The present application claims priority under 35 U.S.C. §119 to Japanese Patent Application No. 2010-167089, filed Jul. 26, 2010 and Japanese Patent Application No. 2010-004380, filed Jan. 12, 2010. The contents of these applications are incorporated herein by reference in their entirety.
1. Field of the Invention
The present invention relates to a synchronous control apparatus.
2. Discussion of the Background
For example, Japanese Patent Application Laid-Open No. 2004-288164 as a conventional technique describes a control apparatus which drives and controls a servo motor by a position controller which outputs a velocity command with a predetermined period based on a position deviation between a position command and a position feedback from a position detector, and by a velocity controller which outputs a torque command with a predetermined period based on the velocity command and a velocity feedback from a velocity detector, and the control apparatus includes a synchronous correction processor which controls in synchronization, two servo motors that drive the same control subject, and which reduces a force applied between the two servo motors based on a force applied between the two servo motors.
According to one aspect of the present invention, a synchronous control apparatus to synchronously control a plurality of motors with respect to a control subject includes a command device and a plurality of motor control devices. The control subject includes the plurality of motors, a plurality of position detectors, and at least one coupler. The plurality of position detectors is configured to detect a plurality of position information of the plurality of motors respectively. The at least one coupler connects movable axes of the plurality of motors. The command device includes a first position controller. The first position controller is configured to compute a work position based on the plurality of position information detected by the plurality of position detectors. The first position controller is configured to compute, based on a difference between a position command and the work position, a new position command. Each of the plurality of motor control devices includes a second position controller. The second position controller is configured to compute commands to drive the plurality of motors based on a difference between the new position command and the plurality of position information.
According to another aspect of the present invention, asynchronous control apparatus to synchronously control two motors with respect to a control subject includes a position measuring device, a command device, first and second motor control devices, and a third motor control device. The control subject is a gantry mechanism. The gantry mechanism includes the two motors, two position detectors, and a coupler. The two position detectors are configured to detect two position information of the two motors respectively. The coupler connects movable axes of the two motors. The position measuring device is configured to measure one of axis coordinate system positions of a work position which is expressed by an XY-axes coordinate system. The command device includes a first position controller. The first position controller is configured to compute, based on a difference between a position command and a work position information according to the one of axis coordinate system positions of the work position measured by the position measuring device, a new position command. Each of the first and second motor control devices includes a second position controller. The second position controller is configured to compute a command to drive the two motors based on a difference between the new position command and the two position information. The third motor control device has a same function as a function of the first or second motor control device. One of the axis coordinate system positions of the work position is input to the third motor control device. The third motor control device outputs the one of the axis coordinate system positions of the work position to the command device.
According to further aspect of the present invention, a synchronous control apparatus includes a first axis, a second axis, and a command device. The first axis to drive a control subject includes a plurality of first motors, a plurality of position detectors, and at least one machine coupler. The plurality of position detectors is configured to detect a plurality of position information of the plurality of first motors respectively. The at least one machine coupler connects movable axes of the plurality of first motors. The second axis to drive another control subject includes a second motor, a position detector, and a machine connector. The position detector is configured to detect position information of the second motor. The machine connector connects a movable axis of the second motor. The command device is configured to make the first axis and the second axis carry out an arc interpolation operation of an XY-axes coordinate system based on a position command. The first axis configures a position integration proportion and velocity proportion control system. The second axis configures a position proportion and velocity integration proportion control system. A first position proportion gain in the first axis is set such that the first position proportion gain matches with a reciprocal of velocity integration time in the second axis. A position integration time in the first axis is set such that the position integration time matches with a reciprocal of a second position proportion gain in the second axis.
A more complete appreciation of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:
The embodiments will now be described with reference to the accompanying drawings, wherein like reference numerals designate corresponding or identical elements throughout the various drawings.
A first embodiment of the present invention will be described with reference to the drawings.
The command device 2 includes a position command generator 21, a position controller 22 and a position information computing unit 23.
The position command generator 21 generates an internal position command 121 for driving motors 5 and 6, and outputs the internal position command 121 to the position controller 22. The position information computing unit 23 inputs detection position information 131 and 141 detected by encoders 7 and 8 through a position information transmission path 126 from the servo amplifiers 3 and 4, and outputs work position information 122 by later-described computation. The position controller 22 inputs a deviation between the internal position command 121 and the work position information 122, computes to perform proportion integration control, and outputs a new position command signal 125 to the servo amplifiers 3 and 4 through the position information transmission path 126. The position information transmission path 126 is, for example, a high-velocity serial communication path, and position information can be transmitted between the servo amplifiers 3 and 4 in synchronization with each other.
