Industrial Roll-to-Roll Printing Register Control Using a Pulse-Width Subdivision Detection Algorithm

Featured Application

The typical application of register control technology proposed in this paper is the industrial gravure printing production line. It is also used in various other kinds of industrial production equipment, such as die-cutting machines, bronzing machines and offset presses. The performance of the register control system is critical to printing production efficiency.

Abstract

Register control systems are a necessary technical measure and an important means of large-scale roll-to-roll industrial printing production. They are effective in reducing the generation of unqualified printing products and improving the accuracy and stability of industrial printing production lines. In this paper, we propose a new register control algorithm that effectively improves the detection accuracy and compensation speed of printing register control systems. Firstly, according to the principle of register color mark detection, a new pulse-width subdivision detection algorithm is proposed, which can greatly improve the accuracy of register error detection without increasing the resolution of external encoder pulse signals. Then, the optimized error compensation method can adaptively adjust the corresponding system parameters, such as the output intensity, error filtering period and output period, according to the current register error size. The new output method greatly improves the error compensation speed without increasing error oscillation. Lastly, the experimental results of 0.01 mm show that the proposed control approach significantly improves the detection accuracy of register errors. Furthermore, the new control algorithm can be applied in the industrial field.

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 tambour 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 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. The proposed approach was tested on an industrial multi-color gravure printing production line, and the fluctuation range of the testing register errors data can be controlled within +/−0.1 mm. To study the fluctuation of control signals, a novel idea using the biological functioning of cells communicating was considered to recognize the optimal register output signal [17]. In ref. [18], a mathematical model of a machine directional (MD) register was derived, where the compensation method was proposed to cancel out the upstream disturbance of the MD register. The proposed MD register model and compensator could be used to improve the performance of the MD register controller in multi-layer roll-to-roll printed electronics. The authors of ref. [19] presented a control strategy for the speed-up phase in the R2R printing system, particularly for printing systems with electronic line shafts. The tension fluctuation caused by torque variation during acceleration is the main cause of register error generation. A mechanical model of R2R printing systems in the speed-up phase was developed based on the principle of mass conservation and torque balance, and a model-based feedforward proportion derivative controller was designed to reduce register errors caused by tension fluctuations. In ref. [20], a feedforward controller based on an active disturbance rejection control (ADRC) strategy was presented to strengthen the accuracy and stability of the register system in multi-color shaftless gravure printing machines. The controller used feedforward control to compensate for the known interference, and ADRC was used to adjust the inputs of the register system and actively estimate and compensate the unknown disturbances in real-time, which greatly improved the accuracy of the register controller. In ref. [21], it was demonstrated by experimental verification that measurement error is generated by the widening and agglomeration of the register mark. The error was shown to differ with the size and shape of the mark under identical printing conditions. The results illustrated the importance of improving the printing quality of the register mark, selecting the desired geometry for register marks with regard to printability and utilizing an edge-detection algorithm in the control program for high-precision register control. The authors of ref. [22] estimated the register errors according to tension fluctuation of the substrate and achieved microscale resolution register control. The experimental results indicate that applying the proposed register algorithm achieved a resolution below +/−30 mu m. In ref. [23], the authors eliminated register coupling between printing units using a fully decoupled proportional-derivative (FDPD) control algorithm, which was effective in processing the impact of different printing roll lengths on register error fluctuations. The authors of ref. [24] studied three different register control algorithms, i.e., model-based feedforward proportional differential (MFPD) and direct-decoupling proportional differential (DDPD). In addition, the performance indicators and industrial implementation difficulty of these algorithms were evaluated and tested. In the field of flexible electronic production, ref. [25] employed the response acceleration input to achieve rapid response in the register control of flexible substrates with a high-precision register control below +/−10 mu m in industrial-scale R2R manufacturing systems. In ref. [26], the engraved marks in the printing cylinder were measured to an accuracy of ±10 μm. In the field of roll-to-roll additive manufacturing [27], the authors investigated the relationship between smearing defects and register error, which can be improved by adjusting the parameters of the control system. In addition, research on the roll-to-roll printing process also refers to the control methods of pressure uniformization [28], adaptive feedforward control [29], multi-roll coordinating optimal control [30] and sensorless tension estimation and disturbance compensation [31].

