KR101731045B1 - Apparatus for precise-adjustment of frame transmission time in the motion control system based on EtherCAT, method thereof and computer recordable medium storing the method - Google Patents
Apparatus for precise-adjustment of frame transmission time in the motion control system based on EtherCAT, method thereof and computer recordable medium storing the method Download PDFInfo
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- KR101731045B1 KR101731045B1 KR1020150127587A KR20150127587A KR101731045B1 KR 101731045 B1 KR101731045 B1 KR 101731045B1 KR 1020150127587 A KR1020150127587 A KR 1020150127587A KR 20150127587 A KR20150127587 A KR 20150127587A KR 101731045 B1 KR101731045 B1 KR 101731045B1
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1679—Programme controls characterised by the tasks executed
- B25J9/1692—Calibration of manipulator
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J13/00—Controls for manipulators
- B25J13/006—Controls for manipulators by means of a wireless system for controlling one or several manipulators
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1679—Programme controls characterised by the tasks executed
- B25J9/1689—Teleoperation
Abstract
The present invention relates to an apparatus for correcting a frame transmission time point of an Ethernet-based motion control system, a method therefor and a computer-readable recording medium on which the method is recorded. The present invention relates to a motion control task including a transmission phase (Publish Phase) for transmitting a frame including a control command to a motor drive
A motion controller for performing a motion control task on the motion control task, the communication controller for communicating with the motion controller performing the motion control task, and a pre-runtime executable file for causing the motion controller to collect the measurement data, And a controller for receiving the measurement data collected by the motion controller through the communication unit from the motion controller and analyzing the received measurement data to calculate a difference A data analysis module for deriving a range of offsets for delaying the starting point of the transmission step so that the offset is within a range of the offset, and a motion control task for delaying the starting point of the transmission step by a determined offset, Executable And a transmission time reflecting module for transmitting the generated transmission time point to the motion controller. The present invention also provides a method for correcting a frame transmission time point, and a computer readable recording medium on which the method is recorded.
Description
The present invention relates to an Ethernet-based motion control system, and more particularly, to an apparatus for precisely correcting a frame transmission time point of an Ethernet-based motion control system, a method therefor, and a computer- .
Motion control systems, which are widely used in surgical robots and various industrial automation fields, are generally a system in which each component is physically and logically coupled strongly by utilizing industrial fieldbus technology. Different applications have different time requirements, but generally require a high level of synchronization. Representative real-time constraints include bounded end-to-end delay and end-to-end delay time variance.
The end-to-end delay time means the time from when the control command is generated from the motion controller to when the corresponding operation is generated in the motor drive. The smaller the value, the higher the precision of the shortening. The minimum cycle time (MCT) of the motion control system can be calculated from the end-to-end delay time. The deviation of the end-to-end delay time means a deviation of operation time between several drives within the same cycle (control cycle), and the smaller the value, the higher the synchronicity with respect to multiple axes.
The motion controller, which is one of the core components of the motion control system, is gradually becoming a universal one according to the requirements of the market to provide various additional functions such as interworking with the management system (MES, ERP) PC-based controllers using desktops and operating systems are becoming increasingly popular, and software is becoming increasingly important. On the other hand, real-time Ethernet (RTE) technology based on Ethernet technology, which is widely used in PC environment, has advantages such as high bandwidth, scalability, and relatively low maintenance cost, . One of the RTE network technologies, EtherCAT, is attracting attention due to its deterministic message communication delay, fast message delivery, global clock-based synchronization, and the flexibility and relatively low price of network topologies.
However, hardware - based frame switching, which is one of the advantages of Ethercat, can guarantee a deterministic data transfer time, but it can only satisfy real - time constraints at the communication network level. In the whole motion control system, And the delay time inside the motion controller and motor drive to account for the deviation, and the message delivery time through the network. In addition, in the case of Distributed Clock (DC) of Ethernet, which is known to provide a deviation of the end-to-end delay time of less than 1 μs, the time of occurrence of the distributed clock synchronization event in the transmission cycle And the delay time due to the internal software of the motion controller and the motor drive must be time-deterministic. Indeed, the biggest factor affecting end-to-end latency on an EtherCAT-based control network is the processing delay by software within the controller.
