Active Magnetic Bearing Rotor System Research Articles

Nonlinear Dynamics and Motion Bifurcations of 12-Pole Variable Stiffness Rotor Active Magnetic Bearings System under Complex Resonance

Nonlinear Dynamics and Motion Bifurcations of 12-Pole Variable Stiffness Rotor Active Magnetic Bearings System under Complex Resonance

Suppression of synchronous current of active magnetic bearings considering radial displacement inconsistency

Suppressing rotor synchronous current is vital for achieving precise control in active magnetic bearing (AMB) rotor systems. The displacement amplitude inconsistency in orthogonal channels presents new challenges for synchronous current suppression. This paper proposes an improved complex least mean square (CLMS) algorithm with error compensation to effectively mitigate rotor unbalanced vibration. Firstly, a dynamic model of the AMB-rotor system with an unbalanced mass is established, and the displacement amplitude inconsistency within the orthogonal channels of the radial magnetic bearings is analyzed. Subsequently, the rotor displacement signal from the orthogonal channels is converted into a complex plane signal. By calculating the negative sequence weight component, the displacement signal is reconstructed, and an error compensation channel based on the CLMS is introduced to enable real-time tracking and compensation of displacement amplitude inconsistencies in the orthogonal channels. Moreover, system stability across the full speed range is ensured through the application of the phase compensation angle method. Finally, experimental validation on a magnetic levitation molecular pump prototype confirms the effectiveness of the proposed algorithm.

Robust Controller Development via Iterative Model Updating for Active Magnetic Bearing Rotor Systems

Robust Controller Development via Iterative Model Updating for Active Magnetic Bearing Rotor Systems

Proportional-derivative control and motion stability analysis of a 16-pole legs rotor-active magnetic bearings system

This paper analyzes the motion stability of a 16-pole rotor-active magnetic bearings (rotor-AMB) system and investigates the complex vibrations under a proportional-derivative (PD) controller. First, electromagnetic theory and Newton’s second law are applied to derive the two-degree-of-freedom differential governing equations for the 16-pole rotor-AMB system, incorporating the PD control terms. The resulting differential equations include parametrically excited, quadratic nonlinear, and cubic nonlinear terms. Subsequently, the multiple time scales perturbation analysis method is performed on the obtained governing equations, yielding four-dimensional averaged equations in both Cartesian and polar coordinates. Finally, numerical simulations including the amplitude–frequency response characteristics, motion trajectories, energy–amplitude relationships, as well as bifurcation and chaotic motion of the system are studied. The results indicate that the PD controller affects the softening and hardening spring characteristics of the system and has significant control effects on the system’s amplitude, energy, and stability. Additionally, increasing the differential gain coefficient [Formula: see text] can change the system’s motion from chaotic to periodic.

Finite element simulation of iron losses for an Active Magnetic Bearing–Rotor system constructed of Hiperco laminations

Iron losses appear in Active Magnetic Bearings (AMBs) mostly because of the rotor's movement, but also because of the fluctuation of the control current in the stator's coils. They can be divided into three categories: the hysteresis losses, the eddy current losses and the excess losses and while they depend significantly on the rotating speed and the magnetic flux density applied on the poles, the most contributing factor is the magnetic material used for the core. In this paper, a 2-D Finite Element Method transient model is used to simulate the rotational motion of the shaft inside the AMB and calculate the iron losses that occur due to the alternating magnetic flux inside the rotor, as well as the mechanical load capacity on the vertical direction of the AMB for each case. A simulation is carried out, at first, for a constant control current value and a speed range of 0–30,000 rpm, followed by a second one, for constant rotational speed and control current values 0–0.5 A. Geometry remains the same for all simulations. When it comes to the materials selected for the stator and the rotor, the cases of Hiperco 27, Hiperco 50 and Hiperco 50 HS laminations are tested. The iron losses of the three alloys are compared to the losses of 3 % silicon-iron. The results show that the three iron cobalt alloys have significantly lower losses than the silicon iron for the same AMB size and rotor's speeds. Hiperco 50 has the lowest loss among the three Hiperco alloys, while Hiperco 50 HS provides slightly higher mechanical load capacity under the same operating conditions.