Analysis of these research results shows that these register control methods mainly depend on the substrate tension coupling model and multi-axis synchronous control technology [32,33]. The processing of decoupling calculations is complex and time-consuming. However, register error detection accuracy on the printed matter is basically achieved by detecting the register color mark, so the key point is understanding how to reliably locate the register color mark. Traditional control schemes usually use photoelectric sensors to detect the register color mark; however, detection results are easily affected by various factors, such as printing quality, color, tension fluctuation, mechanical vibration, mechanical and electrical parameters of photoelectric sensors, detection speed variation and so on. For the research issue of the register color-mark-detection mechanism, there are few research results.

Some researchers have tried to solve printing control problems using machine vision technology, which has been widely used in the printing industry, especially in the application of online printing defect detection [34,35]. In ref. [36], a machine-vision-based register control system was designed for use in chromatic printing machines. The detection algorithm obtains the registration color mark pattern through the CCD (charge-coupled device) and calculates the center of gravity of the color mark, which is compared with the standard position to show whether registration deviation exists or not. In ref. [37], a register error detection method based on the control strip was proposed to realize real-time and online detection of register errors. The translations of the solid block’s edge from the reference block edge in the horizontal and vertical directions were calculated based on the characteristics of the control strip. Lastly, the register error of plates from the reference plate can be obtained. The authors of ref. [38] put forward a relatively effective and discriminative feature region searching algorithm that can automatically detect shapes, such as quasi-rectangular, oval, and so on, as feature regions. The entire image and sub-regional experimental results show that the proposed method can be used to extract ideal shape regions, which can be used as characteristic shape regions for image registration in printing pattern detection systems. However, the real-time reliability of the machine vision register control system need to be further studied and verified in applications of industrial automation.

In summary, traditional register control methods based on decoupling control cannot effectively solve the problem of color mark detection and positioning, and it is difficult to balance the relationship between error compensation speed and register accuracy. The more innovative methods, such as machine vision and machine learning, tend to focus on printing quality monitoring, such as defect detection or fault warning. However, the implementation of image processing combined with motion control systems is expensive, complex and difficult. Moreover, various research limitations and model assumptions make it difficult for many register error models to be applied in engineering practice. In this paper, a new register control algorithm is proposed to improve register color-mark-detection accuracy and error compensation performance without increasing hardware configuration using the pulse-width subdivision detection algorithm. The optimized error compensation strategy provides better control performance than traditional algorithms.

2. Materials and Methods

The architecture of the proposed register control system consists of an encoder and photoelectric sensor-pulse signal input, register controller, data interaction and visualization, machine direction and cross-direction register error compensation output, as shown in Figure 3. Initially, some basic register control–detection methods are introduced, and then we describe the proposed pulse-width subdivision detection algorithm in detail. Variations in color mark shapes and printing quality samples can greatly affect detection accuracy, which leads to false error data. We take the repeat positioning accuracy with color marks to estimate the influence of those interferences. Next, the optimized error compensation method selected in this paper is elaborately described. Lastly, we present the analysis of the experiment results.

2.1. Color Mark Detection and Positioning Model

At present, the register control system usually chooses photoelectric sensors to detect the position of color marks [21]. As shown in Figure 3, input signals consist of the photoelectric sensor-pulse signal and the rotary encoder pulse signal. The output signals are divided into machine-direction and cross-direction register error compensation signals [38]. The incremental rotary encoder converts the timing and phase relationship of its angle coder through two internal photosensitive receivers to obtain the increase or decrease in its angle coder angular displacement. After real-time signal acquisition combined with digital circuits, especially FPGA (field-programmable gate array) or DSP (digital signal Processing), the incremental rotary encoder has the characteristics of real-time and convenient signal acquisition in position detection. According to different coding resolutions and installation methods, the incremental rotary encoder can measure different distances from several microns to hundreds of meters. For the multi-color printing production line, one-to-one independent installation is adopted to avoid the crosstalk of multiple signals. The incremental encoder usually has three signal outputs (six differential signals), namely A, B and Z, which generally use the TTL level. The phase difference between pulse A and pulse B is 90 degrees. Each circle sends out a Z pulse, which can be used as a reference for the mechanical zero position of the printing roller [39].

