Magnetically Suspended Rotor System Research Articles

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.

Improved Second-Order Repetitive Control With Parameter Optimization for Magnetically Suspended Rotor System

In magnetically suspended rotor (MSR) system supported by active magnetic bearings, the mass imbalance of the rotor and the sensor runout lead to multi-frequency vibration of the rotor system, which seriously affects the operation accuracy. In order to suppress the harmonic vibration in the MSR system, an improved second-order repetitive control (SORC) method based on parameter optimization is proposed. Firstly, the dynamic model of MSR system is established. The necessity of restraining the current stiffness force can be confirmed through the division and further analysis of the bearing force. Then, an improved SORC structure diagram is constructed, and the coupling relationship between control gain and weight factor is determined by system stability criterion. Next, for the rapidity, stability and steady-state accuracy in the convergence process, parameters are optimized separately. Then, stage integration can achieve a better balance of performance impacted by parameters. Finally, the simulation results show that the proposed scheme can effectively suppress the multi-frequency vibration of the MSR system.

Hybrid Odd Repetitive Controller for Magnetically Suspended Rotor System

Odd-harmonic current induced by mass unbalance and sensor runout in magnetic bearing coil current of magnetically suspended rotor (MSR) system will cause harmonic vibration. In this paper, a hybrid odd repetitive controller (HORC) is proposed to suppress harmonic current in MSR system. On one hand, frequency robustness of the proposed algorithm is better than that of conventional repetitive controller when the fundamental frequency of harmonic current is fluctuant around the nominal value of rotation frequency. On the other hand, the dynamic response is also accelerated. Meanwhile, a stability criterion is presented to prove the stability of MSR system. The proposed algorithm has good potentials for MSR system. Simulation results verify the effectiveness of the proposed method.

Modified Repetitive Control for Odd-Harmonic Current Suppression in Magnetically Suspended Rotor Systems

In a magnetically suspended rotor (MSR) system, harmonic current mainly caused by mass imbalance and sensor runout would produce harmonic vibration. Repetitive control (RC) is one remarkable approach for eliminating such harmonics. Conventional RC (CRC) attempts to compensate for all frequency components simultaneously. However, in the practical MSR system, it is usual that the current comprises only odd-harmonic components. This paper investigates a modified odd-harmonic RC (MORC) scheme to respond to this issue. The signal generator of arbitrary-order discrete-time periodic signal is established, by which the general forms of CRC and ORC can be obtained. Besides, it is proved that ORC with halved data memory possesses a faster convergence rate, higher repetitive gain, wider frequency bandwidth at the targeted frequency and greater robustness to frequency fluctuation than CRC. The stability criterion for the MORC-controlled MSR system is proved as well. Simulation and experimental results have highlighted the effectiveness of the proposed approach.

Harmonic Current Suppression of Magnetically Suspended Rotor System via Odd-Harmonic Fractional RC

As an efficient actuator for microvibration applications, a magnetically suspended rotor (MSR) system is always stymied by rotor mass imbalance and sensor runout, which will result in a harmonic disturbance in control current and further lead to severe periodic vibrations. In this paper, an odd-harmonic fractional repetitive control strategy is investigated for MSR systems to suppress odd-harmonic current with pertinence at low rotation speed. In contrast with conventional repetitive control (RC), only half of the delay units are required in the proposed control scheme. Therefore, it can achieve less computational burden and a faster convergence rate. Additionally, suppression accuracy of RC is vastly improved by adopting fractional delay filters, especially in fractional scenarios. The inset mode of RC is also modified for a simple system structure. Experimental results on a magnetically suspended flywheel are provided to validate the effectiveness of the proposed method.

Quasi-Resonant Control for Harmonic Current Suppression of a Magnetically Suspended Rotor

In the magnetically suspended rotor (MSR) system of the flywheel, harmonic current produced mainly by mass imbalance and sensor runout would cause undesirable harmonic vibration. Resonant control (RSC) is one of the remarkable performance alternatives for rejecting a set of selected frequency components of the periodic disturbance in a control system. Based on the intrinsic relationship between RSC and repetitive control, which is deduced and clarified, this paper proposes a novel quasi-resonant control (QRSC) scheme for a baseline prestable MSR system to suppress the harmonic current. By introducing a damping factor, QRSC achieves a good balance between stability and dynamic performance. With hybrid phase compensation, it provides system absolute stability and expands the stability margin of the MSR system. Further, as the domination of harmonic current, low-order frequency components are suppressed by parallel QRSCs (PQRSC). A stability criterion with rigorous proof for the plug-in PQRSC-controlled MSR system is addressed as well. Experimental results obtained with a magnetically suspended flywheel prototype corroborate the theoretical approach.

Synchronous vibration control for a class of cross‐coupled antisymmetric MSR systems

A magnetically suspended rotor (MSR) system always suffers from the non-coincidence of the inertia axis and geometric axis, which results in synchronous vibration varied with the rotational speed. To effectively suppress the synchronous vibration torques for the MSR with significant gyroscopic effects, a consolidated vibration control and stability analysis method is proposed here. The MSR system with inherent gyroscopic effects belongs to a class of cross-coupled antisymmetric system. First, a class of cross-coupled antisymmetric system with synchronous vibration influence is modelled. Then, the principle and implementation of the proposed scheme used for synchronous vibration suppression are analysed in detail. Moreover, a stability analysis method for a class of cross-coupled antisymmetric system is developed, which is not limited to the specific MSR system with gyroscopic effects. Finally, the simulation and experiments are performed in the typical magnetically suspended flywheel to demonstrate the effectiveness of the proposed stability analysis method and the vibration suppression algorithm.

