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In this paper, a control strategy based on the inverse system decoupling method and μ-synthesis is proposed to control vibration in a rigid rotor system with active magnetic bearings that are built into high-speed motors. First, the decoupling method is used to decouple the four-degrees-of-freedom state equation of the electromagnetic bearing rigid rotor system; the strongly coupled and nonlinear rotor system is thus decoupled into four independent subsystems, and the eigenvalues of the subsystems are then configured. The uncertain parametric perturbation method is used to model the subsystem, and the multi-objective ant colony algorithm is then used to optimize the sensitivity function and the pole positions to obtain the optimal μ-controller. The closed-loop system thus has the fastest possible response, the strongest internal stability, and the best disturbance rejection capability. Then, the unbalanced force compensation algorithm is used to compensate for the high-frequency eccentric vibration; this algorithm can attenuate the unbalanced eccentric vibration of the rotor to the greatest extent and improve the robust stability of the rotor system. Finally, simulations and experiments show that the proposed control strategy can allow the rotor to be suspended stably and suppress its low-frequency and high-frequency vibrations effectively, providing excellent internal and external stability. [ABSTRACT FROM AUTHOR]

Since the dynamic characteristics of the rotor supported on active magnetic bearings (AMBs) are strongly dependent on the control strategies and control parameters, it is significant to design proper controllers for the AMBs-rotor systems. A robust proportional-differential (PD) control via eigenstructure assignment for an AMBs-rigid rotor system is proposed in this article. First, the dynamic model of the four-degree-of-freedom (4-DOF) AMBs-rigid rotor system was established and was converted into two 2-DOF models by a cross-differential feedback, which radically eliminates the coupling caused by gyroscopic effect. Then, the parametric expressions of the PD feedback matrix and the closed-loop eigenvector matrix for one of the 2-DOF models were obtained by eigenstructure assignment. In order to acquire stability and desired dynamical performance, the eigenvalues were confined in some specific regions in the complex plane. A multiobjective optimization problem was constructed to make the AMBs-rotor system not only be insensitive to the change of the bias current, but also have low amplitudes of the unbalance vibration and unbalance control currents over the full rotational speed range. The system performances corresponding to two Pareto solutions were compared in numerical simulation and experiments, and the results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In order to suppress the synchronous unbalance vibration of the active magnetic bearings (AMBs) rigid rotor system in the full rotational speed range, the polarity switching control (PSC) can effectively suppress the synchronous unbalance vibration of the AMBs-rigid rotor system before and after the rigid cylindrical mode frequency, and the impact of the switching polarity on the system was reduced by using a disturbance observer. However, considering the rigid conical mode, the PSC could not guarantee the synchronous unbalance vibration suppression of the AMBs-rigid rotor system in the full rotational speed range including the rigid cylindrical mode frequency and the rigid conical mode frequency, and the system stability also changes accordingly. This article proposes a synchronous unbalance vibration suppression method based on the four-factor PSC (4-FPSC), which adjusts four polarity factors to suppress the synchronous unbalance vibration before and after two rigid mode frequencies. Besides, the disturbance observer is also avoided. Finally, simulation and experiment results verify the 4-FPSC can effectively suppress the synchronous unbalance vibration of the AMBs-rigid rotor system in the full rotational speed range including the rigid cylindrical and conical mode frequencies. [ABSTRACT FROM AUTHOR]

In active magnetic bearings (AMBs) supported rigid rotor systems, the unbalance compensation strategy based on a notch filter was often used to suppress the synchronous unbalance vibration when the rotor operates in the steady-state rotational speed. Whereas the rotor operates in a rotational-speed range including the critical rotational speeds, conventional notch filters should be improved to suppress the unbalance vibration. In most cases, improving the structure of the notch filter, such as a cross-feedback notch filter, phase-shift notch filter, adding the polarity switch or two-stage switch, was considered to make the notch filter work in the rotational-speed range. However, the improved notch filter may affect the stability of the AMBs rotor systems and result in large vibrations when the polarity switch or two-stage switch shifts. To avoid the shortcomings of these methods, a method using a variable angle compensation algorithm was proposed to suppress the synchronous unbalance vibration in finite iterative seeking processes, directly realizing unbalance compensation according to real-time rotor position. Finally, the effectiveness of the method proposed is verified by simulation and experiment results. [ABSTRACT FROM AUTHOR]