The motion control system must calculate the control message in the motion controller and the data exchange time between the controller and all the drives must be completed within a predetermined execution cycle (Tcycle). At the time when the motor operates and senses to generate accurate motion, (Isochronous Control). Ethercat provides two techniques: frame-based synchronization and DC-based synchronization. Frame-based synchronization is a technique in which a motor drive is driven by a motor drive in synchronization with arrival events of a frame transmitted from a motion controller. Distributed clock-based synchronization places a global clock in the motion control system so that all motor drives are synchronized at this point . The device supporting Ethernet is classified into a device supporting both the above-described two synchronization techniques and a device supporting only the frame-based synchronization technique. For a distributed clock-based synchronization, an appropriate shift time (a specific point in the control cycle) must be selected. Basically, it should be set to a point after the frame arrives at each motor drive so that the data exchange sequence is the same between the motion controller and the motor drive. For the frame arrival time interval should be constant. It is therefore an object of the present invention to provide a uniform frame transmission time point in an Ethernet-based motion control system composed of a motion controller and a plurality of motor drives.
According to an aspect of the present invention, there is provided an apparatus for correcting a frame transmission time, the apparatus comprising: a motion control task including a transmission phase for transmitting a frame having a control command to a motor drive
And a control unit for controlling the motion controller to perform a motion control task and a motion control task, wherein the motion controller is configured to perform a pre-run time execution to collect measurement data including parameters related to the motion control task execution time while the motion controller is executing the motion control task And a controller for receiving the measurement data collected by the motion controller through the communication unit from the motion controller and analyzing the received measurement data to transmit the frame, And an offset for delaying the start time of the transmission step so that the difference between the intervals is minimized A data analysis module for deriving a range of the offset, ), And the determined offset ( And a transmission time reflecting module for generating an execution file to be executed by delaying the start time of the transmission step by a predetermined number of times and transmitting the generated execution file to the motion controller.The motion control task (
) Includes a collection phase (Retrieve Phase) for collecting feedback information, which is information about motions made in a motor connected to the motor drive, from the motor drive, a calculation phase (Computation Phase) for calculating a next motion based on the feedback information, And a transmission phase (Publish Phase) for transmitting a frame including a control command based on the calculated motion, wherein the data analysis module determines that the start point of the transmission step is a point at which the offset And the lower limit of the range is derived.The data analysis module derives an upper limit of the range of the offset so that the execution times of the two consecutive motion control tasks do not overlap.
Wherein the data analysis module determines that the upper limit of the range of the offset is longer than the lower limit of the range of the offset
) The range of the offset is derived.Wherein the data collection module generates a storage code for storing measurement codes for time measurement of the motion control task and measurement data measured in accordance with the measurement code in a stub code to generate the free runtime execution file And transmits the generated free runtime execution file to the motion controller.
