At present, the winding taper tension of the unit-type printing presses produced by our company is mainly linear decreasing. The linear tension taper control is relatively stable in principle, and the tension value decreases with the increase of the winding diameter. For some printed products with normal processes, this taper control method can fully meet the requirements of printed products, but for some special For printed products required by the process, linear tension taper control of this kind is still insufficient, for example, problems such as center wrinkles will occur. In order to further refine and optimize the algorithm of winding tension taper control, we propose another taper control algorithm based on retaining the optimized linear taper control: nonlinear taper control.

Non-linearity includes convex curve and concave curve. In this way, our tension control can realize three control modes: convex curve, concave curve and linear. Users can choose the most suitable taper control on the man-machine interface according to the process requirements of printed products. curve. In this way, it realizes the optimization of control for users, saves costs, and reduces the rejection rate; it is also a quality improvement for our equipment, which can improve the competitiveness of our products in the market to a certain extent.

**First, the basic algorithm**

， **Y=K/X**是在X轴方向无限接近X轴，在Y轴方向无限接近于Y轴的双曲线作为控制算法的数学依据,其中Y作为当前锥度张力；X作为收卷当前直径；K为曲线的曲率系数。 We have selected the inverse proportional function **Y = K / X** , where **Y = K / X** is a hyperbola that is infinitely close to the X-axis in the X-axis direction and close to the Y-axis in the Y-axis direction as the mathematical basis of the control algorithm, where Y is the current taper Tension; X is the current diameter of the winding; K is the curvature coefficient of the curve. 。 Translate the curve by A units in the x-axis direction and B units in the y-axis to obtain the curve **(YB) = K / (XA)** . 平移以后选取第一象限的图示，得到两种曲线： Because the taper tension and roll diameter values we take are usually positive values, we will select the graph of the first quadrant after translating **Y = K / X to** get two kinds of curves:

The first is to translate the convex curve of A1 units to the X axis direction, and the convex curve of B1 units to the Y axis direction. The convex curve is infinitely close to X = A1 in the X axis direction and infinitely close to Y = B1 in the Y axis direction;

The second is to translate the concave curve of A2 units to the X axis direction and the B2 unit of Y axis direction. The concave curve is infinitely close to X = A2 in the X axis direction and infinitely close to Y = B2 in the Y axis direction.

**Figure 1 Inverse proportional function curve shift diagram**

上，那么根据已知点F1和F2可得方程组： In order not to change the normal operating habits, we still choose to enter the starting taper diameter and starting tension F1 (X1, Y1), the ending taper diameter and ending tension F2 (X2, Y2), take two points F1 and F2 in the curve **(YB ) = K / (XA)** , then according to the known points F1 and F2, we can get the equations:

According to the equations: (A1, B1), (A2, B2)

According to the values of (A1, B1) and (A2, B2), two kinds of decreasing curves can be obtained:

The two types of curves extend indefinitely. We can take the longest and short the other. Limit the curve. When the roll diameter is less than or equal to the taper initial roll diameter X1, take the current tension value as the initial tension Y1; when the roll diameter is greater than When the taper ends the winding diameter X2, the current tension value is taken as the ending tension Y2; when the winding diameter is within the interval of X1 and X2, the corresponding curve is selected. which is:

We have made an Excel dynamic curve diagram, which can directly and clearly see the different curves of the tension with the change of the coil diameter as the reference value changes. According to the diagram, when the K value is between 10000 ~ 100,000 The curvature is more suitable for our control requirements.

Here is a schematic diagram of three taper control curves with an initial value of F1 (150.0mm, 70.0%), an end value of F2 (650.0mm, 25.0%), and a K value of 70,000, including our original linearity. Control line. In the figure, the x-axis represents the winding diameter, the unit is mm; the y-axis represents the current tension, the unit is ‰.

**Figure 2 Schematic diagram of the taper control curve**

**Control Principle**

Basic electrical components: 1 man-machine interface, the main stage of the experiment is mainly Siemens MP277; 1 set of Siemens PLC;

Control principle: The reference data of the man-machine interface setting includes: the starting taper diameter, the starting taper tension, the ending diameter of the taper, the ending tension of the taper, and the value of the curvature coefficient K (if the straight-line calculation method is selected) The value of the curvature coefficient K can be omitted), and the taper calculation curve is selected on the man-machine interface (there are three types of curves: the first is a convex curve; the second is a straight line; the third is a concave curve).

S7-300PLC calculates the tension value under the current winding diameter according to the reference data and curve type given by the man-machine interface, and transmits the tension value to the man-machine interface to display according to the accuracy of 0.1%. The value is output to the electro-pneumatic converter in the form of 4 ~ 20mA through the analog output module. The electro-pneumatic converter controls the air pressure setting of the rewinding cylinder and realizes the rewinding taper control.

**Figure 3 Schematic diagram of taper tension control**

**Third, achieve the effect**

Set the relevant parameters of taper control on the man-machine interface, and select the curve form. The curve can be displayed visually through the trend chart, and the diameter change can be clearly shown on the diagram. The operation is simple, the display is intuitive, and the man-machine interaction Strong type.

**1. Rewinding linear taper control curve and output curve of actual electronically controlled converter**

**2. The taper control curve of the winding concave curve and the output curve of the actual electronically controlled converter**

**3. Taper control curve of winding curve and output curve of actual electronically controlled converter**

**4. Actual human-machine interface display screen**

The three types of tension taper control shown in the icon are completely consistent with the actual implementation effect, which fully proves that the nonlinear tension taper control is effective.

**Significance**

With the progress of society and the development of science and technology, users' requirements for equipment are becoming more and more sophisticated and diversified. The multiple choices of this non-linear control method can adapt to the process requirements of different printed products, and the curve display on the man-machine interface And the animation of the current tension with the winding diameter is more intuitive and clear. This not only brings convenience and benefits to users; it also greatly improves the quality of gravure printing equipment.