Analysis of coupled motion constraints and coupling errors for a six-axis magnetic levitation stage

Abstract

This paper presents the coupled motion constraints and coupling errors analysis of a magnetic levitation stage, which are two aspects of the coupling characteristics of magnetic levitation stage caused by force coupling. Aiming at the motion constraint coupling problem, this paper proposes a motion constrain method based on the force distribution matrix of the magnetic levitation stage. By this method, the motion constraint intervals without input saturation for single-degree-of-freedom motion, in-plane motion, and out-of-plane motion of magnetic levitation stage are established. When used for motion control, these constraints can provide the motion constraint specifications for the magnetic levitation stage, avoid the input saturation problem caused by the actuation force coupling, and provide a theoretical basis for magnetic levitation stage trajectory planning. Aiming at reducing the coupling error, this paper proposes a strategy to evaluate the coupling degree of the magnetic levitation stage actuation force by the condition number of the actuation force transfer matrix and the singular value of the force and torque error matrix. On this basis, the force and torque coupling errors caused by the translational and rotational movements of the magnetic levitation stage are studied, and the mechanism and characteristics of the coupling error between the interaction of translational and rotational movements are revealed. Based on the obtained results, the decoupling algorithm of the magnetic levitation stage is designed. Experimental results of the normalized step response demonstrate that the linearity of the magnetic levitation stage will be destroyed by the current saturation, and coupling error can also be introduced. Therefore, it is necessary to study the motion constrain strategy to provide comprehensive criteria for the trajectory planning and controller design. Experimental results of six-axis coupling error analysis show that the coupling error of x- and y-axes translational movement is reduced by 69.34% and 69.60%, respectively. This method provides a theoretical basis for the decoupling of the magnetic levitation stage and reducing the coupling error.