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The active magnetic bearing is highly nonlinear and unstable system. In general most of physical systems, conventional PID control strategies are employed for their stable operation but the dynamics of the system are influenced by input voltage saturation that degrades the performance of the system. The conventional PID control scheme does not work properly alone. In such a situation, PID faces windup phenomenon that leads to instability in the system. To overcome this problem, an anti-windup control scheme leads to stable and smooth operation of active magnetic bearing system.

The proposed anti-windup control strategy is based on dynamic output feedback that is applied on linearized active magnetic bearing (AMB) system to stabilize and avoid the input voltage saturation effect in the actuator.

An anti-windup controller is designed for active magnetic bearing system in presence of input voltage saturation. The stability of AMB system with anti-windup controller is derived in sense of Lyapunov and expressed as linear matrix inequality problem for AMB system and the designed anti-windup controller also enlarges the region of attraction of considered AMB system.

T-S fuzzy technique is used for obtaining local linear model of nonlinear active magnetic bearing system for easy and simple implementation of anti-windup control scheme. In proposed methodology the region of attraction for anti-windup compensator is also discussed. The effectiveness of proposed method is verified by the numerical simulation results for considered active magnetic bearing system and domain of attraction or stability region of closed loop AMB system are also calculated using Eigen Value Optimization technique for both the cases such as with and without anti-windup controller. The comparative result and the contribution of proposed control strategy are also discussed.

This paper aims to study the clearance compatibility of active magnetic bearing (AMB) and gas bearing (GB) to achieve a single-structured hybrid gas-magnetic bearing (HGMB), which uses a single bearing structure to realize both the functions of gas bearing and magnetic bearing.

Because the radial clearance size of the AMB is typically ten times larger than that of the GB, radial clearance compatibility of GB and AMB needs to maximize the radial clearance of GB by adjusting structural parameters. Parametric analysis of structural parameters of GB is explored. Furthermore, a general structural design principle based on static analysis, rotordynamic performance and system stability is established for the single-structured HGMB.

Load capacity is vastly reduced due to the enlarged radial clearance of the GB. A minimum clearance needs to be ensured by increasing the bearing diameter or width to compensate for the reduced load capacity, yet indirectly raising the bearing load. Increased bearing load is conducive to stability, yet it raises the risk of rotor abrasion. In addition, excessively large bearing diameter leads to system instability, and inappropriate bearing width affects critical speeds. A general structural design principle is established and the designed HGMB–rotor processes optimal performances.

A single-structured HGMB is proposed to address the urgent demand for high-speed, cryogenic turboexpanders with frequent starts/stops. This design applies a single-bearing structure to realize the characteristics of both GB and AMB, greatly simplifying the implementation, reducing air friction loss and raising critical speeds. This paper provides a fresh perspective on the development of cryogenic turboexpanders for hydrogen liquefaction. It theoretically validates the feasibility and provides a design guide for a single-structured HGMB system.

HAVING looked at all the problems that one may find in lubrication and wear, one may dream of a bearing which would have no contact between the rotating and static parts: the magnetic bearing is one such dream.

The multi-objective optimization configuration strategy is proposed due to the configuration of EMAs in fault-tolerant control of active magnetic bearing with redundant electromagnetic actuators involving high-dimensional, nonlinear, conflicting goals.

A multi-objective optimization model for bias current coefficients is established based on the nonlinear model of active magnetic bearings with redundant electromagnetic actuators. Based on the non-dominated sorting genetic algorithm III, a numerical method is used to obtain feasible and non-inferior sets for the bias current coefficient.

(1) The conflicting relationship among the three optimization objectives was analyzed for various failure modes of EAMs. (2) For different EMAs' failure modes, the multi-objective optimization configuration strategy can simultaneously achieve the optimal or sub-optimal effective EMF, flux margins, and stability of EMF. Moreover, the characteristics of the optimal Pareto front are consistent with the physical properties of the AMB. (3) Compared with the feasible configuration of C0, the non-inferior configurations can significantly improve the performance of AMB, and the advantages of the multi-objective optimization configuration strategy become more prominent as the asymmetry of the residual supporting structure intensifies.

i) Considering the variation of the rotor displacement during the support reconstruction, a decision-making model that can accurately characterize the dynamic performance of AMB is presented. (ii) The interaction law between AMB and rotor under different failure modes of EMAs is analyzed, and the configuration principles for redundant EMAs are proposed. (iii) Based on the dynamic characteristics of AMB during the support reconstruction, effective EMF, energy consumption, and the Pearson correlation coefficient between the desired EMFs and the decoupled control currents are used as objective functions. iv. The NSGA-III is combined with the decision-making model to address the multi-objective optimization configuration problem of C0.

This paper is concerned with the design and analysis of a bearingless motor.

The bearingless motor is obtained by a regular three-pole active magnetic bearing with an intentionally attached unbalanced mass on the rotor. It is the unbalanced mass that will generate the rotational torque for the motor function. Modeling and control of the unbalanced mass-type bearingless motor have been considered.

It is found through simulations that both functions of motor and magnetic bearing can indeed be achieved in this system.

This novel bearingless motor requires no additional windings and permanent magnets. Thus, it can greatly reduce the cost and design of the bearingless motor.

The purpose of this paper is to create a reliable nonlinear magnetic equivalent circuit (NMEC) of the hybrid magnetic bearing (HMB). Commonly used magnetic equivalent circuits of HMB omit a saturation effect of the magnetic material as well as the leakage and fringing flux. It results in imprecise modelling of the magnetic field distribution. On the other hand, only 3D finite element analysis (FEA) can be used to precisely simulate the magnetic field in this type of the magnetic bearing. The proposed NMEC incorporates the saturation effect of the magnetic material, as well as the leakage and fringing flux.

