# A Real-Time Numerical Decoupling Method for Multi-DoF Magnetic Levitation Rotary Table
## 4 Experiment Results
### Validation of the Real-Time Wrench Model and Current Decoupling Unit  
To evaluate the computation accuracy of the numerical wrench model, the solutions of all coils in the coil set were solved and shown on an oscilloscope, assuming the mover in the maglev system takes motion along the trajectory of Equation (16) for \(0.1\) s. In each subfigure of Figure 7, the left column shows the force components, and the right shows the torque components in the current-wrench transformation matrix. With a \(5\) kHz sampling frequency, there were \(501\) sampling points on each waveform. As the boundary method is very time-consuming, only \(101\) sampling points were calculated here. In this figure, the waveform and the BEM results are very approximate. To quantitatively analyze the accuracy of the proposed real-time numerical wrench model, the relative error ratios of the wrench vector from the FPGA were calculated using BEM results as the benchmark. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Parameter** & \(I_{c}\) & \(w_{c}\) & \(r_{c}\) & \(h_{c}\) & \(I_{m}\) & \(w_{m}\) & \(h_{m}\) & **Remanence** & **Coil Turns** \\ \hline Value & \(60\) mm & \(10\) mm & \(10\) mm & \(10\) mm & \(30\) mm & \(8\) mm & \(8\) mm & \(1.2\) T & \(300\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design parameters for the magnetically levitated rotary actuator shown in Figure 1.  
Figure 6: (**a**) Computation and displaying device for the implementation of numerical current decoupling for the magnetically levitated rotary actuator; (**b**) necessary computation modules in register-transfer level (RTL) structure and peripheral device for evaluation board. Table 3 shows the average relative error of the resultant force and torque considering the 101 sampling points in the BEM model via Equation (17):  
\[(\eta_{\mathbf{F}},\eta_{\mathbf{T}})=\frac{1}{100}\sum_{\text{point}=0}^{101} \left(\frac{\left\|\mathbf{F}_{\text{wm,point}}-\mathbf{F}_{\text{BEM,point}} \right\|}{\left\|\mathbf{F}_{\text{BEM,point}}\right\|},\frac{\left\|\mathbf{T} _{\text{wm,point}}-\mathbf{T}_{\text{BEM,point}}\right\|}{\left\|\mathbf{T}_{ \text{BEM,point}}\right\|}\right)\times 100\%, \tag{17}\]  
where \(\mathbf{F}_{\text{wm}}\), \(\mathbf{T}_{\text{wm}}\), and \(\mathbf{F}_{\text{BEM}}\), \(\mathbf{T}_{\text{BEM}}\) are the resultant force and torque produced by each coil via the numerical wrench model or the BEM software at each sampling point, respectively. Observing the results in Table 3, we concluded that the force and torque error were not beyond 5% and 10%, which highlights that the real-time numerical wrench model has a similar computation accuracy compared with the BEM for the magnetically levitated rotary actuator. Figure 7: Waveform of real-time solutions on the oscilloscope (**up**) and boundary element method (BEM) solution obtained by RadiaTM (**down**). (**a–h**) Results of **Coil 0\(\sim\)Coil 7**, respectively. In order to test the real-time current decoupling unit, the magnetically levitated rotary actuator is assumed to provide a force and torque vector, \([0\;\mathrm{N},0\;\mathrm{N},20\;\mathrm{N},0\;\mathrm{N}\cdot\mathrm{mm},0\; \mathrm{N}\cdot\mathrm{mm},200\;\mathrm{N}\cdot\mathrm{mm}]\), acting on the rotor when it moves along the trajectory of (16) in 0.5 s. The current results for each coil are illustrated as waveforms in Figure 8. Meanwhile, the decoupling current estimated by the BEM solutions are also given as dots in this figure. The real-time numerical current decoupling unit results are not only close to the ones from the off-line emulator, but also can be employed in the controller directly for current regulation in each phase of the coil set. Furthermore, the obtained current value is substituted in the BEM model to solve the magnetic force and torque produced at the corresponding sampling points. In Figure 9, the 101 real-time current solutions shown in Figure 8 are used as the exciting current in the BEM model to calculate force and torque values.