A. S. Andreev, L. V. Kolegova

Ulyanovsk State University (Ulyanovsk, Russia)

Abstract. Proportional-integro-differentiating (PID) controllers are widely used in solving control problems of technical systems, including mechanical ones. For this case, most of works are limited to the study of stabilization problem for steady motions and states; such studies are based on the analysis of model equations in a linear approximation. On the other hand, one of the urgent problems of controlled-motion mechanics is the problem of using PID controllers in tracking the trajectories of multi-link robotic manipulators with semi-global or global stabilization in a non-linear formulation. Practically little studied is the problem of justifying the applicability of such controllers taking into account possible delay in the feedback structure. This paper deals with such a problem. As an application of the theory developed in this paper, the control for a motion of a six-link manipulator is obtained.

Key Words: robotic arm, control, PID controller, delay, Lyapunov functional

For citation: A. S. Andreev, L. V. Kolegova. PID controllers with delay in a problem of stabilization of robotic manipulators’ desired motions. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 24:3(2022), 267–279. DOI: https://doi.org/10.15507/2079-6900.24.202203.267-279

Information about the authors:

Aleksandr S. Andreev, Head of the Department of Information Security and Control Theory, Ulyanovsk State University (42 L. Tolstoy St., Ulyanovsk 432017, Russia), Ph. D. (Physics andMathematics), ORCID: https://orcid.org/0000-0002-9408-0392, asa5208@mail.ru

Lubov V. Kolegova, Assistant Professor, Department of Information Security and Control Theory, Ulyanovsk State University (42 L. Tolstoy St., Ulyanovsk 432017, Russia), https://orcid.org/0000-0002-3160-0602, lyubov_fedorova_1994@mail.ru