When a mechanism system driven by the synchronous control apparatus 1 is an XY-axes coordinate system and the internal position command 121 is a position command on the XY-axes coordinate system, the work position information 122 is a coordinate of a work position (operation center) existing on the XY-axes coordinate system.
The servo amplifier 3 includes a position controller 31, a velocity controller 32, a velocity computing unit 33, and a current controller 34. The servo amplifier 4 also has the same configuration (a position controller 41, a velocity controller 42, a velocity computing unit 43 and a current controller 44).
The position controllers 31 and 41 input deviations between the new position command signal 125 and the detection position information 131 and 141, and compute to perform proportion control, and output a velocity command. The velocity computing units 33 and 34 input detection position information 131 and 141, compute differentiation, and output a velocity feedback signal. The velocity controllers 32 and 42 input a deviation between a velocity command and a velocity feedback signal, and compute to perform proportion control, and output a command for driving the motor.
Since the command for driving the motor drives the motor by applying voltage to a motor winding to flow current, this command is a voltage or current command. The current controllers 34 and 44 compute to control current corresponding to the current command, and supply the current to the motors 5 and 6. The motors 5 and 6 generate a force which is in proportion to the supplied current. For example, if the motor is a synchronous rotation motor, a torque is generated, and if the motor is a linear motor, a thrust force is generated.
As described above, in addition to position control systems formed in the servo amplifiers 3 and 4, the synchronous control apparatus of the first embodiment of the present invention also includes another position control system in the command device 2. Since the position controller 22 in the command device 2 includes integration computation, it is possible to carry out a following operation or a positioning operation with respect to the internal position command 121 which is output from the position command generator 21 without positional deviation of the work position information 122. The position controller 22 can carry out the same operation even with integration control only.
When the first synchronous mechanism (gantry structure) is driven, a command device 14 sends the same position command to the servo amplifiers 15 and 16 which are the same position control configurations through a position information transmission path 126, and controls two axes (X1 axis and X2 axis) in synchronization.
Configurations of the motors 5 and 6, the encoders 7 and 8 and a machine coupling unit 9 shown in
Problems generated when the first synchronous mechanism (gantry structure) is controlled in synchronization will be discussed below.
In the first synchronous mechanism (gantry structure) which fastens mutual axes by the machine coupling unit 9, the higher the rigidity of the machine coupling unit 9 is, the greater the twisting reaction force (invalid reaction force, hereinafter) applied from one of the axes to the other axis and from the other axis to one axis becomes. This invalid reaction force is caused by producing variation of a linear scales 114 and 115, a mounting error with respect to a mechanism, or assembling precision of the mechanism itself, and this exerts influence on both the position control systems as disturbance with respect to the servo amplifiers 15 and 16.
That is, the invalid reaction force becomes a thrust force having a symbol opposite from thrust force command values of the servo amplifiers 15 and 16. In the servo amplifiers 15 and 16, to cancel the invalid reaction force, it is necessary to further increase the thrust force command value (to increase a load ratio) and therefore, energy efficiency is largely deteriorated.
When the invalid reaction force is large, there is an adverse possibility that the invalid reaction force exceeds a thrust force upper limit value that the servo amplifiers 15 and 16 can output. If the invalid reaction force exceeds the thrust force upper limit value, normal position control operation or normal synchronous control cannot be carried out.
In N-axes synchronous control (N is the number of axes and N is a natural number greater than 1), one detection position is defined as a master position and positions of remaining axes (N−1) are defined as slave positions in some cases. For example, in
Next, a method in which the position information computing unit 23 computes the work position information 122 from the detection position information 131 and 141 will be described.
The position information computing unit 23 computes X-coordinates of the work position information 122 using the following equation (1). Here, m is in a range of 0≦m≦1, and m is determined from a work position which is previously designated freely (calculation method of m will be described later).
(X-coordinates of work position information 122)=m×(detection position information 131)+(1−m)×(detection position information 141) (1)
In the configuration of the first synchronous mechanism (gantry structure) shown in
For example, if m in the equation (1) is 0.5, a central position between the X1-axis and the X2-axis can be computed as X-coordinates of the work position information 122. In this manner, if a distance between the X1-axis and the X2-axis is defined as L, work position information in an X-axis direction of mL can be computed.