The structure diagram of register color mark detection and the positioning model is shown in Figure 4. Under the actions of the unwinding traction motor and the guide roller, the web substrate moves forward under constant tension. At the same time, the incremental rotary encoder converts roller displacement into periodic electrical signals, which are converted into counting pulses. When the photoelectric sensor senses the register color mark, the control system locks the code-counting positions of the color mark pulse’s rising and falling edge. The corresponding register error can be calculated by comparing the phase relationship between the color mark position and the printing roller. As shown in Figure 4, $v_w\left(t\right)$ and $v_r\left(t\right)$ illustrate, respectively, the web forward speed and the printing roller linear velocity; $r_x\left(t\right)$ and $p_x\left(t\right)$ represent, respectively, the distance from the register color mark to the printing roller and the distance from the target position to the printing roller start point, where $t$ is the time variable and $L_c^{\ast }$ represents the circumference of the printing roller. The number of roller rotations and target positionings is calculated by counting the number of encoder pulses.

By definition, the register error $e\left(t\right)$ can be expressed as:

$$e\left(t\right)=r_x\left(t\right)-p_x\left(t\right).$$

(1)

In practical applications, due to the influence of web forward-motion characteristics, it is difficult to realize continuous real-time monitoring of register errors. Position detection is reliable and effective only when the color mark is close to the surface of the guide roller under tension and passes through the photoelectric sensor at the focusing position. The time can be defined when the color mark is detected by the photoelectric sensor as $t_0$, then $r_x\left(t_0\right)<L_c^{\ast }$, which is effective in improving real-time control and avoiding adjustment lag. According to the detection model, color mark positioning can be achieved by counting the number of encoder pulses from the color mark pulse to the printing roller, and the calculation formula is expressed as

$$P\left(S_n\right)=\frac{Cnt\left(S_n,P_{ref}\right)L_c^{\ast }}{C^{\ast }}n=\mathrm{1,2},3......,$$

(2)

where $S_n$ is the register color mark; $P$ represents the color-mark-detection position; $Cnt(S_n,P_{ref})$ is the code pulse-counting value from the color mark to the printing roller $P_{ref}$; $L_c^{\ast }$ provides the printing roller circumference; $C^{\ast }$ is the rotary encoder resolution size. Positioning accuracy and detection reliability are crucial to the control system. The system’s theoretical accuracy can be evaluated according to the repetition detection accuracy of the color mark. As shown in

Table 1. Detection accuracy corresponding to different printing roller circumferences and encoder resolutions.

Resolution	1024	2048	3600	4096	5000	8192	10,000	20,000	40,000	Circumference (mm)
Accuracy (mm)	0.39	0.195	0.111	0.097	0.08	0.049	0.04	0.02	0.01	400
	0.488	0.244	0.139	0.122	0.1	0.061	0.05	0.025	0.012	500
	0.585	0.292	0.166	0.146	0.12	0.073	0.06	0.03	0.015	600
	0.683	0.342	0.194	0.171	0.14	0.085	0.07	0.035	0.017	700
	0.781	0.39	0.222	0.868	0.16	0.097	0.08	0.04	0.02	800

, the system detection accuracy corresponding to different encoder resolutions and printing roller circumferences is listed. According to the data analysis, the detection accuracy decreases when the printing roller circumference is larger and increases when the rotary encoder increases in resolution. In theory, system detection accuracy can be improved infinitely by increasing the number of subdivided encoder pulses, such as $L_c^{\ast }=400\mathrm{m}\mathrm{m}$ and $C^{\ast }=\mathrm{200,000}$, in which case the system detection accuracy is then $\mathsf{\tau }=0.002\mathrm{m}\mathrm{m}$ per pulse.