Sliding model control of active magnetic bearing rotor system based on state observer

This paper addresses a novel sliding mode control based on state observer for active magnetic bearing rotor system. Firstly, the state-space model of a radial AMB rotor system is established with considering unbalance disturbance and gyro effect for a vertical flywheel energy storage system. Then a sliding mode function and switching surface are constructed based on an observer. Meanwhile, a separation and decoupling strategy based on Finsler’s lemma is proposed. Through this method, the constraint relationship between the controller gain, active magnetic bearing matrices and the Lyapunov variables is eliminated. After that a method for chattering reduction in the sliding-mode controller is raised. Relied on these techniques, new sufficient conditions for the stability of AMB rotor system are given in the framework of linear matrix inequalities. Finally, the effectiveness of the proposed sliding mode controller is validated on the experimental platform of the flywheel energy storage system.

Self-Calibration Method of Displacement Sensor in AMB-Rotor System Based on Magnetic Bearing Current Control

Displacement sensors are the key components of the active magnetic bearing rotor (AMB-rotor) system to realize the closed-loop control of the rotor displacement. The aging and failure of the displacement sensor components will lead to the changes of sensor sensitivity and zero point, which can directly affect the suspension performance of the rotor and even cause the instability of the AMB-rotor system. Therefore, it is significant to calibrate the sensor regularly. This paper proposes a self calibration method based on the detection and control of the magnetic bearing current without additional calibration equipment and hardware circuits. In addition, a new control structure of the AMB-rotor system is proposed to achieve efficient calibration, which can control the rotor displacement based on current following control method. Finally, experimental results verify the effectiveness of the proposed method on the displacement sensor calibration.

Study on the Mechanism and Suppression of Harmonic Vibration of AMB-Rotor System

The AMB-rotor system is complex and has strong coupling characteristics, which allows multi-harmonic disturbances to enter the system through different ways to produce vibrations with rich spectrum components, which has a great influence on the improvement of micro-vibration accuracy of the rotor system. To further achieve active control of the micro-vibration in the AMB-rotor system, firstly, the mechanism of multi-source disturbance is analyzed according to the working principle of the AMB-rotor system, and the mathematical and physical relationship between the mechanism of disturbance generation and the inducement is deeply studied. Then, the structure of a novel adaptive notch filter, the method of adaptive frequency estimation and analysis of harmonic current suppression in the AMB system are presented. Finally, simulation and experimental research using an MSCMG system demonstrate the feasibility of the proposed method regarding the elimination of harmonic control current.

Self-Identification and Balancing for AMB-Rotor System of Turbomolecular Pumps

Self-Identification and Balancing for AMB-Rotor System of Turbomolecular Pumps

Synchronous Vibration Force Suppression of Magnetically Suspended CMG Based on Modified Double SOGI-FLL

The mass imbalance of the rotor will produce the synchronous vibration force that is transmitted to the magnetically suspended control moment gyroscope (MSCMG) through the magnetic levitation stator, which affects the imaging performance of the satellite. The suppression of the synchronous vibration force needs the speed signal. In order to solve the synchronous vibration force of the MSCMG when the speed measurement sensor fails, this paper proposed an modified double second-order generalized integral frequency-locked loop (SOGI-FLL) method, which uses the frequency of the disturbance signal generated through the mass imbalance of the rotor to adaptively estimate the rotor speed and suppress the synchronous vibration force generated by the active magnetic bearing system. The phase compensation is introduced to ensure the stability of the system in full frequency band. The electromagnetic force is directly used as the input signal of the control algorithm to achieve zero magnetic force control. Simulation and experimental are carried out, and the results are given to prove that the algorithm proposed in this paper can accurately estimate the rotation speed and achieve the vibration force suppression in the full rotation speed range. It is of great significance for the high-precision control of the active magnetic bearing rotor system.

Synchronous disturbance suppression of active magnetic bearing rotor systems using variable period adaptive control algorithm

This paper aims to investigate the issue of suppressing synchronous vibration in active magnetic bearing (AMB) systems. The rotor mass imbalance is a challenging problem for the AMB system, which will cause synchronous vibration and severely affect the system stability and safety. However, existing algorithms based on the iterative feed-forward control strategy find it difficult to simultaneously ensure system’s stability and competent convergence performance. They struggle to maintain tolerable robustness within the system operating bandwidth. This paper proposes a variable period adaptive control algorithm to address these challenges. The overall control scheme can achieve current and displacement elimination separately by switching control structures and is applicable to variable speed conditions. This algorithm can adaptively adjust the iteration period based on rotational speed to ensure both splendid convergence performance and system dynamic performance. Furthermore, this work employs the Lyapunov method to analyze the algorithm’s asymptotic stability and provides a lookup table for algorithm parameters. This could significantly enhance the robustness and stability of the algorithm within the system operating bandwidth. Finally, this methodology has proven to be effective and superior in simulations and experiments.

