Active Magnetic Bearing Control Research Articles

New LMI based gain-scheduling control for recovering contact-free operation of a magnetically levitated rotor

A new approach for the recovery of contact-free levitation of a rotor supported by active magnetic bearings (AMB) is assessed through control strategy design, system modelling and experimental verification. The rotor is considered to make contact with a touchdown bearing (TDB), which may lead to entrapment in a bi-stable nonlinear response. A linear matrix inequality (LMI) based gain-scheduling H∞ control technique is introduced to recover the rotor to a contact-free state. The controller formulation involves a time-varying effective stiffness parameter, which can be evaluated in terms of forces transmitted through the TDB. Rather than measuring these forces directly, an observer is introduced with a model of the base structure to transform base acceleration signals using polytopic coordinates for controller adjustment. Force transmission to the supporting base structure will occur either through an AMB alone without contact, or through the AMB and TDB with contact and this must be accounted for in the observer design. The controller is verified experimentally in terms of (a) non-contact robust stability and vibration suppression performance; (b) control action for contact-free recovery at typical running speeds with various unbalance and TDB misalignment conditions; and (c) coast-down experimental tests. The results demonstrate the effectiveness of the AMB control action whenever it operates within its dynamic load capacity.

Experimental Investigations of Resonance Vibration Control for Noncollocated AMB Flexible Rotor Systems

The resonance vibration control of active magnetic bearing (AMB) supported flexible rotors is a challenging topic in the industrial applications. This work addresses the two issues on the noncollocated AMB flexible rotor systems while passing through the critical speed. A modal separation scheme is established to enhance the observability of the bending mode, and a damping optimization procedure of the electromagnetic force is proposed to provide the maximum control efficiency. First, the rotor imbalance analysis is carried out, and several possible approaches to minimize the vibration of the flexible rotor are presented. Then, the detailed descriptions of the bending mode extraction scheme using notch filters and phase-lead compensators are discussed for a noncollocated flexible rotor system. The root locii of the closed-loop AMB-rotor system with and without additional phase-lead compensator are also performed. A solution to determining the phase angles between the measured rotor displacements to the bearing forces is established using the physical modeling and experimental identification. Finally, simulation and experimental results on a 10 kW magnetically suspended centrifugal compressor show the effectiveness of the proposed methods.

Active Magnetic Bearing Online Levitation Recovery through μ-Synthesis Robust Control

A rotor supported on active magnetic bearings (AMBs) is levitated inside an air gap by electromagnets controlled in feedback. In the event of momentary loss of levitation due to an acute exogenous disturbance or external fault, reestablishing levitation may be prevented by unbalanced forces, contact forces, and the rotor’s dynamics. A novel robust control strategy is proposed for ensuring levitation recovery. The proposed strategy utilizes model-based μ-synthesis to find the requisite AMB control law with unique provisions to account for the contact forces and to prevent control effort saturation at the large deflections that occur during levitation failure. The proposed strategy is demonstrated experimentally with an AMB test rig. First, rotor drop tests are performed to tune a simple touchdown-bearing model. That model is then used to identify a performance weight, which bounds the contact forces during controller synthesis. Then, levitation recovery trials are conducted at 1000 and 2000 RPM, in which current to the AMB coils is momentarily stopped, representing an external fault. The motor is allowed to drive the rotor on the touchdown bearings until coil current is restored. For both cases, the proposed control strategy shows a marked improvement in relevitation transients.

Truncated Predictor Feedback Control for Active Magnetic Bearing Systems With Input Delay

In this brief, we investigate the control of linear systems with input delay with applications to active magnetic bearings (AMBs). This study is motivated by emerging energy explorations that require compressors and other rotating machines to operate in remote locations. The separation between the machine and the control site in these applications, which may extend for several kilometers, introduces a time delay in the transmission of the control signals. Here, we study the effect of input delay in the control of AMBs in remote rotating machines and we present a truncated predictor feedback (TPF) control design to maximize the input delay that the stable closed-loop system can tolerate. The controller corresponding to the maximum input delay is obtained iteratively from the solutions to local linear matrix inequality problems. The capabilities of the designed TPF controller are first verified through simulation and then experimentally validated on an AMB test rig.

Hybrid control of a three-pole active magnetic bearing

The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated while the proposed hybrid controller has a piecewise linear form, i.e., linear in each sub-region. A state-feedback hybrid controller is designed in this study and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the LQR method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law and computational time are advantages of this method over other nonlinear control strategies in AMB systems.

