# Design of a Predictive RBF Compensation Fuzzy PID Controller for 3D Laser Scanning System
## 6 Conclusions  
This paper studies the control of Lidar pitching motion in a 3D laser scanning system. A predictive RBF compensation fuzzy PID controller is proposed, which combines the advantages of a fuzzy algorithm, an RBF neural network and predictive control. Compared with traditional PID, PRFPID eliminates the unknown nonlinear part of the system and has good tracking performance and robustness. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Type**} \\ \cline{2-4}  & **FPID** & **RFPID** & **PRFPID** \\ \hline \(\text{k}_{1},\text{k}_{2},\text{k}_{3},\text{k}_{4},\text{k}_{5}\) & 0.5, 0.5, 50, 25, 20 & 0.5, 0.5, 50, 25, 20 & 0.5, 0.5, 50, 25, 20 \\ RBF nodes & & 5 & 5 \\ \(c\) & & \([-6,-3,0,3,6;-6,-3,0,3,6;-200,-100,0,100,200]\) \\ \(Q\) & & & [500, 0, 0; 500, 0; 0, 0, 500] \\ \(\delta,\gamma\) & & \(10,3\) & \(10,3\) \\ \(P,M,\mu\) & & & \(5,3,0,6\) \\ Set-point & 45 sin(2\(\pi t\)) & 45 sin(2\(\pi t\)) & 45 sin(2\(\pi t\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Controller parameters of sine response. Figure 12: (a) FPID sine response; (b) RFPID sine response; and (c) PRFPID sine response. Through the simulation comparison with the FPID and RFPID controller, the general step response is obtained, and the response time is reduced from 15.298 s to 1.957 s with a steady-state error of 0.07\({}^{\circ}\). Meanwhile, the PRFPID remains as the one with the most favorable response performance for the step input under model mismatch and large disturbance. Moreover, the PRFPID tracks the target curve quickly and accurately and eliminates the deviation in FPID and the fluctuation phenomenon in RFPID by the sinusoidal response comparison. In conclusion, the results show that the PRFPID controller improves the system performance and can effectively control the pitching motion of the 2D Lidar. Conceptualization, X.X. ; validation, X.X. ; writing--original draft preparation, X.X. and M.Z. ; writing--review and editing, M.Z., H.Y. and Z.P. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China, grant number 51805146; the Fundamental Research Funds for the Central Universities, grant numbers B200202221; Changzhou Sci&Tech Program, grant numbers CJ20180047; Jiangsu Key R&D Program, grant numbers BE2018004 and BE2018004-1; Water Resources Department of Jiangsu Province, grant number 2018031. The authors declare no conflict of interest. The authors declare no conflict of interest. References  
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