## 1 Introductions  
Printed electronics refers to the application of printing technologies for the fabrication of electronic circuits and devices. Roll-to-roll gravure printed electronics have received increasing attention in recent years because of its distinctive advantages, including: large surface area, flexible, customizable, low cost, and environmentally friendly. Though printing resolution and accuracy are not as high as conventional semiconductor fabrication, the above advantages are enough to warrant many new applications, such as Radio Frequency Identification (RFID) tags, thin film transistors, solar cells, touch screens, flexible displays, and light emitting devices. Similar to conventional gravure printing processes, some kinds of conductive inks are printed on the moving substrate in sequence in order to achieve the desired functionality in roll-to-roll gravure printed electronics. The gravure printing system can be divided into three main sections: unwinding, printing, and rewinding. The web tension system exists in all the three sections. There are different requirements for web tension in the three sections, because of the different technical requirements. Some researchers have focused their works on the unwinding and rewinding sections [1; 2; 3; 4; 5; 6; 7]. In these research works, the unwinding tension model and rewinding tension model ware studied, and then various kinds of control algorithms were adopted in order to achieve higher tension precision. The control algorithms for unwinding or rewinding tension include Back Propagation (BP) neural network control [1], active disturbance rejection control (ADRC) [2], Fixed-Order H\(\infty\) control [3], fuzzy adaptive Proportional-Integral-Differential (PID) control [4], Non-linear sliding-mode control [5], adaptive gain control [6], and so on. In the printing section, the tension system and the register system are coupled together. Some research works are about the register model and register control algorithm, but these research works are based on the conventional tension model of a roll-to-roll web printing system [8; 9; 10; 11]. Some research groups have studied the web tension system in the printing section, and the tension control algorithm is the research priority. [PERSON]'s group used a back stepping-based control algorithm and fuzzy decoupling method to reduce the propagation of tension disturbances in the roll-to-roll system [12; 13]. [PERSON]'s group analyzed the influence of the master roller placement, velocity, and tension bandwidths on the web tension of roll-to-roll systems [14], and then they developed a three-dimensional (3D) finite element model of the web and applied a robust control algorithm to control the web tension [15]. The aforementioned research works do not take into account the thermal effects in a roll-to-roll printing section. In fact, the effects of temperature on the tension system and register system in a gravure printing section are remarkable, and have attracted some researchers' attention recently. [PERSON]'s group developed a model to determine the temperature distribution in moving webs due to heating by radiation panels [16; 17]. [PERSON]'s group studied the tension behavior through considering the thermal effects in roll-to-roll E-printing [18], and then researched the dynamic thermal characteristic of the register of roll-to-roll multi-layer printing systems [19]. Even so, the research on the thermal characteristics of plastic film tension is not sufficient. There is a lacks of the research on the effects of room temperature and drying temperature on web tension in gravure printed electronics. In the printing section of a gravure printing machine, there are some drying devices behind the printing rollers for drying the printed conductive ink on the substrate. Usually, the web temperature outside the drying devices always changes with the room temperature, and the web temperature inside the drying devices always changes with the drying temperature.