Nonlinear zero-bias current control for active magnetic bearing in power magnetically levitated spindle based on adaptive backstepping sliding mode approach

The zero-bias current controlled way is proposed to cut down the power consumption of the active magnetic bearing in a power magnetically levitated spindle system. The zero-bias current controlled way is easier to realize than the zero-bias flux controlled way, since current can be detected directly, while flux is hard to be measured in practice. Besides, the active magnetic bearing suffers from lumped uncertainty including parameter uncertainty and external load, and the displacement of rotor caused by lumped uncertainty is undesirable. In practice, the upper bound of the lumped uncertainty especially the external load is hard to obtain, making it hard to choose parameters for a traditional sliding mode control. The adaptive backstepping sliding mode control method combining both the advantages of sliding mode procedure and backstepping procedure is proposed to solve this problem. Furthermore, the upper bound of lumped uncertainty is estimated in real time by an adaptive law. In this paper, first a new zero-bias current active magnetic bearing system model with lumped uncertainty is built; then two controllers based on the sliding mode control and adaptive backstepping sliding mode control methods are designed, respectively, and the stability analyses are given for the two controllers via Lyapunov function; finally, the effectiveness of the proposed adaptive backstepping sliding mode control approach for a zero-bias current active magnetic bearing system is verified by the simulation and experiment results.

Uncertainty and disturbance estimator-assisted control of a two-axis active magnetic bearing

In this paper, a robust nonlinear control strategy is developed for a class of second-order nonlinear uncertain systems with uncertainties and disturbances and is applied to two-axis active magnetic bearing position stabilization. The approach is based on a feedback linearization method, robustified by the uncertainty and disturbance estimator, which calculates and robustly cancels system uncertainties and disturbances via appropriate filtering. The controller uses the information regarding the known part of plant dynamics while the terms containing unknown dynamics are treated as additional system uncertainties and disturbances. The algorithm provides excellent performance in stabilizing the active magnetic bearing position and rejecting disturbances both at standstill and under movement. Simulations are given to show the effectiveness of the strategy via an application to an experimentally derived active magnetic bearing model.

Optimization Strategy for PID-Controller Design of AMB Rotor Systems

Most industrial active magnetic bearings (AMBs) are controlled by proportional–integral–derivative (PID) controllers. Usually, a time-consuming iterative manual tuning procedure is required to design these PID controllers. In this contribution, we introduce the strategy, algorithms, and results from an AMB controller design, including optimization using a multiobjective genetic algorithm. We focus on the combination of frequency- and time-domain-based optimization, a strategy for the evaluation of fitness functions for complex PID-controller design, and a sensitivity-based parameter reduction for optimization. Two AMB system controller designs are considered and satisfactory results are obtained using the suggested optimization strategy. For validation purposes, the optimized controller design is experimentally implemented for the first AMB system, which contains a flexible test rotor supported by two AMBs. The maximal rotational speed of 15 000 r/min is achieved for the test rotor. A comparison between simulated and experimental results is presented.

Adaptive Control of Active Magnetic Bearing against Milling Dynamics

For improving the defects in milling processes caused by traditional spindle bearings, e.g., the dimensional discrepancy of a finished workpiece due to bearing wear or oil pollution by lubricant, a novel embedded cylindrical-array magnetic actuator (ECAMA) is designed for milling applications. Since ECAMA is a non-contact type actuator, a control strategy named fuzzy model-reference adaptive control (FMRAC) is synthesized to account for the nonlinearities of milling dynamics and magnetic force. In order to ensure the superior performance of spindle position regulation, the employed models in FMRAC are all constructed by experiments. Based on the experimental results, the magnetic force by ECAMA is much stronger than that by the traditional active magnetic bearing (AMB) design under the same test conditions and identical overall size. The efficacy of ECAMA to suppress the spindle position deviation with the aid of FMRAC has been verified as well via numerical simulations and practical metal cutting.

Optimization-based radial active magnetic bearing controller design and verification for flexible rotors

Engineering costs, especially cost for controller design, are substantial and obstruct active magnetic bearings for broader industrial applications. An optimization-based active magnetic bearing controller design method is developed to solve this problem. Optimization criteria are selected to describe active magnetic bearing practical performance. Controller components are chosen considering that the parameters can be manually interpreted and modified on-site for commissioning. A multi-objective optimization toolbox can be used to tune the controller parameters automatically by minimizing the optimization criteria. The method has been verified within a controller design process for an active magnetic bearing levitated machine. With this method, engineering effort for controller design can be reduced significantly.

