Geodesic
On Modeling a nonlinear integral regulator on the base of the Volterra equations
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 8-18.

Voir la notice de l'article provenant de la source Math-Net.Ru

Synthesis of discrete-time control which solves the problem of stabilization of holonomic mechanical systems’ program motion is considered. Such systems are described by Lagrange equations of the second kind. Digital control signals are used in computer-containing control systems for continuous processes. Development of models for such controlled processes leads to investigation of continuous-discrete systems with state described by a continuous function and discrete control functions. This paper proposes an approach for constructing of controller taking into account non-linearity of the system and non-stationarity of program motion. By means of Lyapunov vector function and the comparison system sufficient conditions of given program motion’s stabilization are obtained. A feature of the article is in solving of the problem by use of Lyapunov vector function with components that explicitly depend on time, and are nonlinear with respect to the generalized coordinates. It allows to solve the stabilization problem in general having the possibility to select the most suitable control parameters for each particular system
Keywords: stabilization, control, discrete-time control, synthesis of control for mechanical systems, Lyapunov vector-function, comparison systems, nonstationary nonlinear dynamical systems. 
@article{SVMO_2016_18_3_a0,
     author = {A. S. Andreev and O. A. Peregudova and S. Y. Rakov},
     title = {On {Modeling} a nonlinear integral regulator on the base of the {Volterra} equations},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {8--18},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a0/}
}
TY  - JOUR
AU  - A. S. Andreev
AU  - O. A. Peregudova
AU  - S. Y. Rakov
TI  - On Modeling a nonlinear integral regulator on the base of the Volterra equations
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2016
SP  - 8
EP  - 18
VL  - 18
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a0/
LA  - ru
ID  - SVMO_2016_18_3_a0
ER  - 
%0 Journal Article
%A A. S. Andreev
%A O. A. Peregudova
%A S. Y. Rakov
%T On Modeling a nonlinear integral regulator on the base of the Volterra equations
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2016
%P 8-18
%V 18
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a0/
%G ru
%F SVMO_2016_18_3_a0
A. S. Andreev; O. A. Peregudova; S. Y. Rakov. On Modeling a nonlinear integral regulator on the base of the Volterra equations. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 8-18. http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a0/

[1] H. Berghuis, H. Nijmeijer, “Global regulation of robots using only position measurements”, Systems and Contr. Letters, 21 (1993), 289-293 | DOI | MR | Zbl

[2] Burkov I.V., “Stabilizatsiya naturalnoi mekhanicheskoi sistemy bez izmereniya ee skorostei s prilozheniem k upravleniyu tverdym telom”, Prikladnaya matematika i mekhanika, 62:6 (1998), 923-933 | MR

[3] Burkov I.V., “Stabilization of position of uniform motion of mechanical systems via bounded control and without velocity measurements”, 3-rd IEEE Multi-conference on Systems and Control. (St. Petersburg), 2009, 400-405

[4] I. M. Ananevskii, V. B. Kolmanovskii, “O stabilizatsii nekotorykh reguliruemykh sistem s posledeistviem”, Avtomatika i telemekhanika, 1989, no. 9, 34-42 | MR

[5] A. S. Andreev, Ustoichivost neavtonomnykh funktsionalno-differentsialnykh uravnenii: monografiya, Izd-vo Ul-GU, Ulyanovsk, 2005, 328 pp.

[6] A. S. Andreev, “Metod funktsionalov Lyapunova v zadache ob ustoichivosti funktsionalno-differentsialnykh uravnenii”, Avtomatika i telemekhanika, 2009, no. 9, 4-55 | Zbl

[7] A. S. Andreev, V. V. Blagodatnov, A.R. Kilmetova, “Uravneniya Volterra v modelirovanii PI- i PID-regulyatorov”, Nauchno-tekhnicheskii vestnik Povolzhya, 2013, no. 1, 84-90 | MR

[8] A. S. Andreev, S. Yu. Rakov, “Ob upravlenii dvukhzvennym robotom-manipulyatorom na osnove PI-regulyatora”, Avtomatizatsiya protsessov upravleniya, 2015, no. 3(41), 69-72

[9] A. S. Andreev, O. A. Peregudova, “Sintez upravleniya dvukhzvennym manipulyatorom bez izmereniya skorostei”, Avtomatizatsiya protsessov upravleniya, 2015, no. 4(42), 81-89

[10] F. L. Chernousko, I. M. Ananevskii, S. A. Reshmin, Metody upravleniya nelineinymi mekhanicheskimi sistemami, Fizmatlit, M., 2006, 326 pp.