged on the right side in the scanning direction. The sub-tank  3  is connected to the four ink cartridges  15  mounted to the cartridge holder  14 , via four tubes  13 . Thereby, the inks of four colors are supplied from the four ink cartridges  15  to the sub-tank  3 . 
     The inkjet head  4  is mounted to the carriage  2 , and is connected to a lower end portion of the sub-tank  3 . Thereby, the inkjet head  4  and the ink cartridges  15  are connected to each other via the tubes  13  and the sub-tank  3 . The inks of four colors are supplied from the sub-tank  3  to the inkjet head  4 . The inkjet head  4  is also configured to discharge the inks from a plurality of nozzles  10  formed in a nozzle surface  4   a  that is a lower surface of the inkjet head and is parallel to the scanning direction and the conveying direction. More specifically, the plurality of nozzles  10  is aligned in the conveying direction to form nozzle rows  9 , so that the inkjet head  4  has four nozzle rows  9  aligned side by side in the scanning direction. From the plurality of nozzles  10 , black, yellow, cyan and magenta inks are discharged from the nozzles  10 , from those configuring the nozzle row  9  on the right side in the scanning direction. 
     The platen  5  is disposed below the inkjet head  4 , and faces the plurality of nozzles  10 . The platen  5  extends over an entire length of the recording sheet P in the scanning direction, and is configured to support the recording sheet P from below. The conveyor roller  6  is disposed upstream of the inkjet head  4  and the platen  5  with respect to the conveying direction. The conveyor roller  7  is disposed downstream of the inkjet head  4  and the platen  5  with respect to the conveying direction. The conveyor rollers  6  and  7  are connected to a conveyor motor  57  (refer to  FIG. 3 ) via a gear and the like (not shown). When the conveyor motor  57  is driven, the conveyor rollers  6  and  7  are rotated to convey the recording sheet P in the conveying direction. 
     The linear encoder  8  includes an encoder scale  18  (“slit member” of the present disclosure) and an encoder sensor  19 . The encoder scale  18  is disposed on the guide rail  12 . The encoder scale  18  extends over an entire length of the guide rail  12  in the scanning direction. As shown in  FIG. 2A , the encoder scale  18  has a plurality of encoder slits  18   a  having translucency and disposed at constant intervals in the scanning direction. 
     The encoder sensor  19  is mounted to the carriage  2 . As shown in  FIGS. 2B and 2C , the encoder sensor  19  has a light-emitting element  19   a  and a light-receiving element  19   b . The light-emitting element  19   a  and the light-receiving element  19   b  are disposed facing each other in the conveying direction. The encoder scale  18  is disposed between the light-emitting element  19   a  and the light-receiving element  19   b  in the conveying direction, and the light-emitting element  19   a  and the light-receiving element  19   b  face each other with the encoder scale  18  being sandwiched therebetween. The light-emitting element  19   a  is configured to irradiate light toward the light-receiving element  19   b.    
     In a state where the encoder sensor  19  (the light-emitting element  19   a  and the light-receiving element  19   b ) is located at the same position as the encoder slit  18   a  of the encoder scale  18  in the scanning direction, as shown in  FIG. 2B , the light irradiated from the light-emitting element  19   a  passes through the encoder slit  18   a  and is then received in the light-receiving element  19   b . On the other hand, in a state where the encoder sensor  19  (the light-emitting element  19   a  and the light-receiving element  19   b ) is located between the two adjacent encoder slits  18   a  of the encoder scale  18  in the scanning direction, as shown in  FIG. 2C , the light irradiated from the light-emitting element  19   a  is blocked by the encoder scale  18  and is not thus received in the light-receiving element  19   b.    
     The encoder sensor  19  is configured to output a signal indicating whether the light from the light-emitting element  19   a  is received in the light-receiving element  19   b . More specifically, the encoder sensor  19  is configured to transmit an encoder signal that is a pulse signal that rises when a state is switched from a state in which the light irradiated from the light-emitting element  19   a  is received in the light-receiving element  19   b  to a state in which the light is not received in the light-receiving element  19   b  and falls when a state is switched from the state in which the light irradiated from the light-emitting element  19   a  is not received in the light-receiving element  19   b  to the state in which the light is received in the light-receiving element  19   b.    
     &lt;Electrical Configuration of Printer&gt; 
     Subsequently, an electrical configuration of the printer  1  is described. Operations of the printer  1  are controlled by a controller  50 . As shown in  FIG. 3 , the controller  50  includes a CPU (Central Processing Unit)  51 , a ROM (Read Only Memory)  52 , a RAM (Random Access Memory)  53 , a flash memory  54 , an ASIC (Application Specific Integrated Circuit)  55  and the like, and is configured to control operations of the carriage motor  56 , the inkjet head  4 , the conveyor motor  57  and the like. The controller  50  is also configured to receive the encoder signal transmitted from the encoder sensor  19 . 
     Note that, the controller  50  may also be configured so that only the CPU  51  executes a variety of processing, only the ASIC  55  executes a variety of processing, or the CPU  51  and the ASIC  55  execute a variety of processing in cooperation with each other. The controller  50  may also be configured so that one CPU  51  solely executes processing or a plurality of CPUs  51  shares and executes processing. The controller  50  may also be configured so that one ASIC  55  solely executes processing or a plurality of ASICs  55  shares and executes processing. 
     &lt;Control Upon Recording&gt; 
     Subsequently, control that is executed when performing recording on the recording sheet P in the printer  1  is described. In the printer  1 , the controller  50  alternately and repeatedly performs a recording pass of controlling the inkjet head  4  to discharge inks from the plurality of nozzles  10  toward the recording sheet P while controlling the carriage motor  56  to move the carriage  2  in the scanning direction, and a conveying operation of controlling the conveyor motor  57  to convey the recording sheet P to the conveyor rollers  6  and  7 , thereby performing recording on the recording sheet P. 
     &lt;Generation of Multiplied Signal&gt; 
     When performing the recording pass, the encoder sensor  19  is moved in the scanning direction together with the carriage  2 , so that the encoder sensor  19  and the encoder scale  18  relatively move in the scanning direction and the encoder signal as described above is output from the encoder sensor  19 . 
     When performing the recording pass, the controller  50  generates multiplied signals that are pulse signals obtained by multiplying the encoder signal received from the encoder sensor  19 . Then, the controller  50  causes the inkjet head  4  to discharge the inks from the plurality of nozzles  10  at a timing at which a rise occurs in the generated multiplied signal, for example. In the below, the generation of the multiplied signals is described. 
     In the first embodiment, when the recording pass starts, the controller  50  executes processing according to a flow shown in  FIG. 4 , thereby generating the multiplied signal. 
     More specifically, when the recording pass starts, the controller  50  first resets a variable N to zero (0) (S 101 ). The variable N corresponds to the number of detection times of the rise of the encoder signal after the carriage  2  starts to move in the recording pass. 
