Active Magnetic Bearing Rotor System Research Articles

Filter Cross-Feedback Control for Nutation Mode of Asymmetric Rotors With Gyroscopic Effects

The nutation mode is an obstacle to the stability improvement of a magnetic-bearing-supported rotor system with significant gyroscopic effects. This article explores a parameter design method of the filter cross feedback for the nutation mode suppression of asymmetric rotor systems supported by active magnetic bearings (AMBs). First, the coupled multi-input multi-output model of the asymmetric AMB rotor system is converted into an equivalent complex single-input single-output model. The equivalent transformation aims at easing the system analysis and extending the classical stability criterion to the complex coefficient frequency domain. Then, the double-frequency bode plot and the Nyquist criterion are used for analyzing the stability of the AMB rotor system and designing the parameters of the filter cross feedback exactly. Simulation results show that the designed filter cross-feedback method has a good performance for suppression of the nutation mode. Finally, the power spectrum level of the nutation component is below $-$ 60 dB after the filter cross-feedback method is implemented in the controller of a large-scale magnetically suspended turbomolecular pump. The experimental results validate the effectiveness of the proposed method.

Active Surge Control for Magnetically Suspended Centrifugal Compressors Using a Variable Equilibrium Point Approach

Surge is one of the main rotor dynamic instabilities limiting the operation of centrifugal compressors. This paper proposes an active surge control scheme for magnetically suspended centrifugal compressors using a variable equilibrium point approach. Multiple uncertainties caused by magnetic air gap adjustment are considered for the active magnetic bearing (AMB) control systems. By using the combination of an analytical model and a finite-element method, the perturbation of bearing force parameters, including the force-current factor and the force-displacement factor, is analyzed. The model uncertainties caused by the perturbation of the power amplifier parameters are identified through the online frequency sweep excitation. Based on the uncertainty analysis of the AMB control system, a μ-synthesis-based controller is designed for the axial magnetic bearing system to suppress the vibration caused by surge. The experiments demonstrate that the proposed method can suppress surge and improve the reliability of the system by using automatic magnetic air gap adjustment of the AMB-rotor system.

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

This work aims to improve the vibrational behaviors of the rotor-active magnetic bearings (AMB) system via proposing a new control methodology for such lateral vibrations. Accordingly, the rotor-AMB system model is modified by integrating the conventional proportional–derivative (PD) controller along with the positive position feedback (PPF) controller to the considered system. The control currents in the rotor-AMB system are designed to become a combination of two control signals: One of them is generated via the PD controller, and the other one comes from the PPF controller. Based on the suggested control method, the whole dynamical system model is derived and then analyzed by the multiple time-scale perturbation method. Then, the bifurcation diagrams of both the spinning speed and rotor eccentricity response curves are investigated before and after control. The obtained analytical results showed that the integrating of the PPF controller to the considered system could mitigate the system lateral vibration close to zero. Moreover, the system quasiperiodic motions have been stabilized after control and the sensitivity to the initial conditions has eliminated. Finally, numerical validations for the obtained analytical results are performed that illustrated an excellent agreement with the analytical ones.

Displacement Self-Sensing Method for AMB-Rotor Systems Using Current Ripple Demodulations Combined With PWM Command Signals

The self-sensing magnetic bearing technology offers significant cost savings and the potential advantages for dynamics performance due to its fundamental sensor-actuator collocation. Based on the active magnetic bearing (AMB) driven by a 2-level pulse width modulation (PWM) switch power amplifier, an analog circuit was designed to estimate the rotor position through extracting the fundamental component information of the current ripples. This paper addresses two key challenges on the displacement self-sensing of AMB-rotor systems: the one is how to accurately extract the fundamental frequency component from the current ripple, and another one is proposing a PWM duty cycle cancellation method to enhance the detecting accuracy of rotor displacement. First, the basic self-sensing principle of demodulation approach is presented. Second, mathematical description of PWM duty cycle cancellation method using driving voltage combined with PWM command signals was deduced. Third, the band-pass filter was designed for extracting the fundamental frequency components of ripple current, and the full-wave rectification was designed for detecting the peak envelope of the fundamental component, and the low-pass filter was designed for filtering out high-frequency noise. Finally, experiments were carried out on a magnetic suspension turbo-molecular pump to evaluate the static and dynamic performance of the designed self-sensing system. The experiment results show that the rotor can be well suspended in a static state, and its speed can reach 6000 rpm. The experiments demonstrate that the designed self-sensing system has the ability to meet the requirement of dynamic performance and stability margin.

