**Yongshun Zhang 1,2, Wanlu Jiang 1,3,\*, Yong Zhu 4,\* and Zhenbao Li <sup>1</sup>**


Received: 31 August 2019; Accepted: 15 October 2019; Published: 2 November 2019

**Abstract:** The rolling mill with hydraulic system is widely used in the production of strip steel. For the problem of vertical vibration of the rolling mill, the effects of different equivalent damping coefficient, leakage coefficient, and proportional coefficient of the controller on the hydraulic screw down system of the rolling mill are studied, respectively. First, a vertical vibration model of a hydraulic screw down system was established, considering the nonlinear friction and parameter uncertainty of the press cylinder. Second, the correlation between different equivalent damping coefficient, internal leakage coefficient, proportional coefficient, vertical vibration was analyzed. The simulation results show that, in the closed-loop state, when Proportional-Integral-Derivative (PID) controller parameters are fixed, due to the change of the equivalent damping coefficient and internal leakage coefficient, the system will have parameter uncertainty, which may lead to the failure of the PID controller and the vertical vibration of the system. This study has theoretical and practical significance for analyzing the mechanism of vertical vibration of the rolling mill.

**Keywords:** rolling mill; hydraulic screw down system; vertical vibration; LuGre model; frictioninduced vibration; flow control; PID controller