The range of the offset is given by the following equation
Lt; / RTI >remind
Is the lower limit of the offset range, Is the upper limit of the offset range, Is the release jitter of the motion control task, Is a time point at which the computation phase of the motion control task ends, Is the execution cycle of the motion control task, Is also the time for performing the control sequence execution time of the current task instance and the time for the control command to update the information of the updated motor drive by traversing all the motor drives to the motion controller, Is a maximum value of a case in which the motion control task instance starts earlier than a predetermined time.According to an aspect of the present invention, there is provided a method for correcting a frame transmission time, the method comprising: transmitting a frame including a control command to a motor drive, (
) Generates a free runtime execution file for collecting measurement data, which is a parameter related to the motion control task execution time, while the motion control task is being performed, and transmits the generated free runtime execution file to the motion controller Receiving the measurement data collected by the motion controller from the motion controller and analyzing the received measurement data to delay the start time of the transmission step so as to minimize a difference in interval between transmission times of the frame, Offset ( ) Within the range of the offset, and deriving a range of the offset ), Determining the determined offset ( Generating a runtime executable file for executing the motion control task so that the start time of the transfer step is delayed and executed by a predetermined number of times.The motion control task (
) Includes a collection phase (Retrieve Phase) for collecting feedback information, which is information about motions made in a motor connected to the motor drive, from the motor drive, a calculation phase (Computation Phase) for calculating a next motion based on the feedback information, And a transmission phase (Publish Phase) for transmitting a frame including a control command based on the calculated motion, wherein the offset ) Derives the lower limit of the range of the offset so that the starting point of the transmission step is performed after the end of the calculation step. The offset ( ) Is derived by deriving an upper limit of the range of the offset so that the execution times of two successive motion control tasks do not overlap.The offset (
) Is such that the upper limit of the range of the offset is longer than the lower limit of the range of the offset ) The range of the offset is derived.The step of transmitting the free runtime executable file may include generating a stuck code for storing a measurement code for time measurement for the motion control task and measurement data measured according to the measurement code in a stub code, And transmits the generated free runtime execution file to the motion controller.
The range of the offset is given by the following equation
, And Is the lower limit of the offset range, Is the upper limit of the offset range, Is the release jitter of the motion control task, Is a time point at which the computation phase of the motion control task ends, Is the execution cycle of the motion control task, Is a time for which the control sequence execution time of the current task instance and the control command are updated to the motion controller by cycling through all the motor drives and updating the information of the motor drive, Is a maximum value of a case where the motion control task starts earlier than a predetermined time.According to another aspect of the present invention, there is provided a computer-readable recording medium having recorded thereon instructions for executing a method for correcting the above-mentioned frame transmission time.
According to the present invention as described above, the measurement data received in the Ethernet-based motion control system including the motion controller and the plurality of motor drives is analyzed and the control command is transmitted so as to minimize the difference in the interval between the transmission times of the frames The transmitting point of the containing frame is offset (
). Accordingly, by providing a uniform frame transmission time point, it is possible to provide the short axis motion precision (precision) and the multi-axis motion synchrony in an ethereal-based motion control system.1 is a block diagram illustrating a configuration of a motion control system according to an embodiment of the present invention.
2 is a block diagram for explaining a configuration of a correction apparatus according to an embodiment of the present invention.
3 and 4 are views for explaining a motion control performing sequence according to an embodiment of the present invention.
5 is a diagram for explaining a method of deriving a range of an offset according to an embodiment of the present invention.
6 is a flowchart illustrating a method for correcting a frame transmission time point of a motion control system according to an embodiment of the present invention.
FIG. 7 is an example of a screen for explaining analysis data derived by analyzing measurement data according to an embodiment of the present invention.
Prior to the detailed description of the present invention, the terms or words used in the present specification and claims should not be construed as limited to ordinary or preliminary meaning, and the inventor may designate his own invention in the best way It should be construed in accordance with the technical idea of the present invention based on the principle that it can be appropriately defined as a concept of a term to describe it. Therefore, the embodiments described in the present specification and the configurations shown in the drawings are merely the most preferred embodiments of the present invention, and are not intended to represent all of the technical ideas of the present invention. Therefore, various equivalents It should be understood that water and variations may be present.
Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Note that, in the drawings, the same components are denoted by the same reference symbols as possible. Further, the detailed description of known functions and configurations that may obscure the gist of the present invention will be omitted. For the same reason, some of the elements in the accompanying drawings are exaggerated, omitted, or schematically shown, and the size of each element does not entirely reflect the actual size.
First, the configuration of a motion control system according to an embodiment of the present invention will be described. 1 is a block diagram illustrating a configuration of a motion control system according to an embodiment of the present invention.
Referring to FIG. 1, a motion control system according to an embodiment of the present invention includes a
The
The
The configuration of the correction apparatus according to the embodiment of the present invention will now be described. 2 is a block diagram for explaining a configuration of a correction apparatus according to an embodiment of the present invention.