The magnetic equivalent circuit of presented HMB is proposed to obtain a reliable model that ensures short calculation time. Developed NMEC incorporates the phenomena as the saturation effect, as well as the leakage and fringing flux. The reluctance of the air gap that includes the fringing flux was calculated using 3D FEA. Kirchhoffs’ laws were used to create a set of nonlinear equations that were iteratively solved by Broyden’s method.

Incorporating into NMEC of the HMB a saturation effect of the magnetic material, as well as the leakage and fringing flux, resulted in the accurate model that was in good agreement with 3 D finite element model and the real object. The developed NMEC offers the calculation time in the range of miliseconds, therefore can be successfully used in the engineering design instead of the FEM.

Presented NMEC can be considered as a fundamental model that can be successfully used for accurate and fast simulation of the HMB. Proposed NMEC includes considerable factors that decide about the model accuracy such as the saturation effect of the ferromagnetic material and the leakage and fringing flux. The developed NMEC can be used in the optimization procedures and for simulations of dynamic responses.

This paper aims to suggest the use of air or iron intervals between axially magnetized rings to increase the forces and stiffness of permanent magnet passive magnetic bearings (PMBs). The paper calculates the stiffness of such bearings through an analytical method and optimizes the dimensions of the magnets for achieving maximum stiffness.

For determining the magnetic fields distribution, forces and stiffness of the bearings, a 2D analytical method is used, based on the subdomain method. For the sake of generalization, all of the parameters are normalized and optimized for maximum normalized stiffness per magnet volume ratio.

The optimum sizes of the magnets as well as the optimum dimensions of the air or iron intervals are calculated in this paper. The optimum sizes of the magnets are around the air gap length and it is very difficult to realize them. Using iron intervals can improve the stiffness to the extremely high values in practical dimensions of the magnets.

This paper presents a novel configuration for improving the performance of PMBs with alternately axially magnetized rings.

This paper aims to present bifurcation analysis of a magnetically supported coaxial rotor model in auxiliary bearings, which includes gyroscopic moments of disks and geometric coupling of the magnetic actuators.

Ten nonlinear equations of motion were solved using the Runge–Kutta method. The vibration responses were analyzed using dynamic trajectories, power spectra, Poincaré maps, bifurcation diagrams and the maximum Lyapunov exponent. The analysis was carried out for different system parameters, namely, the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position.

It was shown that dynamics of the system could be significantly affected by varying these parameters, so that the system responses displayed a rich variety of nonlinear dynamical phenomena, including quasi-periodicity, chaos and jump. Next, some threshold values were provided with regard to the design of appropriate parameters for this system. Therefore, the proposed work can provide an effective means of gaining insights into the nonlinear dynamics of coaxial rotor–active magnetic bearing systems with auxiliary bearings in the future.

This paper considered the influences of the inner shaft stiffness, inter-rotor bearing stiffness, auxiliary bearing stiffness and disk position on the bifurcation behavior of a magnetically supported coaxial rotor system in auxiliary bearings.

The paper presents the results of work on control systems of bearingless electric motors. Authors proposed the applications of bearingless electric machines for aircraft actuation system. Suggested solution characterizes novel concept of on-board equipment design such as More Electric Aircraft. Magnetic suspension technology allows elimination of friction force and the negative performance features of classic bearing system. However, to achieve all these purposes appropriately, dedicated control system must be also applied.

The development of a control system of bearingless electric machine is presented in detail. Mathematical model and construction of induction bearingless motor are widely discussed. Then, proportional–integral-derivative controller algorithm designing for BEM control system was presented using the well pole placement method. Simulation model of BEM control system with use of Matlab-Simulink software was shown. Finally, experimental studies on laboratory stand were introduced. The paper presents design methodology of conventional and advanced control system of bearingless motor.

The presented concept of the bearingless electric machines could be applied in the on-board actuation system. During research, full control system of bearingless electric motor was designed and tested. This system consisted of two subsystems. The first responded for rotary speed stabilization and second one was designed for position control of the rotor in the air gap.

The presented concept of the bearingless electric machines could be applied in the on-board actuation system. During research, full control system of bearingless electric motor was designed and tested. This system consisted of two subsystems. The first responded for rotary speed stabilization and second one was designed for position control of the rotor in the air gap.

The idea of active magnetic suspension system will be implemented for aviation on technology readiness level V. The paper presents unique laboratory stand with bearingless electric motor and experimental studies. The stable time responses of designed control system were presented and discussed. In addition, preliminary considerations of advanced control system with robust controller were introduced as well.

The purpose of this paper is to present the use of artificial immune systems (AISs) to solve constrained design optimization problems for active magnetic bearings (AMBs).

This research applies the AIS approach, more specifically, a representative clonal selection-based AIS called CLONALG, to the single-objective structural design optimization of AMBs. In addition, when compared with a genetic algorithm (GA) developed in the previous work, the CLONALG fails to produce best solutions when a nearly zero feasible ratio occurs in an AMB design problem. Therefore, an AIS called ARISCO (AIS for constrained optimization) is proposed to address the above issue.

A total of six AMB design cases are solved by the GA, CLONALG, and ARISCO. Based on the simulation results, in terms of solution quality, the ARISCO is shown to have better overall performance than the CLONALG and GA. In particular, when solving a problem with a nearly zero feasible ratio, the ARISCO and GA perform equally and both outperform the CLONALG.

In summary, the contributions of this paper include: this research applies the AIS approach, more precisely, the CLONALG, to the single-objective structural design optimization of AMBs; the ARISCO overall produces better AMB designs than the CLONALG and a GA developed in the previous work; in situations where a nearly zero feasible ratio occurs, the ARISCO and GA perform equally, and they both outperform the CLONALG.