Stabilization of Steady Motions for Systems with Redundant Coordinates
- Authors: Krasinskii A.Y.1, Il’ina A.N.2, Krasinskaya E.M.3
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Affiliations:
- Moscow State University of Food Production, Institute of Economics and Management
- Moscow Aviation Institute, Faculty of Information Technologies and Applied Mathematics
- Bauman Moscow State Technical University, Faculty of Fundamental Sciences
- Issue: Vol 74, No 1 (2019)
- Pages: 14-19
- Section: Article
- URL: https://journals.rcsi.science/0027-1330/article/view/164589
- DOI: https://doi.org/10.3103/S0027133019010035
- ID: 164589
Cite item
Abstract
The vector-matrix Shulgin’s equations are used to stabilize the steady motions of mechanical systems with nonlinear geometric constraints in the case of incomplete information on the state. The momenta are introduced only for the cyclic coordinates that are not used to control. Three variants of the measurement vector are used to prove a theorem on the stabilization of control with the help of a part of the cyclic coordinates described by Lagrange variables. The control coefficients and the estimation system coefficients are specified by solving the corresponding Krasovskii linear-quadratic problem for a linear controlled subsystem without the critical variables corresponding to the redundant coordinates and to the introduced momenta. The stability of the complete closed nonlinear system is proved by reducing to a special Lyapunov case and by the application of the Malkin stability theorem in the case of time-varying perturbations.
About the authors
A. Ya. Krasinskii
Moscow State University of Food Production, Institute of Economics and Management
Author for correspondence.
Email: krasinsk@mail.ru
Russian Federation, Volokolamskoe Shosse 11, Moscow, 125080
A. N. Il’ina
Moscow Aviation Institute, Faculty of Information Technologies and Applied Mathematics
Author for correspondence.
Email: happyday@list.ru
Russian Federation, Volokolamskoe Shosse 4, Moscow, 125993
E. M. Krasinskaya
Bauman Moscow State Technical University, Faculty of Fundamental Sciences
Author for correspondence.
Email: krasinsk@mail.ru
Russian Federation, ul. Baumanskaya 5/1, Moscow, 105005
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