Suppression of maglev vehicle–girder self-excited vibration using a virtual tuned mass damper

The self-excited vibration that occurs between a stationary Electromagnetic Suspension (EMS) maglev vehicle and a girder is a practical problem that greatly degrades the performance of a maglev system. As of today, this problem has not been fully solved. In this article, the principle underlying the self-excited vibration problem is explored, and it is found that the fundamental resonance frequency of the maglev girder plays a vital role in the initiation of the self-excited vibration. To suppress the self-excited vibration, a scheme applying a tuned mass damper (TMD) to the maglev girder is proposed, and the stability of the combined system is analyzed. Furthermore, a novel concept of a virtual TMD is introduced, which uses an electromagnetic force to emulate the force of a real TMD acting on the girder. However, in the presence of the time delay caused by the inductance of the electromagnets, the stability analysis of the levitation system combined with the virtual TMD becomes complex. Analysis of the stability shows that there exist some repeated time delay zones within which the overall system is stable. Based on this rule, time delay control is introduced to stabilize the system with a virtual TMD, and a procedure to determine the optimal time delay and gain is proposed. Numerical simulation indicates that the proposed virtual TMD scheme can significantly suppress the self-excited vibration caused by one unstable vibration mode, and is suitable for application to EMS maglev systems.