Nonlinear control laws based on linear ones using odd functions
- Authors: Furtat I.B.1, Gushchin P.A.1, Kopisova E.A.1
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Affiliations:
- Institute of Problems of Mechanical Engineering RAS
- Issue: No 102 (2023)
- Pages: 58-75
- Section: Control systems analysis and design
- URL: https://medbiosci.ru/1819-2440/article/view/363792
- DOI: https://doi.org/10.25728/ubs.2023.102.4
- ID: 363792
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Abstract
The paper investigates nonlinear control laws obtained from linear one by two types of coordinate change by using odd functions. The first coordinate change consists in passing each component of the state vector through a nonlinear function, the second coordinate change is in passing the entire linear control law through a nonlinear function. To study such systems, it is proposed to represent nonlinear functions as linear ones with a nonlinear slope. Such a representation will allow using the methods of linear matrix inequalities (LMI) to study the stability of the closed-loop systems. The stability domains and the domains for the initial conditions are found, obtained as a result of a multi-step solution search procedure using LMI. It is shown that the use of the proposed nonlinear control laws makes it possible to reduce the steady-state error compared to the linear one. The simulations illustrate the theoretical conclusions.
About the authors
Igor Borisovich Furtat
Institute of Problems of Mechanical Engineering RAS
Email: cainenash@mail.ru
St.Peterburg
Pavel Aleksandrovich Gushchin
Institute of Problems of Mechanical Engineering RAS
Email: guschin.p@mail.ru
St.Peterburg
Esenia Alekseevna Kopisova
Institute of Problems of Mechanical Engineering RAS
Email: esyako@ya.ru
St.Peterburg
References
1. АНДРИЕВСКИЙ Б.Р., ФРАДКОВ А.Л. Избранные главытеории автоматического управления с примерами на языкеMATLAB. – СПб.: Наука, 2000. 2. АНТИПОВ А.С., КРАСНОВА С.А., УТКИН В.А. Синтезинвариантных нелинейных одноканальных систем слеже-ния с сигмоидальными обратными связями с обеспечениемзаданной точности слежения Большие отклонения в линей-ных системах при ненулевых начальных условиях // Автома-тика и телемеханика. 3. КРАСНОВА С.А., АНТИПОВ А.С. Иерархический син-тез сигмоидальных обобщенных моментов манипуляторав условиях неопределенности // Проблемы управления. –2016. – № 4. – С. 10–21. 4. КРАСНОВА С.А., УТКИН В.А. Каскадный синтез наблю-дателей состояния динамических систем. – М.: Наука,2006. 5. КРАСНОВА С.А., УТКИН А.В. Сигма-функция в задачахсинтеза наблюдателей состояний и возмущений // Пробле-мы управления. – 2015. – № 5. – С. 27–36. 6. ХАЛИЛ Х.К. Нелинейные системы. – М-Ижевск: НИЦ «Ре-гулярная и хаотическая динамика», Институт компьютер-ных исследований, 2009. 7. BOYD S., GHAOUI L.E., FERON E., BALAKRISHNAN V.Linear Matrix Inequalities in System and Control Theory. –Philadelphia, PA: SIAM, 1994. 8. FRIDMAN E. Introduction to Time-Delay Systems: Analysisand Control. – Springer, International Publishing, 2014. 9. NEKHOROSHIKH A.N., EFIMOV D., POLYAKOV A.,PERRUQUETTI W., FURTAT I.B., FRIDMAN E. On output-based accelerated stabilization of a chain of integrators:Implicit Lyapunov-Krasovskii functional approach // IFAC-PapersOnLine. – 2020. – Vol. 53, no. 2. – P. 5982–5987. 10. NEKHOROSHIKH, A.N., EFIMOV, D., POLYAKOV, A.,PERRUQUETTI, W., FURTAT, I.B. On finite-time stabilizationof a class of nonlinear time-delay systems: Implicit Lyapunov-Razumikhin approach // Proc. IEEE Conf. on Decision andControl, 2020. – P. 1975–1980.
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