Robust Odd Repetitive Controller for Magnetically Suspended Rotor System

The magnetically suspended rotor (MSR) system has advantages of no lubrication, adjustable stiffness, and damping. However, harmonic current induced by mass unbalance and sensor runout will cause harmonic vibration. Wherein, odd-harmonic current occupies the main components of harmonic current in the MSR system and its fundamental frequency is fluctuant. Thus, it is very necessary to suppress odd-harmonic current in the MSR system. The conventional repetitive controller has been proven to be an effective control method to suppress periodic signals in MSR. With notable results on the area, this method appears a deteriorative performance when harmonic current fundamental frequency is fluctuant. To enhance the robustness of the control system, a novel robust odd repetitive control method is investigated in this paper. Experimental results are given to verify the effectiveness and superiority of the proposed method.

Synchronous Force Elimination in the Magnetically Suspended Rotor System With an Adaptation to Parameter Variations in the Amplifier Model

For a magnetically suspended control moment gyro (MSCMG), the mass imbalance of the high-speed magnetically suspended rotor (MSR) will induce a synchronous force, which is the main disturbance for the attitude control of satellites. In this work, an elimination method with an adaption to parameter variations in an amplifier model is presented. First, the MSR system with a hybrid magnetic bearing is modeled. Next, a generalized notch filter is utilized to identify the synchronous displacement, according to which a feedforward controller is designed to generate synchronous current so that the electromagnetic force can counteract the permanent magnetic force precisely. To keep the feedforward controller unaffected by the power amplifiers whose parameters vary with the temperature, another notch filter is adopted to obtain the synchronous coil current, and then two types of adaptive controllers, which can tune the synchronous feedforward controller adaptively, are proposed and compared. Finally, simulations and experiments are carried out to demonstrate the validness of the adaptive control methods in an MSCMG test rig. The proposed control strategy does not need an accurate MSR model, and the methods of adaption to parameter variations in the amplifier model are suitable for various applications according to the elimination precision and computational effort.

Study on stability and rotating speed stable region of magnetically suspended rigid rotors using extended Nyquist criterion and gain-stable region theory

This paper presents a novel and simple method to analyze the absolute stability and the rotor speed stable region of a magnetically suspended rotor (MSR). At the beginning of the paper, a complex variable is introduced to describe the movement of the MSR and a complex coefficient transfer function is obtained accordingly. The equivalent stability relationship between this new variable and the two traditional deflection angles is also demonstrated in a simple way. The detailed characteristics of the open-loop MSR system with time delay are studied carefully based on the characteristics of its Nyquist curve. A sufficient and necessary condition of absolute stability is then deduced by using an extended complex Nyquist stability criterion for MSRs. Based on the relationship between the rotor speed and gain-stable region proposed in this paper, the rotor speed stable region can be solved simply and directly. The usefulness and effectiveness of the proposed approaches are validated by examples and simulations.

Modal decoupling control for a double gimbal magnetically suspended control moment gyroscope based on modal controller and feedback linearization method

To effectively reject the gyroscopic effects and moving-gimbal effects of the double gimbal magnetically suspended control moment gyroscope (DGMSCMG) and to avoid high control effort, this paper proposes a novel control method based on modal decoupling strategy. Modal controller is employed to realize the modal separation of the translation and rotation modes of the magnetically suspended rotor (MSR). Then the dynamic coupling among the two rotation modes of the MSR system and the two rotational motions of the gimbal servo systems have been decoupled by using differential geometry theory. Dynamic compensation filters have been designed to improve the decoupling performance and the system stability without large control resource. Compared with the existing channel decoupling method, the presented one can not only realize the separate control of stiffness and damping of the MSR but also simplify the control system design significantly. The simulation results verify the effectiveness and superiority of the proposed method.

Complex-Coefficient Frequency Domain Stability Analysis Method for a Class of Cross-Coupled Antisymmetrical Systems and Its Extension in MSR Systems

This paper develops a complex-coefficient frequency domain stability analysis method for a class of cross-coupled two-dimensional antisymmetrical systems, which can greatly simplify the stability analysis of the multiple-input multiple-output (MIMO) system. Through variable reconstruction, the multiple-input multiple-output (MIMO) system is converted into a single-input single-output (SISO) system with complex coefficients. The pole locations law of the closed-loop system after the variable reconstruction has been revealed, and the controllability as well as observability of the controlled plants before and after the variable reconstruction has been studied too, and then the classical Nyquist stability criterion is extended to the complex-coefficient frequency domain. Combined with the rigid magnetically suspended rotor (MSR) system with heavy gyroscopic effects, corresponding stability criterion has been further developed. Compared with the existing methods, the developed criterion for the rigid MSR system not only accurately predicts the absolute stability of the different whirling modes, but also directly demonstrates their relative stability, which greatly simplifies the analysis, design, and debugging of the control system.