**1. Introduction**

The linear induction motor (LIM) has been widely studied as a transportation system running in urban areas owing to its low noise, environmentally friendly factors that do not generate dust, and its excellent performance on slopes and around sharp curves. An LIM is a system that levitates and is propelled through the interaction of the rails and vehicles using the power of an electromagnet. It comprises, primarily, a levitation system and a propulsion system. In the levitation system, as shown in Figure 1b, the train guide generates an attraction force through the lower part of the rail to levitate the train. As shown in Figure 1a, the propulsion system generates magnetic flux using an electromagnet mounted on the train, linking it to the rail. Subsequently, the linkage magnetic flux generates a counteracting flux in the direction of the train on the rail. Consequently, the train and rail are attracted and repelled by the correlation between the magnetic flux generated by the electromagnet mounted on the train and the counteracting magnetic flux of the rail. The LIM generate thrust for propulsion through attraction and repulsion—a normal force being generated in the rail direction. Therefore, to generate the thrust required to propel the train, a normal force that does not contribute to the propulsion of the train is generated. In addition, because the normal force is generated in the opposite direction of the levitation force of the train, the levitation system must overcome gravity and normal

forces, and float the train. In other words, the unnecessarily generated normal force is a factor that destabilizes the levitation system of the train, it being a potential safety problem due to train levitation failure. It also induces additional energy consumption in both the propulsion system and the levitation system, thereby reducing efficiency [1]. Therefore, for the efficient operation of trains, a train control technique that reflects the characteristics of linear devices is required.

**Figure 1.** Structure of maglev train: (**a**) Structure of trains and rails and (**b**) Structure of levitation system.

For LIM control, a control method using slip frequency and a method using indirect vector control were widely studied. The slip-frequency control method was used because of its independence from parameter fluctuations and ease of implementation. Because the linear motor is based on an induction motor, the size of final load *RL* fluctuated according to slip, as shown in Figure 2a. Accordingly, the ratio of the current for magnetization and the current for propulsion fluctuated. As shown in Figure 2b, the magnitude of the input current required for operation based on the slip increased when the slip was large, and decreased when the slip was small [2–5].

**Figure 2.** Efficiency fluctuation due to slip: (**a**) Induced motor equivalent circuit and (**b**) Input current and slip.

Because the LIM is a system based on an induction motor that cannot directly control the slip, the slip frequency (having a proportional relationship to the slip) was used. Accordingly, a study was conducted on a method of improving efficiency through the size of the slip frequency [6–8]. However, slip is a factor related to the normal force that affects the potential failure of the train. There is also a problem in that normal force increases when the size of slip frequency decreases [9].

In [8], a fixed slip-frequency control method was proposed that used fixed high slip frequency that did not fail to levitate the train. However, by using the same slip frequency in the operating bands of all trains, a problem occurred in that operating efficiency was lowered by using the same slip frequency, even in sections where high slip frequency was not required (on the basis of train operating conditions). Subsequently, a study of a variable slip-frequency control method was conducted to change the slip

frequency on the basis of the operating conditions of the train to lower the slip frequency while limiting the normal force of the LIM [10].

Second, as a method, an indirect vector control method was proposed that is widely used in rotary induction motors with fast response and excellent performance [11]. However, for indirect vector control, the air-gap magnetic flux must be kept constant, but is difficult to apply in the LIM because the air-gap magnetic flux fluctuates during train operation owing to the characteristics of linear devices. In [12–15], a method was presented using the current of the *d* axis, which is the axis where the magnetic flux of the motor is generated during the vector control of an induction motor. The attenuated magnetic flux was compensated by controlling *d*-axis current *id*. However, this method also had a problem, in that *iq* associated with the thrust force fluctuated to maintain the slip frequency constant when *id* was changed to compensate for the attenuated magnetic flux, as shown in slip angular velocity Equation (1) of indirect vector control (here, *iq* means the current in the *q* axis generating torque in the *d*-*q* axis for vector control):

$$
\omega\_{sl} = \frac{1}{T\_r} + \frac{i\_q}{i\_d} \tag{1}
$$

where <sup>ω</sup>*sl* is the slip angular velocity, *Tr* = *Lr Rr* , *Lr* is rotor winding impedance, *Rr* is rotor winding resistance, *id* is the d-axis current (air-gap magnetic flux), and *iq* is the q-axis current (thrust).

Accordingly, in [16], a control method using both indirect vector control and variable slip-frequency control was proposed. When the *id* value was changed to compensate for the air-gap magnetic flux, ω*sl* changed using *iq* such that the slip value was within the allowable range. However, because this method was not a result derived through mutual mathematical analysis of train operating conditions, it was difficult to guarantee safety because the exact normal force was unknown. In addition, because all input values for each condition must be derived through direct experiments, the process costs much time and money. For this reason, maglev trains currently in operation utilize a fixed slip-frequency control method that can guarantee train safety. Therefore, in order to improve train efficiency while ensuring safety, it is necessary to analyze the mutual influence through mathematical analysis of the slip, normal force, and propulsion force. On the basis of the analyzed data, if the calculated slip frequency is instantaneously changed on the basis of the operating conditions of the train, it is possible to safely and efficiently operate the train (the proposed method increases efficiency by using the ratio of slip frequency, normal force, and traction force, which are the characteristics of electromagnetic-suspension-type LIM. Therefore, it is difficult to apply this method to types of maglev trains with different structures and driving methods).

The remainder of this paper is organized as follows. In Section 2, the mathematical relationship between normal/propulsion force and slip frequency is analyzed through an investigation of the relationship among normal force, propulsion force, slip, and slip frequency. After that, through the derived equation, the change in efficiency within the limited normal force is presented. Consequently, a control algorithm for controlling the proposed method is presented. In Section 3, the effect is shown through simulation. In Section 4, experimental evaluation conducted using actual vehicles running on the island of Yeongjong, Korea is summarized. Lastly, Section 5 presents our conclusions.

### **2. Control Method**