Unbalance response of a magnetic suspended dual-rotor system

The magnetic suspended dual-rotor system applied in more electric aero-engine can eliminate the wear and lubrication system of mechanical bearings and solve the vibration control issue of system effectively, which provides the possibility to improve the performance of aero-engine significantly. This research focuses on the unbalance response of the magnetic suspended dual-rotor system. First, a structure of dual-rotor system supported by two active magnetic bearings and two permanent magnetic bearings is presented. With proportional derivative (PD) control adopted, the bearing characteristics of active magnetic bearings are modeled as the equivalent stiffness and equivalent damping, and the permanent magnetic bearings are modeled as elastic support. Then, the Riccati transfer matrix method with good numerical stability is used to establish the model of the magnetic suspended dual-rotor system unbalance response. Subsequently, the validity of the present formulation has been tested against some known results available in literature and the simulation results obtained by finite element method (FEM). Finally, the dynamic characteristics of the unbalance response are investigated. The results reveal that the influence of the inner rotor imbalance excitation on the magnetic suspended dual-rotor system unbalance response is much larger than that of the outer rotor imbalance excitation. In addition, the critical speeds increase with the proportional coefficient, and the derivative coefficient can affect the amplitudes of the unbalance response, but not critical speeds. From the perspectives of the maximum bearing capacity and maximum displacement of active magnetic bearing-rotor system, the possibility of the magnetic suspended dual-rotor system safely crossing the critical speeds of the first three orders is investigated.

Fault Diagnosis of Active Magnetic Bearing⁻Rotor System via Vibration Images.

As important sources in fault diagnosis of rotary machinery, vibration signals are usually processed in the time or frequency domain as features to distinguish different classes of faults. However, these kinds of processing methods always ignore the corresponding relations among multiple signals, resulting in information loss. In this paper, a new fault description strategy named vibration image is proposed, based on which three new kinds of features are extracted, containing coupling information between different channels of vibration signals. Additionally, a new feature fusion method called two-layer AdaBoost is designed to train the fault recognition model, which avoids overfitting when the dataset is not large enough. Features based on vibration images combined with two-layer AdaBoost are adopted to diagnose faults of rotary machinery. Taking an active magnetic bearing-rotor system as the experimental platform, a dataset with four classes of faults is collected and our algorithm achieves good performance. Meanwhile, features based on vibration images and two-layer AdaBoost are both proved to be efficient separately.

Unbalance Compensation and Automatic Balance of Active Magnetic Bearing Rotor System by Using Iterative Learning Control

Active control is one of the most important advantages of active magnetic bearing (AMB), and also can be used to suppress the imbalance of AMB rotor system (AMB-RS). This paper aims at dealing with periodic vibration problem caused by unbalanced force existing in AMB-RS as the rotor spins. Firstly, with the advantages of iterative learning control (ILC) over repetitive problems, a novel ILC algorithm based on the system information of the iteration before last iteration is put forward to achieve parallel computing of real-time control, real-time acquisition and signal extraction in AMB digital control system (DCS). Then, two compound control modes are proposed on the basis of AMB closed-loop feedback control system (CFCS), one is a parallel compound control mode (PCCM) that is used to achieve unbalance compensation, the other one is a serial compound control mode (SCCM) that is used to achieve automatic balance, and corresponding compound control systems are designed on the basis of an AMB experimental system. Finally, numerical simulation and experimental research are carried out, and the results show that the control methods proposed in this paper have significant control effect on the periodic vibrations produced by the unbalanced force of AMB-RS. Therefore, the research achievements can provide theoretical references and experimental basis for the further application of AMB in the high-precision and high-speed fields.

Average power balance method for power failure compensation control of high‐speed turbo molecular pump with AMB system

High-speed permanent magnet motors supported by an active magnetic bearing (AMB) have been widely used in the industrial field. However, the AMB-rotor system will lose its magnetic force if the mains power fails, and high-speed rotor will crash the stator severely and bring a fatal damage to the system. To solve this problem, a power failure compensation control method based on the average power balance control was proposed. Firstly, a motor energy feedback model was proposed. Secondly, a non-linear controller with double closed loops was designed. And the Lyapunov function was built and analysed to ensure the system stability. Finally, a series of experiments based on the high-speed magnetically suspended vacuum turbo molecular pump was carried out. The experiment results verified the validity and feasibility of the proposed method, and the safety of the AMB system was improved greatly.

A Multifrequency Disturbances Identification and Suppression Method for the Self-Sensing AMB Rotor System

The self-sensing active magnetic bearing (SAMB) rotor systems own the benefits of reduced cost and better system integration, from the substitution of rotor displacement estimation for external sensors. However, the self-sensing errors between the real and estimated rotor displacement, together with the unbalance force and sensor runout, will act as disturbances that affect the SAMB rotor system, inducing current fluctuations and rotor vibrations. This paper presents a disturbance suppression method for the modulation-type SAMB rotor systems, in which both the amplitude and phase of disturbances are identified and real-time updated. A lumped multifrequency disturbances model is established. And a disturbances identification algorithm with object function value-based step vectors is proposed. The system stability and method convergence conditions are analyzed. The convergence rate, overshoot and antinoise capacity of the method are verified through simulations. In the end, the effectiveness and performance of the suppression method are validated through steady state and varying rotational speed experiments on a 4-DOF radial SAMB rigid rotor platform.