     Then, the controller  50  stands by until a rise (“signal change” of the present disclosure) of the encoder signal is detected (S 102 : NO), and increase the variable N by 1 when the rise of the encoder signal is detected (S 102 : YES) (S 103 ). In a case where the variable N is 1 (S 104 : YES), the controller  50  generates the multiplied signals every [TE 1 /PA 1 ] (S 105 ), and proceeds to S 111 . Herein, TE 1  and PA 1  are values set in advance by a test and the like, and are stored in the flash memory  54  and the like. 
     Note that, since the processing of multiplying the encoder signal to generate the multiplied signals in S 103  or S 205 , S 305  and S 406 , which will be described later, is well known, as disclosed in Japanese Patent No. 3,622,628, for example, the detailed descriptions thereof are omitted herein. 
     When the variable N is 2 or greater (S 104 : NO), the controller  50  determines whether TR N−1  is equal to or longer than a predetermined TR 1  (“predetermined first time” of the present disclosure) and equal to or shorter than a predetermined TR 2  (“predetermined second time” of the present disclosure) (S 106 ). Herein, TR N−1  is an actual length of a period of time (([N−1] th  detection time period) from detection of an [N−1] th  rise of the encoder signal to detection of a N th  rise of the encoder signal. 
     In the recording pass, when contaminants and the like are not attached to the encoder scale  18  and the carriage  2  moves at a predetermined speed, a variation occurs in the length of the detection time period due to variation in the moving speed of the carriage  2 . TR 1  is, for example, a lower limit value of the variation in the length of the detection time period. TR 2  is, for example, an upper limit value of the variation in the length of the detection time period. 
     When it is determined that TR N−1  is equal to or longer than TR 1  and equal to or shorter than TR 2  (S 106 : YES), the controller  50  executes first multiplied signal generation processing (S 107 ), and proceeds to S 111 . 
     When it is determined that TR N−1  is not equal to or longer than TR 1  and equal to or shorter than TR 2  (S 106 : NO), the controller  50  determines whether TR N−1  is shorter than TR 1  (S 108 ). When it is determined that TR N−1  is shorter than TR 1  (S 108 : YES), the controller  50  executes second multiplied signal generation processing (S 109 ), and proceeds to S 111 . When it is determined that TR N−1  is longer than TR 2  (S 108 : NO), the controller  50  executes third multiplied signal generation processing (S 110 ), and proceeds to S 111 . 
     In S 111 , the controller  50  determines whether the recording pass is completed. When it is determined that the recording pass is not completed (S 111 : NO), the controller  50  returns to S 102 , and when it is determined that the recording pass is completed, the controller  50  ends the processing. 
     &lt;First Multiplied Signal Generation Processing&gt; 
     Subsequently, the first multiplied signal generation processing of S 107  is described. As shown in  FIG. 5 , in the first multiplied signal generation processing, the controller  50  first determines whether the variable N is 2 (S 201 ). When it is determined that the variable N is 2 (S 201 : YES), the controller  50  calculates a target value P N  of the number of multiplied signals that are generated for a N th  detection time period, based on P N =PA N +(P N−1 −PR N−1 ) (S 202 ). 
     Herein, P N−1  is a target value of the number of multiplied signals that are generated during an [N−1] th  detection time period. PA N  is a standard value of the number of multiplied signals that are generated during the N th  detection time period, and is stored in advance in the flash memory  54 . PR N−1  is the number of multiplied signals actually generated during the [N−1] th  detection time period. 
     When it is determined that the variable N is not 2, i.e., the variable N is 3 or greater (S 201 : NO), the controller  50  determines whether TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2  (S 203 ). When it is determined that TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2  (S 203 : YES), the controller  50  calculates P N , based on P N =PA N +(P N−1 −PR N−1 ), in a similar manner to described above (S 202 ). 
     When it is determined that TR N−2  is not equal to or longer than TR 1  and equal to or shorter than TR 2  (shorter than TR 1  or longer than TR 2 ) (S 203 : NO), the controller  50  calculates P N , based on P N =PA N +(P N−1 −PR N−1 )−(P N−2 −PR N−2 ) (S 204 ). 
     After calculating P N  in S 202  or S 204 , the controller  50  generates the multiplied signals every [TE N /P N ] (S 205 ). Herein, TE N  is an expected value of the N th  detection time period. TE N  is, for example, an average value of a predetermined number of times of past detection time periods before the N th  detection time period. Alternatively, TE N  may also be preset and stored in the flash memory  54 . 
     &lt;Second Multiplied Signal Generation Processing&gt; 
     Subsequently, the second multiplied signal generation processing of S 109  is described. As shown in  FIG. 6 , in the second multiplied signal generation processing, the controller  50  executes processing of S 301  to S 304  similar to S 201  to S 204  of the first multiplied signal generation processing. After calculating P N  in S 302  or S 304 , the controller  50  generates the multiplied signals every [(2×TE N −TR N−1 )/P N ] (S 305 ). 
     &lt;Third Multiplied Signal Generation Processing&gt; 
     Subsequently, the third multiplied signal generation processing of S 110  is described. As shown in  FIG. 7 , in the third multiplied signal generation processing, the controller  50  first determines whether the variable N is 2 (S 401 ). When it is determined that the variable N is 2 (S 401 : YES), the controller  50  calculates P N , based on P N =(M N−1 +1)×PA N +(P N−1 −PR N−1 ) (S 402 ). Herein, M N−1  is the number of the encoder slits  18   a  that are not detected during the [N−1] th  detection time period. A value of M N−1  is set as processing is executed according to a flow shown in  FIG. 8 , which will be described later. 
     When it is determined that the variable N is 3 or greater (S 401 : NO), the controller  50  determines whether TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2  (S 403 ). When it is determined that TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2  (S 403 : YES), the controller  50  calculates P N , based on P N =(M N−1 +1)×PA N +(P N−1 −PR N−1 ), in a similar manner to described above (S 402 ). 
     When it is determined that TR N−2  is not equal to or longer than TR 1  and equal to or shorter than TR 2  (shorter than TR 1  or longer than TR 2 ) (S 403 : NO), the controller  50  calculates P N , based on P N =(M N−1 +1)×PA N +(P N−1 −PR N−1 )−(P N−2 −PR N−2 ) (S 404 ). 
     After calculating P N  in S 402  or S 404 , the controller  50  calculates a value of C N−1  that is a standard value of the length of the [N−1] th  detection time period (S 405 ). In S 405 , the controller  50  calculates, as the value of C N−1 , an average value of lengths of a predetermined number of times of past detection time periods before the N th  detection time period. Then, the controller  50  generates the multiplied signals every [(2×TE N −TR N−1 +M N−1 ×C N−1 )/P N ] (S 406 ). 
