Control algorithm to reject the effect of iron sleepers for magnetic levitation vehicle using LSM with PM Halbach and ironless coil

In magnetic levitation (maglev) system, suspension, guidance and propulsion are provided by magnetic forces. Basically, there are two kinds of linear motors utilized to provide propulsion force for maglev vehicles [1, 2]. One design is called linear synchronous motor (LSM), and the other is linear induction motor (LIM). LSM possesses the dominant advantage of high efficiency, and is widely applied in high-speed maglev vehicles, such as Germany TR maglev vehicle and Japan MLU/MLX superconductive maglev vehicle. LIM is widely used in low-speed maglev systems, such as Japan HSST maglev vehicle. The reason is that LIM suffers from the influence of eddy current [3], which in return generates acceleration resistance for the maglev vehicle. As the increase of people’s demands for rapidity and energy-saving, it is appreciable that the tendency of propulsion system for maglev vehicles is toward LSM. Typically, LSM in the maglev system is composed of iron coils on the guideway supplying primary magnetic field and electromagnets on the vehicle offering secondary magnetic field. There are energy-consuming in both the electromagnets and the iron coils in this kind of LSM. One method to reduce the energy-consuming on the vehicle is to replace electromagnets with Permanent Magnets (PMs) [4, 5], which can provide field without power supply. The improvement of the performance of PM materials [6] and the present of Halbach array [7] greatly promote the application of PM in LSM. Currently the maximum magnetic energy product of permanent magnets applicable to commercial manufacture has achieved at 397.9 kJ/m. And Halbach array is an innovative combination of PMs arranged with different magnetization directions and it can enhance the magnetic field on one side while weaken the magnetic field on the other side. Iron coils should not be utilized if the magnetic field on the vehicle is provided by PM Halbach, or there will be strong attractive force (normal force) between the PMs on the vehicle and the iron on the guideway. Thus LSM with PM Halbach and ironless coil is a good candidate to maglev propulsion system, and it has the characteristics of zero power supply on the vehicle and zero normal force. This innovative structure of LSM has been successfully utilized in American GA maglev vehicle. The magnetic field and force generated by LSM with PM Halbach and ironless coil are studied in previous literatures. H. Bergh et al. presented the approximate analytical solution to magnetic field of Halbach near the surface and deduced the propulsion and normal force generated by the LSM [8]. To investigate the magnetic field far away from the surface, J.F. Hoburg analyzed the static magnetic field of dual Halbach array for GA maglev vehicle by magnetization charge theory, but the results are quite complicated [9]. C.S. Li et al. investigated the optimization technique of PM Halbach array for electrodynamic suspension (EDS) maglev [10]. Magnetic field and optimization design of rotary motor using PM Halbach are conducted by Z.P. Xia et al. [11] and M. Markovic et al [12]. X. Zhang et al. investigated the magnetic field and the magnetic force of LSM with PM Halbach and ironless coil by introducing surface current theory [13]. However, no attention has been paid to the iron sleepers on the guideway, with which attractive force can be generated between the PM Halbach and the guideway. The direction of this attractive force is opposite to the suspension force, which will increase the suspension load and affect the suspension performance. This paper focuses on analysis of the effect of the iron sleepers on the suspension system using LSM with PM Halbach and ironless coil and the design of the control strategy to reject this effect. The analytical model of the attractive force is proposed by introducing the approximate analytical expression for the field of PM Halbach. And then the suspension performance under consideration of the iron sleepers on the guideway is testified by simulation, which demonstrates that the effect of iron sleepers on the suspension system cannot be ignored. The control strategy to reject this effect is designed, and its effectiveness is illustrated by simulation. This paper is organized as follows. Section 2 presents the structure of LSM with PM Halbach and ironless coil, and the iron sleepers on the guideway. Section 3 introduces the analytical description of the magnetic field of PM Halbach, and develops analytical solution to attractive force generated by PM Halbach and iron sleepers. Section 4 investigates the effect of iron sleepers on the suspension system by adding the proposed force to suspension system, and simulation result shows that the attractive force brings resonance to suspension system with typical state feedback controller. In section 5, a nonlinear controller is designed using a feedback linearization technique, and simulation result shows that it is quite effective to reject the resonance resulting from sleepers. Finally, a brief summary are discussed in Section 6.