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The capacity of improving the control accuracy and dynamic performance of a four degree-of-freedom (DOF) permanent magnet biased active magnetic bearing (PMBAMB) system is critical to developing and maintaining a high precision application in a magnetically suspended direct-driven spindle system. The 4-DOF PMBAMB system, however, is a multivariable, strong coupled and nonlinear system with unavoidable and unmeasured external disturbances, in addition to having parameter variations. The satisfactory control performance cannot be obtained by using traditional strategies. Therefore, it is important to present a novel control scheme to construct a robust controller with good closed-loop capability. This paper proposes a new decoupling control scheme for a 4-DOF PMBAMB in a direct-driven spindle system based on the neural network inverse (NNI) and 2- degree-of-freedom (DOF) internal model control method. By combining the inversion of the 4-DOF PMBAMB system with its original system, a new pseudolinear system can be developed. In addition, by introducing the 2-DOF internal model controller into the pseudolinear system to design extra closed-loop controllers, we can effectively eliminate the influence of the unmodeled dynamics to the decoupling control accuracy, as well as adjust the properties of tracking and disturbance rejection independently. The experimental results demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

• The operation of a four degree of freedom hybrid magnetic bearing (4-DOF HBM) can be considered as a repetitive process. • Iterative learning control is advantageous to deal with repetitive control problems. • The iteration variant disturbances are considered. • A modified iterative learning controller with an extended state observer (ESO) is presented. • Good performances of anti-disturbance and stability for HMBs system are achieved. Iterative learning control (ILC) is an iterative control strategy which calculates a new input according to the error in previous cycles. It is widely used in industries with repetitive operations. Since magnetic bearing systems can be considered as running in a repetitive task, the ILC could be applied. Hence, this paper proposes a modified iterative learning control (ILC) strategy for a four degree-of-freedom (DOF) hybrid magnetic bearing system to reject the disturbance based on an extended state observer (ESO). The feasibility of applying the ILC to the four-DOF magnetic bearing system is analyzed firstly. It is proved that the tracking error can converge by selecting suitable controller parameters. Secondly, to accurately obtain the uncertainties in the operation process, an ESO is designed. As for a repetitive rotation process, the iteration variant disturbance may have a certain influence on the performance of the system which is not usually considered. Therefore, the iteration variant disturbance is introduced and the effectiveness is derived. Finally, simulations and experiments are carried out to demonstrate the effectiveness of the proposed method. The classical proportion-integration-differentiation (PID) control and an existing proposed neural network inverse (NNI) control are implemented for comparison. The results show that the proposed strategy can achieve better reference tracking and disturbance suppression ability than PID and NNI control. [ABSTRACT FROM AUTHOR]