     &lt;Position Parameter&gt; 
     Subsequently, a position parameter U is described. In the first embodiment, the controller  50  acquires position information of the carriage  2  in the scanning direction, based on a value of a position parameter U. In the first embodiment, when performing the recording pass, the controller  50  performs processing according to the flow shown in  FIG. 8 , in parallel with processing according to the flow shown in  FIG. 4 , thereby updating the value of the position parameter U. The processing is performed according to the flow shown in  FIG. 8 , values of M 1 , M 2 , . . . are also set. 
     More specifically, when the recording pass starts, the controller  50  resets all of M 1 , M 2 , . . . to 0 (S 501 ), and resets the variable K to 2 (S 502 ). Then, when a rise of the encoder signal is detected (S 503 : YES), if the carriage  2  moves to the left side (“one side in the scanning direction” of the present disclosure) (S 504 : YES), the controller  50  increases the value of the position parameter U by 1 (S 505 ), and if the carriage  2  moves to the right side (“the other side in the scanning direction” of the present disclosure) (S 504 : NO), the controller  50  decreases the value of the position parameter U by 1 (S 506 ). After the processing of S 505  or S 506 , when the recording pass is not completed (S 507 : NO), the controller  50  returns to S 502 , and when the recording pass is completed (S 507 : YES), the controller  50  ends the processing. 
     When a rise of the encoder signal is not detected (S 503 : NO), if K×TE N  does not elapse since the previous rise of the encoder signal (S 508 : NO), the controller  50  returns to S 503 . 
     If K×TE N  elapses since the previous rise of the encoder signal (S 508 : YES), the controller  50  increases M N  by 1 (S 509 ). Herein, the value of N in TE N  in S 508  and M N  in S 508  is the value of N set in the processing according to the flow shown in  FIG. 4 . 
     Subsequently, when the carriage  2  moves leftward (S 510 : YES), the controller  50  increases the value of the position parameter U by 1 (“predetermined value” of the present disclosure) (S 511 ), and when the carriage  2  moves rightward (S 510 : NO), the controller  50  decreases the value of the position parameter U by 1 (S 512 ). After the processing of S 509  or S 510 , the controller  50  increases the value of the variable K by 1 (S 513 ). Then, when the recording pass is not completed (S 514 : NO), the controller  50  returns to S 503 , and when the recording pass is completed (S 514 : YES), the controller  50  ends the processing. 
     In the first embodiment, the processing is executed according to the flow shown in  FIG. 8 , as described above, so that when the carriage  2  moves to the left side in the scanning direction, the value of the position parameter U increases by 1 each time a rise of the encoder signal is detected. When a rise of an [ N+1 ] th  encoder signal is not detected until a time of 2×TE N  elapses since the N th  rise of the encoder signal is detected, the value of the position parameter U increases by 1. Thereafter, the value of the position parameter U increases by 1 each time a time of TE N  elapses until an [N+1] th  rise of the encoder signal is detected. 
     When the carriage  2  moves to the right side in the scanning direction, the value of the position parameter U decreases by 1 each time a rise of the encoder signal is detected. When a rise of the [N+1] th  encoder signal is not detected until the time of 2×TE N  elapses since the N th  rise of the encoder signal is detected, the value of the position parameter U decreases by 1. Thereafter, the value of the position parameter U decreases by 1 each time the time of TE N  elapses until an [N+1] th  rise of the encoder signal is detected. 
     In the first embodiment, when the carriage  2  moves leftward, the value of the position parameter U is increased, and when the carriage  2  moves rightward, the value of the position parameter U is decreased. However, the present invention is not limited thereto. For example, when the carriage  2  moves leftward, the value of the position parameter U may be decreased, and when the carriage  2  moves rightward, the value of the position parameter U may be increased. In this case, the right side in the scanning direction corresponds to “one side in the scanning direction” of the present disclosure, and the left side of the scanning direction corresponds to the other side in the scanning direction of the present disclosure. 
     The amount of increase in the position parameter U in S 504  and S 509  and the amount of decrease in the position parameter U in S 505  and S 510  may also be a predetermined value larger than or smaller than 1. 
     In the first embodiment, the processing is executed according to the flow shown in  FIG. 8 , so that when a rise of the [N+1] th  encoder signal is not detected until the time of 2×TE N  elapses since the N th  rise of the encoder signal is detected, the value of M N  increases by 1. The value of M N  increases by 1 each time the time of TE N  elapses until a rise of the [N+1] th  encoder signal is detected. 
     &lt;Effects&gt; 
     In the first embodiment, in a case where TR N−1  is short, the number of multiplied signals that are generated during the [N−1] th  detection time period becomes small, and PR N−1  becomes smaller than P N−1 . In a case where TR N−1  is long, the number of multiplied signals that are generated during the [N−1] th  detection time period becomes small, and PR N−1  becomes greater than P N−1 . Therefore, in the first embodiment, in a case where TR N−1  is equal to or longer than TR 1  and equal to or shorter than TR 2 , P N  is calculated based on P N =PA N−1 +(P N−1 −PR N−1 ), and when a N th  rise of the encoder signal occurs, the multiplied signals are generated every [TE N /P N ]. Thereby, when the number of the multiplied signals for the [N−1] th  detection time period becomes small, it is possible to increase the number of the multiplied signals for the N th  detection time period. When the number of the multiplied signals for the [N−1] th  detection time period becomes large, it is possible to decrease the number of the multiplied signals for the N th  detection time period. 
     In a case where TR N−1  is within a range of TR 1  or longer and TR 2  or shorter, when the multiplied signals are generated as described above, it is possible to generate the multiplied signals at appropriate time intervals. However, when TR N−1  becomes extremely short due to influences of contaminants and the like attached to the encoder scale  18 , PR N−1  becomes extremely smaller than P N−1  and P N  that is calculated based on P N =PA N−1 +(P N−1 −PR N−1 ) becomes extremely large. For this reason, when a N th  rise of the encoder signal occurs, if the multiplied signals are generated in a similar manner to the case where TR N−1  is equal to or longer than TR and equal to or shorter than TR 2 , the time intervals of the multiplied signals become extremely short. 
     Therefore, in the first embodiment, when a N th  rise of the encoder signal occurs, if TR N−1  is shorter than TR 1 , the multiplied signals are generated for each time calculated as [(2×TE N −TR N−1 )/P N ]. Thereby, P N  increases as described above. However, when TR N−1  is short, since [2×TE N −TR N−1 ] increases, the time calculated as [(2×TE N −TR N−1 )/P N ] is not extremely lengthened or extremely shortened. Thereby, even when contaminants are attached to the encoder scale  18 , it is possible to generate the multiplied signals at appropriate time intervals. 
     On the other hand, when TR N−1  becomes extremely long due to influences of contaminants and the like attached to the encoder scale  18 , PR N−1  becomes extremely larger than P N−1 , and P N  that is calculated based on P N =PA N−1 +(P N−1 −PR N−1 ) becomes extremely small. For this reason, when a N th  rise of the encoder signal occurs, if the multiplied signals are generated in a similar manner to the case where TR N−1  is equal to or longer than TR and equal to or shorter than TR 2 , the time interval of the multiplied signals becomes extremely longer. 