2.2. Register Control Algorithm Based on Pulse Width Subdivision

2.2.1. Pulse-Width Subdivision Color Mark Positioning Model

The detected position of a color mark can be defined as the pulse rising-edge position $P_{rise}$ and the pulse falling-edge position $P_{down}$. The corresponding color mark width can be obtained by counting the number of encoder pulses from the rising edge to the falling edge $Cnt(P_{rise},P_{down})$. However, many interference factors can affect the detection results, such as mechanical vibration, transmission error, edge jitter, color saturation characteristics, surface reflection characteristics, sensor electrical characteristics, color mark print quality, etc. In this paper, the average value of the rising and falling-edge positions is used as the detected position:

$$P_m=\frac{1}{2}\left(P_{rise}+P_{down}\right).$$

(3)

Figure 5 shows the proposed pulse width subdivision detection model, and the color mark position $P_m$ and width $W_m$ can be expressed as:

$$\left\{\begin{array}{l}{P}_m=\frac{\tau }{2}\left[Cnt\right({0,t}_{rise})+\frac{{t_1-t}_r}{t_1}+Cnt(0,t_{down})+\frac{{t_2-t}_d}{t_2}]\\ W_m=\tau [\frac{t_r}{t_1}+Cnt({t\prime }_{rise}{,t\prime }_{down})+\frac{{t_2-t}_d}{t_2}],\hspace{1em}\tau =\frac{L_c^{\ast }}{C^{\ast }}\end{array}\right.,$$

(4)

where $\tau =L_c^{\ast }/C^{\ast }$ is the actual length corresponding to each coded pulse; $Cnt\left({t\prime }_{rise}{,t\prime }_{down}\right)$ indicates the integer number of encoder pulses contained between the rising and falling edge, excluding the two “edge coded pulses”; $t_1$ and $t_2$ represent the width time of the coded pulse corresponding to the rising and falling edge; $t_r$ and $t_d$ are the width time from the rising and falling edge to the next nearest coded pulse jump edge in microseconds.

By subdividing the two “edge coded pulses”, the positioning accuracy of color mark detection can be achieved, in theory, to the maximum extent, and the complexity of external electrical configuration can be reduced. Even if a low-resolution rotary encoder is selected, high-precision positioning and detection accuracy can be achieved. When the system detection resolution is insufficient, the proposed subdivision detection algorithm is effective in overcoming this problem.

2.2.2. Optimized Feedforward Register Control

After obtaining the accurate and reliable register error data, the controller then outputs the compensation signal to the printing roller servo drive mechanism in real-time according to the error detection results; the error compensation operation is performed by increasing or decreasing the running speed of the printing roller in a limited time so as to align the color mark patterns. In Figure 6, the register error compensation output block diagram is shown. The PD controller adaptively adjusts the optimal output parameters according to the output strategy, including the register error size, running speed, filter period and other parameters, outputs the compensation signal to the printing roller servo motor and finally, achieves the purpose of the printing register by superposing the printing roller speed through the mechanical transmission system.

The output compensation formula of register error is expressed as:

$$e_r=\epsilon \ast ∆V_i\ast t_{output},t_{output}<\frac{L_c^{\ast }}{V_i^{\ast }},$$

(5)

where $\epsilon$ is the output strength influence factor or speed superposition influence factor, which is a constant determined by the ratio of the servo driver electronic gearbox and the mechanical transmission ratio, and $t_{output}$ represents the output time in milliseconds. Generally, the execution time is linear with the size of the error, and $∆V_i$ is the printing roller’s superimposed speed, which is a constant in normal operations. According to Formula (5), the larger $\epsilon$, $∆V_i$ and $t_{output}$ are, the faster the error compensation speed. However, it is also more prone to error oscillation. On the contrary, when error adjustment accuracy is higher, execution speed is slower. When there is a large register error, such as a joint of two webs, fast adjustment can complete error compensation in a short time, but this can easily cause error oscillation due to an adjustment resolution that is too large. Therefore, the adaptive adjustment of influence factors and output period according to the size of the register error is an effective method to improve control system performance.

