# Suppression of Harmonic Current in Magnetic Bearing-Rotor System with Redundant Structure
## 1 Introduction  
Compared with mechanical bearings, magnetic bearings are considered to be superior with characteristics of no physical contact, low rotation friction, high speed, and long life. These advantages have led magnetic bearings to become the key components of important industrial fields, such as aero engines, turbine generators, and energy storage flywheels [1, 2, 3]. However, mechanical component damage and electrical part failure will render the system unable to continue working, and the rotor will fail. Therefore, the fault-tolerant design of magnetic bearings is an effective way to solve the problem that will improve the reliability of the magnetic-levitated bearing system while under extreme conditions [1, 4, 5]. On the basis of the strongly coupled fluxes and equivalent magnetic circuit model of the heteropolar magnetic bearing, [PERSON] and [PERSON] et al. first proposed magnetic bearings with redundant structures and designed the fault-tolerant control strategy when different coils fail [6]. The core of fault-tolerant control is to obtain the current distribution matrix and make the magnetic bearing generate the desired force with residual normal coils. Furthermore, the bias current linearization theory and current distribution matrix providean approach to achieve the fault-tolerant control for magnetic bearings with redundant structures. After the theory was proposed, related research was further carried out. [PERSON] and [PERSON] [7] proposed the Lagrange multiplier approach to obtain the current distribution matrix and analyzed the position stiffness and voltage stiffness of the magnetic bearing with redundant structures. They adopted the simulation and experiment to verify the validity of the fault-tolerant control strategy [8]. Moreover, [PERSON] [9] established a fault-tolerant controller for the eight-pole symmetrical radial magnetic bearing with redundant structures and carried out an experiment on a turbo-molecular vacuum pump. They realized that the rotor remained levitated with the failure of three simultaneous coils at the rotor speed of 4200 rpm. Considering the magnetic leakage, eddy current, and reluctance of the ferromagnetic material path factors in the magnetic bearing, [PERSON] and [PERSON] [10; 11; 12] introduced a compensation coefficient to the force of magnetic bearing and obtained the corresponding current distribution matrix. Recently, [PERSON] [13] proposed an unbiased control theory to design a fault-tolerant controller for magnetic bearings with redundant structures, which can be applied to the encompassed bearings with an arbitrary number of poles. The current distribution matrix reflects the mapping relationship between electromagnetic force and current. [PERSON] and [PERSON] [14; 15] extended the theory of calculating the current distribution matrix from the equilibrium position to nonequilibrium position and designed an improved fault-tolerant controller. The simulation results showed an improvement in the performance of the magnetic bearing-rotor system with the proposed fault-tolerant control strategy. For stators with the characteristics of an even number of evenly spaces poles of equal area, [PERSON] and [PERSON] [16] proposed an effectively simplified method to design a fault-tolerant controller while some coils fail in magnetic bearings. Different bias current coefficients can lead the magnetic bearing to produce different characteristics of electromagnetic force. [PERSON] and [PERSON] [17] proposed an optimal algorithm to acquire the reasonable bias current coefficient, and the simulation results illustrated that the proposed approaches improve the system performance. Furthermore, according to the need of a fault-tolerant controller applied to magnetic bearings with redundant structures, they designed a fault-tolerant control scheme that includes dual DSP microprocessors and a power amplifier [18]. However, for magnetic bearings with redundant structures, most research has focused on obtaining the current distribution matrix when different coils fail.