In the case of the configuration of the first synchronous mechanism (gantry structure) shown in
Like the X1-axis and the X2-axis, the Y-axis also includes another servo amplifier (for Y-axis), configures a position control system, and drives another motor (for Y-axis) based on another position command (for Y-axis) from the command device 2. In this case, as will be described later, a value of m can be calculated based on Y-axis coordinates which intersect with the coordinates of the X1-axis and the X2-axis. That is, a position of the Y-axis is Y-coordinate of the work position information 122, and a position calculated by the equation (1) using m is X-coordinate of the work position information 122.
A calculation expression of m will be described below.
In this case, m can be calculated using the following equation (2).
m=(Py+dY2)/(dY1+Ly+dY2) (2)
In
In this manner, the work position information in the X-axis direction can be calculated from a position of the Y-axis. When an operation head 113 which moves in the Y-axis is mounted on the machine coupling unit 9 shown in
The synchronous control apparatus of this embodiment of the present invention is achieved by paying attention to a fact that in the N-axes synchronous control (N is the number of axes and N is a natural number greater than 1), the same number of encoder positions as that of the axes and a machine position of the actual synchronous mechanism do not strictly match with each other, a fact that an invalid reaction force is generated by rigidity of a coupling member which fastens movable axes of the same number of motors as that of the axes to each other, and a fact that an invalid reaction force and a deviation between the axes of the same number of encoder positions as that of the axes are mutually contradictory.
That is, the synchronous control apparatus of this embodiment of the present invention is configured based on a fact that in the N-axes synchronous control (N is the number of axes and N is a natural number greater than 1), the number of detection positions which match with the position command should not be two or more, but one, and a fact that a position control system should be provided for each of the servo amplifiers, and the position control system using one detection position for the position command is required.
The representative invention of the present application includes a configuration that in the N-axes synchronous control (N is the number of axes and N is a natural number greater than 1), a work position is calculated from a plurality of encoder positions, and the work position is made to follow a position command, a configuration that integration computation in each servo amplifier is eliminated (In the integration computation, as the motion becomes lower frequency, the gain is increased. Therefore, at the time of stop when the positioning operation is completed, an invalid reaction force is increased. The increase in the invalid reaction force is suppressed by eliminating the integration computation), and a configuration that one new position control system is added to an outer side of the servo amplifier, and only this position control system is provided with the integration computation.
As described above, in the representative invention of the present application, precision of a machine which is a control subject is also comprehensively and essentially considered. It is possible to suppress an invalid reaction force which is applied between axes using a general electric part (a motor, a servo amplifier or a command device) with respect to a machine which drives coordinate axes in the same direction of a plurality of motors, and it is possible to precisely perform synchronous control with respect to the work position.
That is, thrust forces (torques) of a plurality of motors which should operate in synchronization with each other can be made substantially equal to each other, and it is possible to realize the synchronization operation having a small invalid reaction force when the positioning operation is carried out or after the positioning operation is completed only by the position information transmission path through which position data is transmitted (utilizing general serial communication). Deviation caused by influence of rigidity or viscous friction of a machine coupling unit can be reduced, and work position information in the command device can strictly match with a position command when the positioning operation is completed.
In the representative invention of the present application, a transmission path other than the position information transmission path (for example, a position deviation transmission path or a torque command transmission path) is not required between axes of the servo amplifiers. Therefore, the servo amplifier can be formed from general products, and the servo amplifier is more excellent than a special product in terms of cost and maintenance.
The detection position information corresponds to position information described in claims, the internal position command corresponds to the position command described in claims, the work position information corresponds to the work position described in claims, the command device corresponds to a command apparatus, and the servo amplifier corresponds to a motor control apparatus described in claims.
Examples of applications of the synchronous control apparatus according to the embodiment of the present invention will be described in sequence with respect to various synchronous mechanisms.
Next, a second embodiment of the present invention will be described with reference to the drawings.
The second embodiment is different from the first embodiment in that the synchronous control apparatus 10 inputs detection position information of the laser interferometer 101 to the servo amplifier 17, inputs the same to the position information computing unit 23 in the command device 2 through a position information transmission path 126 as detection position information 171, and in that the position information computing unit 23 uses the detection position information 171 of only the laser interferometer 101, but does not use the detection position information 131 and the detection position information 141 from the servo amplifiers 3 and 4.