The identification of axial magnetic bearing system based on LS-PSO algorithm

System identification is an important basis of adaptive control and fault identification of active magnetic bearing (AMB) system. Among all the identification algorithms, least square method (LS) is a comparatively simple one with small calculation amount but a poor performance as well under colored noise, and particle swarm optimization algorithm (PSO) has a good performance under colored noise but a huge calculation amount. Taking advantage of the complementation of LS and PSO, the identification based on LS-PSO algorithm was proposed, which combines the briefness of LS and the high precision of PSO. In the novel algorithm, PSO updates the poles of identified transfer function model, and LS estimates the numerator optimally. The output error variance is minimized by repeating the procedure. In simulation, the calculation amount declined by 91.4% on average comparing with PSO, and the experiments validated that the error variance of LS-PSO declined by 92.92% relative to LS. The experimental results show that LS-PSO retains high precision of PSO under colored noise, while its calculation amount is greatly reduced by introducing LS, which is significant to practical application.

Enhancing working performance of active magnetic bearings using improved fuzzy control and Kalman-LMS filter

This paper develops a novel control approach to enhance working performance of eight-pole radial active magnetic bearings (AMB). In the proposed method, the improved fuzzy proportional-integral-derivative (PID) control based on variable universes of proportional scaling is designed firstly to obtain better identification performance and flexibility of AMB control. Then, a Kalman filter is implemented to estimate the rotor displacement to reduce the noise disturbance and undesirable parameter adjustments caused by fuzzy control scheme. Finally, the least mean square (LMS) filter is connected with fuzzy control to compensate the unknown mass unbalance which might induce serious vibrations of AMB facilities. The simulation results show that the improved fuzzy PID control plays better performance than PID control in overshoot control, and the transient time of improved fuzzy PID is much shorter compared to conventional fuzzy PID. Meanwhile, the impacts of noise disturbance can be significantly limited by connecting with Kalman filter, and the maximum steady-state error can be decreased to about 85%. It is also shown that the LMS filter algorithm can effectively compensate the unknown mass unbalance in relatively short time without affecting the stability of AMB system.

Vibration control of high-speed rotor supported by hybrid foil-magnetic bearing with sudden imbalance

A hybrid foil-magnetic bearing (HFMB) was successfully studied as a vibration isolator by introducing a sudden imbalance or an unexpected disturbance during turbine/rotor operation. This HFMB is used to achieve stability during transient vibration behavior. The HFMB consists of two oil-free bearing technologies: an active magnetic bearing (AMB) and air foil bearing (AFB). Using both technologies takes advantage of the strengths of each bearing while compensating for their inherent weaknesses. In addition, the HFMB has good dynamic characteristics, and the damping can be adjusted using the appropriate gain selection for the AMB controller. Based on these unique features, dynamic stability can be enhanced, even if a sudden imbalance occurs while the rotor is operating. In this study, a rigid rotor was operated at up to 12,000 rpm and tested using a control algorithm to reduce the sudden imbalance vibration amplitudes. The experiment was conducted under the situation that the mass dropped out at 6,000 rpm. In order to validate the stability performance of the HFMB with a sudden mass loss, the vibration response results for the AFB and HFMB were compared. When applying the HFMB, the asynchronous vibration was suppressed, and the 1x vibration results showed reductions of almost 30%. When the sudden mass loss occurred, the magnetic control force was remarkably effective at reducing the asynchronous vibration of the rotor supported by the HFMB. In conclusion, it was experimentally verified that using the HFMB made sudden imbalance vibration control possible during rotor operation with an air foil bearing. In this respect, the HFMB has the characteristics of high stiffness/damping, which prevent rubbing and suppress excessive vibration due to a sudden imbalance event.

Control of Magnetic Bearing With Material Saturation Nonlinearity

In this paper, a nonlinear modeling and control method for magnetic bearings is designed, considering the core material nonlinear high flux behavior for the first time. A combination of the generalized Lur'e method and linear matrix inequalities is used during the modeling and control design process. It is common to include a margin of safety in amplifiers and other active magnetic bearing (AMB) components. The nonlinear modeling makes it possible to operate an existing industrial AMB system with larger electric currents and thus achieve a larger maximum load capacity than existing AMB modeling and control practices allow. As a result, existing industrial AMB's can be tuned to become more resilient in dealing with external disturbances. In addition, smaller and lighter AMBs can be designed by using the proposed method, which enables achievement of the same maximum force requirement of present-day larger AMB systems.

High-Precision Cutting Tool Tracking With a Magnetic Bearing Spindle

A method is presented for tool tracking in active magnetic bearing (AMB) spindle applications. The method uses control of the AMB air gap to achieve the desired tool position. The reference tracking problem is transformed from the tool coordinates into the AMB control axes by bearing deflection optimization. Therefore, tool tracking can be achieved by an off-the-shelf AMB controller. The method is demonstrated on a high-speed AMB boring spindle with a proportional integral derivative (PID) control. The hypothetical part geometries are traced in the range of 30 μm. Static external loading is applied to the tool to confirm disturbance rejection. Finally, a numerical simulation is performed to verify the ability to control the tool during high-speed machining.