For the unbalance vibration of the rigid rotor system on active magnetic bearings (AMBs) supported high-speed motors in the full rotational speed range, a method based on the polarity switching tracking filter (PSTF) and the disturbance observer (DO) is proposed to achieve vibration suppression. To identify the synchronous unbalance vibration, a positive polarity tracking filter and a negative one are adopted before and after the rigid critical rotational speed range, respectively. The rigid critical rotational speed is in this range whose lower/upper limit is the negative/positive polarity switching frequency. Although the PSTF can effectively reduce the rotor vibration when it rotates at subcritical rotational speed range and supercritical range, the vibration increases evidently and even destabilize the system within the rigid critical rotational speed range. It means that the PSTF cannot suppress the rotor unbalance vibration in the full rotational speed range. However, this vibration during the rigid critical rotational speed range can be considered as a kind of disturbance and the DO is adopted to observe it, then the vibration identified is compensated in the control current to reduce the rotor unbalance vibration in the rigid critical rotational speed range. Therefore, the method based on the PSTF and the DO can suppress the unbalance vibration in the full rotational speed range. Finally, simulation and experiment results demonstrate that the method proposed can effectively suppresses the synchronous unbalance vibration of the AMBs-rigid rotor system in the full rotational speed range. [ABSTRACT FROM AUTHOR]

Nowadays, high-frequency switching power amplifiers (SPA) have been studied widely; bulk of the researches were focused on audio power amplifiers. In active magnetic bearing (AMB) systems, high-frequency electromagnetic excitation caused by rotor imbalance can affect the performance of the SPA, so the traditional SPA cannot meet the requirements of the AMB systems. Therefore, on the premise of ensuring larger power, the frequency of the SPA should be improved to ensure the normal operation of the AMB system. Two-level pulsewidth modulation (PWM) current-mode SPAs are widely used in AMB systems. In order to broaden the bandwidth and to reduce the average steady-state error current, SiC power devices based SPA with a high bus voltage and a high switching frequency was designed. The basic principle and the linearized control model of SPAs are introduced. Then, the duty ratio stability and average steady-state error current of the SPAs are analyzed based on the output ripple current. When the PWM modulator is designed by either the discrete devices or the integrated chips, the critical gains to ensure the duty ratio stability are, respectively, analyzed based on the slope matching and the nonideal characteristic of operational amplifiers. Hence, two methods to reduce the average steady-state error current are proposed, respectively. One is to adjust the offset voltage of triangular carrier for the P controller, the other is to use a proportional integral (PI) controller. The offset adjusting method allows the SPA to achieve better dynamic performance and wider bandwidth. The proportional integral (PI) controller can reduce the average steady-state error current but narrows the bandwidth. Finally, the experiment results are in good agreement with the theoretical analyses. [ABSTRACT FROM AUTHOR]

To achieve high‐precision position control for the active magnetic bearing high‐speed flywheel rotor system (AMB‐HFRS), a novel control strategy based on inverse system method and extended two‐degree‐of‐freedom (2‐DOF) proportional–integral–derivative (PID) controller is proposed in this study. First, the inverse system method is employed to decouple the AMB flywheel rotor system with strong non‐linear and coupling, into four independent subsystems. Subsequently, extended 2‐DOF PID controllers are used to regulate the decoupled subsystems, to obtain good performances of disturbance rejection and tracking simultaneously. In the extended 2‐DOF PID controller, a differential signal is produced by a velocity observer to improve the ability of against noise. Finally, the characteristics of stability, tracking, disturbance rejection and robustness of the control strategy proposed are analysed in theory, and its ability and effectiveness to control the radial position of the AMB‐HFRS are further studied by simulations and experiments. It is shown that the control strategy proposed can keep the AMB‐HFRS suspending stably from static state to the speed of 24,000 rpm, has the advantages of good tracking, high disturbance rejection, strong robustness and good ability of against noise. [ABSTRACT FROM AUTHOR]

To eliminate the influence of gyroscopic effect on system stability and to improve the control performances for the active magnetic bearing (AMB) high‐speed flywheel rotor system, a novel control strategy based on the modal separation and inverse system method is proposed. The translational motions and rotational motions of the AMB flywheel rotor system are firstly decoupled by the modal separation, then the rotational motions are decoupled by the inverse system method, so that the AMB flywheel rotor system, which is a multivariable and strong coupled system, is decoupled into four subsystems. Finally, the subsystems are regulated by four two‐degrees‐of‐freedom (2‐DOF) internal model controllers, respectively. Furthermore, the stability, tracking and robustness of the novel control strategy are analysed theoretically, and its effectiveness on vibration control of the AMB high‐speed flywheel rotor system is further investigated by simulations and experiments. The results show that the novel control strategy can achieve stable suspension and effectively suppress the vibration of the AMB high‐speed flywheel rotor system from static state to 24,000 rpm, with the advantages of high stability, strong robustness, and good performances of tracking and disturbance rejection simultaneously. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

