On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm
Abstract This article presents the Proportional Integral Resonant Controller (PIRC-controller) as a novel control strategy to suppress the lateral vibrations and eliminate nonlinear bifurcation characteristics of a vertically supported rotor system. The proposed control algorithm is incorporated int...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Springer
2022-12-01
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| Series: | SN Applied Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/s42452-022-05245-z |
| _version_ | 1797817857427374080 |
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| author | Nasser A. Saeed Osama M. Omara M. Sayed Jan Awrejcewicz Mohamed S. Mohamed |
| author_facet | Nasser A. Saeed Osama M. Omara M. Sayed Jan Awrejcewicz Mohamed S. Mohamed |
| author_sort | Nasser A. Saeed |
| collection | DOAJ |
| description | Abstract This article presents the Proportional Integral Resonant Controller (PIRC-controller) as a novel control strategy to suppress the lateral vibrations and eliminate nonlinear bifurcation characteristics of a vertically supported rotor system. The proposed control algorithm is incorporated into the rotor system via an eight-pole electromagnetic actuator. The control strategy is designed such that the control law (PIRC-controller) is employed to generate eight different control currents depending on the air-gap size between the rotor and the electromagnetic poles. Then, the generated electrical currents are utilized to energize the magnetic actuator to apply controllable electromagnetic attractive forces to suppress the undesired lateral vibrations of the considered rotor system. According to the suggested control strategy, the whole system can be represented as a mathematical model using classical mechanics' principle and electromagnetic theory, in which, the rub-impact force between the rotor and the stator is included in the derived model. Then, the obtained discrete dynamical model is analyzed using perturbation techniques and validated numerically through bifurcation diagrams, frequency spectrums, Poincare maps, time responses, and steady-state whirling orbit. The obtained results illustrate that the proposed control algorithm can mitigate the nonlinear vibration and eliminate the catastrophic bifurcations of the rotor system when the control gains are designed optimally. In addition, the system dynamics are analyzed when the rub-impact occurrence between the rotor and the pole housing is unavoidable. The acquired results revealed that the system may perform periodic-1, periodic-n, or quasiperiodic motion with one of two oscillation modes depending on both the impact stiffness coefficient and the dynamic friction coefficient. Article Highlights Nonlinearity dominates the uncontrolled rotor response, where it suffers from the jump phenomenon and multiple solutions. The proposed controller forces the Jeffcott rotor to respond as a linear system with small oscillation amplitudes. The rotor oscillates with full-annular-rub or partial-rub-impact mode when rub-impact occurs between the rotor and stator. |
| first_indexed | 2024-03-13T08:59:38Z |
| format | Article |
| id | doaj.art-a33f5c4726a44d299fb4278e80cbff44 |
| institution | Directory Open Access Journal |
| issn | 2523-3963 2523-3971 |
| language | English |
| last_indexed | 2024-03-13T08:59:38Z |
| publishDate | 2022-12-01 |
| publisher | Springer |
| record_format | Article |
| series | SN Applied Sciences |
| spelling | doaj.art-a33f5c4726a44d299fb4278e80cbff442023-05-28T11:24:56ZengSpringerSN Applied Sciences2523-39632523-39712022-12-015113910.1007/s42452-022-05245-zOn the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithmNasser A. Saeed0Osama M. Omara1M. Sayed2Jan Awrejcewicz3Mohamed S. Mohamed4Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia UniversityDepartment of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia UniversityDepartment of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia UniversityDepartment of Automation, Biomechanics, and Mechatronics, Faculty of Mechanical Engineering, Lodz University of TechnologyDepartment of Mathematics and Statistics, College of Science, Taif UniversityAbstract This article presents the Proportional Integral Resonant Controller (PIRC-controller) as a novel control strategy to suppress the lateral vibrations and eliminate nonlinear bifurcation characteristics of a vertically supported rotor system. The proposed control algorithm is incorporated into the rotor system via an eight-pole electromagnetic actuator. The control strategy is designed such that the control law (PIRC-controller) is employed to generate eight different control currents depending on the air-gap size between the rotor and the electromagnetic poles. Then, the generated electrical currents are utilized to energize the magnetic actuator to apply controllable electromagnetic attractive forces to suppress the undesired lateral vibrations of the considered rotor system. According to the suggested control strategy, the whole system can be represented as a mathematical model using classical mechanics' principle and electromagnetic theory, in which, the rub-impact force between the rotor and the stator is included in the derived model. Then, the obtained discrete dynamical model is analyzed using perturbation techniques and validated numerically through bifurcation diagrams, frequency spectrums, Poincare maps, time responses, and steady-state whirling orbit. The obtained results illustrate that the proposed control algorithm can mitigate the nonlinear vibration and eliminate the catastrophic bifurcations of the rotor system when the control gains are designed optimally. In addition, the system dynamics are analyzed when the rub-impact occurrence between the rotor and the pole housing is unavoidable. The acquired results revealed that the system may perform periodic-1, periodic-n, or quasiperiodic motion with one of two oscillation modes depending on both the impact stiffness coefficient and the dynamic friction coefficient. Article Highlights Nonlinearity dominates the uncontrolled rotor response, where it suffers from the jump phenomenon and multiple solutions. The proposed controller forces the Jeffcott rotor to respond as a linear system with small oscillation amplitudes. The rotor oscillates with full-annular-rub or partial-rub-impact mode when rub-impact occurs between the rotor and stator.https://doi.org/10.1007/s42452-022-05245-zPIRC-controllerRub-impactPeriodic-n, and quasiperiodic motionsFull-annular-rub modePartial-rub-impact mode |
| spellingShingle | Nasser A. Saeed Osama M. Omara M. Sayed Jan Awrejcewicz Mohamed S. Mohamed On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm SN Applied Sciences PIRC-controller Rub-impact Periodic-n, and quasiperiodic motions Full-annular-rub mode Partial-rub-impact mode |
| title | On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm |
| title_full | On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm |
| title_fullStr | On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm |
| title_full_unstemmed | On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm |
| title_short | On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm |
| title_sort | on the rub impact force bifurcations analysis and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with pirc control algorithm |
| topic | PIRC-controller Rub-impact Periodic-n, and quasiperiodic motions Full-annular-rub mode Partial-rub-impact mode |
| url | https://doi.org/10.1007/s42452-022-05245-z |
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