## 5 Conclusions  
The purpose of this article was to investigate the disturbance behavior of the sun-tracking solar arrays. Firstly, a disturbance torque model, which took the friction torque and the flexibility of the solar array into consideration, was proposed. Secondly, the dynamic characteristic of a multi-fold solar array was analyzed, with the analysis results revealing that the torsional mode contributed most of the dynamic response inspired by the SADA. Based on the finding, a SAS was designed to simulate the torsional mode dynamic behavior of the solar array. Then, the disturbance torque generated by the SADA-driven SAS was tested by the micro-disturbance force/torque measurement platform, which was built based on a Kistler 6-component piezoelectric sensor. According to the results, the disturbance of the SADA-driven SAS has the following characteristics: (1) The frequency components of the disturbance torque consist of two parts: (a) the first torsional natural frequency of the SAS; (b) the motor-driving frequency and its harmonics. (2) When the moment of inertia is constant, the disturbance torque amplitude at the torsional mode frequency increases with the increase of the mode frequency. (3) When the torsional mode frequency of the SAS is constant, the amplitude of each frequency component of the disturbance torque increases with the increase of the moment of inertia of the solar \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Components** & **Natural Frequency** & **Driving Frequency** & **2 nd-Order Harmonic** & **3 rd-Order Harmonic** \\ \hline \hline \begin{tabular}{c} Experiments (Nm) \\ Simulation (Nm) \\ Absolute error (Nm) \\ Relative error (\%) \\ \end{tabular} & \begin{tabular}{c} 0.0038 \\ 0.00399 \\ 0.00019 \\ 5.00 \\ \end{tabular} & \begin{tabular}{c} 0.04344 \\ 0.03661 \\ 0.00683 \\ 15.72 \\ \end{tabular} & \
\begin{tabular}{c} 0.01021 \\ 0.01249 \\ 0.00228 \\ 22.33 \\ \end{tabular} &
\begin{tabular}{c} 0.00181 \\ 0.002198 \\ 0.000388 \\ 21.44 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of simulation/test amplitudes. Figure 16: Simulation and test results of the disturbance torque. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Components** & **Natural Frequency** & **Driving Frequency** & **2 nd-Order Harmonic** & **3 rd-Order Harmonic** \\ \hline \hline \begin{tabular}{c} Test (Hz) \\ Simulation (Hz) \\ Absolute error (Hz) \\ Relative error (\%) \\ \end{tabular} & \begin{tabular}{c} 1.189 \\ 1.18749 \\ 0.00151 \\ 0.127 \\ \end{tabular} & \
\begin{tabular}{c} 53 \\ 53.31217 \\ 0.036683 \\ 0.68683 \\ 0.68683 \\ 0.68683 \\ 0.648 \\ \end{tabular} &
\begin{tabular}{c} 106 \\ 159.0625 \\ 159.999 \\ 159.999 \\ 0.93650 \\ 0.5888 \\ 0.5888 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of simulation/test frequencies. array. Finally, the proposed disturbance torque model was validated by comparing the simulation and test results, which illustrated that the predicted frequency error of the model is less than 0.648%, and the amplitude error of the corresponding frequency is less than 22.33%. Therefore, the model can effectively predict the disturbance torque produced by the sun-tracking solar array. The disturbance torque model established in this paper can be used to predict the disturbance torque at the design stage of sun-tracking solar arrays. The SAS proposed in this paper makes the ground experiments on the solar array feasible, which serves as a reference for other research. Conceptualization, J.Y. and Y.G. ; data curation, J.Y. and C.Z. ; formal analysis, J.Y. ; funding acquisition, L.Z. ; investigation, J.Y. ; methodology, J.Y. and D.Z. ; project administration, L.Z. ; resources, D.Z. and S.C.; software, J.Y. ; validation, J.Y. ; visualization, L.Z. ; writing--original draft, J.Y. ; writing--review and editing, Y.G. and S.C. All authors have read and agreed to the published version of the manuscript. This research was funded by National Key Research and Development Plan of China, Grant No.2016 YFB0500904.