Therefore, in the synchronous control apparatus 10, a motor is not connected to the servo amplifier 17, and uses the servo amplifier 17 as a data converter which transmits only the detection position information 171 of the laser interferometer 101 to the position information transmission path 126. With this configuration, the synchronous control apparatus can be formed only from general products.
When detection resolving power of the encoders 7 and 8 (length per one pulse: e.g., 0.1 μm/1 pulse) and detection position resolving power of the laser interferometer 101 are different from each other, electronic gear computation is carried out in the position information computing unit 23 to equalize both the resolving powers.
In the second embodiment, a position near the work position is detected by the laser interferometer 101, this is feedback to the position control system in the command device 2 as the work position information 122 in the command device 2. Therefore, it is possible to make the work position in the X direction precisely follow the command position as compared with the first embodiment.
The laser interferometer corresponds to a position measuring apparatus described in claims.
Next, a third embodiment of the present invention will be described with reference to the drawings.
The third embodiment is different from the first embodiment in that the synchronous control apparatus 11 synchronously controls the synchronous mechanism including three axes (e.g.,
Configurations of the motors 5, 6 and 18, the encoders 7, 8 and 19 (corresponding to linear scale heads 7, 8, and 19 shown in
The position information computing unit 23 in the command device 2 calculates the work position information 122 based on detection position information 131, 141 and 171 from the servo amplifiers 3, 4 and 17. For example, the calculation method of two axes using the equation (1) described in the first embodiment may be developed into three axes (see equations (3) and (4)).
In
When three linear scale heads are mounted on one linear scale to detect a position for example, if a true value of detection position information X1 detected from the linear scale through the servo amplifier 3 is defined as θ [rad] and a minute value corresponding to an error is defined as δ, and if it is assumed that an error of one cycle is generated in the linear scale, X1 becomes equal to θ+δ sin(θ).
If liner scale heads are disposed on a circumference of the linear scale every 120° (2π/3), detection position information X2 of the servo amplifier 4 and detection position information X3 of the servo amplifier 17 are as follows: X2=θ+δ sin(θ−2π/3) and X3=θ+δ sin(θ−4π/3). Here, the three liner scale heads are deviated in position by 120° from each other, but since values of the true values θ become equal to each other if one original position is commonly used for the three motors, an error of one cycle depends on a physical position, and the values are deviated from θ by 120° and 240°.
The position information computing unit 23 in the synchronous control apparatus of the third embodiment of the present invention carries out averaging computation of the work position information 122 using the following equation (3).
(work position information 122)=((detection position information 131)+(detection position information 141)+(detection position information 171))/3 (3)
The equation (3) is expressed by the following equation (4).
(work position information 122)=θ+δ(sin(θ)+sin(θ−2π/3)+sin(θ−4π/3)) (4)
Here, since sin(θ)+sin(θ−2π/3)+sin(θ−4π/3)=0, (work position information 122)=θ, and the work position information 122 is obtained as a true value having no error. When the number of arc linear motors is m, liner scale heads should be disposed every 360/m°=2π/m, and the position information computing unit 23 should carry out the averaging computation of the m number.
The synchronous control apparatus of the third embodiment of the present invention includes another position control system in the command device 2 in addition to the position control systems constituted in the servo amplifiers 3, 4 and 17. Since the position controller 22 in the command device 2 includes integration computation, the work position information 122 can carry out the following operation or the positioning operation without positional deviation with respect to the internal position command 121 which is output by the position command generator 21. It is possible to reduce an error of N-cycle (N is a natural number) per one rotation generated by a mounting error of the linear scale by the averaging computation of the position information computing unit 23.
As described above, according to the third embodiment, it is possible to easily increase the number of axes which synchronously control, and to suppress an invalid reaction force of each axis to a lower level. As the number of axes which synchronously control is increased, the control configuration between the axes becomes complicated, and adjustment of control gain is also complicated. According to the third embodiment, when a synchronous control system with respect to the N-axis (N is a natural number greater than 1) is configured, it is only necessary to prepare the same number of servo amplifiers (e.g., general servo amplifiers) having the same control system as that of the N-axes.