     Therefore, in the first embodiment, when a N th  rise of the encoder signal occurs, if TR N−1  is longer than TR 2 , P N  is calculated based on P N =(M N−1 +1)×PA N−1 +(P N−1 −PR N−1 ), and the multiplied signals are generated for each time calculated as [(2×TE N −TR N−1 +M N−1 ×C N−1 )/P N ]. 
     When P N  is calculated in this way, if PR N−1  is large, P N  becomes small. P N  takes into consideration the number M N−1  of the encoder slits  18   a  that are not detected. Thereby, it is possible to reduce the number of the multiplied signals for the N th  detection time period by the increased number of the multiplied signals for the [N−1] th  detection time period. In this case, although P N  becomes small, as described above, when TR N−1  is long, [2×TE N −TR N−1 +M N−1 ×C N−1 ] is reduced. For this reason, the time calculated as [(2×TE N −TR N−1 +M N−1 ×C N−1 )/P N ] is prevented from being extremely lengthened or extremely shortened. Thereby, even when contaminants are attached to the encoder scale  18 , it is possible to generate the multiplied signals at appropriate time intervals. 
     Contaminants are attached to the encoder scale  18  in diverse forms. Therefore, in the first embodiment, as described above, in each of cases where TR N−1  is shorter than TR 1  and where TR N−1  is longer than TR 2 , the multiplied signals are generated by processing different from the case where TR N−1  is equal to or longer than TR 1  and equal to or shorter than TR 2 . However, in this case, it may be problematic if the time interval for generating the multiplied signals is determined as described above. 
     Therefore, in the first embodiment, when TR N−2  is shorter than TR 1  and when TR N−2  is longer than TR 2 , a value of P N  is set as a value obtained by subtracting [P N−2 −PR N−2 ] from a value of P N  when TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2 . Thereby, it is possible to generate the multiplied signals at appropriate time intervals. 
     As a specific example, a case where contaminants D as shown in  FIGS. 9A and 9B  are attached to the encoder scale  18 , a case where contaminants D as shown in  FIGS. 10A and 10B  are attached to the encoder scale  18  and a case where contaminants D as shown in  FIGS. 11A and 11B  are attached to the encoder scale  18  are considered. 
     In this case, when the encoder sensor  19  reaches positions shown in  FIGS. 9A, 10A and 11A , a rise of the encoder signal occurs, and TR N−1  becomes shorter than TR 1 . TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2 . 
     In this case, as described above, when a N th  rise of the encoder signal occurs, P N  is calculated based on P N =PA N +(P N−1 −PR N−1 ) (S 302 ), and the multiplied signals are generated for each time calculated as [(2×TE N −TR N−1 )/P N ] (S 305 ). Thereby, it is possible to generate the multiplied signals at appropriate time intervals. 
     On the other hand, when the encoder sensor  19  reaches a position shown in  FIG. 9B , a rise of the encoder signal occurs, TR N  becomes equal to or longer than TR 1  and equal to or shorter than TR 2 . As described above, TR N−1  is shorter than TR 1 . In this case, TR N−1  is short, so that the number PR N−1  of the multiplied signals generated during the [N−1] th  detection time period is smaller than the target value P N . For this reason, unlike the first embodiment, if P N+1  is calculated based on P N+1 =PA N+1 +(P N −PR N ), a value of P N+1  is affected by [P N−1 −PR N−1 ] (&gt;0) and becomes large. As a result, when an [N+1] th  rise of the encoder signal occurs, if the multiplied signals are generated every [TE N+1 /P N+1 ], the time interval for which the multiplied signals are generated becomes extremely short. 
     Therefore, in the first embodiment, in this case, when an [N+1] th  rise of the encoder signal occurs, P N+1  is calculated based on P N+1 =PA N +(P N −PR N )−(P N−1 −PR N−1 ) (S 204 ) and the multiplied signals are generated every [TE N+1 /P N+1 ] (S 205 ). Thereby, P N+1  is not affected by [P N−1 −PR N−1 ], so that it is possible to generate the multiplied signals at appropriate time intervals. 
     When the encoder sensor  19  reaches a position shown in  FIG. 10B , a rise of the encoder signal occurs and TR N  becomes shorter than TR 1 . As described above, TR N−1  is shorter than TR 1 . In this case, TR N−1  is short, so that the number PR N−1  of the multiplied signals generated during the [N−1] th  detection time period is smaller than the target value P N−1 . For this reason, unlike the first embodiment, if P N+1  is calculated based on P N+1 =PA N+1 +(P N −PR N ), a value of P N+1  is affected by [P N−1 −PR N−1 ] (&gt;0) and becomes large. In the meantime, a value of (2×TE N+1 −TR N ) is determined by a value of TR N , irrespective of a value of TR N−1 . As a result, when an [N+1] th  rise of the encoder signal occurs, if the multiplied signals are generated every [(2×TE N +−TR N )/P N+1 ], the time interval for which the multiplied signals are generated becomes extremely short. 
     Therefore, in the first embodiment, in this case, when an [N+1] th  rise of the encoder signal occurs, P N+1  is calculated based on P N+1 =PA N+1 +(P N −PR N )−(P N−1 −PR N−1 ) (S 304 ) and the multiplied signals are generated every [(2×TE N+1 −TR N )/P N+1 ] (S 305 ). Thereby, P N+1  is not affected by [P N−1 −PR N−1 ], so that it is possible to generate the multiplied signals at appropriate time intervals. 
     When the encoder sensor  19  reaches a position shown in  FIG. 11B , a rise of the encoder signal occurs and TR N  becomes longer than TR 2 . As described above, TR N−1  is shorter than TR 1 . In this case, TR N−1  is short, so that the number PR N−1  of the multiplied signals generated during the [N−1] th  detection time period is smaller than the target value P N−1 . For this reason, unlike the first embodiment, if P N+1  is calculated based on P N+1 =(M N+1 )×PA N+1 +(P N −PR N ), P N+1  is affected by [P N−1 −PR N−1 ] (&gt;0) and becomes large. In the meantime, a value of [2×TE N −TR N +M N ×C N ] is determined by a value of TR N , irrespective of a value of TR N−1 . As a result, when an [N+1] th  rise of the encoder signal occurs, if the multiplied signals are generated every [(2×TE N+1 −TR N +M N ×C N )/P N+1 ], the time interval for which the multiplied signals are generated becomes extremely short. 
     Therefore, in the first embodiment, in this case, when an [N+1] th  rise of the encoder signal occurs, P N+1  is calculated based on P N+1 =(M N+1 )×PA N+1 +(P N −PR N )−(P N−1 −PR N−1 ) (S 404 ) and the multiplied signals are generated every [(2×TE N+1 −TR N +M N ×C N )/P N+1 ] (S 405 ). Thereby, P N+1  is not affected by [P N−1 −PR N−1 ], so that it is possible to generate the multiplied signals at appropriate time intervals. 