Referring to FIG. 2, the
The communication unit 310 is for communication with the
The input unit 320 receives a user's key operation for controlling the
The display unit 330 visually provides a menu of the
The storage unit 340 stores programs and data necessary for the operation of the
The control unit 350 may control the overall operation of the
The control unit 350 includes a data collection module 351, a data analysis module 353, and a transmission
Next, a motion control execution sequence according to an embodiment of the present invention will be described. 3 and 4 are views for explaining a motion control performing sequence according to an embodiment of the present invention.
The motion control execution sequence according to the embodiment of the present invention is assumed to be implemented in the form of a single task as shown in FIG. 3, and a single motion control task is assumed as a user-level task having the highest priority in the
Motion control task (
A collection phase for collecting feedback information using the network from theAccording to general real-time system theory, each task instance (
) Is released every fixed period. The release time of the task instance is then . However, interference occurs due to the timer resolution (TMR) or kernel level tasks of the
As a result, the i-th control command observation point (
Is a time point at which the i-th control frame is released in the motion controller 100 ) And the control frame transmission delay to the corresponding motor drive 200 ). ≪ / RTI >The control frame transmission delay is the delay time by the link layer (
And the frame switching time in the motor drive 200 ( ), And transmission time by cable ( ). ≪ / RTI > Frame switching time and transmission time by cable ( + ) Is considered to be 1 [mu] s, It is also expressed as a constant. Therefore, the control frame transmission delay to the motor drive 200 ) Is a constant, and eventually the i-th control command observation point ( Can be expressed by the following equation (2).
In order for each motor attached to each of the motor drives 200 to receive a control command and operate at a precise uniform timing, the arrival time of two consecutive control commands observed by the
Finally, as shown in
Therefore, instead of making these
Actually, when the control frame including the control command is released from the motion controller 200
) Is very difficult to adjust when the network device starts transmitting packets to the external port, and it is difficult to adjust the network device driver stack by the version of the operating system mounted on the platform of theTherefore, the present invention adjusts the starting point of the transmission phase (Publish Phase) of each instance of the motion control task so that the time interval at which the control command is released from the
The following Equation (5) represents the starting point of the transmission phase (Publish Phase)
Represents the completion point of the computation phase of the i-th task instance.
3, the start of a publish phase of each task instance according to an embodiment of the present invention may include an offset
). Equation (6) is an offset ) Is applied and the execution timing of the delayed transmission phase (Publish Phase) ).
According to the present invention, the execution phase of the first task instance (publish phase)
), And then the execution phase of all task instances (Publish Phase) starts with a delay after the scheduled release time, ). That is, according to the present invention, the transmission step of the task instance is offset (i.e., ), And then performs the delay.The pseudo code according to the embodiment of the present invention is shown in Table 1 below.
retrieving sensed values;
computing motion command;
/ * Pseudo Code start from here * /
if first_iter:
/ * Delay transmission time at first task instance * /
time2transmit = first_release_time + ;
else
/ * Next transmission time is determined by
sum of previous transmission time and task period * /
time2transmit + = TSK_PERIOD;
endif
now = get current system time;
/ * Waiting for the time to transmit * /
while (now <time2transmit)
now = get current system time;
endwhile
time2transmit = now;
/ * Pseudo Code end here * /
publishing motion command;
wait until next task activation;
endwhile
Then, in accordance with an embodiment of the present invention,
Will now be described in more detail. FIG. 5 is a diagram illustrating an offset ) In the case of the first embodiment of the present invention.Referring to FIG. 5, an offset ("
The following three conditions must be satisfied.First, for all control cycles
. That is, it indicates that for all task instances, the execution phase of the publish phase should be corrected to be done after the computation phase is over. This condition is offset ( ) Is the lower limit of Respectively.Second, the execution of two consecutive control cycles is not overlapped. In other words, after performing a coordinated transfer phase (Publish Phase), there must be some spare time until the next task instance is released. If the condition is not met, the next control cycle must wait for the arrival of the feedback information transmitted from the
third,
. If this condition is not met, it means that there is not enough time to complete the motion control sequence (Retrieve, Computation and Publish Phase) within the control period.Jitter
) And when the computation phase is completed ( ) Shows a random distribution, so the exact offset lower limit ( ) Is difficult to determine. Also, the offset upper limit ( ), The worst case task release jitter occurs (the maximum value of the case where the next task instance starts earlier than the scheduled time: ), There must be enough time between the release of the control frame of the current task instance and the release of the next task instance. Therefore, the transmission time offset upper / lower limit ( , ) Is estimated through pre-runtime analysis before actual application execution.Also, after all the control frames including the control sequence execution time and the control command of the current task instance have traversed the N motor drives 200, the time for updating the information of the updated
The range of the transmission time offset satisfying the above three constraints is expressed by Equation (7).
