On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System

The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. Acc...

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Autores principales:	Sabry M. El-Shourbagy, Nasser A. Saeed, Magdi Kamel, Kamal R. Raslan, Emad Abouel Nasr, Jan Awrejcewicz
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	cubic position-velocity controller stability bistable solutions tristable solutions Poincaré map bifurcation diagram Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/32840d376efe4eda90aaf7e515244cf6
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id	oai:doaj.org-article:32840d376efe4eda90aaf7e515244cf6
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spelling	oai:doaj.org-article:32840d376efe4eda90aaf7e515244cf62021-11-25T19:06:29ZOn the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System10.3390/sym131120692073-8994https://doaj.org/article/32840d376efe4eda90aaf7e515244cf62021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2069https://doaj.org/toc/2073-8994The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. According to the proposed control law, the nonlinear system model is established and then investigated with perturbation analysis. Nonlinear algebraic equations that govern the steady-state oscillation amplitudes and the corresponding phases are derived. Depending on the obtained algebraic equations, the different frequency response curves and bifurcation diagrams are plotted for the studied model. Sensitivity analysis for the linear and nonlinear controllers’ gains is explored. Obtained analytical results demonstrated that the studied model had symmetric bifurcation behaviours in both the horizontal and vertical directions. In addition, the integration of the cubic position controller made the control algorithm more flexible to reshape system dynamical behaviours from the hardening spring characteristic to the softening spring characteristic (or vice versa) to avoid resonance conditions. Moreover, the optimal design of the cubic position gain and/or cubic velocity gain could stabilise the unstable motion and eliminate the nonlinear effects of the system even at large disc eccentricities. Lastly, numerical validations for all acquired results are performed, where the presented simulations show accurate correspondence between numerical and analytical investigations.Sabry M. El-ShourbagyNasser A. SaeedMagdi KamelKamal R. RaslanEmad Abouel NasrJan AwrejcewiczMDPI AGarticlecubic position-velocity controllerstabilitybistable solutionstristable solutionsPoincaré mapbifurcation diagramMathematicsQA1-939ENSymmetry, Vol 13, Iss 2069, p 2069 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	cubic position-velocity controller stability bistable solutions tristable solutions Poincaré map bifurcation diagram Mathematics QA1-939
spellingShingle	cubic position-velocity controller stability bistable solutions tristable solutions Poincaré map bifurcation diagram Mathematics QA1-939 Sabry M. El-Shourbagy Nasser A. Saeed Magdi Kamel Kamal R. Raslan Emad Abouel Nasr Jan Awrejcewicz On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System
description	The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. According to the proposed control law, the nonlinear system model is established and then investigated with perturbation analysis. Nonlinear algebraic equations that govern the steady-state oscillation amplitudes and the corresponding phases are derived. Depending on the obtained algebraic equations, the different frequency response curves and bifurcation diagrams are plotted for the studied model. Sensitivity analysis for the linear and nonlinear controllers’ gains is explored. Obtained analytical results demonstrated that the studied model had symmetric bifurcation behaviours in both the horizontal and vertical directions. In addition, the integration of the cubic position controller made the control algorithm more flexible to reshape system dynamical behaviours from the hardening spring characteristic to the softening spring characteristic (or vice versa) to avoid resonance conditions. Moreover, the optimal design of the cubic position gain and/or cubic velocity gain could stabilise the unstable motion and eliminate the nonlinear effects of the system even at large disc eccentricities. Lastly, numerical validations for all acquired results are performed, where the presented simulations show accurate correspondence between numerical and analytical investigations.
format	article
author	Sabry M. El-Shourbagy Nasser A. Saeed Magdi Kamel Kamal R. Raslan Emad Abouel Nasr Jan Awrejcewicz
author_facet	Sabry M. El-Shourbagy Nasser A. Saeed Magdi Kamel Kamal R. Raslan Emad Abouel Nasr Jan Awrejcewicz
author_sort	Sabry M. El-Shourbagy
title	On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System
title_short	On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System
title_full	On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System
title_fullStr	On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System
title_full_unstemmed	On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System
title_sort	on the performance of a nonlinear position-velocity controller to stabilize rotor-active magnetic-bearings system
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/32840d376efe4eda90aaf7e515244cf6
work_keys_str_mv	AT sabrymelshourbagy ontheperformanceofanonlinearpositionvelocitycontrollertostabilizerotoractivemagneticbearingssystem AT nasserasaeed ontheperformanceofanonlinearpositionvelocitycontrollertostabilizerotoractivemagneticbearingssystem AT magdikamel ontheperformanceofanonlinearpositionvelocitycontrollertostabilizerotoractivemagneticbearingssystem AT kamalrraslan ontheperformanceofanonlinearpositionvelocitycontrollertostabilizerotoractivemagneticbearingssystem AT emadabouelnasr ontheperformanceofanonlinearpositionvelocitycontrollertostabilizerotoractivemagneticbearingssystem AT janawrejcewicz ontheperformanceofanonlinearpositionvelocitycontrollertostabilizerotoractivemagneticbearingssystem
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On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System

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