     For example, a case where contaminants D as shown in  FIGS. 12A and 12B  are attached to the encoder scale  18 , a case where contaminants D as shown in  FIGS. 13A and 13B  are attached to the encoder scale  18  and a case where contaminants D as shown in  FIGS. 14A and 14B  are attached to the encoder scale  18  are considered. 
     In this case, when the encoder sensor  19  reaches positions shown in  FIGS. 12A, 13A and 14A , a rise of the encoder signal occurs, and TR N−1  becomes longer than TR 2 . TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2 . 
     In this case, as described above, when a N th  rise of the encoder signal occurs, P N  is calculated based on P N =(M N−1 +1)×PA N +(P N−1 −PR N−1 ) (S 402 ), and the multiplied signals are generated for each time calculated as [(2×TE N −TR N −+M N−1 ×C N−1 )/P N ] (S 405 ). Thereby, it is possible to generate the multiplied signals at appropriate time intervals. 
     On the other hand, when the encoder sensor  19  reaches a position shown in  FIG. 12B , a rise of the encoder signal occurs, and TR N  becomes equal to or longer than TR 1  and equal to or shorter than TR 2 . As described above, TR N−1  is longer than TR 2 . In this case, TR N−1  is long, so that the number PR N−1  of the multiplied signals generated during the [N−1] th  detection time period is larger than the target value P N . For this reason, unlike the first embodiment, if P N+1  is calculated based on P N+1 =PA N +(P N −PR N ), a value of P N+1  is affected by [P N−1 −PR N−1 ] (&lt;0) and becomes small. As a result, when an [N+1] th  rise of the encoder signal occurs, if the multiplied signals are generated every [TE N+1 /P N+1 ], the time interval for which the multiplied signals are generated becomes extremely long. 
     Therefore, in the first embodiment, in this case, when an [N+1] th  rise of the encoder signal occurs, P N+1  is calculated based on P N+1 =PA N +(P N −PR N )−(P N−1 −PR N−1 ) (S 204 ) and the multiplied signals are generated every [TE N+1 /P N+1 ] (S 205 ). Thereby, P N+1  is not affected by [P N−1 −PR N−1 ], so that it is possible to generate the multiplied signals at appropriate time intervals. 
     When the encoder sensor  19  reaches a position shown in  FIG. 13B , a rise of the encoder signal occurs and TR N  becomes shorter than TR 1 . As described above, TR N−1  is longer than TR 2 . In this case, TR N−1  is long, so that the number PR N−1  of the multiplied signals generated during the [N−1] th  detection time period is larger than the target value P N−1 . For this reason, unlike the first embodiment, if P N+1  is calculated based on P N+1 =PA N +(P N −PR N ), a value of P N+1  is affected by [P N−1 −PR N−1 ] (&lt;0) and becomes small. In the meantime, a value of (2×TE N+1 −TR N ) is determined by a value of TR N , irrespective of a value of TR N−1 . As a result, when an [N+1] th  rise of the encoder signal occurs, if the multiplied signals are generated every [(2×TE N +−TR N )/P N+1 ], the time interval for which the multiplied signals are generated becomes extremely long. 
     Therefore, in the first embodiment, in this case, when an [N+1] th  rise of the encoder signal occurs, P N+1  is calculated based on P N+1 =PA N +(P N −PR N )−(P N−1 −PR N−1 ) (S 304 ) and the multiplied signals are generated every [(2×TE N+1 −TR N )/P N+1 ] (S 305 ). Thereby, P N+1  is not affected by [P N−1 −PR N−1 ], so that it is possible to generate the multiplied signals at appropriate time intervals. 
     When the encoder sensor  19  reaches a position shown in  FIG. 14B , a rise of the encoder signal occurs and TR N  becomes longer than TR 2 . As described above, TR N−1  is longer than TR 2 . In this case, TR N−1  is long, so that the number PR N−1  of the multiplied signals generated during the [N−1] th  detection time period is larger than the target value P N−1 . For this reason, unlike the first embodiment, if P N+1  is calculated based on P N+1 =(M N+1 )×PA N+1 +(P N −PR N ), a value of P N+1  is affected by [P N−1 −PR N−1 ] (&lt;0) and becomes small. In the meantime, a value of [2×TE N +−TR N +M N ×C N ] is determined by a value of TR N , irrespective of a value of TR N−1 . As a result, when an [N+1] th  rise of the encoder signal occurs, if the multiplied signals are generated every [(2×TE N+1 −TR N +M N ×C N )/P N+1 ], the time interval for which the multiplied signals are generated becomes extremely long. 
     Therefore, in the first embodiment, in this case, when an [N+1] th  rise of the encoder signal occurs, P N+1  is calculated based on P N+1 =(M N+1 )×PA N+1 +(P N −PR N )−(P N−1 −PR N−1 ) (S 404 ) and the multiplied signals are generated every [(2×TE N+1 −TR N +M N ×C N )/P N+1 ] (S 405 ). Thereby, P N+1  is not affected by [P N−1 −PR N−1 ], so that it is possible to generate the multiplied signals at appropriate time intervals. 
     In this way, in the first embodiment, when TR N−2  is shorter than TR 1  and when TR N−2  is longer than TR 2 , the value of P N  is set as a value obtained by subtracting [P N−1 −PR N−1 ] from a value of P N  when TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2 , so that it is possible to generate the multiplied signals at appropriate time intervals. 
     In the first embodiment, a value of C N−1  is calculated as an average value of lengths of the past detection time periods before the N th  detection time period. Thereby, the calculated time interval of the multiplied signals can be made appropriate. 
     In the first embodiment, when a rise of the encoder signal is detected, the value of the position parameter U is increased or decreased according to the moving direction of the carriage  2 . When the time of 2×TE N  elapses from the N th  rise of the encoder signal without an [N+1] th  rise of the encoder signal, the value of the position parameter U is also increased or decreased according to the moving direction of the carriage  2 . Thereafter, the position parameter U is increased or decreased each time the time of TE N  elapses until an [N+1] th  rise of the encoder signal occurs, according to the moving direction of the carriage  2 . Thereby, the value of the position parameter U accurately corresponds to the position of the carriage  2  in the scanning direction, taking into consideration the encoder slits  18   a  that are not detected due the influences of contaminants and the like attached to the encoder scale  18 . Thereby, it is possible to accurately acquire the position information of the carriage  2  in the scanning direction, based on the value of the position parameter U. 
     Second Embodiment 
     A second embodiment of the present disclosure is described. 
