## 3 Results
### Industrial Application  
In Figure 13, a multi-color gravure printing experimental platform filmed in an industrial printing production factory site is employed to test the proposed control algorithm. The first printing station is used as the reference color mark pattern for open-loop continuous printing, and the register errors of the following patterns are calculated using the first or previous color mark position. The web width is 820 mm, and the maximum working speed is 150 m/min. The tension sensor is installed to detect and control web tension in the process of unwinding, winding and transmission. The final register error can be detected and verified using the register controller data display, image processing algorithm and manual recheck. The schematic diagram of the experimental platform is shown in  
Figure 11: Synchronous rotation experimental platform. Figure 12: Register color mark repeated-detection accuracy using rotary encoder with different resolutions and the proposed detection method. Figure 14, including the printing unit, register control system, oscilloscope and printing quality detection system. It is effective to observe the electrical characteristics and stability of each pulse signal using an oscilloscope in Figures 9 and 14. The photoelectric sensor is installed at the position one cycle before the printing roller. Figure 15 shows the register control accuracy curve in the industrial printing production line using the proposed detection method and an encoder with a resolution of 5000. The blue curve represents the traditional error fluctuation data without subdivision, and the red curve provides the proposed method's experimental result using the pulse-width subdivision algorithm. Each point corresponds to register error detection data, and the error fluctuation range of the blue curve is \(\pm\)0.12 mm, while the error fluctuation range of the red curve can be basically controlled within \(\pm\)0.04 mm. The remaining \(\pm\)0.06 mm error is mainly caused by the influence of the mechanical transmission error. However, the error curve results show that the algorithm is superior to traditional detection methods. In addition, the comparison of register errors using different control algorithms is shown in Table 2. Compared with the MFPD and well-tuned PD control, the proposed pulse-width subdivision control greatly reduces register errors and can achieve faster compensation speed. It must be noted that the listed register errors may correspond to different printing process parameters, and there are also significant differences in the fluctuation range of upstream and downstream register errors. Therefore, different operations should be considered to achieve control accuracy within the range of \(\pm\)0.1 mm to \(\pm\)0.05 mm. Figure 14: The schematic diagram of the experimental platform. Figure 13: Experimental platform for multi-color printing experimental testing platform. The register error curve of the optimized error compensation method and the traditional output compensation method is shown in Figure 16, in which the abscissa is the number of printing cycles, the ordinate represents the register error in millimeter and the running speed is 60 m/min. Obviously, it has to deal with a large register error within the range of 0.25 mm-0.5 mm in Figure 16a,b. Due to the slow compensation speed, the system needs a long time to complete task (a). However, curve (b) presents the continuous oscillation phenomenon with the increase in compensation speed. In high-speed printing production, both conditions can cause a large number of unqualified printing products to decrease production efficiency. The optimized register error compensation results are drawn in curves (c) and (d) and compared with curves (a) and (b); they have better control performance and can quickly complete compensation without redundant oscillation data.