# A New Rotor Position Measurement Method for Permanent Magnet Spherical Motors
## 5 Conclusions  
Rotor position measurement (RPM) is a precondition for closed-loop operation of spherical motors. This paper presents a novel RPM method for a PMSM based on image processing. In the proposed RPM, a LSGM was installed at the top of a PMSM rotor shaft, where three LEDs in the LSGM were arranged in a straight line with different distances to form three optical feature points (OFFPs). A high-speed  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measurement Method** & \multicolumn{2}{c}{**Photoelectric Sensor**} & \multicolumn{2}{c}{**Hall-Effect Sensor**} & \multicolumn{2}{c}{**High-Speed Camera**} \\ \hline \multirow{3}{*}{Tilting motion} & \(e_{\theta}(^{\circ})\) & 0.65 & 1.55 & 0.32 \\  & \(e_{\varphi}(^{\circ})\) & 0.58 & 1.62 & 0.3 \\  & \(e_{\omega}(^{\circ})\) & 0.49 & 1.47 & 0.31 \\ \hline \multirow{3}{*}{Spinning motion at Center point} & \(e_{\theta}(^{\circ})\) & 0.59 & 1.29 & 0.25 \\  & \(e_{\varphi}(^{\circ})\) & 0.51 & 1.36 & 0.3 \\  & \(e_{\omega}(^{\circ})\) & 0.47 & 1.28 & 0.3 \\ \hline \multirow{3}{*}{Edge spinning motion} & \(e_{\theta}(^{\circ})\) & 0.69 & 1.87 & 0.22 \\  & \(e_{\varphi}(^{\circ})\) & 0.62 & 1.83 & 0.3 \\ \cline{1-1}  & \(e_{\omega}(^{\circ})\) & 0.51 & 1.31 & 0.45 \\ \hline \hline \end{tabular}  
* \(e_{\theta}\) is the error of tilting angle\(\_\theta\); \(e_{\varphi}\) is the error of yaw angle\(\_\theta\); \(e_{\omega}\) is the error of spinning angle\(\_\omega\).  
\end{table}
Table 4: Comparison of different rotor position measurement methods.  
Figure 22: Experimental results of edge spinning motion of PMSM rotor: (**a**) Experimental and analytical results of \(\theta\); (**b**) difference between experimental and analytical results of \(\theta\); (**c**) experimental and analytical results of \(\varphi\); (**d**) difference between experimental and analytical results of \(\varphi\); (**e**) experimental and analytical results of \(\omega\); (**f**) difference between experimental and analytical results of \(\omega\).  
camera was used to capture the images of these three OFPs. The coordinate values of the three OFPs in the images were extracted to compute the tilting angle_\(\theta\), the yaw angle_\(\varphi\) and the spinning angle_\(\omega\) of the PMSM rotor, and thus obtain the rotor position of a PMSM. As there was no physical contact between a high-speed camera and a PMSM, extra moment of inertia and friction resistance, which may compromise the working performances of spherical motors, were avoided. The experimental platform was set up to verify the effectiveness of the proposed RPM method with high detection precision. In the future, we will install a tiny camera in a PMSM to measure the rotor position, which has negligible influence on the motion of rotor and structure of a PMSM. Combining with the other sensors, we will use the multiple sensor fusion method to further improve the precision of the RPM.  
[PERSON] and [PERSON] designed the architecture of rotor position measurement device, [PERSON], [PERSON] and [PERSON] helped the experiments. All of the authors wrote and revised the paper.  
This work is supported by the key project of the China National Natural Science Foundation (51637001).  
The authors declare no conflict of interest.