     &lt;Schematic Configuration of Printer&gt; 
     As shown in  FIG. 15 , a printer  101  of the second embodiment (“liquid discharge apparatus” of the present disclosure) includes four inkjet heads  102  (liquid discharge head” of the present disclosure), a platen  103 , conveyor rollers  104  and  105  (“conveyor” of the present disclosure), and the like. 
     The four inkjet heads  102  are disposed side by side in the conveying direction. Each of the inkjet heads  102  includes four head units  106 , and a head holding member  107 . 
     The head unit  106  has a plurality of nozzles  110  aligned at equal intervals in the scanning direction. The four head units  106  of the inkjet head  102  are aligned in two rows in the scanning direction, and some nozzles  110  of the head units  106  configuring a row on an upstream side with respect to the conveying direction and some nozzles  110  of the head units  106  configuring a row on a downstream side with respect to the conveying direction are overlapped in the conveying direction. Thereby, in the inkjet head  102 , the plurality of nozzles  110  of the four head units  106  are aligned in the scanning direction over an entire length of the recording sheet P. That is, the inkjet head  102  is a line head. 
     The head holding member  107  is a plate-shaped member having a length direction in the scanning direction, and is configured to hold the four head units  106 . 
     The four inkjet heads  102  are configured to discharge black, yellow, cyan and magenta inks from the plurality of nozzles  110 , from those disposed on the upstream side with respect to the conveying direction. The head units  106  of the four inkjet heads  102  are supplied with inks of corresponding colors from ink cartridges (not shown). 
     The platen  103  is disposed below the four inkjet heads  102 , extends over the entire length of the recording sheet P in the scanning direction, and extends over the four inkjet heads  102  in the conveying direction. 
     The conveyor roller  104  is disposed upstream of the four inkjet heads  102  with respect to the conveying direction. The conveyor roller  105  is disposed downstream of the four inkjet heads  102  with respect to the conveying direction. The conveyor rollers  104  and  105  are connected to a conveyor motor  156  via a gear and the like (not shown). When the conveyor motor  156  is driven, the conveyor rollers  104  and  105  are rotated to convey the recording sheet P in the conveying direction. 
     As shown in  FIG. 15 , in the printer  101  of the second embodiment, the conveyor roller  104  is provided with a rotary encoder  120 . Note that, the rotary encoder  120  may also be provided to the conveyor roller  105 . 
     The rotary encoder  120  includes an encoder disk  121  (“slit member” of the present disclosure), and an encoder sensor  122 . As shown in  FIG. 16A , the encoder disk  121  is a circular plate-shaped member. The encoder disk  121  is attached to the conveyor roller  104 , and is configured to rotate together with the conveyor roller  104 . The encoder disk  121  has also a plurality of encoder slits  121   a . The plurality of encoder slits  121   a  has translucency, and is aligned at equal intervals in a circumferential direction (“predetermined direction” of the present disclosure) of the encoder disk  121 . 
     As shown in  FIGS. 16B and 16C , the encoder sensor  122  includes a light-emitting element  122   a  and a light-receiving element  122   b . The light-emitting element  122   a  and the light-receiving element  122   b  are disposed facing each other in the scanning direction. The encoder disk  121  is disposed between the light-emitting element  122   a  and the light-receiving element  122   b  in the scanning direction, and the light-emitting element  122   a  and the light-receiving element  122   b  face each other with the encoder disk  121  being sandwiched therebetween. The light-emitting element  122   a  is configured to irradiate light toward the light-receiving element  122   b.    
     In a state where the encoder sensor  19  (the light-emitting element  122   a  and the light-receiving element  122   b ) faces the encoder slit  121   a  of the encoder disk  121 , the light irradiated from the light-emitting element  122   a  passes through the translucent encoder slit  121   a  and is then received in the light-receiving element  122   b , as shown in  FIG. 16B . On the other hand, in a state where the encoder sensor  122  (the light-emitting element  122   a  and the light-receiving element  122   b ) faces a part between the two adjacent encoder slits  121   a  of the encoder disk  121 , the light irradiated from the light-emitting element  122   a  is blocked by the encoder disk  121  and is not thus received in the light-receiving element  122   b , as shown in  FIG. 16C . 
     The encoder sensor  122  is configured to output a signal indicating whether the light from the light-emitting element  122   a  is received in the light-receiving element  122   b . More specifically, the encoder sensor  122  is configured to transmit an encoder signal that is a pulse signal that rises when a state is switched from a state in which the light irradiated from the light-emitting element  122   a  is received in the light-receiving element  122   b  to a state in which the light is not received in the light-receiving element  122   b  and falls when a state in switched from the state in which the light irradiated from the light-emitting element  122   a  is not received in the light-receiving element  122   b  to the state in which the light is received in the light-receiving element  122   b.    
     &lt;Electrical Configuration of Printer&gt; 
     Subsequently, an electrical configuration of the printer  101  is described. Operations of the printer  101  are controlled by a controller  150 . As shown in  FIG. 17 , the controller  150  includes a CPU  151 , a ROM  152 , a RAM  153 , a flash memory  154 , an ASIC  155  and the like, and is configured to control operations of the head unit  106 , the conveyor motor  156  and the like. The controller  150  is also configured to receive the encoder signal transmitted from the encoder sensor  122 . In the second embodiment, the printer  101  includes the plurality of head units  106 . However, in  FIG. 17 , for convenience of sake, only one head unit  106  is shown. 
     Note that, the controller  150  may also be configured so that only the CPU  151  executes a variety of processing, only the ASIC  155  executes a variety of processing, or the CPU  151  and the ASIC  155  execute a variety of processing in cooperation with each other. The controller  150  may also be configured so that one CPU  151  solely executes processing or a plurality of CPUs  151  shares and executes processing. The controller  150  may also be configured so that one ASIC  155  solely executes processing or a plurality of ASICs  155  shares and executes processing. 
     &lt;Processing Upon Recording&gt; 
     Subsequently, control that is executed when performing recording on the recording sheet P in the printer  101  is described. In the printer  101 , the controller  150  causes the plurality of head units  106  to discharge inks from the plurality of nozzles  110  while controlling the conveyor motor  156  to cause the conveyor rollers  104  and  105  to convey the recording sheet P in the conveying direction, thereby performing recording on the recording sheet P. 
     &lt;Generation of Multiplied Signal&gt; 
     When performing recording on the recording sheet P, as described above, the encoder disk  121  is rotated together with the conveyor roller  104 , so that the encoder sensor  122  and the encoder disk  121  relatively move in the circumferential direction of the encoder disk  121  and the encoder signal as described above is output from the encoder sensor  122 . 
     When performing recording on the recording sheet P, the controller  150  generates multiplied signals by multiplying the encoder signal received from the encoder sensor  122 . Then, the controller  150  causes the head units  106  to discharge the inks from the plurality of nozzles  110  at a timing at which a rise occurs in the generated multiplied signal, for example. In the below, the generation of the multiplied signals is described. 
