**5. Conclusions**

In this paper, the effects of different equivalent damping coefficients, leakage coefficients in the hydraulic cylinder, and proportional coefficients of the PID controller on the vertical vibration of the rolling mill were studied. The following conclusions are obtained:


**Author Contributions:** Conceptualization, W.J. and Y.Z. (Yong Zhu); methodology, Y.Z. (Yongshun Zhang); investigation, Y.Z. (Yongshun Zhang); writing—original draft preparation, Y.Z. (Yongshun Zhang); writing—review and editing, Y.Z. (Yong Zhu) and Z.L.

**Funding:** This research was funded by [the National Natural Science Foundation of China] grant number [No. 51875498, 51805214], [Key Program of Hebei Natural Science Foundation] grant number [No. E2018203339], [China Postdoctoral Science Foundation] grant number [No. 2019M651722], and [Young issues in the special project of basic research of Yanshan University] grant number [No. 15LGB005].

**Conflicts of Interest:** The authors declare no conflict of interest.
