Design the high speed control system for the synchronization between the rotary table and linear motion lead screw

MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING GRADUATION PROJECT ELECTRONICS AND ELECTRONIC ENGINEERING TECHNOLOGY DESIGN THE HIGH-SPEED CONTROL SYSTEM FOR THE SYNCHRONIZATION BETWEEN THE ROTARY TABLE AND LINEAR MOTION LEAD SCREW ADVISOR : NGUYEN TU DUC, MS STUDENTS: NGUYEN DANG DAT NGUYEN THANH PHONG SKL010588 Ho Chi Minh City, December 2022 HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING    GRADUATION PROJECT TOPIC: DESIGN THE HIGH-SPEED CONTROL SYSTEM FOR THE SYNCHRONIZATION BETWEEN THE ROTARY TABLE AND LINEAR MOTION LEAD SCREW Name/Student’s ID: NGUYEN DANG DAT - 18142011 NGUYEN THANH PHONG - 18142053 Major: ELECTRICAL AND ELECTRONIC ENGINEERING TECHNOLOGY Advisor: NGUYEN TU DUC, MS Ho Chi Minh City, December 2022 Graduation Thesis THE SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom– Happiness Ho Chi Minh City, December 28th, 2022 GRADUATION PROJECT ASSIGNMENT Student name: Nguyen Dang Dat Student ID: 18142011 Student name: Nguyen Thanh Phong Student ID: 18142053 Major: Electrical and Electronic Engineering Technology Class: 18142CLA Advisor: Nguyen Tu Duc, MS Date of assignment: 27/12/2022 Phone number: 0332194223 – Dat 0937289626 – Phong Date of submission: 27/12/2022 Project title: Design the high-speed control system for the synchronization between the rotary table and linear motion lead screw Initial materials provided by the advisor:     MR-J3-B Servo amplifier instruction manual Motion Controller Q series using CPU Motion Q173DS Learn the principles of operation and how to control the Servo Motor Learn about Ladder code programming languages, GX-Works2 programming Software and GT Designer 3 Content of the project:     How to communicate between PLC with computer, servo drivers MR-J3B Programming in Ladder language and loading into the control CPU, testing multiple times, and correctly correcting if the error occurs when programming Controlling Multi-axis synchronous Servo Learn about related software Final product: 3-axis synchronous control system moves according to the precise moving point on the turntable with high speed CHAIR OF THE PROGRAM (Sign with full name) ADVISOR (Sign with full name) Graduation Thesis THE SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom– Happiness Ho Chi Minh City, December 28th, 2022 ADVISOR’S EVALUATION SHEET Student name: Nguyen Dang Dat Student ID: 18142011 Student name: Nguyen Thanh Phong Student ID: 18142053 Major: Electrical and Electronic Engineering Technology Project title: Design the high-speed control system for the synchronization between the rotary table and linear motion lead screw Advisor: Nguyen Tu Duc, MS EVALUATION Content of the project: …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… Strengths: …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… Weaknesses: …………………………………………………………………………………………………… …………………………………………………………………………………………………… Approval for oral defense? (Approved or denied) …………………………………………………………………………………………………… Overall evaluation: (Excellent, Good, Fair, Poor) …………………………………………………………………………………………………… Ho Chi Minh City, , 2022 ADVISOR (Sign with full name) Graduation Thesis THE SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom– Happiness Ho Chi Minh City, December 28th, 2022 PRE-DEFENSE EVALUATION SHEET Student name: Nguyen Dang Dat Student ID: 18142011 Student name: Nguyen Thanh Phong Student ID: 18142053 Major: Electrical and Electronic Engineering Technology Project title: Design the high-speed control system for the synchronization between the rotary table and linear motion lead screw Name of Reviewer: EVALUATION Content and workload of the project Strengths: Weaknesses: Approval for oral defense? (Approved or denied) Reviewer’ questions for project valuation Mark: …………… (in words: .) Ho Chi Minh City, _, 2022 REVIEWER (Sign