The printing roller of the output time is the printing roller one-cycle operation time $\mathrm{T}=L_c^{\ast }/V_i^{\ast }$, as shown in Figure 7, while the register error output time-segment model ignores the influence of time $L_c^{\ast }/∆V_i$. Then, each printing cycle time can be divided into three sections, namely, detection time $t_u$, output delay $t_v$ and adjustable time $t_w$. Obviously, the executable time decreases with an increase in running speed, and the adjustable amount of error also decreases. In order to avoid the output execution time exceeding one printing cycle, the maximum compensation limit at one time can be set to $e_{max}=\epsilon \ast ∆V_i\ast T$. The new compensation error is obtained from the next detection result, and the register errors shall not be accumulated and stacked. The optimized feedforward error compensation strategy is expressed as

$$\left\{\begin{array}{c}\epsilon ={\epsilon }^{\ast },e\left(t\right)<=0.1\mathrm{m}\mathrm{m}\\ \epsilon ={p_0\left[e\left(t\right)+0.9\right]\epsilon }^{\ast },0.1\mathrm{m}\mathrm{m}<e\left(t\right)<=1.1\mathrm{m}\mathrm{m},0<p_0<=1\\ \epsilon ={p_1\epsilon }^{\ast },e\left(t\right)>1.1\mathrm{m}\mathrm{m},p_1>1\end{array}\right..$$

(6)

We define the output intensity influence factor as constant ${\epsilon }^{\ast }$. When the register error $e\left(t\right)\le 0.1\mathrm{m}\mathrm{m}$, the output mode remains unchanged; when $0.1\mathrm{m}\mathrm{m}<e\left(t\right)\le 1.1\mathrm{m}\mathrm{m}$, the output intensity influence factor changes linearly according to the current error size; when $e\left(t\right)>1.1\mathrm{m}\mathrm{m}$, the output intensity influence factor is directly scaled to accelerate the compensation speed. $p_0$ and $p_1$ are the corresponding system constants.

2.2.3. Analysis of Detection Reliability and Influencing Factors

The printing quality and geometric shape of the register color mark are two important factors that affect detection stability. Figure 8 shows the color mark shape positioning model, in which $p_{rise}$ and $p_{down}$ indicate the rising and falling edge of the color mark pulse, respectively, and $w_m$ is the detected color mark width. Generally, these shapes are considered rectangular and triangular and are taken to detect the machine direction and cross-direction register errors. However, the rectangular color mark can only be used for machine direction register control. Because the triangular mark has a bevel, its detection and positioning results are affected by both directions. Therefore, the right-angle side of the triangle mark can be used to achieve machine direction register control, and the triangle mark width can be used as the basis for detecting cross-direction register errors.

According to the proposed encoder pulse-width subdivision positioning model in Figure 5, the color mark electrical detection error comes from the pulse edge jitter. When positioning the rectangular color mark, its edge jitter can present a symmetrical relationship between left and right, and its positioning accuracy is better than the single-edge-detection method after taking the average of the rising and falling-edge positions. However, due to the existence of the bevel, the jitter of the color mark bevel can be significantly higher than the positioning accuracy of the right-angle edges, and there is also crosstalk between the transverse and longitudinal registrations (machine direction and cross-direction).

The qualified and unqualified register color mark patterns and detection-edge jitter oscilloscope display waveforms, as shown in Figure 9. It can be seen that color marks (a), (c) and (e) are unqualified printing patterns, the colors of the patterns are not full enough and the edge is irregular. Color marks (b), (d) and (f) are qualified printing patterns with full color and clear and regular edges. On the right, (g) and (h) are the pulse waveforms measured using an oscilloscope, including four pulse signals; from top to bottom, these are color mark pulse (blue), encoder pulse A (green), B (purple) and Z (yellow). According to the operation principle of the incremental rotary encoder, A and B pulses are two orthogonal pulse signals with a phase difference of 90 degrees [40]. Based on the phase relationship, the frequency doubling and direction discrimination function can be realized, and Z is the starting signal of each printing cycle. The real-time monitoring waveforms are presented in (g) and (h). When the encoder pulse signal remains stable without fluctuation, the width-time of an encoder pulse is 25 microseconds according to the oscilloscope display, and its register error fluctuation range is plus or minus one encoder pulse accuracy. Therefore, low-quality printed patterns obviously cannot meet the requirements of control system detection accuracy.