     In the second embodiment, when the recording on the recording sheet P starts, the controller  150  executes processing according to a flow shown in  FIG. 8 , thereby generating the multiplied signal. 
     More specifically, when the recording on the recording sheet P starts, the controller  150  executes processing from S 601  to S 610  similar to S 101  to S 110  of the first embodiment. In S 102  of the first embodiment, it is determined whether a rise of the encoder signal from the linear encoder  8  is detected. However, in S 602  of the second embodiment, it is determined whether a rise of the encoder signal from the rotary encoder  120  is detected. 
     Then, after executing processing of any one of S 605 , S 607 , S 609  and S 610 , the controller  150  determines whether the recording on the recording sheet P is completed (S 611 ). When it is determined that the recording on the recording sheet P is not completed (S 611 : NO), the controller  150  returns to S 602 , and when it is determined that the recording on the recording sheet P is completed (S 611 : YES), the controller  150  ends the processing. 
     &lt;Effects&gt; 
     In the second embodiment also, similar to the first embodiment, in a case where TR N−1  is equal to or longer than TR 1  and equal to or shorter than TR 2 , P N  is calculated based on P N =PA N−1 +(P N−1 −PR N−1 ), and the multiplied signals are generated every [TE N /P N ] when a N th  rise of the encoder signal occurs. Thereby, when the number of the multiplied signals for the [N−1] th  detection time period becomes small, the number of the multiplied signals for the N th  detection time period can be increased. When the number of the multiplied signals for the [N−1] th  detection time period becomes large, the number of the multiplied signals for the N th  detection time period can be reduced. 
     In the second embodiment also, similar to the first embodiment, in a case where TR N−1  is shorter than TR 1 , the multiplied signals are generated for each time calculated as [(2×TE N −TR N−1 )/P N ] when a N th  rise of the encoder signal occurs. Thereby, even when contaminants are attached to the encoder scale  18 , it is possible to generate the multiplied signals at appropriate time intervals. 
     In the second embodiment also, similar to the first embodiment, in a case where TR N−1  is longer than TR 2 , P N  is calculated based on P N =(M N−1 +1)×PA N−1 +(P N−1 −PR N−1 ) and the multiplied signals are generated for each time calculated as [(2×TE N −TR N−1 +M×C N−1 )/P N ]. Thereby, even when contaminants are attached to the encoder slits, it is possible to generate the multiplied signals at appropriate time intervals. 
     In the second embodiment also, in each of cases where TR N−1  is shorter than TR 1  and where TR N−1  is longer than TR 2 , the processing for determining the time interval for generating the multiplied signals is made different from the case where TR N−1  is equal to or longer than TR 1  and equal to or shorter than TR 2 . However, in this case, it may be problematic if the time interval for generating the multiplied signals is determined as described above. 
     Therefore, also in the second embodiment, similar to the first embodiment, when TR N−2  is shorter than TR 1  and when TR N−2  is longer than TR 2 , a value of P N  is set as a value obtained by subtracting [P N−1 −PR N−1 ] from a value of P N  when TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2 . Thereby, it is possible to generate the multiplied signals at appropriate time intervals. 
     Modified Embodiments 
     In the above, the first and second embodiments of the present disclosure have been described. However, the present invention is not limited to the first and second embodiments and can be diversely modified within the scope of the claims. 
     For example, in the first and second embodiments, as the value of C N−1  that is a standard value of the length of the [N−1] th  detection time period, the average value of lengths of the predetermined number of times of past detection time periods before the N th  detection time period is used. However, the present invention is not limited thereto. 
     In a modified embodiment 1, as shown in  FIG. 19A , a printer  200  includes a temperature sensor  201  for detecting a temperature, in addition to a configuration similar to the printer  1  of the first embodiment. The temperature sensor  201  is mounted to the carriage  2 , for example. 
     In the modified embodiment 1, as shown in  FIG. 19B , in the third multiplied signal generation processing, the controller  50  executes processing of S 701  to S 704  similar to S 401  to S 404  of the first embodiment. Then, after calculating P N  in processing of S 702  or S 704 , the controller  50  acquires temperature information, based on a signal from the temperature sensor  201  (S 705 ). Then, the controller  50  determines a value of C N−1 , based on the acquired temperature information (S 706 ), and executes processing of S 707  similar to S 406  of the first embodiment by using the determined value of C N−1 , thereby generating the multiplied signal. 
     In a modified embodiment 2, a table in which the temperature and C N−1  are associated with each other is stored in advance in the flash memory  54 , for example, and in S 706 , the controller  50  determines C N−1 , based on the table and the temperature acquired in S 705 . Alternatively, for example, data of a relation equation between the temperature and C N−1  is stored in advance in the flash memory  54 , and in S 706 , the controller  50  determines C N−1 , based on the data of the relation equation and the temperature acquired in S 705 . 
     A viscosity of grease applied between the carriage  2  and the guide rails  11  and  12  is changed by the temperature, so that the moving speed of the carriage  2 , i.e., the detection time period when there are no contaminants and the like attached to the encoder scale  18  is changed due to the influence. In the modified embodiment 1, the controller  50  calculates C N−1  based on a detection result of the temperature sensor  201 . Thereby, the time interval of the multiplied signals calculated based on C N−1  can be made appropriate. 
     In the modified embodiment 2, values of C 1 , C 2 , . . . are stored in advance in the flash memory  54  (“memory” of the present disclosure). The stored values of C 1 , C 2 , . . . are obtained in advance by a test and the like. 
     In the modified embodiment 2, as shown in  FIG. 20 , in the third multiplied signal generation processing, the controller  50  executes processing of S 801  to S 804  similar to S 401  to S 404  of the first embodiment. Then, after calculating P N  in processing of S 802  or S 804 , the controller  50  reads out the value of C N−1  stored in the flash memory  54  (S 805 ), and executes processing of S 806  similar to S 406  of the first embodiment by using the read value of C N−1 , thereby generating the multiplied signal. 
     In the modified embodiment 2, since the appropriate value of C N−1  is obtained by a test and the like and is stored in the flash memory  54 , it is not necessary to execute the processing for calculating C N−1 . 
     In the first embodiment, the value of the position parameter U that is increased or decreased each time a rise of the encoder signal is detected is corrected to increase or decrease when the time of 2×TE N  elapses from the detection of the encoder and each time TE N  elapses thereafter. Thereby, the position parameter U can accurately correspond to the position of the carriage  2  in the scanning direction. However, the present invention is not limited thereto. For example, the position parameter U that is increased or decreased each time a rise of the encoder signal is detected may be corrected by other methods so that the value corresponds to the position of the carriage  2 . 
