# Research on Multiple-Axis Contour Error Suppression Method Based on Composite Layered Control
## 5 Conclusions  
This paper presents a novel approach for contour error suppression based on composite hierarchical control, where the spatial three-dimensional contour is divided into distinct layers, each being addressed by a tailored controller. Prior to investigating the holistic contour control methodology, we introduced an improved sliding-mode disturbance observer controller based on an enhanced S-shaped function to enhance the single-axis positioning accuracy. Through comparative simulations and analyses with traditional exponential convergence law methods and the approach proposed in reference [23], the results indicate that the single-axis controller advocated in this paper not only exhibits superior tracking precision but also demonstrates faster response times, significantly mitigating oscillations in the sliding-mode control system.  
Preserving the prerequisite of single-axis positioning accuracy, the introduction of the composite hierarchical control significantly enhances the adaptability in the spatial contour controller design. Different levels of accuracy requirements are accommodated through the design of distinct controllers for each level. For the XY plane's lower-level contour, a fuzzy PID controller is employed to address the complex and strongly nonlinear  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Three-Dimensional Contour Error**} \\ \cline{2-4}  & **MAX** & **MEAN** & **IAE** \\ \hline Layered CCC & 1.3566 & 0.2115 & 1.2053 \\ \hline Reference [34] & 2.0028 & 1.0684 & 1.9886 \\ \hline Reference [35] & 3.1176 & 0.5862 & 3.8591 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Contour error comparison table.  
Figure 30: Spatial curves with multiple curvatures.  
environment of the multi-axis servo control system. Comparative simulation experiments with the traditional centered combination control (CCC) method illustrated that the fuzzy-PID-based lower-level control approach not only enhances the accuracy of the XY plane's lower-level contour by 84.39% but also further improves the overall contour accuracy by 84.45%.  
In terms of the upper-level contour control, a proportional controller is adopted. Comparative analysis with the CCC method based on fuzzy PID lower-level control revealed that this design strategy further enhances the accuracy of the three-dimensional overall contour by 61.9%, achieving a 94% enhancement compared to the traditional CCC method. Ultimately, the overall contour error remains around an average of 0.0115 mm. Through rigorous simulation analysis and validation experiments, the effectiveness of the proposed method was comprehensively demonstrated.  
These findings collectively indicate that the proposed composite hierarchical-control-based contour error suppression method holds significant promise for elevating contour control precision and presents a new technological avenue for the application of multi-axis servo control systems in high-precision machining domains.  
Conceptualization, X.L.; Methodology, C.X.; Validation, C.X.; Formal analysis, B.X.; Investigation, K.C. and B.X.; Resources, X.L.; Data curation, S.L.; Writing-original draft, K.C.; Writing-review & editing, C.W.; Supervision, S.L.; Funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript. This research was funded by Chunyang Wang grant number 80923010202.  
Not applicable.  
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. The codes used and/or analyzed during the current study are available from the corresponding author on reasonable request. The data are not publicly available due to the involvement of national defense and military projects in the project, it has not been fully disclosed yet.  
The authors declare no conflict of interest.