with full name) CỘNG HÒA XÃ HỘI CHỦ NGHĨA VIỆT NAM Độc lập – Tự – Hạnh phúc *** XÁC NHẬN CHỈNH SỬA ĐỒ ÁN TỐT NGHIỆP Họ tên SV1: Nguyễn Đặng Đạt MSSV: 18142011 Họ tên SV2: Nguyễn Thành Phong MSSV: 18142053 Lớp: 18142CLA Khóa: Ngày bảo vệ: 5/1/2023 2018 - 2022 Chuyên ngành: CNKT Điện – Điện tử - Khoa Đào tạo Chất lượng cao (hệ CLA) Căn ý kiến nhận xét Hội đồng chấm Khóa luận tốt nghiệp (HĐ số 5) Giảm thiểu phần lý thuyết thuyết trình báo cáo Powerpoint Đưa kết trọng tâm mà sinh viên thực Powerpoint Nhóm sinh viên sửa chữa, hoàn chỉnh số nội dung sau: STT Nội dung cũ Powerpoint gồm biểu đồ cột sai số tính tốn thực tế, biểu đồ đường đường cong mơ hình hoạt động tính tốn thực tế Powerpoint gồm đồ thị tọa độ (Stroke graph) đồ thị vận tốc (Velocity graph) Powerpoint gồm video nằm sau phần thuyết trình Powerpoint gồm phụ lục mơ tả cơng thức tính tốn Nội dung chỉnh sửa Trang + Tổng hợp đồ thị sai số đồ thị tọa độ tính tốn/thực tế thành 26 đường cong hoạt động mơ hình + Tổng hợp đồ thị tọa độ đồ thị vận tốc thành kết hoạt động 28; 29 mơ hình + Bổ sung video kết mơ hình thực tế bên phần “6.3 30 Result” + Loại bỏ phần phụ lục (I, II, III) Tp Hồ Chí Minh, ngày tháng năm 2023 SV THỰC HIỆN GV HƯỚNG DẪN Graduation Thesis DISCLAIMER Subject: Design the High-speed control system for the synchronization between the rotary table and linear motion lead screw Instructor: Nguyen Tu Duc MS Name/Student’s ID: Nguyen Dang Dat - 18142011 Email: 18142011@student.hcmute.edu.vn Nguyen Thanh Phong - 18142053 Email: 18142053@student.hcmute.edu.vn Promise: We hereby declare that this is our own research work The data and results stated in the thesis are honest and have never been published in any other works Ho Chi Minh City, December 28th, 2022 (Signature and full name) Graduation Thesis ACKNOWLEDGEMENTS The thesis was completed at Ho Chi Minh City University of Technology and Education Ho Chi Minh City for months During the process of making the graduation thesis, the group of students received a lot of help to complete this thesis First of all, our team would like to thank the teachers of the Faculty of Electrical and Electronics Engineering, as well as the teachers of the Ho Chi Minh City University of Technology and Education, for imparting valuable knowledge in learning, as well as other skills skills during research and working with teachers during the time students are at the school Thereby, we have the professional knowledge to this graduation project Our team would like to thank Mr Le Hoang Lam for guiding and giving useful suggestions so that we can successfully complete this graduation project Besides that teacher has supported us with hardware devices to meet the requirements given Once again, thank you very much to everyone around me, family, relatives, friends and teachers who have been by my side, supporting us on the path of studying, working and finding new directions Graduation Thesis TABLE OF CONTENT Contents DISCLAIMER ACKNOWLEDGEMENTS TABLE OF CONTENT LIST OF FIGURES LIST OF TABLES 12 ABSTRACT 13 CHAPTER 1: OVERVIEW OF THE PROJECT 15 1.1 Problem: 15 1.2 Objectives of the topic: 15 1.3 Research subjects: 15 1.4 Research methods: 16 CHAPTER 2: THEORETICAL BASIS 17 2.1 Overview of project: 17 2.2 General introduction to PLC: 17 2.3 AC Servo Motor: 23 2.4 Servo Driver: 25 2.5 Overview of Synchronous Control: 29 2.6 Motion SFC programming language: 34 2.7 Overview related software: 36 CHAPTER 3: HARDWARE DESIGN 38 3.1 Introduction to the project: 38 3.2 Configuration option – DAQ: 38 3.3 Electrical part design: 39 3.4 Mechanical part design: 57 3.5 Result: 61 CHAPTER 4: CONTROL PROCESS 62 4.1 Overall operation of system: 62 4.2 Synchronous operation: 63 4.3 Programming solution: 67 4.4 Synchronous operation calculation: 92 Graduation Thesis 4.5 HMI Design: 113 CHAPTER 5: CONCLUTION AND THESIS DEVELOPMENT ORIENTATIONS 117 5.1 Result: 117 5.2 Conclusion: 117 5.3 Development orientations: 