The synchronous control apparatus (the synchronous control apparatus of the first embodiment of the present invention when the number of axes is two) according to the third embodiment of the present invention which synchronously controls the N-axis can be applied to industrial machines such as a press machine and an injection molding machine.
In the case of the industrial machines such as the press machine and the injection molding machine of a mechanism in which two motors and one drive gear are coupled to each other, when the coupling is a rigid body, even if only a motor of one of the axes is controlled in position to make the other motor follow, encoder rotation angles of both the motors match with each other. Therefore, the synchronous control apparatus of the first or third embodiment of the present invention can be applied.
When this coupling rigidity is low, since a rotation angle of the drive gear and a rotation angle of the motor of two axes do not always match with each other, computation of the following equation (5) is carried out by the position information computing unit in the command device.
The rotation angle of the drive gear=a rotation angle of a motor of a first axis+(torsional moment/torsional rigidity×distance from an encoder of the first axis to the drive gear) (5)
In this manner, if the rotation angle of the drive gear is used as work position information, it is possible to make the rotation angle of the drive gear flow the command position and thus, the synchronous control apparatus of the first or third embodiment of the present invention can be applied.
The torsional moment is given by a torque of a motor of the first axis, and torsional rigidity is given by material and shape of the coupling. The distance from the encoder of the first axis to the drive gear is geometrically determined when the motor is assembled in the machine.
The synchronous control apparatus according to the third embodiment of the present invention which synchronously controls the N-axis (the synchronous control apparatus according to the first embodiment of the present invention when the number of axes is two) can be applied also to synchronous control of a wire saw sending-out axis and a wire saw take-up axis (an external sensor measures a sending-out amount from a reference position of a wire saw, and the measured value is defined as a feedback position to the command device), and also to synchronous control of a film sending-out axis and a film take-up axis (an external sensor measures a sending-out amount from a reference position of a film, and the measured value is defined as a feedback position to the command device).
The synchronous control apparatuses of the first to third embodiments of the present invention have the above-described configurations. Therefore, in the N-axis synchronous control (N is the number of axes, and is a natural number greater than 1), torques (thrust forces) of the axes at the time of acceleration and deceleration can be balanced (see
Next, a fourth embodiment of the present invention will be described with reference to the drawings. In the synchronous control apparatus of the first embodiment of the present invention (
It is an object of the first embodiment of the present invention to position the work position information 122, i.e., to match the internal position command 121 and the work position information 122 with each other. Therefore, the difference between the detection position information 131 and 132 of the servo amplifiers 3 and 4 and the new position command signal 125 when the positioning operation is completed does not cause a problem. However, when the rigidity of the machine coupling unit 9 is low or viscous friction is high, this difference becomes large. In this case, if control systems of the velocity controllers 32 and 42 in the servo amplifiers 3 and 4 are changed to imperfect integration, this difference can be reduced.
In the case of the imperfect integration, if an imperfect integration ratio is increased, the control becomes close to proportion control, and if the imperfect integration ratio is reduced, the control becomes close to integration control. Therefore, when the machine rigidity is low, since a component of an invalid reaction force by motor torque or thrust force is small, an imperfect integration ratio should be adjusted to a small value within a permissible range (if the imperfect integration ratio is reduced, this difference becomes small, but the invalid reaction force is increased. If the imperfect integration ratio is increased, the difference becomes large, and the invalid reaction force is reduced).
In the synchronous control apparatuses of the first to fourth embodiments of the present invention, each of the command device and the servo amplifiers has the position control system, but even if the apparatus is integrally provided with the command device and the servo amplifiers, the same operation and effect can be obtained. The apparatus may input a position command which comes from outside, and may include two identical position control systems.
Next, a fifth embodiment of the present invention will be described with reference to the drawings. A machine tool having a gantry mechanism as shown in
The control systems of the synchronous control apparatuses used for the machine tools are position proportion and velocity integration proportion control systems in many cases. Here, since the Y-axis in
However, to keep balance of the control systems, in the X-axis of the twin drive, the position controller 22 in
When an arc interpolation operation is carried out, if corresponding gain settings of control systems in the X-axis and the Y-axis are made equal to each other as usual, a locus is distorted as shown in
To solve this problem, it is necessary to establish a gain setting equation. In the X-axis of the twin drive, if transfer functions from the position command of the position integration proportion and velocity proportion control system to the detection position information are put in order, it can be expressed as in the following equation (6).
