А -Е Е Е А Ы Е , Е А
е яб ь–к яб ь 2016 16№ 5 ISSN 2226-1494 http://ntv.ifmo.ru/ SCIENTIFIC AND TECHNICAL JOURNAL OF INFORMATION TECHNOLOGIES, MECHANICS AND OPTICS September–October 2016 Vol. 16 No 5 ISSN 2226-1494 http://ntv.ifmo.ru/en
62-503.57
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15.06.16, 01.08.16
doi: 10.17586/2226-1494-2016-16-5-787-795 –
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-, . 2016. . 16. № 5. . 787–795. doi: 10.17586/2226-1494-2016-16-5-787-795
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№ 16-38-00638
_a
DISTURBANCE ERROR INVARIANCE IN AUTOMATIC CONTROL SYSTEMS
FOR TECHNOLOGICAL OBJECT TRAJECTORY MOVEMENT
A.V. Lekareva
a aVladimir State University named after Alexander and Nikolay Stoletovs, Vladimir, 600000, Russian Federation
Corresponding author: tasya671@rambler.ru
Article info
Received 15.06.16, accepted 01.08.16 doi: 10.17586/2226-1494-2016-16-5-787-795 Article in Russian
For citation: Lekareva A.V. Disturbance error invariance in automatic control systems for technological object trajectory movement.
Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 5, pp. 787–795. doi: 10.17586/2226-1494-2016-16-5-787-795
Abstract
The essence of the first method lies in injection of additional component into the already established control signal and
formation of the channel for that component. Control signal correction during the signal synthesis stage in the control device
constitutes the basis for the second method. Research results have shown high efficiency of application for both correction
methods. Both methods have roughly the same precision. We have shown that the correction in the control device is
preferable because it has no influence on the inner contour of the system. We have shown the necessity of the block usage
with the variable transmission coefficient, which value is determined by technological trajectory parameters. Research results
can be applied in practice for improvement of the precision specifications of automatic control systems for trajectorial
manipulators.
Keywords
combined control, the fourth modified invariance form, adaptation contour, technological trajectory, handling robot
Acknowledgements
Research is carried out under financial support of the Russian Foundation for Basic Research as part of the scientific project
No. 16-38-00638 mol_a.
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References
1. Morozovskii V.T. Mnogosvyaznye Sistemy Avtomaticheskogo Upravleniya [Multiconnected Systems of the Automatic Control]. Moscow, Energiya Publ., 1970, 288 p.
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2,
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32
1
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* 3
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0,4
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2
1
3
. .: , 1990. 128 .
3. . .
. Ч. II. .: , 1980. 96 .
4. . . .
, 1963. 376 .
5. . ., . ., . .,
. . .
.: , 1963. 475 .
6. . ., . ., . ., . .
. : , 2005.
276 .
7. . ., . .
//
. 2013. . 18, №22(125). . 102– 105.
8. . ., . ., . .
. : , 2010. 166 .
9. . ., . ., . ., Щ . .
- . .: ,
1975. 264 .
10. . ., . ., . ., . .
//
. 2014. № 3. . 114.
11. . ., . ., . ., . .
// . 2014. № 6. . 74.
12. . ., . ., . .
//
. . 2015. №3. . 50-56.
13. . ., . ., . ., . .,
. . // . 2014. № 6. . 73.
14. . ., . ., . ., . .,
. .
// . 2015. № 2-24. . 5329–5334.
15. . ., . .
// . 2015. №11-12. . 201–205.
Л а ваА а а ияВ а и и в а – ,
, , 600000,
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2. Miroshnik I.V. Soglasovannoe Upravlenie Mnogokanal’nymi Sistemami [Coordinated Control of Multi-Channel Systems]. Leningrad, Energoatomizdat Publ., 1990, 128 p.
3. Potapov A.M. Bases of Calculation and Design of Linear Servo Systems. Part II. Leningrad, LMI Publ., 1980, 96 p. (In Russian) 4. Kukhtenko A.I. Problema Invariantnosti v Avtomatike [The
Problem of Invariance in Automation]. Kiev, 1963, 376 p. 5. Yavorskii V.N., Bessonov A.A., Korotaev A.I., Potapov A.M.
Designing of Invariant Servo Drives. Moscow, Vysshaya Shkola Publ., 1963, 475 p.
6. Egorov I.N., Kobzev A.A., Mishulin Yu.E., Nemontov V.A.
Upravlenie Robototekhnicheskimi Sistemami s Silomomentnym Ochuvstvleniem [Robotic Systems Management with Force-Torque Sensing]. Vladimir, VlSU Publ., 2005, 276 p.
7. Kobzev A.A., Mahfouz A.A. Features of realization of the fourth form of invariancy in systems of programmed control.
Izvestia VSTU, 2013, vol. 18, no. 22, pp. 102–105.
8. Legaev V.P., KobzevA.A., Generalov L.K. Model'noe Upravlenie Tochnost'yu Obrabotki na Metallorezhushchikh Stankakh [Modal Control of Processing Precision at Metal Cutting Machines]. Vladimir, VlSU Publ., 2010, 166 p. 9. Novoselov B.V., Gorokhov Yu.S., Kobzev A.A., Shchitov A.I.
Avtomaty-Nastroishchiki Sledyashchikh Sistem [Automatic-Adjusters of Servo Systems]. Moscow, Energiya Publ., 1975, 264 p.
10. Kobzev A.A., Novikova N.A., Lekareva A.V., Mahfouz A.A. Research of the dynamic movement correction in robot systems.
Modern Problems of Science and Education, 2014, no. 3, p. 114.
11. Kobzev A.A., Novikova N.A., Lekareva A.V., Mahfouz A.A. Analysis of the program trajectory correction algorithms in device that produces control signals to drives of robot systems.
Modern Problems of Science and Education, 2014, no. 6, p. 74. 12. Kobzev A.A., Novikova N.A., Lekareva A.V.Analysis of the
algorithms of adaptation of the managing detector of influence for drives of robotic systems by means of the simulator of intercoordinate perturbations. Russian Electromechanics, 2015, no. 3, pp. 50–56.
13. Arkhipov A.N., Kobzev A.A., Lekareva A.V., Mahfouz A.A., Petukhov E.N. Analysis of robotization of process of hydrocutting of oil pipelines. Modern Problems of Science and Education, 2014, no. 6, p. 73.
14. Arkhipov A.N., Kobzev A.A., Eropova E.V., Lekareva A.V., Mahfouz A.A. Coordination of axes of object and the manipulator when hydrocutting oil pipelines. Fundamental Research, 2015, no. 2–24, pp. 5329–5334.
15. Kobzev A.A., Lekareva A.V. Axes matching of mobile robot technology and manipulation object. Oboronnaya Tekhnika, 2015, no. 11-12, pp. 201–205.