117 REFERENCES 118 APPENDICES 119 Graduation Thesis 4.4.5 Results: 4.4.5.1 The result of high-speed synchronous control of X-axis:  Stroke graph:  Speed graph: Figure 4.48: The line chart illustrate the high speed synchronous control of X-Axis Figure 4.49: Actual speed of X-axis at synchronous motion 111 Graduation Thesis 4.4.5.2 The result of high-speed synchronous control of Y-axis:  Stroke graph:  Speed graph: Figure 4.50: The line chart illustrate the high-speed synchronous control of Y-Axis Figure 4.51: Actual speed of Y-axis in synchronous motion 112 Graduation Thesis 4.4.5.3 Explanation: To begin with the description, it is obvious that the horizontal axis (Length per Cycle) of each graph is in the range from 0° to 21400° with one 360°-cycle of rotary table, which means that the synchronous control operation would be executed during 59,4 revolutions of the rotary table After that, the synchronization will stop and wait for next operation or return the beginning of its operation The stroke graph illustrates that during the synchronous operation with 59,4 cycles of rotary table, the output value of that axis will be shown as given pictures By following to this kind of graph, it is convenient to observe the detailed motion ordinates to compare with the setting data for the precision insurance Besides that, the speed graph could indicate the stability of operation at each level of speed Dealing with speed observation, it is essential to compare the satisfied graph at actual motion with the calculated velocity It is to ensure that the created cam curve could be used for maximum speed To sum up, those graphs describes the motion with the combination of precision (Stroke graph) and high-speed motion (Speed graph) with 120 rpm 4.5 4.5.1 HMI Design: Main Screen: Figure 4.52: Initial interface at system startup The screen displays information about the names, student numbers of our team members and instructors Besides, that is the hardware image that our team has completed the design At the bottom of the screen is the name of the screen that we are communicating with and two buttons to switch the screen page 113 Graduation Thesis 4.5.2 Synchronous Control Screen: Figure 4.53: Synchronous Control Screen The monitoring screen displays the measure of the axes moving on the system, along with the positions of the objects placed on the pole, the turntable and the indicator light showing the status of the operation In the frame “CURRENT FEED VALUE” displays the addresses of the axes that are standing outside the actual waiting To be able to identify the system is faulty or have some problems, in the "ERROR" frame will display the error data of the motor axes to capture the problem that needs to be handled The right corner is the buttons to control the system to run, drop objects automatically and display the system warning screen When pressing the “AUTO ON” button, the system will start to run automatically bringing the objects from the cylinder to the position of the rotating round table And the “AUTO OFF” button will stop the system if any unforeseen circumstances occur Besides, there are screen switching buttons in the “NAVIGATION” frame + The yellow button “ALARM SCREEN” switches the display of the system problem warning screen + LOG OUT: is the button to log out the account you are accessing and return to the original main screen 114 Graduation Thesis 4.5.3 Control Panel: Figure 4.54: Control Panel Screen The buttons in the “Test Operation” frame are used to move the independent axes to the desired locations: + JOG is a button that controls the axis to move when held down in the negative or positive direction + ABS is the button that controls the axis to move to the position set in “SETTING POSITION” + INC is the button that controls the axis to move one more segment set in “SETTING POSITION” In the "Position Control Setting" frame control the axes simultaneously: + “HOME ALL” is the button that controls the axes to move to the position where the DOG sensor returns the values to + “XY LINEAR” is the button that controls the X and Y axes to move to the position where the program has been written + “SETTING POSITION” is a screen switch to set parameters to control axes according to needs In the frame “MAGNET CONTROL” are the buttons to control the magnet As soon as the system is started, to control the servo motor it is necessary to activate the address so that the Servo enters the standby state And the “Operation Adjustment” box will take care of that Synchronous control will be through the buttons in the “Synchronous Operating” frame Here, when synchronous mode is turned on, the X, Y and Z axes cannot be commanded, but instead will be controlled through the turntable axis to operate 115 Graduation Thesis Finally, the yellow buttons at the “RESET ERROR” frame will reset the system error when the problems have been fixed 4.5.4 Position Setting Screen: Figure 4.55: Position Setting Screen Thanks to this screen, it is possible to set the JOG speed parameters, address and the operating speed of the axes motor To be able to return to the control screen, we can click the “BACK” arrow at the bottom to return to the previous screen 4.5.5 Alarm Screen: Figure 4.56: Alarm Screen The screen shows the operating error of the system and describes it so that the operator can identify the problem that needs to be resolved Besides, it also reports the number of times that error is encountered to grasp the dangerous situation of the system 116 Graduation Thesis CHAPTER 5: CONCLUTION AND THESIS DEVELOPMENT ORIENTATIONS 5.1 Result:  Successfully built a 4-axis synchronous control system according to the set requirements  Separate control of main motor circular axis and X, Y, Z axes  The system is stable during operation  Motor runs precisely at high speed  Design control interface for automatic product picking system using GX Work2, MT Developer 2, GT-Designer software  Design the right part of the control screen and display warnings for the system 5.2 Conclusion: After a period of research and perfecting the model: "Design the high-speed control system for the synchronization between the rotary table and linear motion lead screw", the group of students has drawn the advantages and disadvantages of the topic:  Advantages:  The model can control multiple AC Servo motors at the same time  The system runs correctly  The system can run in many modes, the value can be changed to suit different requirements  Disadvantages:  The system is still limited to complex shapes  The model is small, so the scope of operation is limited  Cannot run stably and accurately when sucking too heavy objects  The system operation is only to pick and place the objects without any recognization such as vision or barcode reading  The ability of synchronous axes to follow a moving object on a circular trajectory traveling only on one trajectory of one diameter 5.3 Development orientations:  Can combine other systems to work simultaneously  Adjust the pick-and-drop operation cycle to suit your requirements  The magnet device can be replaced with a robot hand for more flexible operation  The space of the axes can be expanded to operate other functions within the allowed area  It is possible to rotate the motor in reverse or for the shaft to pick up and drop the object from the turntable to pillar 117 Graduation Thesis REFERENCES [1] GENERAL-PURPOSE AC SERVO “SERVO MOTOR INSTRUCTION MANUAL (Vol.2) [2] GENERAL-PURPOSE AC SERVO “SSCNET III INTERFACE / MODEL MR-J3_B / SERVO AMPLIFIER INSTRUCTION MANUAL” [3] “I/O Module Type Building Block User's Manual” [4] “MOTION CONTROLLER Q-Series (Q173DSCPU/Q172DSCPU/Q173DSCPU(S1)/Q172DSCPU(-S1)) User Manual“ [5] “Q173DSCPU/Q172DSCPU Motion Controller (SV22) Programming Manual (Advanced Synchronous Control)” [6] “Q173DSCPU/Q172DSCPU Motion