Current-Bounded Commutation of a Long-Stroke Magnetically Levitated Stage with Moving Coils

Magnetically levitated stages（MLS） have potentials to obtain good motion performances in high vacuum environment. Yet the electromagnetic forces/torques corresponding to six degrees of freedom（DOF） motions have coupling relationship with each current of coil array, and this coupling is still associated with the relative positions between the mover and the stator of the stage. So it is quite difficult to control the 6-DOF motions of the stage. By reasonable commutation of coil array, this complicated coupling relationship can be decoupled. The analytical force/torque-decomposing model of the stage is established first. Then the initial currents of coil array are commutated based on the pseudo inverse of the analytical force/torque-decomposing model matrix. And then the coil array currents are commutated again with different current bounds given to the initial currents as well as in the sense of minimum 2-norm of currents vector. Using the long stroke magnetically levitated stage with moving coils under investigation as examples, the currents of coil array are commutated with different current bounds adopting the proposed commutation method, the determination of current bound and the current bounds＇ influences on the heat-losses in coil array are analyzed, and the effectiveness of implementation algorithm of proposed commutation method is discussed. Simulation, analysis and discussion results indicate that the currents of coil array within the given current bound can be solved analytically by proposed commutation method, and the implementation algorithm does not need any searching or iteration. By the current-bounded commutation method proposed, the amplitude of coil array currents can be limited within an appropriate current bound（This is very beneficial to the improvement of the reliability and motion performance of the stage）, as well as these currents can also generate the desired forces and torques.

A solution using only electromagnetic coils for relative pose control in satellite docking

This paper proposes an electromagnetic coil topology and its control strategy,which can be incorporated into the electromagnetic docking device to achieve relative pose control in satellite docking.The target satellite has a main coil;the chaser satellite possesses a main coil of the same size accompanied by six and four evenly arranged secondary coils inside and outside the main coil,respectively.The coil on the target satellite is DC energized,while the currents in the coils of the chaser satellite are regulated.To remove the coupling between the pitch/yaw torque and translational force,the internal and external secondary coils of the chaser satellite interact with the main coil of the target satellite to perform the control of relative pitch/yaw and relative translation,respectively,so relative pose control can be achieved.The torque and force vectors exerted by the secondary coils of the chaser satellite are synthesized onto the pitch and yaw axes of the body frame.According to their spatial composition relationship,the formulas are proposed,which obtain the magnetic moment vectors of the coils from the set torques and forces.The controllers regulating pitch/yaw,translation,and distance utilize a three-loop cascaded structure that consists of an outer position loop,a middle velocity loop and an inner current loop.The control strategy is verified by dynamics simulation.

Relative roll control of satellite docking using electromagnetic coils

An electromagnetic coil topology and its control strategy,which can be incorporated into the electromagnetic docking device,have been proposed for the relative roll control of two satellites in space.The target satellite and the chaser satellite are respectively embarked with four and six coils evenly arranged around the docking axis.All the coils on the target satellite are Direct Current(DC)energized,while the currents in the coils of the chaser satellite are regulated to achieve the relative roll control.The electromagnetic force/torque model is built by utilizing the frequentlyused far field model.Based on the fundamental components extracted from that model,this paper proposes a real-time magnetic moment vector distribution formula that simply generates a constant roll torque.This paper not only presents an equation for calculating the relative roll angle through the Euler angles of two satellites,but also an equation that converts the roll torque setpoint to the setpoints of the coil currents.A 3-closed-loop positioning controller composed of angle,angular velocity,and current loop is developed.The proposed topology is verified by finite element simulation,and the control strategy is validated by dynamics simulation and ground-based tests.