Study of the characteristics of linear flexible object control system
- Autores: Romadov S.V.1, Kozyr A.V.1, Efromeev A.G.1
-
Afiliações:
- Tula State University
- Edição: Nº 113 (2025)
- Páginas: 58-72
- Seção: Mathematical control theory
- URL: https://journal-vniispk.ru/1819-2440/article/view/289707
- ID: 289707
Citar
Texto integral
Resumo
The paper solves a flexible object control problem. The issues of constructing a mathematical model of an inhomogeneous flexible link based on the Euler-Bernoulli equation are considered. The simple design model was chosen, which, for example, can describe the vibrations of a single-link manipulator, load bending during aerial transportation, or a helicopter blade. A universal algorithm for determining the parameters of an elastic system is presented. A convenient method is used to analytically determine mode shapes of an inhomogeneous structure. Vibrations model was built by the method of initial parameters with discretization of distributions of mass and bending rigidity. The system dynamics equations are obtained by integrating the Euler-Bernoulli equation, which makes mathematical formulation universal. The resulting mathematical model describes with sufficiently high accuracy the dynamics of objects, which are characterized by a constant or stepwise distribution of mass and stiffness along their length. The control system, providing high speed with minimal fluctuations, is developed using LQR and LMI methods. It is shown that the LMI method allows one to directly limit the control action and more intuitively set the required characteristics of the system, however, it is less resistant to changes in the parameters of the control object. Control system needs to be done more robust, and thus further research is necessary.
Palavras-chave
Sobre autores
Sergey Romadov
Tula State University
Email: romadovsergey5@gmail.com
Tula
Andrey Kozyr
Tula State University
Email: Kozyr_A_V@mail.ru
Tula
Andrey Efromeev
Tula State University
Email: age.sau@mail.ru
Tula
Bibliografia
- АВРАМЕНКО А.А. Метод Рэлея – Ритца и метод начальных параметров в задаче расчета динамических характеристик составных упругих конструкций балоч-ного типа // Вестник Самарского университета. Серия естествознания. – 2019. – №1. – С. 44–56.
- ОГОРОДНИКОВ Ю.И. Синтез наблюдателей состояния для линейных моделей упругих конструкций // Современ-ные технологии. Системный анализ. Моделирование. – 2016. – №4. – С. 25–36.
- ХАЗАНОВ Х.С. Механические колебания систем с рас-пределенными параметрами: учеб. Пособие. – Самара, Изд-во СГАУ, 2002. – 80 с.
- ABDULLAHI M.A., ZAHARUDDIN M., MUS-TAPHA M. Vibration control comparison of a single link flexible manipulator between fuzzy logic control and pole placement control // Int. Journal of Scientific & Technol-ogy Research. – 2013. – No. 2. – P. 236–241.
- EL-ZOBAIDI H., CHAUDHURI B., PAL B.C. et al. LMI approach to normalised H∞ loop-shaping design of pow-er system damping controllers // IET Proc. on Generation Transmission and Distribution. – 2005. – No. 6(152). – P. 952–960.
- HICKNER M., FASEL U., NAIR A.G. et al. Data-driven unsteady aeroelastic modeling for control // ARC. – 2022. – Vol. 61, No. 2. – P. 123–146.
- MARTINS R.J., ZAHARUDDIN M., OSMAN TOKHI M. Approaches for dynamic modelling of flexible manipula-tor systems // IEE Proc. Control Theory and Applications. – 2003. – No. 4(150). – P. 401–411.
- RAHIMI H.N., NAZEMIZADEH M. Dynamic analysis and intelligent control techniques for flexible manipula-tors: A review // Advanced Robotics. – 2014. – No. 28(2). – P. 63–76.
- SCHERER C., WEILAND S. Linear Matrix Inequalities in Control. – Germany, University of Stuttgart, 2015. – 293 p.
- SHI P., LIU F., GU Y. et al. The Development of a Flight Test Platform to Study the Body Freedom Flutter of BWB Flying Wings // Aerospace. – 2021. – No. 8. – P. 390–408.
- WARMINSKI J., KLODA L., LATALSKI J. et al. Nonlin-ear vibrations and time delay control of an extensible slowly rotating beam // Nonlinear dynamics. – 2021. – No. 103(8). – P. 3255–3281.
- WERNER H. Controller design using linear matrix ine-qualities // Control systems, robotics, and automation. – 2009. – Vol. IX. – P. 168–201.
- YINAN W., XIAOWEI ZH., RAFAEL P. et al. Aeroelastic Simulation of High Aspect Ratio Wings with Intermittent Leading-Edge Separation // AIAA JOURNAL. – 2021. – 32 p.
- ZHANG C., ZHOU Z., ZHU X. et al. A Comprehensive Framework for Coupled Nonlinear Aeroelasticity and Flight Dynamics of Highly Flexible Aircrafts // Applied Sciences. – 2020. – Vol. 10, No. 3. – P. 949–966.
- ZHANG Y., LI B., CUI P. et al. Numerical simulation of support interference characteristics on a low-aspect ratio flying-wing model // J. Phys. Conf. Ser. – 2020. – 8 p.
- ZHAO W., GUPTA A., MIGLANI J. et al. Finite Element Model Updating of Composite Flying-wing Aircraft using Global/Local Optimization // Proc. of the AIAA Scitech-2019 Forum, 2019.
- ZHAO X., ZHANG S., LIU Z. et al. Vibration control for flexible manipulators with event triggering mechanism and actuator failures // IEEE Trans. on Cybernetics. – 2021. – P. 7591–7601.
- ZHAO Z., HE X., AHN C.K. Boundary disturbance ob-serv-er-based control of a vibrating single-link flexible manipulator // IEEE Trans. on Systems, Man, and Cyber-netics: Systems. – 2021. – No. 51(4). – P. 2382–2390.
- ZHAO Z., LIU Z. Finite-time convergence disturbance re-jection control for a flexible Timoshenko manipula-tor // IEEE/CAA Journal of Automatica Sinica. – 2021. – No. 8(1). – P. 157–168.
- ZHILING T. Modeling and control of flexible link robots. – Singapore, National University of Singapore, 2004. – 153 p.
Arquivos suplementares