A method of obtaining a range of the above-described offset, selecting an offset in the range of the obtained offset, and reflecting it to the motion control task will be described. 6 is a flowchart illustrating a method for correcting a frame transmission time point of a motion control system according to an embodiment of the present invention. FIG. 7 is an example of a screen for explaining analysis data derived by analyzing measurement data according to an embodiment of the present invention.
The motion control application according to an embodiment of the present invention is created by a user according to the need or intention of the user. It is assumed that the motion control application is created using the
Next, the data acquisition module 351 provides the pre-runtime execution file to the
Next, the
An offset (or motion) that increases the precision and concurrency of motion over the control cycle of the currently set motion application
) Is calculated in consideration of the timing information of the measured motion control task, the number of motor drives, and the data size.Also, the data analysis module 353 may display an analysis screen including analysis data through the display unit 330 in step S160. An example of such a screen is shown in Fig. As shown, the analysis screen displays the task's release jitter (
), The calculation step is completed ( ) And the time at which the frame including the control command is transmitted ), And a graph of the probability density function for each item is displayed based on the measured statistical value. Further, the analysis screen can display the range of the offset as shown in Equation (7). Meanwhile, the data analysis module 353 can output the graph file and the statistical summary table in the form of a text file when there is a request according to the input of the user.On the other hand, the user can browse the analysis data through this screen. In particular, the user may browse the range of offsets and may select the offsets within the range of such offsets through input 320. When the user inputs an offset (a numerical value) selected by the user through the input unit 320, the transmission
Then, the transmission
Then, the transmission
On the other hand, in the embodiment described above, the
Meanwhile, a method for correcting a frame transmission time of an Ethernet-based motion control system according to an embodiment of the present invention may be implemented in a form of a program readable by various computer means and recorded in a computer-readable recording medium. Here, the recording medium may include program commands, data files, data structures, and the like, alone or in combination. Program instructions to be recorded on a recording medium may be those specially designed and constructed for the present invention or may be available to those skilled in the art of computer software. For example, the recording medium may be a magnetic medium such as a hard disk, a floppy disk and a magnetic tape, an optical medium such as a CD-ROM or a DVD, a magneto-optical medium such as a floppy disk magneto-optical media, and hardware devices that are specially configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions may include machine language wires such as those produced by a compiler, as well as high-level language wires that may be executed by a computer using an interpreter or the like. Such a hardware device may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.
While the present invention has been described with reference to several preferred embodiments, these embodiments are illustrative and not restrictive. It will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit of the invention and the scope of the appended claims.