Sliding mode control with deep learning method for rotor trajectory control of active magnetic bearing system

Active magnetic bearing (AMB) is competent in rotor trajectory control for potential applications such as mechanical processing and spindle attitude control, while the highly nonlinear and coupled dynamic characteristics especially in the condition of rotor large motion are obstacles in controller design. In this paper, a controller of AMB is proposed to achieve rotor 3D trajectory control. First, the dynamic model of the AMB-rotor system containing a nonlinear electromagnetic force model is introduced. Then the DCNN-SMC (deep convolutional neural network - sliding mode control) controller is proposed. Sliding mode control is used to achieve the tracking control with high robustness and responsiveness, and a deep convolutional neural network based on deep learning method is designed to compensate the uncertainties of the system. Finally, simulation of a 5-degree of freedom (DOF) system on various trajectories demonstrates evident control effect of the proposed controller in precision and significant effect of DCNN based on deep learning method in compensation control.

Unbalance Compensation for Active Magnetic Bearing Rotor System Using a Variable Step Size Real-Time Iterative Seeking Algorithm

It is necessary to reduce the vibration of rotors supported on active magnetic bearings (AMBs) with high displacement precision requirement in operation. An unbalance compensator for an AMB-rigid rotor system is studied. The dynamic model of an AMB-axially symmetric rigid rotor system was first established. Then, the specific form of compensating currents in the AMBs was obtained. At last, an unbalance compensator based on real-time variable step size (VSS) polygonal iterative seeking algorithm for equivalent unbalance coefficients of the rotor at the AMBs positions was proposed. With the compensator, the AMBs produce additional forces that are of same magnitudes but opposite phases as the equivalent unbalance forces at the AMBs positions to reduce the rotor vibration. Since the equivalent unbalance coefficients, which represent the equivalent imbalance of the rotor at the AMBs positions, are independent of the rotating speed, thus, the compensator is suitable for application in both steady state and varying-speed operations. With the VSS method, both the accuracy and the convergence rate of the identification algorithm could be realized. Numerical simulations and experiments confirmed the effectiveness of the proposed method for suppressing the unbalance vibration of the AMB-rotor system in steady states and varying-speed operations.

Tracking Compensation Control for Nutation Mode of High-Speed Rotors With Strong Gyroscopic Effects

Due to the strong gyroscopic effects, the stable control for the nutation vibration of high-speed rotors is an important concern in magnetically suspended control moment gyros (MSCMGs). This paper addresses the two key challenges on the nutation mode control of AMB-rotor systems: using the complex coefficient representation method to obtain the accuracy nutation frequency, and proposing an adaptive tracking approach to ensure stable operations over the entire speed ranges. In order to improve the phase margin of the nutation mode, this paper proposes a nutation mode tracking compensation method based on the cross-feedback-control scheme. First, the analytical calculation for the nutation frequency of the high-speed rotor under the closed-loop condition is carried out. Then, the compensation control method using an adaptive tracking filter in the nutation control path is proposed to provide an adequate damping for the nutation mode. Simulation results show that the nutation mode tracking compensation provides a greater phase lead for the nutation mode compared to the conventional nutation mode filtering approach. Finally, the experimental results on a developed double-gimbal MSCMG prototype validate the effectiveness of the proposed method.

The Terminal Sliding Mode Control of 4-DoF Active Magnetic Bearing Rotor System

This paper deals with the application of terminal sliding mode control theory of 4 degree of freedom rigid Active Magnetic Bearing System (AMB). The virtual control inputs are introduced, and the controller is designed by Lyapunov stability. The actual control input currents are observed by the relationship between the virtual and the actual input current, to achieve a rapid and stable magnetic levitation rotor. The simulation results show that the proposed scheme can suppress the disturbance effectively, and the system is fast and stable at the equilibrium position because the initial state of the system is on the sliding surface.

Dynamic Analysis for the Rotor Drop Process and Its Application to a Horizontal Rotor-Active Magnetic Bearing System in Helium Gas

The high-temperature gas-cooled reactor pebble-bed modular (HTR-PM) has been proposed by the Institute of Nuclear and New Energy Technology of Tsinghua University, in which the active magnetic bearings (AMBs) are equipped to support the high-speed rotor in the helium circulator system. In the case of AMB failures, emergencies, or overload conditions, the auxiliary bearing is applied as the backup protector to provide temporary mechanical support and displacement constraint for the dropping rotor. A detailed dynamic model is established to reveal the behavior of the dropping rotor. This model is able to describe the rotor displacement and inclination around each axis. The left and right rotor orbits are revealed. Dropping experiments are also carried out to reveal the actual behavior of the dropping rotor in helium. The predicted and experimental results will benefit further study, design, and application of the auxiliary bearing in HTR-PM helium circulator.