In the Y-axis of the single axis drive, if transfer functions from the position command of the position proportion and velocity integration proportion control system to the detection position information are put in order, it can be expressed as in the following equation (7).
If the equations (6) and (7) match with each other, the detection position information matches with the position command in the arc interpolation operation. That is, the detection position information follows the position command. Especially, since a denominator of a transfer function called characteristic polynomial determines response characteristics of the transfer function, it is only necessary to determine a gain setting value such that coefficients in the denominators of the equations (6) and (7) match with each other, and to satisfy the following equations (8) and (9).
Kp1Kv=Kv/Ti (8)
Kp1Kv/Tir=KpKv/Ti (9)
That is, from the equation (8), the following equation (10) is established:
Kp1=1/Ti (10)
the equation (10) is substituted into the equation (9) to establish
Tir=1/Kp (11).
At that time, numerators of the equations (6) and (7) match with each other.
When the gain setting values obtained from the equations (10) and (11) are used, it can be found from
Next, a sixth embodiment of the present invention will be described with reference to the drawings. In the fifth embodiment, the position controller 22 shown in
In the X-axis of the twin drive, if transfer functions from the position command of the position proportion integration and velocity proportion control system to the detection position information are put in order, it can be expressed as in the following equation (12).
On the other hand, in the Y-axis of the single axis drive, if transfer functions from the position command of the position proportion and velocity proportion integration control system to the detection position information are put in order, it can be expressed as in the following equation (13).
Here, if the equation (12) and the equation (13) match with each other, the detection position information matches with the position command in the arc interpolation operation. That is, the detection position information follows the position command. Especially, since a denominator of a transfer function called characteristic polynomial determines response characteristics of the transfer function, it is only necessary to determine a gain setting value such that coefficients in the denominators of the equations (12) and (13) match with each other, and to satisfy the following equations (14) and (15).
2Kp1Kv=Kv/Ti+KpKv (14)
Kp1Kv/Tir=KpKv/Ti (15)
That is, from the equation (14), the following equation (16) is established:
Kp1=1/(2Ti)+Kp/2 (16)
the equation (16) is substituted into the equation (15) to establish
Tir=1/(2Kp)+Ti/2 (17).
However, unlike the fifth embodiment, only the equations (16) and (17) are satisfied, numerators in the equations (12) and (13) do not match with each other, and the detection position information does not completely match with the position commands of the X-axis and the Y-axis. To match the transfer functions including the numerators with each other, it is necessary to satisfy the following equation (18) in addition to the equations (16) and (17).
Ti=1/Kp (18)
When gain setting values obtained from the equations (16) to (18) are used, it can be found from
Next, a seventh embodiment of the present invention will be described with reference to the drawings. When detection delays of the detection position information 131 and 141 with respect to a new position command signal 125 in
However, when the detection delays of the detection position information 131 and 141 with respect to the new position command in
A configuration of the synchronous control apparatus 12 in
It is possible to avoid the problem that the detection delay of the detection position information is increased by inputting the position deviation 124 and the work position information 122, and by forming the position observer 24 which outputs a new detection position information 123 in which the delay is compensated. This position observer 24 can be configured as shown in
Even in the sixth embodiment, the position observer 24 exhibits the same operation and effect. In the fifth to seventh embodiments, it is described that the X-axis is a machine tool having a gantry mechanism which is the twin drive, but the same operation and effect can be obtained even if a movable table has three or more, i.e., a plurality of axes drive as the X-axis as in wide and extra-large machineries.
Especially, the position deviation 124 and the work position information 122 in which detection position information of a plurality of axes are computed by the position information computing unit 23 are input to the position observer 24 of the seventh embodiment, the work position information 122 is computed and output and thus, there is an effect that it is unnecessary to change the design even if the twin axis is changed to the plurality of axes. Even if feedback is carried out using the laser interferometer shown in the second embodiment (
Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.
Number | Date | Country | Kind |
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P. 2010-004380 | Jan 2010 | JP | national |
P. 2010-167089 | Jul 2010 | JP | national |
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Entry |
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Japanese Office Action for corresponding JP Application No. 2011-191023, Nov. 22, 2012. |
Japanese Office Action for corresponding JP Application No. 2010-167089, Aug. 17, 2011. |
Japanese Office Action for corresponding JP Application No. 2011-191023, May 21, 2013. |
Number | Date | Country | |
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20110169441 A1 | Jul 2011 | US |