Division Linearization Zero-Bias Current Control for AMBs–Rotor System With Uncertainties and Saturation

Traditional constant current sum (CCS) distribution strategy is always employed in the nonlinear active magnetic bearing (AMB) system control for linearization, but the bias current in CCS causes extra power consumption and limits the AMBs' capacity. In this paper, a division linearization zero-bias current (DLZBC) distribution strategy is proposed as a substitution for CCS strategy. Under this strategy, a linear active disturbance rejection controller (LADRC) with a static anti-windup compensator (SAWC) is applied to deal with model uncertainties and current saturation. For different types of AMB-supported machines, a partial normalized nonlinear model is established. Subsequently, the performance of the CCS strategy is analyzed, and a DLZBC strategy is presented to reduce the power consumption and transform the system into a linear plant with a lumped uncertain parameter. Afterward, a LADRC is designed to enhance robustness, whose parameters are chosen according to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu -$</tex-math></inline-formula> synthesis framework and are convenient for adjustment practically. For anti-saturation, a SAWC is developed to help the system escape quickly from current saturation and enlarge the stability domain of the saturated system. Comparative simulations and experiments results show that the proposed control method can significantly reduce power consumption and achieve good response in AMB-rotor system.

Stiffness Compensation Control for Centrifugal Compressors Based on Online Parameter Identification of Magnetic Bearings

Significant temperature rise will degrade the stability of the active magnetic bearing (AMB) rotor system, which is an obstacle to the industrial implementation of magnetically suspended centrifugal compressors (MSCCs) with high power density. Aiming to ensure stable operation of the suspended rotor at high temperatures, this paper presents a stiffness compensation method based on online parameter identification. First, the linearized model at the operating point is derived through the establishment of a magnetic circuit model. The analysis of the temperature factor of bearing stiffness parameters is conducted. Then, the forgetting factor recursive least squares online identification algorithm is employed to obtain the coil resistance affected by bearing temperature in real time. Finally, a stiffness compensation control scheme is designed based on the identification results and current rotor displacement, in combination with series and feedback compensation to apply the same electromagnetic force to the rotor during temperature rise. Simulation and experimental results validate that the proposed method can effectively suppress the low-frequency fluctuation and guarantee the stability of the AMB rotor system.

Nonlinear dynamics of two dimensional rotor-active magnetic bearing system with generalized-pole legs: stability state diagram and control strategy

Nonlinear dynamics of two dimensional rotor-active magnetic bearing system with generalized-pole legs: stability state diagram and control strategy

Feedback Linearization and Robust Control for Whirl Mode With Operating Point Deviation in Active Magnetic Bearings-Rotor System

The whirl mode, seriously affecting the stability of active magnetic bearings (AMBs), is a hot issue in the AMBs-rotor system. This article stresses a whirl mode problem accompanied by the operating point deviation when the magnetically suspended control moment gyro outputs torque. A feedback linearization controller is proposed to decouple the whirl mode effects from the system state-space representation. A robust controller for uncertain systems is also used to solve the operating point deviation problem. First, the AMBs-rotor system's state-space representation containing the whirl mode terms is described. Next, a system uncertainty caused by the operating point deviation is discussed. Then, a feedback linearization controller combined with a robust controller for uncertain systems is designed. Finally, simulations and experiments for validity verification are presented, and comparative experiments with a PID controller and a robust controller are shown and compared in this article.

Dynamic analysis and vibration control of a rotor-Active magnetic bearings system with base motion

High-speed and high-precision rotating machinery is widely applied in industry, which promotes the rapid development of non-contact bearings represented by active magnetic bearings (AMBs). The rotor-AMBs system is usually installed on the base. Due to the base motion, it affects the dynamic characteristics of the rotor-AMBs system. In this paper, the dynamic analysis of the rotor-AMBs system with base motion is carried out. The dynamic model of the system with base motion is first derived, and the control model is then established. The influence of the inherent property of the base, the excitation mode of the base motion, and the control method for the rotor-AMBs system are analyzed with numerical simulation. In addition, the combination of feedforward control and PID control is employed to eliminate the vibration disturbance caused by the base motion and improve the suspension accuracy of the rotor. The experimental results show that the proposed hybrid control can effectively reduce the vibration of the rotor-AMBs system with base motion.

