On the Resonant Vibrations Control of the Nonlinear Rotor Active Magnetic Bearing Systems
Nonlinear vibration control of the twelve-poles electro-magnetic suspension system was tackled in this study, using a novel control strategy. The introduced control algorithm was a combination of three controllers: the proportional-derivative (PD) controller, the integral resonant controller (IRC),...
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| Veröffentlicht in: | Applied sciences Jg. 12; H. 16; S. 8300 |
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| Abstract | Nonlinear vibration control of the twelve-poles electro-magnetic suspension system was tackled in this study, using a novel control strategy. The introduced control algorithm was a combination of three controllers: the proportional-derivative (PD) controller, the integral resonant controller (IRC), and the positive position feedback (PPF) controller. According to the presented control algorithm, the mathematical model of the controlled twelve-poles rotor was established as a nonlinear four-degree-of-freedom dynamical system coupled to two first-order filters. Then, the derived nonlinear dynamical system was analyzed using perturbation analysis to extract the averaging equations of motion. Based on the extracted averaging equations of motion, the efficiency of different control strategies (i.e., PD, PD+IRC, PD+PPF, and PD+IRC+PPF) for mitigating the rotor’s undesired vibrations and improving its catastrophic bifurcation was investigated. The acquired analytical results demonstrated that both the PD and PD+IRC controllers can force the rotor to respond as a linear system; however, the controlled system may exhibit the maximum oscillation amplitude at the perfect resonance condition. In addition, the obtained results demonstrated that the PD+PPF controller can eliminate the rotor nonlinear oscillation at the perfect resonance, but the system may suffer from high oscillation amplitudes when the resonance condition is lost. Moreover, we report that the combined control algorithm (PD+IRC+PPF) has all the advantages of the individual control algorithms (i.e., PD, PD+IRC, PD+PPF), while avoiding their drawbacks. Finally, the numerical simulations showed that the PD+IRC+PPF controller can eliminate the twelve-poles system vibrations regardless of both the excitation force magnitude and the resonant conditions at a short transient time. |
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| AbstractList | Nonlinear vibration control of the twelve-poles electro-magnetic suspension system was tackled in this study, using a novel control strategy. The introduced control algorithm was a combination of three controllers: the proportional-derivative (PD) controller, the integral resonant controller (IRC), and the positive position feedback (PPF) controller. According to the presented control algorithm, the mathematical model of the controlled twelve-poles rotor was established as a nonlinear four-degree-of-freedom dynamical system coupled to two first-order filters. Then, the derived nonlinear dynamical system was analyzed using perturbation analysis to extract the averaging equations of motion. Based on the extracted averaging equations of motion, the efficiency of different control strategies (i.e., PD, PD+IRC, PD+PPF, and PD+IRC+PPF) for mitigating the rotor’s undesired vibrations and improving its catastrophic bifurcation was investigated. The acquired analytical results demonstrated that both the PD and PD+IRC controllers can force the rotor to respond as a linear system; however, the controlled system may exhibit the maximum oscillation amplitude at the perfect resonance condition. In addition, the obtained results demonstrated that the PD+PPF controller can eliminate the rotor nonlinear oscillation at the perfect resonance, but the system may suffer from high oscillation amplitudes when the resonance condition is lost. Moreover, we report that the combined control algorithm (PD+IRC+PPF) has all the advantages of the individual control algorithms (i.e., PD, PD+IRC, PD+PPF), while avoiding their drawbacks. Finally, the numerical simulations showed that the PD+IRC+PPF controller can eliminate the twelve-poles system vibrations regardless of both the excitation force magnitude and the resonant conditions at a short transient time. Nonlinear vibration control of the twelve-poles electro-magnetic suspension system was tackled in this study, using a novel control strategy. The introduced control algorithm was a combination of three controllers: the proportional-derivative ( PD ) controller, the integral resonant controller ( IRC ) , and the positive position feedback ( PPF ) controller. According to the presented control algorithm, the mathematical model of the controlled twelve-poles rotor was established as a nonlinear four-degree-of-freedom dynamical system coupled to two first-order filters. Then, the derived nonlinear dynamical system was analyzed using perturbation analysis to extract the averaging equations of motion. Based on the extracted averaging equations of motion, the efficiency of different control strategies (i.e., PD, PD+IRC, PD+PPF, and PD+IRC+PPF ) for mitigating the rotor’s undesired vibrations and improving its catastrophic bifurcation was investigated. The acquired analytical results demonstrated that both the PD and PD+IRC controllers can force the rotor to respond as a linear system; however, the controlled system may exhibit the maximum oscillation amplitude at the perfect resonance condition. In addition, the obtained results demonstrated that the PD+PPF controller can eliminate the rotor nonlinear oscillation at the perfect resonance, but the system may suffer from high oscillation amplitudes when the resonance condition is lost. Moreover, we report that the combined control algorithm ( PD+IRC+PPF ) has all the advantages of the individual control algorithms (i.e., PD, PD+IRC, PD+PPF ), while avoiding their drawbacks. Finally, the numerical simulations showed that the PD+IRC+PPF controller can eliminate the twelve-poles system vibrations regardless of both the excitation force magnitude and the resonant conditions at a short transient time. |
| Author | Raslan, Kamal R. Saeed, Nasser A. Kamel, Magdi Awrejcewicz, Jan Gepreel, Khaled A. El-Shourbagy, Sabry M. |
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| Cites_doi | 10.20855/ijav.2019.24.21309 10.1115/DETC2017-67105 10.1177/1077546307074577 10.1016/j.chaos.2005.04.003 10.1016/j.chaos.2007.02.002 10.1016/j.apm.2021.01.008 10.1007/s10846-010-9487-7 10.1016/j.ymssp.2018.01.010 10.1007/s10409-016-0577-z 10.1016/j.jsv.2020.115365 10.1177/14613484221104818 10.1002/0471705195 10.3390/sym13081502 10.1016/j.chaos.2006.05.095 10.1016/j.cnsns.2014.10.011 10.1007/s11071-014-1706-5 10.1016/j.euromechsol.2020.104145 10.1016/S0020-7462(01)00136-6 10.3390/pr10020271 10.1007/s11071-005-3937-y 10.1006/jsvi.2000.3257 10.3390/sym13112069 10.1109/ACCESS.2020.3012447 10.1007/s11071-005-7959-2 10.1002/stc.423 10.1007/s11071-019-05256-3 10.1016/j.apm.2020.11.005 10.1109/ACCESS.2021.3081397 10.1016/j.chaos.2007.06.044 10.1142/S021812740802063X 10.1016/j.euromechsol.2020.104120 10.1016/j.cnsns.2010.04.055 10.1016/j.mechatronics.2004.10.003 10.1016/j.mechatronics.2012.10.001 10.1006/jsvi.2000.2916 10.1002/9783527651894 10.3390/app112210839 10.1002/9783527617586 10.1016/j.ymssp.2017.07.033 |
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| SubjectTerms | Control algorithms Dynamical systems forward whirling motion Investigations IRC-control algorithm Mathematical models Military helicopters nonlinear vibration control PD-control algorithm PPF-control algorithm rotor electro-magnetic suspension system |
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| Title | On the Resonant Vibrations Control of the Nonlinear Rotor Active Magnetic Bearing Systems |
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