Active Magnetic Bearing 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

Control the Axial Displacement of the Rotor Position with Load and No Load Condition in an Active Magnetic Bearing System

Control the Axial Displacement of the Rotor Position with Load and No Load Condition in an Active Magnetic Bearing System

Dynamic Analysis and PD Control in a 12-Pole Active Magnetic Bearing System

This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton’s second law, a two-degree-of-freedom control equation of the system, including PD control terms and gravitational effects, is constructed. This equation involves not only parametric excitation, quadratic nonlinearity, and cubic nonlinearity but also a more pronounced coupling effect between the magnetic poles due to the presence of gravity. Secondly, using the multi-scale method, a four-dimensional averaged equation of the system in Cartesian and polar coordinates is derived. Finally, through numerical analysis, the system’s amplitude–frequency response, motion trajectory, the relationship between energy and amplitude, and global dynamic behaviors such as bifurcation and chaos are discussed in detail. The results show that the PD controller significantly affects the system’s spring hardening/softening characteristics, excitation, amplitude, energy, and stability. Specifically, increasing the proportional gain can quickly suppress the rotor’s motion, but it also increases the system’s instability. Adjusting the differential gain can transition the system from a chaotic state to a stable periodic motion.

Measurement-based Dynamic Modelling in Levitated Active Magnetic Bearing Systems

Commissioning Active Magnetic Bearings (AMB) requires a well-designed control system to reject external disturbances while supporting process loads. An accurate dynamic model is essential for predicting responses to various excitations and disturbances, aiding in controller design. Current models for AMB commissioning are either nonparametric estimations, which provide limited information, or finite element models, which may not capture all system dynamics. This paper presents a black-box method to develop a parametric model that captures all dynamics within an AMB system using measurement data. Frequency domain measurement data was used to construct a segmental linear model to simulate dynamic interactions. The controller, actuation, and sensor components were derived from SKF Magnetic Mechatronics design calculations to isolate the rotor from the plant model and reconstruct the closed-loop system model. The frequency response of the identified rotor model was compared to direct measurements, and the resulting system model was compared to direct measurements of the closed-loop response. Results show that the proposed segmental AMB system model predicts frequency response with 97.9% accuracy compared to direct measurements. This model will be used to design control methods to improve AMB system performance.

Stability Assessment of the High-Speed Flywheel with AMBs on a Rotating Platform

With the continuous improvement of the performance and capabilities of spacecrafts, the application of active magnetic bearings (AMBs) has become a major focus in current research. The AMBs-flywheel system is not only responsible for attitude control but also provides the required energy during shadow periods. In magnetically suspended single gimbal control moment gyroscope (SGCMG), self-excited vibration caused by high-speed rotor rotation significantly affects the stability of the AMB system. The research focus lies in magnetically supporting the flywheel at high speeds with low power consumption to explore gyroscopic mechanics at ultra-high speeds and assess the corresponding stability. This study presents an assessment of the stability performance of a high-speed flywheel equipped on a single gimbal with an angular momentum of 75 Nm. To achieve ultra-high-speed operation under low driving power, a high-precise dynamic balance was performed followed by a novel unbalance control strategy of a radial and axial automatic balancing algorithm to suppress effectively synchronous vibrations due to nutation and precession. Corresponding experiments including static stable suspension experiments as well as low-speed, high-speed, and series-based stability assessments were conducted. Stable suspension at any speed ranging from 0 to 30,000 r/min was successfully implemented. The stability performance of the high-speed flywheel on a rotating platform at different gimbal speeds was verified, with a maximum speed reaching 31,200 r/min. The entire output torque process within the range of 30,000 r/min was revealed.

Model adaptive reference tracking control for uncertain robotic manipulators with input disturbance

AbstractThis article presents a simple approach for designing a linear adaptive controller, employing the model reference systems concept, to enable the tracking of uncertain robotic manipulators under the influence of input disturbances. The combined impact of model uncertainties and matched disturbances on the robot's behavior is considered as a total matched disturbance, attributed to a double integral system. Subsequently, a novel linear disturbance estimator, augmented by a feed‐forward correction term, is employed to estimate this lumped disturbance within the double integrator system. As a result of this procedure, the requisite adaptive law, based on the model reference system, is formulated for the nominal control parameter instead of arbitrary free‐parameter selections. The effectiveness of the proposed approach is theoretically justified and further supported by its application in the analysis of an active magnetic bearing system.

A Disturbance Compensation Control Strategy for Rotational Speed Standard Device Based on AMB System.

