# A Real-Time Numerical Decoupling Method for Multi-DoF Magnetic Levitation Rotary Table
## 4 Experiment Results
### Computation Resource  
The RTL implementation processing the floating-point data always spends many hardware resources in FPGA. Here, the required hardware resources and the occupation ratio, containing the look-up table (LUT), Flip Flop (FF), and digital signal processor (DSP), are given in Table 4 for each module. The current decoupling unit contains two parts: the numerical wrench model and matrix operation. The former is constructed by the **FT** and SUM IP cores, and the latter uses the **MO** IP core. The trajectory, display, and data-storing module for testing also consumes some resources. The total occupied computation resources are not beyond 20%. Thus, there are enough spare resources for the next control algorithm design. Low resource occupation benefits from the pipelined RTL structure in which only one numerical FT IP core is employed. Meanwhile, as only the 7 nearest magnets to the current-carrying region were selected for force and torque computation, the computation burden significantly decreases. Computation efficiency can further develop if more **FT** IP cores are employed in the implementation. However, referring to the existing magnetic levitation system, we assumed that the 5 kHz sampling frequency is high enough for the design of the matching controller.  
Discussion of FPGA-Based Numerical Current Decoupling Unit for Magnetically Levitated Rotary Actuator  
The FPGA-based numerical current decoupling unit for the maglev actuator is based on the numerical wrench model and the matrix operation module. The experiments prove the effectiveness of the current decoupling RTL component in two aspects. First, the solutions of the numerical wrench model were compared with the unified BEM program package Radia(tm). The error ratios of the results from the numerical wrench model were not beyond 5% and 10%, and these results were assumed to reflect the real performance of the maglev actuator. Second, the current vector solved by the current decoupling unit was substituted in the boundary element model to evaluate validity. Even if there exists some force and torque ripples in the simulation results, these deviations could be inhibited by the feedback control in the real magnetic levitation system.  
Computation efficiency and the occupied computation resources of the decoupling unit affect its application in the real controller. Referring to the computation unit amount calculated by Equation (13) and the synthesis reports from HLS(tm), the computation delay was less than 200 \(\upmu\)s, which is high enough for the sampling cycle of a real maglev system controller. Furthermore, the data given in Table 4 also show that the implementation of the decoupling unit is not a burden for the existing  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**FPGA Resources**} & \multicolumn{3}{c}{**Current Decoupling Module**} & \multicolumn{3}{c}{**Data Displaying and Storing Modules**} \\ \cline{2-6}  & **Wrench Model** & **Matrix Operation** & **Trajectory** & **DAC Connector** & **SDIO Driver** \\ \hline LUT & 45,672 (15.04\%) & 5664 (1.87\%) & 6433 (2.12\%) & 1606 (0.53\%) & 869 (0.29\%) \\ FF & 38,806 (6.39\%) & 9329 (1.54\%) & 4546 (0.75\%) & 680 (0.11\%) & 502 (0.08\%) \\ DSPs & 245 (8.75\%) & 76 (2.71\%) & 56 (2.00\%) & 16 (0.57\%) & 0 (0.0\%) \\ \hline \hline \end{tabular}
\end{table}
Table 4: FPGA resource utilization for hardware implementation. DPSs—digital signal processors; FF—Flip Flop; LUT— look-up table.  
Figure 9: Magnetic force and torque simulation results solved by Radia(tm) using current solutions from the real-time numerical current decoupling unit shown in Figure 8.  
FPGA evaluation board. In future work, the magnetically levitated rotary table will be fabricated, and the multi-DoF motion controller will be constructed based on the proposed FPGA-based current decoupling unit.