To represent the support characteristic of active magnetic bearings (AMB), the commonly used parameters are the equivalent stiffness and the equivalent damping, which inherit the parameters of the stiffness and the damping from traditional mechanical bearings. First, by analyzing the diversity and the similarity between traditional mechanical bearing and AMB, the prior condition for applying the parametric representation of equivalent stiffness and equivalent damping to AMB is illuminated. Then, a method for measuring the equivalent stiffness and the equivalent damping of AMB-rotor system is proposed with multi-frequency excitation. One of its outstanding features is that the proposed method is based on the multi-degree of freedom (DOF) rotor model, not the single- DOF model, because the single DOF model cannot be suitably applied to the multi-DOF AMB-rotor systems. Otherwise, in order to decrease the identification error, the multi-frequency excitation can achieve the lowest peak value by means of appropriate selection for the relative phasing of each component, so that the possibility of the rotor displacement exceeding clearances of AMB and the magnetic force reaching saturation is minimized. Finally, the experiments, which are carried out on an AMB-rotor test rig with a vertical shaft, indicate that the proposed method can efficiently reduce the peak value for the superimposed multi-frequency excitation and correctly identify the equivalent stiffness and equivalent damping of AMB-rotor system. [ABSTRACT FROM AUTHOR]

The undesired synchronous vibration due to rotor mass imbalance is a main disturbance source in all rotating machinery including active magnetic bearing (AMB)-rotor systems. In the AMB-rotor system, imbalance compensation, which causes the AMB actuators to spin a rotor about its geometric axis, and automation balancing, which spins a rotor about its inertial axis, are two kinds of common control aim for the rotor imbalance control. In this study, the internal relation between the imbalance compensation and the automation balancing is analyzed and a uniform control method is proposed. With the identical control algorithm, the proposed control method can realize the automation balancing or the imbalance compensation, respectively, by switching the controller's junction position in the original control loop. The proposed control method does not depend on the dynamic plant model, because its algorithm is based on the real-time identification for the Fourier coefficient of the rotor imbalance disturbance. In this paper, the process of identification algorithm is given in detail and all the possible junction forms of the controller are illustrated. By the simulations, the identification performances of the control algorithm are compared in the conditions with three variable factors, including the signal noise ratio (SNR), the imbalance phase and the identification delay time. The noise level has considerable influence on the identification precision, but the imbalance phase has little. To prolong the identification delay time will be of benefit to improve the identification precision but slow down the identification process. Experiments, which are carried out on an AMB-rigid rotor test rig, indicate that by switching the junction position of the controller in control loop, both kinds of rotor imbalance control can achieve the good effectiveness. [ABSTRACT FROM AUTHOR]

Abstract: A method for multi-frequency periodic vibration suppressing in active magnetic bearing (AMB)-rotor systems is proposed, which is based on an adaptive finite-duration impulse response (FIR) filter in time domain. Firstly, the theoretic feasibility of the method is proved. However, two problems would be unavoidable, if the conventional adaptive FIR filter is adopted in practical application. One is that the convergence rate of the different frequency components may be highly disparate in multi-frequency vibration control. The other is that the computational complexity is significantly increased because the long memory FIR filter is required to match the transient response time of the AMB-rotor system. To overcome the problems above, the Fast Block Least Mean Square (FBLMS) algorithm is adopted to efficiently implement the computation in frequency domain at a computational cost far less than that of the conventional FIR filter. By the FBLMS algorithm, regardless of the number of the considered frequency components in vibration disturbance, the computational complexity would be invariable. Moreover, filter’s weights in the FBLMS algorithm have the intuitional relation with signal’s frequency. As a result, the convergence rate of each frequency component can be adjusted by assigning the individual step size parameter for each weight. Experiments with the reciprocating simulating disturbance test and the rotating harmonic vibration test were carried out on an AMB-rigid rotor test rig with a vertical shaft. The experiment results indicate that the proposed method with the FBLMS algorithm can achieve the good effectiveness for suppressing the multi-frequency vibration. The convergence property of each frequency component can be adjusted conveniently. Each harmonic component of the vibration can be addressed, respectively, by reconfiguring the frequency components of the reference input signal. [Copyright &y& Elsevier]

The dynamic characteristics of a cracked rotor with an active magnetic bearing (AMB) are theoretically analyzed in this paper. The effects of using optimal controller parameters on the dynamic characteristics of the cracked rotor and the effect of a crack on the stability of the active control system are discussed. It is shown that the dynamic characteristics of the cracked rotor with AMBs are clearly more complex than that of the traditional cracked rotor system. Adaptive control with AMBs may hide the fault characteristics of the cracked rotor, rather than helping to diagnose a crack; this will depend on the controller strategy used. It is very difficult to detect a crack in the rotor with an AMB support system when the vibration of the rotor system is fully controlled. Monitoring the super-harmonic components of 2× and 3× revolution in the sub-critical speed region can be used as an index to detect a crack in the rotor with an AMB system. If the effect of the crack is not taken into account at the design stage of the controller, then the rotor–AMB system will lose its stability in some cases when cracks appear. [Copyright &y& Elsevier]