# Electromagnetic Characteristics Analysis of a Tubular Moving Magnet Linear Generator System
## 2 Linear Generator Design
### Linear Generator Controller Design  
When driven by the high-speed reciprocating motion of FPEs, the electromotive force (EMF) of the designed linear generator in the last section is quasi-sine ware. The frequency of the EMF will be equal to the frequency of the reciprocating motion. This is because the reciprocating motion stroke is short than the pole pitch of the linear generator, and the direction of the EMF will be constant during a stroke. Current commutation is not needed during a stroke. This characteristic makes the current control of the single-phase linear generator easier than that of the reported designs.  
\begin{table}
\begin{tabular}{c c} \hline
**Items** & **Value** \\ \hline Stator diameter & 138 mm \\ Stator length & 155 mm \\ Mover diameter & 58 mm \\ PM length & 30 mm \\ Pole pitch & 47 mm \\ Max stroke & 40 mm \\ \hline \end{tabular}
\end{table}
Table 1: Main dimensions of the designed linear generator.  
Figure 2: The structure of the designed linear generator.  
Figure 3 shows the designed power convertor for the control of the linear generator. A pulse width modulation (PWM) H-bridge power converter is designed to control the generating process of the linear generator. A standard sine ware is selected for the aimed generating current. The amplitude of the generating current is adjusted according to the needed power output. A discrete proportion integration differentiation (PID) algorithm is used for the current feedback control.  
The equivalent circuit of the designed linear generator is also shown in Figure 3. The linear generator can be equivalent to a series of the coil resistance, the coil inductance, and the EMF voltage source. The EMF can further equal the product of the EMF coefficient and the mover moving speed of the linear generator. The three electromagnetic parameters will be calculated by the finite element model, which will be created and validated in the next section.  
Table 2 lists the main parameters for the control of the designed linear generator, including the control parameters and characteristic parameters of the selected power switch devices. As shown in the table, a kind of insulated gate bipolar translator (IGBT) is selected for the power switch to enable a large generating current of up to 120 A. The restricted unipolar method is used for the pulse width modulation (PWM) control. The control method can reduce the electromagnetic loss of the controller as much as possible. The parameters will be used by the model during the simulation.  
The parameters for the control of the linear generator are selected according to the electromagnetic characteristics of the designed linear generator. The voltage of the battery is selected to be higher than the maximum terminal voltage of the linear generator when it is working at the rated conditions. This is because the H-bridge power convertor works in boost mode when it uses as a rectifier. The PWM frequency is selected according to the coil inductance of the linear generator. The servo frequency is selected according to the requirement of the control accuracy. The power switch devices are selected according to the latest technology of the automotive IGBT chips.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Value** \\ \hline Voltage of the battery & 200 V \\ Max current of IGBT & 120 A \\ IGBT saturation voltage & 1.5 V \\ Diode forward voltage & 1.65 V \\ Filter capacitor & 400 \(\mu\)F \\ PWM Frequency & 20 kHz \\ Servo Frequency & 10 kHz \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main parameters for the control of the linear generator.  
Figure 3: Power convertor designed for the linear generator.