Lateral vibration control and stabilization of the quasiperiodic oscillations for rotor-active magnetic bearings system

Saeed, Nasser A.; Kandil, Ali

doi:10.1007/s11071-019-05256-3

Cited by 31 publications

(26 citation statements)

References 32 publications

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“…By solving the obtained nonlinear algebraic equations (i.e., Equation ( 21)) in terms of different system parameters utilizing σ 1 or f as a bifurcation control parameter, one can obtain different response curves given Section 2.3. Moreover, the stability of the obtained solution can be explored by examining the eigenvalues of the Jacobian matrix of the righthand side of Equation (19). To derive the stability criteria, let a 10 , a 20 , ϕ 10 and ϕ 20 is the steady-state solution of Equation (20), while a 11 , a 21 , ϕ 11 and ϕ 21 is a small perturbation about that steady-state solution.…”

Section: Steady-state Vibration and Stability Investigationsmentioning

confidence: 99%

“…Numerical simulations for temporal oscillations of the main system and the connected controllers according to Figure 16 for three different values of the excitation frequency Ω (i.e., Ω = 0.9, 1, 1.1) are illustrated in Figures 17,18,and 19,respectively. Figure 17 simulates the main system temporal oscillations before and after control according to Figure 16 when Ω = 0.9.…”

Section: Comparison Between the Ppf And Appf Controllersmentioning

confidence: 99%

“…Syed [16] introduced a comparison between the positive position feedback controller and negative velocity feedback controller to control the nonlinear oscillation of a flexible link manipulator. Saeed et al [17][18][19] applied the PPF controller to suppress the lateral vibrations and the corresponding whirling motion of the rotating machinery. The authors reported that the PPF controller can mitigate the rotating shafts lateral vibration close to zero when the controller's natural frequency is tuned to have the same value as the shaft spinning speed.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

et al. 2021

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The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

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Section: Steady-state Vibration and Stability Investigationsmentioning

confidence: 99%

Section: Comparison Between the Ppf And Appf Controllersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

et al. 2021

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“…Therefore, AMBs is an inherently nonlinear system, where every design for AMBs has its own dynamical behaviors. Therefore, many research articles have been dedicated to explore the nonlinear dynamics for different configurations of Rotor-AMBs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Ji et al [1] explored the nonlinear dynamical behaviors of the four-pole Rotor-AMBs.…”

Section: Introductionmentioning

confidence: 99%

Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

et al. 2020

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Rotor active magnetic bearings system is the most efficient supporting technique of high-speed rotating machinery. This work aims to explore the dynamical behaviors of the 6-pole rotor active magnetic bearings system for the first time. Two different control strategies are introduced to mitigate the considered system lateral vibrations and the corresponding whirling motions. The first control technique (Radial control) is suggested such that the attractive magnetic force in each pole is proportional to both the radial displacement and radial velocity of the rotating disk toward that pole. The second control strategy (Cartesian control) is proposed such that the controlled magnetic force in each pole is designed to be proportional to both the cartesian displacement and cartesian velocity of the rotating disk in two perpendicular directions. Based on the proposed control strategies, two nonlinear dynamical models are derived and then analyzed by applying perturbation methods. Different response-curves and bifurcation diagrams are plotted utilizing the disk spinning-speed and the disk eccentricity as bifurcation control parameters. The main obtained analytical and numerical results illustrated that the considered system can perform a circular forward whirling motion only under the first control technique, while four whirling modes (that are forward whirling , backward whirling, both forward and backward whirling, and oscillation along a straight line) are noticed in the second control method depending on the disk spinning speed. Moreover, it is found that the radial control method is robust against the system instability than the cartesian control one, especially at large disk eccentricity. However, the cartesian control method could exhibit a vibration suppression efficiency higher than the radial control one at small disk eccentricity.

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“…In recent years, the rise of deep learning has provided a good solution to this kind of problem, and scholars in various countries have researched it. Of which, there are many studies on the control of electromagnetic bearing targeting at rotor control and optimization [4][5][6]. Reddy et al (2018) proposed a self-designed fuzzy logic controller based on an adaptive multi-population genetic algorithm to control active electromagnetic bearing [7].…”

Section: Introductionmentioning

confidence: 99%

Control of hybrid electromagnetic bearing and elastic foil gas bearing under deep learning

Sun

2020

PLoS ONE

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The hybrid electromagnetic and elastic foil gas bearing is explored based on the radial basis function (RBF) neural network in this study so as to improve its stabilization in work. The related principles and structure of hybrid electromagnetic and elastic foil gas bearings is introduced firstly. Then, the proportional, integral, and derivative (PID) bearing controller is introduced and improved into two controllers: IPD and CPID. The controllers and hybrid bearing system are controlled based on the RBF neural network based on deep learning. The characteristics of the hybrid bearing system are explored at the end of this study, and the control simulation research is developed based on the Simulink simulation platform. The effects of the PID, IPD, and CIPD controllers based on the RBF neural network are compared, and they are also compared based on the traditional particle swarm optimization (PSO). The results show that the thickness, spread angle, and rotation speed of the elastic foil have great impacts on the bearing system. The proposed CIPD bearing control method based on RBF neural network has the shortest response time and the best control effect. The controller parameter tuning optimization starts to converge after one generation, which is the fastest iteration. It proves that RBF neural network control based on deep learning has high feasibility in hybrid bearing system. Therefore, the results provide an important reference for the application of deep learning in rotating machinery.

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Lateral vibration control and stabilization of the quasiperiodic oscillations for rotor-active magnetic bearings system

Cited by 31 publications

References 32 publications

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

Control of hybrid electromagnetic bearing and elastic foil gas bearing under deep learning

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