## 6 Conclusions  
This paper presented the neural network based sliding mode control for tracking control of the 3-DOF manipulator with the presence of uncertainties and external payload variation. The structure of the neural network sliding mode control as well as the correlation between the slope of the sliding surface and robust term in the control signal are derived. The conventional sliding mode controller (SMC) is described by nonlinear terms, the sliding surface and the robust term with gain \(K\), and \(\alpha\) via the term \"\(K\)s- \(\alpha\)sign(s)\" to generate the tracking performance. As mentioned in the introduction and in Section 3.2, despite its strong robustness, fixed gains cannot satisfy the tracking performance with the variant uncertainties or external disturbances. Previous works proposed many control schemes for the SMC with adaptive gains by using intelligent techniques without considering the slope of the sliding surface that affects the convergence rate to zero of the system errors. Besides, suitable gains are not discussed clearly. Based on a missing in constructing an advanced algorithm on constructing an advanced algorithm, this paper employed the neural network with gradient descent method for adjusting the robust term and the slope of the sliding surface (same function as nonlinear PD control) to a suitable value such that the stability is guaranteed, and higher tracking performance can be achieved. The proposed controller is tested on the 3 DOF hydraulic manipulator to validate its effectiveness and workability. Comparisons of tracking performance between the proposed algorithm with the conventional sliding mode and traditional PD control are given in both simulation and experiments under the presence of the uncertainties and the external payload. The results indicate that the proposed algorithm can exhibit high precision in tracking performance.  
However, in this study, the learning rate parameters are set manually based on several experiments as mentioned in the above remarks. These parameters should be automatically adopted with system behavior. Besides, we ignored use of the intelligent technique as compensation like other convention adaptive sliding mode controller schemes. Therefore, the neural network SMC proposed in this study is a premise to develop an adaptive learning rate and can be considered as the first step to get a suitable value for a novel adaptive control with intelligent techniques (radial basis function or adaptive control) in future works.  
Figure 15: The slope adjusted for the sliding surface of the (**a**) first joint, (**b**) second joint, (**c**) third joint.  
**Author Contributions**: [PERSON] was the supervisor providing funding and administrating the project, and he reviewed and edited the manuscript. [PERSON] did the investigation, methodology, analysis, and the validation, made the MATLAB software, and wrote the original draft. [PERSON] checked the introduction, structure of the paper and experiment results. All authors contributed to this article and accepted the final report.  
**Funding**: This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean government (MEST) (NRF-2017R1A2B3004625) and by the Ministry of Trade, Industry & Energy (MOTIE, Korea) under Industrial Technology Innovation Program (No.10067184).  
**Conflicts of Interest**: The author declares no conflict of interest.