The rotational speed standard device that can carry loads is the key device for calibrating passive rotational speed sensors. The rotor of the passive rotational speed sensor is connected to the rotor of the standard speed device through a coupling, and the standard reference speed is provided by the standard device. Due to the rotor eccentricity, the unbalanced force of the rotor occurs, and it can not only affect the rotational speed accuracy but can also damage the mechanical bearings of the standard speed device. To solve this issue, a method for suppressing the unbalanced force of the speed standard device based on an active magnetic bearing (AMB) force compensation system is proposed. First, the overall structure of the system is briefly introduced. Then, the force feedback control system model with the AMB as the force actuator is established, and a PI controller is designed to achieve the disturbed force control. Finally, a semi-physical simulation experimental platform is built to verify the effectiveness of the proposed method. The experimental results show that the AMB force compensation system can reduce 84.4%, 81.6%, and 79.8% of the unbalanced vibration force at the frequency of 30 Hz, 90 Hz, and 150 Hz, respectively.

A novel three-module real-time adjustable accuracy speed estimator for active magnetic bearing system

This research aims to investigate the rotational speed estimation in active magnetic bearing (AMB) system. Rotational speed sensors are commonly employed for speed acquisition. Nevertheless, with the continuous advancement of AMB system, the inherent weaknesses of the speed sensors are becoming increasingly prominent in practical applications. Therefore, achieving online speed estimation can effectively address the engineering challenges arising from deficiencies in speed sensors. However, in terms of robustness, accuracy, and tracking performance, the existing speed estimation algorithms are insufficient to simultaneously meet the requirements of the AMB system. Moreover, present techniques are challenging to address prevalent issues in the AMB system, such as noise, harmonic interference, amplitude variations, and misalignment of the rotor axis trajectory. To tackle these problems, this work designs a novel three-module real-time adjustable accuracy speed estimator for AMB system. The algorithm employs displacement signals to estimate the rotational speed. And, it can flexibly adjust its noise resistance and accuracy through parameter tuning. Additionally, it can significantly diminish the influence of noise, harmonic interference, amplitude variations, and misalignment of the rotor axis trajectory. Finally, the simulation and experimental results demonstrate the effectiveness of this algorithm and validate its superior performance in robustness, accuracy, and tracking performance.

Modified Nested Saturated Control for Uncertain Multiple Integrators With High-Order Nonlinear Perturbation.

This article studies the global asymptotic stability problem of multiple integrators subject to uncertain parameters and high-order nonlinear perturbation. By introducing a modified saturation function with positive tunable parameters, three types of modified nested saturated controllers with different parameter assignments are proposed to handle the uncertain integrators with high-order nonlinear perturbation. The specific mechanism of the modified nested saturated controllers with different parameter assignments, in which control parameters appear before states, saturation functions, or saturation levels, is comprehensively analyzed. With the help of a modified saturation function, the global convergence domain of each state can be kept invariable in the saturation reduction analysis. Meanwhile, a large saturation level is obtained by adjusting positive tunable parameters. Combining with derivatives calculation and M -matrix-based comparison theory, proposed saturated control schemes are utilized to handle the considered system. Finally, an active magnetic bearing (AMB) system is revisited as an uncertain mechanical system and used to verify the feasibility of the proposed control designs.

Nonlinear vibration control of magnetic bearing system considering positive and negative stiffness

The nonlinear dynamics are studied for an active magnetic bearing (AMB) system under the low-frequency sinusoidal excitation, which can affect the operational stability of a high-speed magnetic bearing. A single-degree-of-freedom nonlinear dynamics model of magnetic bearing was developed with a c-type active magnetic bearing as the research target. The characteristics of the magnetic bearing system show positive and negative stiffness for different feedback gains. The amplitude–frequency response curves of the vibration characteristics of the positive stiffness magnetic bearing system were obtained by using the method of multiple scales. The influence of each parameter on the resonance amplitude and nonlinearity of the magnetic bearing system is understood by analyzing the amplitude–frequency response curve. The bifurcation diagram for the rotor with rotor mass, and control parameters is derived from the numerical simulation of the negative stiffness magnetic bearing system. The parameter intervals that cause single-cycle vibration, double-cycle vibration, and chaotic state of the magnetic bearing rotor are discovered by analyzing the bifurcation diagrams of each parameter. The simulation results show that the magnetic bearing system exhibits complex nonlinear dynamic characteristics when it is a negative stiffness system.

Fault Detection in Active Magnetic Bearings Using Digital Twin Technology

Active magnetic bearings (AMBs) are widely used in different industries to offer non-contact and high-velocity rotational support. The AMB is prone to failures, which may result in system instability and decreased performance. The efficacy and reliability of magnetic bearings can be significantly affected by failures in the sensor and control systems, leading to system imbalance and possible damage. A digital twin is an advanced technology that has been increasingly used in different industrial fields. It allows for the creation and real-time monitoring of virtual replicas of physical systems. This paper proposes a novel method for fault detection of Active Magnetic Bearings (AMBs) using digital twin technology and a neural network. The digital twin model serves as a virtual representation that accurately replicates the actual AMB system’s efficiency and features, allowing continuous real-time monitoring and detection of faults. The conventional neural network (CNN) is used as the primary tool for identifying faults in the Active Magnetic Bearing (AMB) within a digital twin model. Experiments proved the effectiveness and robustness of the suggested approach method to fault detection in the AMB.