Vibration Suppression by Seeking Unbalance Mass-radius Product in Active Magnetic Bearing-rotor System with Varying Speed Condition

Vibration Suppression by Seeking Unbalance Mass-radius Product in Active Magnetic Bearing-rotor System with Varying Speed Condition

Identification of dynamic parameters of active magnetic bearings in a flexible rotor system considering residual unbalances

Active magnetic bearings (AMBs) support rotors using electromagnetic forces rather than mechanical forces. It is necessary to identify the AMB force coefficients (equivalent stiffness and damping) since they play key roles in the rotordynamic analysis. The identification is usually performed by analyzing the unbalance response. However, the presence of unknown residual unbalances reduces the identification accuracy and a rigid rotor model is only valid when the rotating speed is far below the first bending critical speed. Therefore, this paper proposes an identification algorithm to estimate the stiffness and damping parameters for a flexible rotor AMB system in the presence of unknown residual unbalances by using two independent unbalance response data sets. The proposed algorithm is first evaluated by numerical calculation for accuracy and then applied experimentally in the identification of a flexible rotor AMB system operating at speeds ranging from 3,000 rpm (50 Hz) to 30,000 rpm (500 Hz). The identification results are verified in the end.

Improving Dynamic Response of AMB Systems in Control Moment Gyros Based on a Modified Integral Feedforward Method

During gimbal maneuvering, the dynamic characteristics of the active magnetic bearing (AMB) rotor system is an important concern for the applications of the magnetically suspended double-gimbal control moment gyro (MSDGCMG). Both the static torques caused by the gimbal motions and the dynamic torques by the rotor twisting motion will have an impact on the dynamic performance of the magnetically suspended high-speed rotor. This paper explores a modified current integral feedforward (CIF) control scheme to improve its dynamic response. Using a dynamic regulator, the CIF method is applied to supply the static torque by the permanent magnets and simultaneously improve the stability margin of the AMB rotor system. Then, the multiple compensation method is proposed to compensate the dynamic torque to further improve the response speed. The influence of rotor tilting on the output torque precision of MSDGCMG is also analyzed. Finally, the experimental results on a developed MSDGCMG prototype validate the effectiveness of the proposed method. The modified CIF combined with dynamic torque compensation resulted in a step response settling time of 0.13 s as compared with the traditional method with a settling time of 2.5 s.

A Novel Cross-Feedback Notch Filter for Synchronous Vibration Suppression of an MSFW With Significant Gyroscopic Effects

To effectively suppress the synchronous vibration torques for a magnetically suspended rotor (MSR) with significant gyroscopic effects and serious coupling dynamics, a novel cross-feedback notch filter is proposed in this paper. First, the coupled multi-input-multi-output active magnetic bearing rotor system is converted into an equivalent complex single-input single-output (SISO) system. The equivalent transformation aims at easing the controller design and extending the classical stability criterion to the complex coefficient frequency domain. Then, the principle and implementation of the proposed scheme used for synchronous vibration suppression over an entire rotational speed range is analyzed in details. The performance compared with the conventional decentralized notch filter is investigated. Moreover, the closed-loop stability, which based on the equivalent complex SISO system and complex-coefficient stability criterion is given. Experimental results on a magnetically suspended flywheel demonstrate the significant effect of the proposed method on both synchronous vibration suppression and stability preservation.

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

Abstract In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton’s second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.

Power Consumption Reduction for Magnetic Bearing Systems During Torque Output of Control Moment Gyros

The power consumption of actuators is an important concern for the spacecraft attitude control system. This paper presents a power consumption reduction method for permanent magnet biased active magnetic bearings (AMBs) during torque output of control moment gyros (CMGs). For simplicity of analysis, a simple single degree-of-freedom (DOF) AMB system undergoing an external load force is first presented. An operating point adaptive regulation based on current-integral feedforward method is proposed to realize the coil current reduction with a reference position offset. Then the proposed method is extended to the case of the 4-DOF AMB-rotor system. In order to improve the dynamic response of the current-integral output, a dynamic regulator is incorporated into the feedforward loop. The parameter range for stability and dynamic properties of the AMB-rotor system with and without using the dynamic regulator have also be compared and discussed. Finally, experimental results on a developed magnetically suspended double-gimbal CMG prototype validate the effectiveness of the proposed method.