A method for modeling of the dynamics characteristics for a 5-phase permanent magnet tubular linear motor (PMTLM) is presented. Its electromagnetic nonlinear field analysis with finite element method (FEM) has been coupled with the circuit model. The calculation model includes the equations for electrical circuits and mechanical quantities as well. They have been obtained using Lagrange's method. The calculated and measured waves of the mover position have been compared for several values of the excitation current. This comparison yields a good agreement. Presented calculation model is very useful in designing and optimization of the PMTLM and in the calculation of the parameters for the control algorithms intended for such a type of actuators.

Different from the synchronization mechanism of synchronous generators, the non-synchronous generators must be synchronized with the grid through a controller. Generally, the virtual synchronous generator (VSG) control strategy is adopted for this purpose. In view of the current situation, where the control loops are not comprehensively considered in the research of the synchronization stability of the VSG, this paper considers multiple control loops, such as active frequency loops, virtual governors, power filters and current constraint control, to establish the mathematical model of the VSG and infinite system. On this basis, the correlation formula between power angle difference and control parameters is deduced. Adopting the phase plane method, the influence of different control loops and their parameters on the transient synchronization stability is analyzed. Finally, a setting principle of the frequency modulation coefficient of virtual governors is proposed, which not only meets the response speed of control systems, but also has good control performance.