Controller (SV13/SV22) Programming Manual (REAL MODE)” [7] “Q173DSCPU/Q172DSCPU Motion Controller (SV13/SV22) Programming Manual (Motion SFC)” [8] “Mitsubishi Programmable Controller Training Manual Q Maintenance (for GX Works2) [9] “MELSEC-Q/L Structured Programming Manual (Common Instructions)” [10] “Motion Controller School Textbook (Advanced Synchronous Control Edition) Windows PC Compatible MT Works2” [11] Website: “https://ocw.metu.edu.tr/pluginfile.php/6886/mod_resource/content/1/ch8/ 8- 3.htm” Author: Arthur Hays Sulzberger [12] Website: “https://www.youtube.com/watch?v=HdtyczafhI4&t=1s” Name’s video: “Disk Tracking Machine - Motion control made by Schneider Electric” 118 Graduation Thesis APPENDICES  Ladder program: 119 Graduation Thesis  Calculated speed of two X and Y axes: Radius 360 ꙍ=10000 deg/min Vx Vy (rpm) (rpm) ꙍ=18000 deg/min Vx Vy (rpm) (rpm) ꙍ=28800 deg/min Vx Vy (rpm) (rpm) ꙍ=43200 deg/min Vx Vy (rpm) (rpm) -248.804 569.652 -447.847 1025.374 -716.555 1640.598 -1074.832 2460.897 -188.279 585.555 -338.902 1053.999 -542.243 1686.398 -813.364 2529.597 -126.321 597.001 -227.378 1074.602 -363.804 1719.364 -545.706 2579.046 -63.402 603.904 -114.123 1087.028 -182.597 1739.244 -273.895 2608.866 0.000 606.211 0.000 1091.180 0.000 1745.888 0.000 2618.832 63.402 603.904 114.123 1087.028 182.597 1739.244 273.895 2608.866 126.321 597.001 227.378 1074.602 363.804 1719.364 545.706 2579.046 188.279 585.555 338.902 1053.999 542.243 1686.398 813.364 2529.597 248.804 569.652 447.847 1025.374 716.555 1640.598 1074.832 2460.897 307.435 549.414 553.383 988.945 885.413 1582.312 1328.119 2373.468 355 350 345 340 335 330 325 320 315 120 Graduation Thesis 310 363.727 524.994 654.708 944.989 1047.533 1511.983 1571.299 2267.975 417.250 496.579 751.050 893.842 1201.680 1430.148 1802.520 2145.221 467.598 464.385 841.676 835.892 1346.682 1337.428 2020.023 2006.141 514.387 428.656 925.897 771.581 1481.435 1234.529 2222.152 1851.794 557.262 389.665 1003.071 701.397 1604.913 1122.235 2407.370 1683.353 595.895 347.708 1072.611 625.875 1716.177 1001.400 2574.266 1502.100 629.993 303.106 1133.987 545.590 1814.380 872.944 2721.570 1309.416 659.297 256.196 1186.734 461.153 1898.774 737.844 2848.161 1106.766 683.582 207.336 1230.448 373.205 1968.717 597.129 2953.076 895.693 702.666 156.899 1264.799 282.418 2023.678 451.869 3035.517 677.804 716.402 105.267 1289.523 189.481 2063.237 303.170 3094.855 454.755 724.685 52.835 1304.433 95.103 2087.093 152.164 3130.639 228.246 727.453 0.000 1309.416 0.000 2095.065 0.000 3142.598 0.000 724.685 -52.835 1304.433 -95.103 2087.093 -152.164 3130.639 -228.246 716.402 -105.267 1289.523 -189.481 2063.237 -303.170 3094.855 -454.755 702.666 -156.899 1264.799 -282.418 2023.678 -451.869 3035.517 -677.804 683.582 -207.336 1230.448 -373.205 1968.717 -597.129 2953.076 -895.693 659.297 -256.196 1186.734 -461.153 1898.774 -737.844 2848.161 -1106.766 629.993 -303.106 1133.987 -545.590 1814.380 -872.944 2721.570 -1309.416 595.895 -347.708 1072.611 -625.875 1716.177 -1001.400 2574.266 -1502.100 557.262 -389.665 1003.071 -701.397 1604.913 -1122.235 2407.370 -1683.353 514.387 -428.656 925.897 -771.581 1481.435 -1234.529 2222.152 -1851.794 467.598 -464.385 841.676 -835.892 1346.682 -1337.428 2020.023 -2006.141 417.250 -496.579 751.050 -893.842 1201.680 -1430.148 1802.520 -2145.221 363.727 -524.994 654.708 -944.989 1047.533 -1511.983 1571.299 -2267.975 307.435 -549.414 553.383 -988.945 885.413 -1582.312 1328.119 -2373.468 248.804 -569.652 447.847 -1025.374 716.555 -1640.598 1074.832 -2460.897 188.279 -585.555 338.902 -1053.999 542.243 -1686.398 813.364 -2529.597 126.321 -597.001 227.378 -1074.602 363.804 -1719.364 545.706 -2579.046 63.402 -603.904 114.123 -1087.028 182.597 -1739.244 273.895 -2608.866 305 300 295 290 285 280 275 270 265 260 255 250 245 240 235 230 225 220 215 210 205 200 195 190 185 180 175 170 165 121 Graduation Thesis 160 0.000 -606.211 0.000 -1091.180 