Real-time application of a dynamic disturbance suppression control approach for an axial active magnetic bearing system

Active Magnetic Bearings (AMBs) use magnetic forces to suspend the rotor, allowing contactless operation and the ability to adjust stiffness and damping. However, compared to mechanical bearings, magnetic bearings are much weaker in terms of rigidity. A large external force can lead to rotor/stator collision. This study proposes a Dynamic Stiffness Controller (DSC) for AMBs. The DSC dynamically adjusts the AMB stiffness to counter external disturbance forces in real-time. Experimental results show the effective change of AMB stiffness by DSC based on the magnitude of the external load. Furthermore, not only the AMB stiffness can be real-time adjusted to counterbalance disturbances but the steady-state energy consumption is improved as there is little disturbances applied to the system. The AMB-DSC system exhibiting only 33% energy consumption compared to AMBs with constant stiffness. DSC for AMB systems offers benefits like lower risk of rotor-stator collisions, preventing coil burnouts, and improved energy efficiency.

Adaptive gain scheduling based event-triggering control design for robust performance of active magnetic bearing

This article proposes an efficient adaptive robust control for the eight-pole active magnetic bearing based on a heteropolar structure. Due to the uncertain behavior of active magnetic bearing, the mathematical model of active magnetic bearing is considered to be highly nonlinear and uncertain. As the rotor displacement and velocity are the measurable states, sliding mode control is designed to estimate state variables. Also, a matched disturbance term is used to deal with undesirable disturbances in the active magnetic bearing system. The controller is developed for an active magnetic bearing using the event-triggering-based sliding mode control technique. However, the stability of the proposed scheme has been achieved with the help of Lyapunov theory. Furthermore, the adaptive gain scheduling approach based on a neural network has been augmented to adjust the gain of the proposed controller for active magnetic bearing adaptively. The simulation studies have been performed in detail to demonstrate the use of proposed scheme for the robust control of active magnetic bearings. Finally, a comparative analysis of the proposed control design scheme with a conventional controller has been performed to achieve improved performance satisfying the plant constraints.

Harmonic vibration suppression in active magnetic bearing systems with adaptive notch filter and repetitive control

Harmonic vibration suppression in active magnetic bearing systems with adaptive notch filter and repetitive control

Distributed Modeling of Isolated Active Magnetic Bearings Considering Magnetic Leakage and Material Nonlinearity

In order to expand the application field of magnetic bearings, this article studies a novel radially isolated active magnetic bearing (IAMB) system in which the stator and the rotor are separated by a layer of metal isolation sleeve. Aimed at the shortcomings of existing modeling methods, a distributed magnetic circuit model (DMCM) was proposed based on the magnetic field segmentation theory for IAMBs. Considering material nonlinearity and leakage flux, the flux distributions of the isolation sleeve and air gap are calculated accurately. Finally, the 3D finite element model (3D FEM) and experimental platform were built to verify the feasibility of the IAMB and the correctness of the DMCM.

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.

Comparative Study of PID, PD-FLC and PID-FLC for Active Magnetic Bearing

In this manuscript, a closed loop active magnetic bearing system (AMB) is proposed, dynamically modelled and linearized in form of unstable transfer function. To achieve proper bearing operation, the proposed AMB system is controlled by two separate controllers, one to control the current in the electromagnet coils by forming an inner closed loop and second to stabilize the position of the suspending object at equilibrium. To maintain the position of suspending object at equilibrium, for the proposed AMB system (considering inner closed loop as unity) a conventional PID controller, a PD-fuzzy logic controller (PD-FLC) and a PID-fuzzy logic controller (PID-FLC) is designed and their performance is observed and compared. Later, the effect of designed controllers on the complete proposed AMB system is studied with the help of control system plots and improvement among their performances is observed. The plotted step responses and calculated transient state parameters will verify that by changing the conventional PID controller to a PID-FLC could result in 48.34% improvement in overshoot, 41.52% increment in speed of response and 32.23% increment in the relative stability.

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.

Fuzzy variable gain robust control of active magnetic bearings rigid rotor system

AbstractA high speed rigid rotor system supported by active magnetic bearings (AMBs) puts forward higher requirements on the performance of controllers. The fuzzy variable gain H‐infinity robust control (FVGRC) method is proposed to simplify controller design while suppressing system uncertainty. First, the T‐S fuzzy model of four‐degree‐of‐freedom (4‐DOF) AMBs was established based on the 4‐DOF AMBs rigid rotor equivalent coupling model optimised by the μ‐gap metric. Then, based on the fuzzy models of AMBs systems under different operating conditions, the relative optimal weight function value of H‐infinity robust controller was calculated when AMBs system was at value of the speed endpoint, and the fuzzy variable gain H‐infinity robust (FVGR) controller was designed on this basis. Finally, the simulation and experimental results showed that the FVGRC can simplify the model of controller and ensure the stable operation of AMBs rigid rotor system in the full speed range under high‐speed conditions.