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ARTICLE
Servo constraint control for mechanical systems: friction force depending on control design
| 1 | SAIC GM, Wuling Automobile Co., Ltd., Liuzhou, Guangxi, China |
| 2 | School of Vehicle and Mobility, Tsinghua University, China |
Submission date: 2020-12-18
Final revision date: 2021-03-14
Acceptance date: 2021-04-15
Online publication date: 2021-06-08
Publication date: 2021-07-15
KEYWORDS
TOPICS
ABSTRACT
In this paper, the problem of motion of controlled mechanical systems under a servo constraint
is considered. The servo constraint which is prescribed by the designer is supposed
to be non-ideal, that is, it does work in a virtual displacement. The second order form constraint
is introduced to obtain a closed-form (i.e., analytical form) control input. The final
servo control contains two parts: the first one generates the constraint force so that the
constraint is exactly followed, while the second one can be designed by the designer for the
facility, such as to compensate the effects of the friction force. After geometrical analysis
applied to the Coulomb friction forces, we found that they actually depend on the control
forces (i.e., the two are coupled). Application to a 3-DOF robot manipulator is made.
REFERENCES (20)
1.
Abraham R., Marsden J.E., Ratiu T., 1988, Tensor Analysis, and Applications, 2nd ed., Springer Verlag, New York.
2.
Anderson B.D.O., Moore J.B., 1969, Linear system optimization with prescribed degree of stability, Proceedings of IEEE, 116, 2083-2087.
3.
Cabannes H., 1968, General Mechanics, 2nd ed. (translated, original in French), Blaisdell/Ginn, Waltham, MA.
4.
Chen Y.H., Leitmann G. H., Chen J. S., 1998, Robust control for rigid serial manipulators: A general setting, Proceedings of the 1998 American Control Conference, Philadelphia, PA, 2, 912-916.
5.
Chen Y.H., 1999, Equations of motion of constrained mechanical systems: given force depends on constraint force, Mechatronics, 9, 4, 411-428.
6.
Chen Y.H., 2009, Constraint-following servo control design for mechanical system, Journal of Vibration and Control, 15, 3, 369-389.
7.
Hamel G., 1949, Theoretische Mechanik (in German), Springer Verlag, Berlin.
8.
Huang J., Chen Y.H., Zhong Z., 2013, Udwadia-Kalaba approach for parallel manipulator dynamics, Journal of Dynamic Systems Measurement and Control, 135, 6, 061003.
9.
Hui Y., Chen Y., Yu D., 2018, Vehicle motion control under equality and inequality constraints: a diffeomorphism approach, Nonlinear Dynamics, 95, 175-194.
10.
Kirgetov V.I., 1967, The motion of controlled mechanical systems with prescribed constraints (servoconstraints) (in English, translated from the original Russian), Journal of Applied Mathematics and Mechanics 31, 3, 433446.
11.
Noble B., Daniel J.W., 1977, Applied Linear Algebra, 2nd ed., Prentice Hall, Englewood Cliffs, N.J.
12.
Papastavridis J.G., 2002, Analytical Mechanics, Oxford University Press, New York, NY.
13.
Rosenberg R.M., 1977, Analytical Dynamics of Discrete Systems, Plenum, New York.
14.
Sciavicco L., Siciliano B., 2000, Modeling and Control of Robot Manipulators, 2nd ed., Springer Verlag, UK.
15.
Sun H., Zhao H., Zhen S., Huang K., Zhao F., Chen X., Chen Y-H., 2015, Application of the Udwadia-Kalaba approach to tracking control of mobile robots, Nonlinear Dynamics, 83, 389-400.
16.
Udwadia F.E., Kalaba R.E., 1996, Analytical Dynamics: A New Approach, Cambridge University Press, Cambridge, UK.
17.
Udwadia F.E., Kalaba R.E., 2000, Nonideal constraints and Lagrangian dynamics, Journal of Aerospace Engineering, 13, 17-22.
18.
Xu J., Du Y., Chen Y.-H., Guo H., 2018, Adaptive robust constrained state control for nonlinear maglev vehicle with guaranteed bounded airgap, IET Control Theory and Applications, 12, 11, 1573-1583.
19.
Yin H., Chen Y.-H., Huang J., Lü H., 2020, Tackling mismatched uncertainty in robust constraint-following control of under actuated systems, Information Sciences, 520, 337-352.
20.
Zhao R., Chen Y.H., Wu L., Pan M., 2020, Robust trajectory tracking control for uncertain mechanical systems: servo constraint-following and adaptation mechanism, International Journal of Control, 93, 7, 1696-1709.
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