## 1 Introduction  
The roll-to-roll production process is widely used in the field of industrial automation, including in battery diaphragm production [1], web handling [2], inkjet printing [3], printed circuit boards [4], textiles [5] and the printing industry [6; 7; 8; 9; 10]. Register error detection in roll-to-roll printing refers to the accurate printing of each part of the printed pattern in the required substrate area by controlling the printing roller of each color [11]. Register accuracy depends on each step of the whole printing process. The register controller calculates the machine direction and cross-direction relative distance of each color mark by detecting the special shape patterns on the printed matter, thus calculating the printing offset of each printing unit before transmitting the error compensation signal to the servo drive systems, which act on the machine direction and cross-direction operation for each printing roller motor. Figure 1 shows an example of an industrial printing production line, and Figure 2 presents typical six-color register color mark patterns as follows: (a) qualified register position relationship and (b) unqualified register position relationship. This paper is organized as follows. We present related studies in Section 2, and Section 3 discusses the methodology, which includes the architecture of the proposed color-mark-detection algorithm, the analysis of the influencing factors and the optimized error compensation method. The experimental results and industrial applications are shown in Section 4. Section 5 presents the conclusions and future works. Many register control methods have been proposed for roll-to-roll printing processes, and these methods can effectively detect and compensate for register errors in real-time. The authors of ref. [12] studied the mechanism of generating register errors and the related influencing factors according to the characteristics of RTR printing systems. The test results using the proposed high-accuracy register controller indicate that inherent factors in register controllers have a significant impact on control accuracy, and the approximate range of substrate length required for error compensation is \(+/-10\)-\(30\) m.  
In ref. [13], a gravure register controller was employed using active disturbance rejection control (ADRC) to achieve the high-precision control of multicolor register systems. It effectively improved the control precision, speed and production efficiency of gravure printing. The influence of different register control strategies on web movement and register quality in a production-scale gravure printing machine was examined in ref. [14]. Based on different material conditions, 13 different paperboard qualities were produced, and each was printed using three different register control strategies. It was found that the cross-direction position on the tumour is the most influential board-side parameter on lateral web movement and register quality. A register control strategy with an increasing gain per printing unit was the most effective in improving register quality for this runnability behavior. The authors of ref. [15] presented a novel register control method that uses an active-motion-based roller (AMBR) to reduce register error in R2R gravure printing. Instead of shifting the phase of the downstream printing roller, which leads to undesired tension disturbance, the one degree-of-freedom (1-DOF) mechanical device AMBR was used  
Figure 1: Industrial printing production equipment. Figure 2: Typical six-color register color mark patterns: (**a**) qualified register position relationship and (**b**) unqualified register position relationship. to compensate for web elongation by controlling its motion according to the register error. The proposed register control method could maintain a register error of under \(+/-0.15\) mm. The authors of ref. [16] utilized the model-based feedforward PD (MFPD) control method to suppress the impact of upstream tension fluctuations on adjacent downstream printing units.