Mismatched Disturbance Rejection Control for Voltage-Controlled Active Magnetic Bearing via State-Space Disturbance Observer

A novel composite control method based on disturbance observer for the precision suspension of a voltage-controlled active magnetic bearing (AMB) system is presented in this study. The voltage-controlled AMB system always suffers from the mismatched disturbances, which act on the system via different channels from the control inputs. In this study, we reconstruct a new system, which is equivalent to the original voltage-controlled AMB dynamical system. The reconstructed system targets to divide the mismatched disturbances into the matched component and the mismatched component. The matched component is attenuated by the feedback robust controller, and the mismatched component is rejected on the basis of disturbance observer. Both simulations and experiments demonstrate the effectiveness in rejecting the mismatched disturbances on the voltage-controlled AMB system in a magnetically suspended control moment gyro. The proposed control method handles the mismatched disturbances from the state variable and preserves the nominal performance of the baseline robust controller to the best.

Research on Inverse Control of Active Magnetic Bearing Based on Fuzzy Inverse Model

For magnetic bearing system with characteristics of zero damping, negative stiffness and nonlinearity, this paper put forward a method of inverse control based on the fuzzy inverse model. The fuzzy system with fuzzifier and defuzzifier was used as an interpolator to approximate the inverse model of magnetic bearing. Then we connected the fuzzy inverse model in series with the magnetic bearing system to form a generalized pseudo linear plant, and selected a PID controller to control the pseudo linear plant. The fuzzy inverse model and the PID controller together formed an inverse controller to implement the closed-loop inverse control of the system. The simulation results demonstrate that the inverse control can reduce the overshoot, shorten the settling time, and make the rotor levitate in a larger range.

Using Fuzzy Bang-Bang Relay Controller for a Single-Axis Magnetic Bearing System

This paper presents a new type of fuzzy controller for active magnetic bearing applications. Active magnetic bearing (AMB) applications in rotating machinery are fast growing due to their precise and contact less support of the rotating shaft. AMB are open loop unstable due to nonlinear relationship between electromagnetic force,attraction distance and the electromagnetic current. To regulate the electromagnetic forces acting on the bearing, external control is required. Feedback control for AMB systems such as proportional and derivative is only restricted to linearized region. For nonlinear control systems, artificial intelligence techniques such as fuzzy and hybrid techniques are being investigated. Bang-bang control is an old but effective technique to control nonlinear system in optimal time. Bang-bang control combined with fuzzy logic decision-making flexibility results in a robust control system. In this work an integrated fuzzy bang-bang relay controller (FBBRC) is presented to control the AMB system. FBBRC is simple to design than conventional fuzzy controllers. Comparison with other widely used AMB control techniques demonstrate improved results.

A Field Balancing Technique Based on Virtual Trial-Weights Method for a Magnetically Levitated Flexible Rotor

For a magnetically levitated flexible rotor (MLFR), the amount of residual imbalance not only generates undesired vibrations, but also results in excessive bending, which may cause it hit to the auxiliary bearings. Thus, balancing below the critical speed is essential for the MLFR to prevent the impact. This paper proposes a balancing method of high precision and high efficiency, basing on virtual trial-weights. First, to reduce the computed error of rotor's mode shapes, a synchronous notch filter is inserted into the active magnetic bearing (AMB) controller, achieving a free support status. Then, AMBs provide the rotor with the synchronous electromagnetic forces (SEFs) to simulate the trial-weights. The SEFs with the initial angles varying from 0 deg to 360 deg in the rotational frame system result in continuous changes in the MLFR's deflection. Last, correction masses are calculated according to the changes. Compared to the trail-weights method, the new method needs not test-runs, which improves the balancing efficiency. Compared to the no trail-weights method, the new method does not require a precise model of the rotor-bearing system, which is difficult to acquire in the real system. Experiment results show that the novel method can reduce the residual imbalance effectively and accurately.

Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing

For a magnetically suspended control moment gyroscope, stiffness and damping of magnetic bearing will influence modal frequency of a rotor. In this paper the relationship between modal frequency and stiffness and damping has been investigated. The mathematic calculation model of axial passive magnetic bearing (PMB) stiffness is developed. And PID control based on internal model control is introduced into control of radial active magnetic bearing (AMB), considering the radial coupling of axial PMB, a mathematic calculation model of stiffness and damping of radial AMB is established. According to modal analysis, the relationship between modal frequency and modal shapes is achieved. Radial vibration frequency is mainly influenced by stiffness of radial AMB; however, when stiffness increases, radial vibration will disappear and a high frequency bending modal will appear. Stiffness of axial PMB mainly affects the axial vibration mode, which will turn into high-order bending modal. Axial PMB causes bigger influence on torsion modal of the rotor.