A General Double-Input Synchronous Signal Processor for Imbalanced Vibration Mitigation in AMB-Rotor Systems

Imbalanced vibration is an urgent yet challenging problem in active magnetic bearings (AMBs) rotor manufacturing due to the rotor mass imbalance effect. The virtue of active control in AMB systems lies in enabling substantial online mitigation of imbalanced vibrations. However, in practice, due to the lack of speed sensors in most of the existing AMB-rotor systems, efficient rotational speed feedback is still on the way. As a remedy, this article proposes a rotational speed sensor-free synchronous signal processor (SSP) with the double inputs: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$</tex-math> </inline-formula> -and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$</tex-math> </inline-formula> -axes direction displacement measurements of radial AMBs. The proposed SSP is capable of estimating the rotational speed and accordingly generating synchronous signals of the imbalanced vibrations by filtering noise in both directions. Such signals are afterward implemented as a feedforward compensator for eliminating the periodical imbalance effects. With the assistance of the Lyapunov theory, the conditions of the proposed SSP method together with the feedforward imbalance compensator are derived to guarantee the stability of the closed-loop AMB-rotor system. Extensive experimental results substantiate the effectiveness and superiority of the proposed SSP method in terms of imbalanced vibration suppression.

Influence of displacement sensor runout on active magnetic bearing-rotor system and control analysis

In the active magnetic bearing (AMB)-rotor system, a displacement sensor is one of the indispensable components. It detects the displacement of the rotor in real time and feeds back to the control system to realize the stable suspension of the rotor. However, due to electromagnetic interference, unstable power supply, poor grounding, and uneven rotor surface, the signal runout of the displacement sensor can often occur, resulting in rotor vibration. Given the above problems, this paper establishes the control model of the AMB-rotor system, lists three typical sensor runout signals, then analyzes the influence of different types of sensor runout on the system, and discusses the control methods under different sensor runout conditions. The research results have a specific guiding significance for vibration control of the maglev rotor under sensor runout influence.

Unbalanced Magnetic Pull Disturbance Compensation of Magnetic Bearing Systems in MSCCs

Unbalanced magnetic pull (UMP) disturbance seriously affects the stable operation of the magnetically suspended rotor (MSR) system. This article proposes an UMP disturbance suppression method based on a linear extended state observer (LESO) and adaptive peak filter (APF). The cascade structure of LESO and APF can accurately estimate the UMP disturbance in the whole speed range. First, the dynamic model of the active magnetic bearing rotor systems is established and the UMP caused by the dynamic eccentricity in the MSR system is analyzed. Second, a third-order LESO and an APF are designed. The performance evaluation of the LESO indicates that estimation error of disturbance decreases with the increase of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega _{o}$</tex-math></inline-formula> , and the addition of APF can make UMP disturbance estimation unaffected by the high-frequency noise. After adding this method, the closed-loop system remains stable within the working rotation speed range. Finally, simulation results show that the UMP disturbance can be estimated and compensated. Experimental results validate the proposed method can well suppress the large vibration of the UMP on the rotor.

Dynamic Characteristics Analysis of Magnetic Levitation Rotor Considering Unbalanced Magnetic Pull

The working principle of the motor can cause unbalanced magnetic pull (UMP) between stator and rotor unavoidably. Previous research about nonlinear vibration excited by UMP was focused on the rotor supported by traditional mechanical bearings or gas bearings. However, the magnetic levitation rotor is particular due to the low rigidity provided by the active magnetic bearing (AMB). UMP amplifies rotor vibration in the resonant zone and further excites the nonlinear electromagnetic force, thus producing different vibration phenomena. The paper calculates rotor orbit, spectra analysis, and time-history plot with numerical methods and studies the influence of the rotation speed, eccentricity, key control parameters, and UMP on rotor dynamics in detail. Results illustrate displacement response spectra of the magnetic levitation rotor are quite different from previous research results. The appearing frequency components are inducted by universal formulas in this paper. Furthermore, research shows a slight adjustment of the control parameters affect significantly harmonic components and vibration characteristics. The research results have practical reference significance for fault diagnosis, feature recognition, and controller optimization of the AMB-rotor system.