3. Results

3.1. Establishment of the Register Controller Experimental Platform

The experimental platform adopts the STM32+FPGA hardware structure system, and FPGA is regarded as an STM32 peripheral expansion device, which is different from the usual master–slave access response mechanism to realize the interaction between the single-chip computer and FPGA. In order to ensure the real-time requirements of the register error compensation output, the register error is directly output by the FPGA hardware system. At the same time, the detected relevant operation data are uploaded to STM32 for drawing and display, and the man–machine interface interaction operation is complete to achieve minimum-system-output delay operation.

Figure 10 shows the hardware platform of the register controller, which mainly includes the encoder pulse signal input, external signal input for each printing cycle, photoelectric sensor signal input, error compensation signal output, communication interface, etc. Real-time acquisition and calculation of various high-frequency pulse signals are realized by writing Verilog HDL code using the software version number of IEEE P1364-2005/D3. The external cycle signal input is equivalent to a group of translation signals of the rotary encoder Z signal, which can more conveniently locate the starting position of the printing roller and facilitate subsequent multi-color mark identification.

3.2. Establishment of Register Controller Experimental Platform

Before adjusting the printing process parameters, such as oven temperature or printing tension, it is necessary to determine that the detection accuracy of the register system itself is stable and reliable through a synchronous simulation experiment. The color-mark-detection synchronous-following rotation experimental platform is designed and built to test system detection accuracy with different encoder resolutions and the proposed pulse-width subdivision algorithm. As shown in Figure 11, two standard color marks are fixed on two independent electronic axes for synchronous following and rotating operation. Then, the register error fluctuation in the two color marks is calculated to evaluate system detection accuracy. The two motors are driven by independent servo systems, and the color mark or magnet is directly fixed on the rotation shaft to minimize interference caused by the transmission of the mechanical and electronic gear ratio. The two electronic axes, A and B, rotate synchronously at the same speed. For the simulation experiment on the industrial printing production line, due to the appearance, size and power that are far greater than that of the simulation test platform and the interference with mechanical transmission, the speed of different printing axes may not be fully synchronized, resulting in the unstable operation of the register control system. The register error is detected and positioned using a photoelectric sensor and rotary encoder. The color marks with full-color, clear-edge dots and weak surface reflection are selected to test, such as red or black color marks.

The repeated-detection accuracy of the register color mark is positioned using the rotary encoder with different resolutions. The proposed detection method is shown in Figure 12, in which the error fluctuation dates in 60 m/min with 30 consecutive cycles are included. Three incremental encoders with different resolutions were selected for testing, namely 4096, 8192 and 20,000 resolutions. If the corresponding printing roller circumference is 400 mm, the accuracy can be calculated as 0.092, 0.04 and 0.02, respectively.

As shown in Figure 12, the error curves are represented by black, green, blue and red curves, and each point represents a detection result. The x-axis coordinate provides the number of rotations, and the y-axis coordinate represents the color-mark-detection positioning error in millimeters. Obviously, the system detection error has at least one encoder pulse jitter regardless of pulse resolution, which is caused by the random overlap between the photoelectric sensor detection pulse edge and the encoder pulse edge. The electrical and mechanical edge jitter may cause at least one encoder pulse jitter. System detection accuracy increases with the increase in encoder resolution from 0.184 mm (black) to 0.04 mm (blue). However, detection accuracy using the pulse-width subdivision method is still much better than using traditional detection methods, and the detection accuracy can be controlled within 0.01 mm. Detection accuracy is shown to be the best in the red curve.

3.3. 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 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 Figure 9 and Figure 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 ±0.12 mm, while the error fluctuation range of the red curve can be basically controlled within ±0.04 mm. The remaining ±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. The comparison of register errors using different control algorithms (mm).

