Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator
Within this work, the radial Proportional Derivative (PD-) controller along with the eight-poles electro-magnetic actuator are introduced as a novel control strategy to suppress the lateral oscillations of a non-linear Jeffcott-rotor system. The proposed control strategy has been designed such that...
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MDPI AG
2022-07-01
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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 | Within this work, the radial Proportional Derivative (PD-) controller along with the eight-poles electro-magnetic actuator are introduced as a novel control strategy to suppress the lateral oscillations of a non-linear Jeffcott-rotor system. The proposed control strategy has been designed such that each pole of the magnetic actuator generates an attractive magnetic force proportional to the radial displacement and radial velocity of the rotating shaft in the direction of that pole. According to the proposed control mechanism, the mathematical model that governs the non-linear interactions between the Jeffcott system and the magnetic actuator has been established. Then, an analytical solution for the obtained non-linear dynamic model has been derived using perturbation analysis. Based on the extracted analytical solution, the motion bifurcation of the Jeffcott system has been investigated before and after control via plotting the different response curves. The obtained results illustrate that the uncontrolled Jeffcott-rotor behaves like a hard-spring duffing oscillator and responds with bi-stable periodic oscillation when the rotor angular speed is higher than the system’s natural frequency. It is alsomfound that the system, before control, can exhibit stable symmetric motion with high vibration amplitudes in both the horizontal and vertical directions, regardless of the eccentricity magnitude. In addition, the acquired results demonstrate that the introduced control technique can eliminate catastrophic bifurcation behaviors and undesired vibration of the system when the control parameters are designed properly. However, it is reported that the improper design of the controller gains may destabilize the Jeffcott system and force it to perform either chaotic or quasi-periodic motions depending on the magnitudes of both the shaft eccentricity and the control parameters. Finally, to validate the accuracy of the obtained results, numerical simulations for all response curves have been introduced which have been in excellent agreement with the analytical investigations. |
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| language | English |
| last_indexed | 2024-03-09T22:07:03Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-f3fdd107b24c4de8aed1cbae1d20cfcd2023-11-23T19:41:00ZengMDPI AGApplied Sciences2076-34172022-07-011213668810.3390/app12136688Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings ActuatorNasser A. Saeed0Osama M. Omara1M. Sayed2Jan Awrejcewicz3Mohamed S. Mohamed4Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, EgyptDepartment of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, EgyptDepartment of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, EgyptDepartment of Automation, Biomechanics, and Mechatronics, Faculty of Mechanical Engineering, Lodz University of Technology, 90924 Lodz, PolandDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaWithin this work, the radial Proportional Derivative (PD-) controller along with the eight-poles electro-magnetic actuator are introduced as a novel control strategy to suppress the lateral oscillations of a non-linear Jeffcott-rotor system. The proposed control strategy has been designed such that each pole of the magnetic actuator generates an attractive magnetic force proportional to the radial displacement and radial velocity of the rotating shaft in the direction of that pole. According to the proposed control mechanism, the mathematical model that governs the non-linear interactions between the Jeffcott system and the magnetic actuator has been established. Then, an analytical solution for the obtained non-linear dynamic model has been derived using perturbation analysis. Based on the extracted analytical solution, the motion bifurcation of the Jeffcott system has been investigated before and after control via plotting the different response curves. The obtained results illustrate that the uncontrolled Jeffcott-rotor behaves like a hard-spring duffing oscillator and responds with bi-stable periodic oscillation when the rotor angular speed is higher than the system’s natural frequency. It is alsomfound that the system, before control, can exhibit stable symmetric motion with high vibration amplitudes in both the horizontal and vertical directions, regardless of the eccentricity magnitude. In addition, the acquired results demonstrate that the introduced control technique can eliminate catastrophic bifurcation behaviors and undesired vibration of the system when the control parameters are designed properly. However, it is reported that the improper design of the controller gains may destabilize the Jeffcott system and force it to perform either chaotic or quasi-periodic motions depending on the magnitudes of both the shaft eccentricity and the control parameters. Finally, to validate the accuracy of the obtained results, numerical simulations for all response curves have been introduced which have been in excellent agreement with the analytical investigations.https://www.mdpi.com/2076-3417/12/13/6688Jeffcott-rotorradial controllerelectro-magnetic actuatornon-linear vibrationsquasi-periodic motionchaotic motions |
| spellingShingle | Nasser A. Saeed Osama M. Omara M. Sayed Jan Awrejcewicz Mohamed S. Mohamed Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator Applied Sciences Jeffcott-rotor radial controller electro-magnetic actuator non-linear vibrations quasi-periodic motion chaotic motions |
| title | Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator |
| title_full | Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator |
| title_fullStr | Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator |
| title_full_unstemmed | Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator |
| title_short | Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator |
| title_sort | non linear interactions of jeffcott rotor system controlled by a radial pd control algorithm and eight pole magnetic bearings actuator |
| topic | Jeffcott-rotor radial controller electro-magnetic actuator non-linear vibrations quasi-periodic motion chaotic motions |
| url | https://www.mdpi.com/2076-3417/12/13/6688 |
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