Abstract
The problem of control of the traction force direction in the course of the motion of an inertial object is considered. The maximum possible value of the traction force is constant and is determined by the maximum dry friction force. Within a finite time range, the problem of bringing an object to a given rectilinear trajectory with simultaneous velocity maximization in the appropriate direction is considered.
REFERENCES
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Gordon&Breach, New York, 1986).
Ya. N. Roitenberg, Automatic Control (Nauka, Moscow, 1971) [in Russian].
V. K. Isaev, “L. S. Pontryagins’s maximum principle and optimal programming of rocket thrust,” Automat. Remote Control 22 (8), 881–893 (1961).
A. E. Bryson and Y.-C. Ho, Applied Optimal Control: Optimization, Estimation, and Control (Blaisdell Pub. Co., Waltham, MA, 1969).
V. N. Afanas’ev, V. B. Kolmanovskii, and V. R. Nosov, Mathematical Theory of Control System Design (Vysshaya shkola, Moscow, 2003) [in Russian].
V. Ph. Zhuravlev, “Friction laws in the case of combination of slip and spin,” Mech. Solids 38 (4), 52–58 (2003).
V. Ph. Zhuravlev, “On the dry frictions model in the rigid body dynamics problems,” Usp. Mekh., No. 3, 157–158 (2005).
V. V. Andronov and V. Ph. Zhuravlev, Dry Friction in Problems of Mechanics (Regular and Chaotic Dynamics, Izhevsk, Moscow, 2010) [in Russian].
V. Ph. Zhuravlev, “Flat dynamics of a homogeneous parallelepiped with dry friction,” Mech. Solids 56 (1), 1–3 (2021).
G. M. Rozenblat, “On optimal rotation of a rigid body by applying internal forces,” Dokl. Math. 106 (1), 291–297 (2022).
N. N. Krasovskii, Game Problems on Motions Meeting (Nauka, Moscow, 1970) [in Russian].
S. A. Reshmin, “Synthesis of control of a manipulator with two links,” J. Comput. Syst. Sci. Int. 36 (2), 299–303 (1997).
S. A. Reshmin and F. L. Chernousko, “Control synthesis in a nonlinear dynamic system based on a decomposition,” J. Appl. Math. Mech. 62 (1), 115–122 (1998).
I. M. Anan’evskii and S. A. Reshmin, “Decomposition-based continuous control of mechanical systems,” J. Comput. Syst. Sci. Int. 53 (4), 473–486 (2014).
Funding
The research work was financially supported by the Russian Science Foundation, project no. 23-11-00128, https://rscf.ru/project/23-11-00128/.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares that he has no conflicts of interest.
Additional information
Translated by O.Polyakov
Publisher’s Note.
Allerton Press remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Reshmin, S.A. Optimal Traction Control in High-Speed Maneuvering under Dry Friction Conditions. Mech. Solids 58, 2574–2585 (2023). https://doi.org/10.3103/S0025654423070191
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654423070191