Periods	MFPD		Periods	Well-Tuned PD		Periods	Traditional	Proposed
2	−0.05	0.19	1	−0.04	−0.07	5	0.03	0.05
7	−0.07	0.10	6	0.10	−0.05	6	0.11	0.02
12	0.03	0.16	13	0.13	0.05	7	0.08	−0.01
17	0.19	0.24	20	0.22	0.15	11	0.08	0.01
22	0.08	0.08	27	0.12	0.05	13	0.11	0.04
27	−0.01	−0.03	34	0.02	0.06	14	0.12	−0.01
32	−0.08	−0.13	40	−0.06	−0.04	15	−0.02	0.05
37	−0.22	−0.15	47	−0.08	−0.06	17	−0.12	−0.01
42	−0.15	−0.07	53	−0.02	−0.16	20	−0.08	−0.02
47	0.07	−0.15	60	0.06	−0.15	21	0.03	−0.01
52	0.10	−0.14	67	0.10	−0.12	23	−0.08	0
57	0.16	−0.04	74	−0.02	−0.09	26	−0.05	0
62	0.20	0.02	82	−0.14	−0.13	28	−0.08	0.02
67	0.16	0.04	90	−0.03	−0.01	30	−0.02	0

. 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 ±0.1 mm to ±0.05 mm.

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.

4. Discussion

The pulse-width subdivision detection algorithm proposed in this paper can, in theory, completely solve the problem of insufficient encoder pulse resolution. The simulation experiment test results verify the effectiveness of the algorithm presented in Figure 12. However, according to the industrial-application production test results in Figure 15, the register error of the final printed products is also affected by many other factors, such as color difference variation, mechanical vibration and transmission error, etc. In Figure 16, it is obvious that a longer error compensation time results in more printing waste produced in a high-speed printing situation (e.g., 150–180 m/min production speed). The optimized error compensation strategy has a good effect on improving this problem. However, the setting of appropriate, relevant parameters (e.g., stacking velocity) depends on various external conditions, such as printing speed, photoelectric sensor installation position and web tension, etc. Therefore, there is still a lot of room for improvement in the intelligence level of the printing register control system. To sum up, for the improvement of the final production efficiency, the impact of each operating link must be comprehensively considered.

In comparison with similar register control approaches, such as fully decoupled proportional-derivative control or model-based feedforward proportional differential control, the novelty of this work can be summarized as the efficiency and practicality of the proposed control algorithm. Existing control algorithms are based on complex, time-consuming tension decoupling mathematical models and are difficult to apply in engineering practice. The impacts of color mark detection accuracy are also rarely considered in the existing research literature. The proposed register control approach is based on engineering application practice, studying the principle of color mark detection, printing pattern quality influence and the output compensation mechanism, significantly improving the accuracy and speed of the register control system.

5. Conclusions

In this work, a new register control method using the pulse-width subdivision detection algorithm is proposed to improve the accuracy of register error detection without increasing the resolution of external encoder pulse signals. The specific contributions are as follows:

(1)

We studied the principle of register color mark detection. It was identified that the resolution of the encoder pulse, sensor electrical edge jitter, color mark printing quality and mechanical vibration are the main interference factors that show that the most traditional detection method based on the encoder and photoelectric sensor cannot effectively work.

(2)

The proposed pulse-width subdivision detection algorithm can effectively improve the accuracy of register error detection based on the same hardware platform configuration.

(3)

Different compensation output intensities can greatly affect execution time; we also found that for all output policy parameters, an optimal value exists for the control speed and stability, but if this is too fast or too slow, the compensation time reduces production efficiency.

The current detection system mainly solves the problem of insufficient positioning accuracy of the color mark; however, the color mark printing quality must meet the requirements of relevant printing process technical indicators, so further works on the detection system should identify more types of register color marks. In addition, the calibration and quantification of photoelectric sensor detection results cannot be realized yet, which leads to uncertainty in the register reference position. Future work should study how to realize automatic register, further reduce manual operation and apply the machine vision method to calculate the calibrated register error.