# An Experimental Validated Control Strategy of Maglev Vehicle-Bridge Self-Excited Vibration
## 1 Introduction  
Compared with the traditional railway train system, the electromagnetic maglev system has advantages of less exhaust fumes emission, lower noise and the ability to climb steeper slopes, which has attracted wide attention in recent years [1; 2; 3]. Maglev's rapid development and its potential commercial applications depict a bright future. However, there are still some issues to be solved urgently, such as the vehicle-bridge stationary self-excited vibration [4; 5]. When the maglev train is suspended on some special bridges with minor weight per meter, the maglev train and bridges may vibrate vertically and continuously, which degrade the stability of the levitation control and the ride comfort. In magnetic engineering, due to its clear physical meaning and excellent performance, the cascaded-loop control architecture with displacement-loop and current-loop to control the electromagnetic force is widely adopted [6; 7]. According to the formulation of the electromagnetic force, the electromagnetic force is related to the levitation gap and current. To some extent, the electromagnetic force, the levitation gap and the current are interactive and complex. As we all know, from the perspective of the magnetic flux, the electromagnetic force is solely determined by the magnetic flux [8]. The relationship between the electromagnetic force and magnetic flux is simple and clear, if the magnetic flux-loop instead of the traditional current-loop is adopted to control the electromagnetic force, it may be favorable for the stabilization of interaction system. Hence, the magnetic flux will be discussed and adopted in this paper. To master the underlying principles of the self-excited vibration, plenty of studies have been carried out from different perspectives. [PERSON] et al. [9; 10] pointed out that the American magnetic levitation system was successfully suspended in Florida, but it was incapable of achieving stable suspension when the vehicle was moved to the old Dominican university campus. They believed that the over-flexibility of the latter bridge was the main reason for the difficulties of stable suspension. [PERSON] et al. believed that the self-excited vibration is caused by the inappropriate frequency relationship between the various components of the Maglev vehicle-bridge interaction system [11]. Therefore, the proper frequency distribution is an effective strategy to avoid the resonance. The center manifold method was carried out to discuss the underlying principles of the self-excited vibration in the literature [12; 13]. It is believed that the self-excited vibration results from the bifurcations and chaos. The aforementioned studies about the roots of the self-excited vibration provide us inspiration to avoid the vibration. In this paper, based on the proposed minimum model, the underlying principles of the self-excited vibration will be explored from the real parts of its characteristic roots. To eliminate the self-excited vibration, the methods, including optimization of the parameters and minimization of the time-delay of feedback channels [14], virtual tuned mass damper algorithm [15] and the virtual energy harvester algorithm [16] are explored by different scholars. They believed that these control strategies can avoid the self-excited vibration for the given bridge. [PERSON] intends to develop a neuro-PI (proportional-integral) controller to control the dynamic response of the maglev vehicles around an allowable prescribed acceleration, numerical simulations demonstrate that a trained neuro-PI controller has the ability to control the acceleration amplitude for running maglev vehicles [17]. However, due to the complexity, the robustness to bridges with different modal frequencies awaits further research. In this paper, by the analysis of the block diagrams in depth, we find that removing the displacement feedback of bridge instead of the feedback in pairs is an effective technique to enable levitation subsystem passivity and to solve the problem of self-excited vibration theoretically.