100: Motion controller 200: Motor driver
300: Correction device 310:
320: input unit 330:
340: storage unit 350: control unit
351: Data collection module 353: Data analysis module
355: Transmission point reflection module
Claims (13)
A motion control task including a transmission phase (Publish Phase) for transmitting a frame having a control command to the motor drive A communication unit for communicating with the motion controller performing the motion control;
A data collection module for generating a free runtime execution file for collecting measurement data including parameters related to the motion control task execution time while the motion controller executing the motion control task through the communication unit and transmitting the generated free runtime execution file to the motion controller;
Wherein the control unit receives the measurement data collected by the motion controller from the motion controller through the communication unit and analyzes the received measurement data to delay the start time of the transmission step so as to minimize a difference in interval between transmission times of the frame, Offset ( A data analysis module for deriving a range of the data; And
Within the range of the offset, an offset ( ), And the determined offset ( And a transmission time reflecting module for generating an execution file to be executed by delaying the start time of the transmission step by a predetermined number of times and transmitting the generated execution file to the motion controller,
The motion control task ( ) Includes a collection phase (Retrieve Phase) for collecting feedback information, which is information about motions made in a motor connected to the motor drive, from the motor drive, a calculation phase (Computation Phase) for calculating a next motion based on the feedback information, And a transmission phase (Publish Phase) for transmitting a frame including a control command based on the calculated motion,
Wherein the data analysis module derives a lower limit of the range of the offset so that the starting point of the transmission step is performed after the end of the calculation step.
Wherein the data analysis module derives an upper limit of the range of the offset so that the execution times of two successive motion control tasks do not overlap.
The data analysis module
The upper limit of the range of the offset is longer than the lower limit of the range of the offset ) Deriving a range of the offset.
The data collection module
Generating a storage code for storing a measurement code for time measurement of the motion control task and measurement data measured in accordance with the measurement code in a stub code to generate a free run time execution file, And transmits an execution file to the motion controller.
The range of the offset is
Equation
Lt; / RTI >
remind Is the lower limit of the offset range,
remind Is the upper limit of the offset range,
remind Is the release jitter of the motion control task,
remind Is the time when the computation phase of the motion control task ends,
remind Is the execution cycle of the motion control task,
remind Is also the time at which the control sequence execution time of the current task instance and the control command update the information of the updated motor drive by traversing all the motor drives to the motion controller,
remind Is a maximum value of a case where the motion control task instance starts earlier than a predetermined time.
A motion control task including a transfer phase (Publish Phase) for transmitting a frame including a control command to the motor drive ) Generates a free runtime execution file for collecting measurement data, which is a parameter related to the motion control task execution time, while the motion control task is being performed, and transmits the generated free runtime execution file to the motion controller ;
An offset calculating unit for receiving the measurement data collected by the motion controller from the motion controller and analyzing the received measurement data to calculate an offset for delaying a start time of the transmission step so that a difference between intervals at which the frame is transmitted is minimized );
Within the range of the offset, an offset ( ); And
The determined offset ( Generating a runtime executable file for executing the motion control task to cause the start time of the transfer step to be delayed and executed by a predetermined number of times,
The motion control task ( ) Includes a collection phase (Retrieve Phase) for collecting feedback information, which is information about motions made in a motor connected to the motor drive, from the motor drive, a calculation phase (Computation Phase) for calculating a next motion based on the feedback information, And a transmission phase (Publish Phase) for transmitting a frame including a control command based on the calculated motion,
The offset ( ) Deriving a lower limit of the range of the offset so that the starting point of the transmitting step is performed after the end of the calculating step.
The offset ( Gt;) < / RTI >
Wherein an upper limit of the range of the offset is derived so that the execution times of two successive motion control tasks do not overlap.
The offset ( Gt;) < / RTI >
The upper limit of the range of the offset is longer than the lower limit of the range of the offset ) ≪ / RTI > wherein a range of the offset is derived.
The step of transmitting the free runtime executable file
Generating a pre-runtime executable file by generating a measurement code for time measurement of the motion control task and measurement data measured according to the measurement code in a stub code, generating the pre-run execution file, And transmitting the frame to the motion controller.
The range of the offset is
Equation
Lt; / RTI >
remind Is the lower limit of the offset range,
remind Is the upper limit of the offset range,
remind Is the release jitter of the motion control task,
remind Is the time when the computation phase of the motion control task ends,
remind Is the execution cycle of the motion control task,
remind Is also the time at which the control sequence execution time of the current task instance and the control command update the information of the updated motor drive by traversing all the motor drives to the motion controller,
remind Is a maximum value of a case where the motion control task starts earlier than a predetermined time.
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