0.000 -1745.888 0.000 -2618.832 -63.402 -603.904 -114.123 -1087.028 -182.597 -1739.244 -273.895 -2608.866 -126.321 -597.001 -227.378 -1074.602 -363.804 -1719.364 -545.706 -2579.046 -188.279 -585.555 -338.902 -1053.999 -542.243 -1686.398 -813.364 -2529.597 -248.804 -569.652 -447.847 -1025.374 -716.555 -1640.598 -1074.832 -2460.897 -307.435 -549.414 -553.383 -988.945 -885.413 -1582.312 -1328.119 -2373.468 -363.727 -524.994 -654.708 -944.989 -1047.533 -1511.983 -1571.299 -2267.975 -417.250 -496.579 -751.050 -893.842 -1201.680 -1430.148 -1802.520 -2145.221 -467.598 -464.385 -841.676 -835.892 -1346.682 -1337.428 -2020.023 -2006.141 -514.387 -428.656 -925.897 -771.581 -1481.435 -1234.529 -2222.152 -1851.794 -557.262 -389.665 -1003.071 -701.397 -1604.913 -1122.235 -2407.370 -1683.353 -595.895 -347.708 -1072.611 -625.875 -1716.177 -1001.400 -2574.266 -1502.100 -629.993 -303.106 -1133.987 -545.590 -1814.380 -872.944 -2721.570 -1309.416 -659.297 -256.196 -1186.734 -461.153 -1898.774 -737.844 -2848.161 -1106.766 -683.582 -207.336 -1230.448 -373.205 -1968.717 -597.129 -2953.076 -895.693 -702.666 -156.899 -1264.799 -282.418 -2023.678 -451.869 -3035.517 -677.804 -716.402 -105.267 -1289.523 -189.481 -2063.237 -303.170 -3094.855 -454.755 -724.685 -52.835 -1304.433 -95.103 -2087.093 -152.164 -3130.639 -228.246 -727.453 0.000 -1309.416 0.000 -2095.065 0.000 -3142.598 0.000 -724.685 52.835 -1304.433 95.103 -2087.093 152.164 -3130.639 228.246 -716.402 105.267 -1289.523 189.481 -2063.237 303.170 -3094.855 454.755 -702.666 156.899 -1264.799 282.418 -2023.678 451.869 -3035.517 677.804 -683.582 207.336 -1230.448 373.205 -1968.717 597.129 -2953.076 895.693 -659.297 256.196 -1186.734 461.153 -1898.774 737.844 -2848.161 1106.766 -629.993 303.106 -1133.987 545.590 -1814.380 872.944 -2721.570 1309.416 -595.895 347.708 -1072.611 625.875 -1716.177 1001.400 -2574.266 1502.100 -557.262 389.665 -1003.071 701.397 -1604.913 1122.235 -2407.370 1683.353 -514.387 428.656 -925.897 771.581 -1481.435 1234.529 -2222.152 1851.794 -467.598 464.385 -841.676 835.892 -1346.682 1337.428 -2020.023 2006.141 -417.250 496.579 -751.050 893.842 -1201.680 1430.148 -1802.520 2145.221 155 150 145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 122 Graduation Thesis 10 -363.727 524.994 -654.708 944.989 -1047.533 1511.983 -1571.299 2267.975 -307.435 549.414 -553.383 988.945 -885.413 1582.312 -1328.119 2373.468 -248.804 569.652 -447.847 1025.374 -716.555 1640.598 -1074.832 2460.897  The calculated information and actual data of two axis X and Y running: Angle 360 355 350 345 340 335 330 325 320 315 310 305 300 295 290 285 280 275 270 265 260 255 250 245 240 235 230 225 220 215 210 205 200 195 190 185 Calculation Xcal Ycal 308121.8 53977.5 309215.2 50509.7 310002.2 46959.8 310476.8 43354.8 310635.4 39722.1 310476.8 36089.4 310002.2 32484.4 309215.2 28934.5 308121.8 25466.7 306730.3 22107.4 305051.3 18882.1 303097.7 15815.4 300884.1 12930.7 298427.6 10249.9 295746.8 7793.4 292862.1 5579.8 289795.4 3626.2 286570.1 1947.2 283210.8 555.7 279743.0 -537.7 276193.1 -1324.7 272588.1 -1799.3 268955.4 -1957.9 265322.7 -1799.3 261717.7 -1324.7 258167.8 -537.7 254700.0 555.7 251340.7 1947.2 248115.4 3626.2 245048.7 5579.8 242164.0 7793.4 239483.2 10249.9 237026.7 12930.7 234813.1 15815.4 232859.5 18882.1 231180.5 22107.4 Practical Xpra Ypra 308481.5 52989.5 309752.6 49302.5 310405 45626.2 310596.7 42016.9 310635.4 38460.2 310384.8 34784.9 309725 31216.2 308812.8 27846.2 307569.5 24429.7 306035.2 21071 304216.5 17867.3 302263.7 14886.4 299873 11988.9 297248.9 9406.2 294482.5 6927.6 291619.4 4886.9 288529.8 3264 285085.4 1609.3 281831.5 157.7 278408.7 -674.2 274842.2 -1340.5 271226.2 -1693.1 267537.8 -1903.8 264100.9 -1266.2 260601.8 -850 257007.6 202.4 253390.5 1284 249966.7 2653.2 246961.6 4508.6 244009.8 6750.4 241187.1 9240.6 238689.8 11474.4 236427.6 14262.4 234216.2 17163.3 232607.8 20191.8 230834.2 23657.3 Absolute error (=