Multicriteria Parametric Optimization of Nonlinear Robust Control with Two Degrees of Freedom by a Discrete-Continuous Plant

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DOI https://doi.org/10.15407/pmach2023.03.042
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher Anatolii Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN  2709-2984 (Print), 2709-2992 (Online)
Issue Vol. 26, no. 3, 2023 (September)
Pages 42-53
Cited by J. of Mech. Eng., 2023, vol. 26, no. 3, pp. 42-53

 

Authors

Borys I. Kuznetsov, Anatolii Pidhornyi Institute of Mechanical Engineering Problems of NAS of Ukraine (2/10, Pozharskyi str., Kharkiv, 61046, Ukraine), e-mail: kuznetsov.boris.i@gmail.com, ORCID: 0000-0002-1100-095X

Ihor V. Bovdui, Anatolii Pidhornyi Institute of Mechanical Engineering Problems of NAS of Ukraine (2/10, Pozharskyi str., Kharkiv, 61046, Ukraine), e-mail: ibovduj@gmail.com, ORCID: 0000-0003-3508-9781

Olena V. Voloshko, Anatolii Pidhornyi Institute of Mechanical Engineering Problems of NAS of Ukraine (2/10, Pozharskyi str., Kharkiv, 61046, Ukraine), e-mail: vinichenko.e.5@gmail.com, ORCID: 0000-0002-6931-998X

Tetyana B. Nikitina, Educational scientific professional pedagogical Institute Ukrainian Engineering Pedagogical Academy (9a, Nosakov str., Bakhmut, 84511, Ukraine), e-mail: tatjana55555@gmail.com, ORCID: 0000-0002-9826-1123

Borys B. Kobylianskyi, Educational scientific professional pedagogical Institute Ukrainian Engineering Pedagogical Academy (9a, Nosakov str., Bakhmut, 84511, Ukraine), e-mail: nnppiuipa@ukr.net, ORCID: 0000-0003-3226-5997

 

Abstract

A multicriteria parametric optimization of nonlinear robust control with two degrees of freedom by a discrete-continuous plant has been developed to increase accuracy and reduce sensitivity to uncertain plant parameters. Such plants are mounted on a moving base, on which sensors for angles, angular velocities and angular accelerations are installed. To increase the accuracy of control, systems with two degrees of freedom, which include control with feedback and a closed-loop, and with direct connections and open-loop control of the setting and disturbing effects, are used. The multicriteria optimization of nonlinear robust control with two degrees of freedom by a discrete-continuous plant is reduced to the solution of the Hamilton-Jacobi-Isaacs equations. The robust control target vector is calculated as a solution of a zero-sum antagonistic vector game. The vector payoffs of this game are direct indexes performance vector presented in the system in different modes of its operation. The calculation of the vector payoffs of this game is related to the simulation of the synthesized nonlinear system for different operating modes of the system, input signals and values of the plant parameters. The solutions of this vector game are calculated on the basis of the system of Pareto-optimal solutions, taking into account the binary relations of preferences, on the basis of the stochastic metaheuristic of Archimedes optimization algorithm by several swarms. Thanks to the synthesis of nonlinear robust control with two degrees of freedom by a discrete-continuous object, it is shown that the use of synthesized controllers made it possible to increase the accuracy of control of an electromechanical system with distributed parameters of the mechanical part to reduce the time of transient processes by 1.5–2 times, reduce dispersion of errors by 1.3 times and reduce the sensitivity of the system to changes in the plant parameters in comparison with typical controllers used in existing systems. Further improvement of control accuracy is restrained by energy limitations of executive mechanisms and information limitations of measuring devices.

 

Keywords: discrete-continuous plant, nonlinear robust control, Hamilton-Jacobi-Isaacs equation, multicriteria parametric optimization, stochastic metaheuristic optimization algorithm.

 

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References

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Received 25 May 2023

Published 30 September 2023