## 1 Introduction  
CRPMs with hydraulic tension represent a key piece of experimental equipment to simulate the cold-rolling process. As shown in Figure 1, hydraulic cylinders on each side of the mill apply constant tension to the workpiece. For CRPMs with hydraulic tension, only a small piece of metal strip is used as a workpiece, so they have lower energy and material consumption than traditional CRPMs with coilers [1]. In the cold-rolling process, the tension can significantly reduce deformation resistance by changing the stress state of the deformation zone and reducing the longitudinal compressive stress. As a result, the tension directly influences the thickness accuracy, flatness,  
Figure 1: Schematic of a CRPM with hydraulic tension. and surface quality. Therefore, in the cold-rolling process, the tension must be accurately controlled in order to obtain high-quality cold-rolled products [2; 3; 4]. However, the tension control for a CRPM with hydraulic tension has its own particularities and difficulties, as described in Section 2. First, the forward and backward tensions are coupled with each other. Second, tension cylinders are required to track the rolling speed while achieving closed-loop tension control in typical hydraulic load control systems, where there is strong extraneous force disturbance [5; 6]. Third, the forward and backward tensions are affected by many factors, such as work roller radius, rolling speed, friction coefficient, pass reduction, the type of strip material and its geometric dimensions, etc. Fourth, the stiffness of the workpiece changes in real time. Last, limited by the stroke of the tension cylinder and the length of the strip, the rolling process is often in a stage of acceleration or deceleration, which is detrimental for tension control. Thus, how to ensure the stability of tension is the most critical technical issue that has to be solved in CRPMs with hydraulic tension. Currently, the design of CRPMs with hydraulic cylinders is mostly finished by VARTRON in Austria or Northeastern University in China. In the hydraulic design of VATRON, both the ring and piston sides of the tension cylinders are controlled by an independent servovalve. Damping holes are set between the ring sides and the oil-return pipeline, and damping holes are also set between the piston sides and the oil-return pipeline. The control system, with four servovalves, is flexible, but the controlled objects are coupled with each other, making the program very complex. In addition, the equipment is very expensive. The damping holes are set to eliminate excess force, but a large amount of high-pressure fluid will flow through them and back to the oil tank during work, resulting in huge amounts of noise and energy loss. Reports on tension control for CRPMs with hydraulic cylinders are mainly from Northeastern University in China. [PERSON] designed a method to realize constant tension control with proportional pressure relief valves [7] (marked as method 1). During the rolling process, the outlet of the hydraulic pump is directly connected with the ring side of the entry tension cylinder through pipelines, and constant tension control is achieved through the proportional relief valve. However, due to the impact of the high-frequency flow pulsation of the pump and the fluid inertia effect [8; 9], the accuracy of tension control is limited. Furthermore, when used to control \(T_{\text{H}}\), the flow of the proportional relief valve includes the pump flow and the output flow from the entry-tension cylinder, which makes it necessary to designate a large nominal size (at least 10 mm) for the proportional relief valves. It can be seen from the user manual that the larger the nominal size of the valve, the slower its response speed, thereby affecting the dynamic effect of tension control. In order to solve the problems existing in the above method, Sun provided a control technique combining a speed feedforward controller with a tension feedback controller [10] (marked as method 2).