     In the first and second embodiments, assuming that contaminants are attached to the encoder scale  18  or the encoder disk  121  in diverse aspects, in each of cases where TR N−1  is shorter than TR 1  and where TR N−1  is longer than TR 2 , the processing for determining the time interval for generating the multiplied signals is made different from the case where TR N−1  is equal to or longer than TR 1  and equal to or shorter than TR 2 . When TR N−2  is shorter than TR 1  and when TR N−2  is longer than TR 2 , the value of P N  is set as a value obtained by subtracting [P N−1 −PR N−1 ] from the value of P N  when TR N−2  is equal to or longer than TR 1  and equal to or shorter than TR 2 . However, the present invention is not limited thereto. 
     In a modified embodiment 3, in the printer  1  of the first embodiment, the controller  50  executes processing according to a flow shown in  FIG. 21 , thereby generating the multiplied signal. 
     More specifically, processing of S 901  to S 904  and S 910  of the flow shown in  FIG. 21  is similar to the processing of S 101  to S 105  and S 111  of the first embodiment. In the modified embodiment 3, when N is 2 or greater (S 904 : NO), the controller  50  calculates P N  based on P N =PA N +(P N−1 −PR N−1 ) (S 906 ). When TR N−1  is equal to or longer than TR 1  (S 907 : NO), the controller  50  generates the multiplied signals every [TE N /P N ] (S 908 ), and proceeds to S 910 . When TR N−1  is shorter than TR 1  (S 907 : YES), the controller  50  generates the multiplied signals every [(2×TE N −TR N −)/P N ] ( 909 ), and proceeds to S 910 . 
     In a modified embodiment 4, in the printer  101  of the second embodiment, the controller  50  executes processing according to a flow shown in  FIG. 22 , thereby generating the multiplied signal. Processing of S 1001  to S 1009  of the flow shown in  FIG. 22  is similar to the processing of S 901  to S 909  of the modified embodiment 3. Processing of S 1010  of the flow shown in  FIG. 22  is similar to S 611  of the second embodiment. 
     For example, contaminants are little attached to the encoder scale  18  or the encoder disk  121 , and even when contaminants are attached, an amount of attachment thereof may be relatively small, depending on the printers. In this case, TR N−1  is expected to be shorter than TR 1  but TR N−1  is not expected to be longer than TR 2 . In this case, it is assumed that a plurality of contaminants is not attached to a part close to the encoder scale  18  or the encoder disk  121 , and when TR N−1  is shorter than TR 1 , TR N−2  is equal to or longer than TR 1  and becomes TR 2 . 
     In such printer, like the modified embodiments 3 and 4, when TR N−1  is shorter than TR 1 , the processing for generating the multiplied signals is made different from the case where TR N−1  is equal to or longer than TR 1 . Thereby, it is possible to generate the multiplied signals at appropriate time intervals. 
     In a modified embodiment 5, in the printer  1  of the first embodiment, the controller  50  executes processing according to a flow shown in  FIG. 23 , thereby generating the multiplied signal. 
     More specifically, processing of S 1101  to S 1105  and S 1111  of the flow shown in  FIG. 23  is similar to the processing of S 101  to S 105  and S 111  of the first embodiment. In the modified embodiment 5, when N is 2 or greater (S 1104 : NO) and TR N−1  is equal to or shorter than TR 2  (S 1106 : NO), the controller  50  calculates P N  based on P N =PA N +(P N−1 −PR N−1 ) (S 1107 ), generates the multiplied signals every [TE N /P N ] (S 1108 ), and proceeds to S 1111 . 
     On the other hand, when N is 2 or greater ( 1104 : NO) and TR N−1  is longer than TR 2  (S 1106 : NO), the controller  50  calculates P N  based on P N =(M N−1 +1)×PA N +(P N−1 −PR N−1 ) (S 1109 ), generates the multiplied signals every [(2×TE N −TR N−1 )/P N ] (S 1110 ), and proceeds to S 1111 . 
     In a modified embodiment 6, in the printer  101  of the second embodiment, the controller  50  executes processing according to a flow shown in  FIG. 24 , thereby generating the multiplied signal. Processing of S 1201  to S 1210  of the flow shown in  FIG. 24  is similar to the processing of S 1101  to S 1110  of the modified embodiment 4. Processing of S 1211  of the flow shown in  FIG. 24  is similar to S 611  of the second embodiment. 
     For example, contaminants are little attached to the encoder scale  18  or the encoder disk  121 , the intervals between the encoder slits  18   a ;  121   a  are short, and when contaminants are attached, the contaminants may extend over the entire length of the encoder slit  18   a ;  121   a , depending on the printers. In this case, TR N−1  is expected to be longer than TR 2  but TR N−1  is not expected to be shorter than TR 1 . In this case, it is assumed that a plurality of contaminants is not attached to a part close to the encoder scale  18  or the encoder disk  121 , and when TR N−1  is longer than TR 2 , TR N−2  is equal to or longer than TR 1  and becomes TR 2 . 
     In such printer, like the modified embodiments 5 and 6, when TR N−1  is shorter than TR 1 , the processing for generating the multiplied signals is made different from the case where TR N−1  is equal to or longer than TR 1 . Thereby, it is possible to generate the multiplied signals at appropriate time intervals. 
     In the first and second embodiments, the multiplied signals are generated based on the rise timing of the encoder signal, for example. However, the present invention is not limited thereto. For example, the multiplied signals may be generated based on a fall timing of the encoder signal. In this case, a fall of the encoder signal corresponds to “signal change” of the present disclosure. 
     In the first embodiment, the linear encoder  8  has such configuration that the light-emitting element  19   a  and the light-receiving element  19   b  of the encoder sensor  19  are disposed with the encoder scale  18  being sandwiched therebetween, and when the light-emitting element  19   a  and the light-receiving element  19   b  face the encoder slit  18   a  of the encoder scale  18 , the light irradiated from the light-emitting element  19   a  is received in the light-receiving element  19   b . However, the present invention is not limited thereto. For example, in the first embodiment, the linear encoder may have such configuration that the light-emitting element and the light-receiving element are provided on the same side with respect to the encoder scale, and when the light-emitting element and the light-receiving element do not face the encoder slit, the light irradiated from the light-emitting element is reflected on the encoder scale and is then received in the light-receiving element. Similarly, in the second embodiment, the rotary encoder may have such configuration that the light-emitting element and the light-receiving element are provided on the same side with respect to the encoder disk, and when the light-emitting element and the light-receiving element do not face the encoder slit, the light irradiated from the light-emitting element is reflected on the encoder disk and is then received in the light-receiving element. 
     In the above, the present disclosure is applied to the printer configured to discharge the inks from the nozzles, thereby performing recording on the recording sheet P. However, the present invention is not limited thereto. For example, the present disclosure can also be applied to a liquid discharge apparatus configured to record an image by discharging inks to a to-be-recorded medium other than the recording sheet, such as a T-shirts, a sheet for outdoor advertisement, a case of a portable terminal such as a smartphone, a corrugated cardboard, a resin member and the like. The present disclosure can also be applied to a liquid discharge apparatus configured to discharge liquid other than ink, such as liquidous resin or metal.