Web tension measurement method for web printing machine based on extended state observer

Abstract

The present invention discloses a web printing press material belt tension measurement method based on an extended state observer. According to the mechanical relationship between the swing roller mechanism rotation angle and the material belt tension to be measured, a mathematical model of the swing roller mechanism tension system is established. The swing roller mechanism rotation angle and its first-order and second-order derivatives are estimated by using the extended state observer. The estimated values ​​of the swing roller rotation angle and its first-order and second-order derivatives are substituted into the swing roller mechanism tension system model to obtain the material belt tension value. The tension measurement method proposed by the present invention utilizes the filtering performance of the extended state observer to effectively filter out the interference in the swing roller rotation angle measurement process, solves the problem of amplifying the interference in the process of obtaining the first-order and second-order derivatives of the swing roller rotation angle, and realizes the high-precision measurement of the web printing press material belt tension.

Description

Technical Field

[0001] The invention belongs to the technical field of web printing equipment control, and in particular relates to a method for measuring the tension of a web printing machine belt based on an expansion state observer. Background Art

[0002] High-precision control of the web tension is the guarantee for web printing presses to produce high-fidelity multi-color prints, and it is also the basis for the promotion of web printing presses to the field of printed electronics. As the most widely used component in the measurement of web tension in web printing presses, the measurement accuracy of the swing roller mechanism is the core factor in achieving high-precision tension control. However, the tension system of the swing roller mechanism, which takes the swing roller mechanism angle as input and the web tension as output, is a typical second-order differential system, which leads to the problem of amplified interference when directly collecting the swing roller mechanism angle to obtain the web tension. In engineering applications, the swing roller mechanism tension system model is more often simplified to a proportional system model, resulting in low accuracy in the swing roller measurement of web tension, which cannot meet the requirements of tension control during high-speed, high-precision multi-color printing. Therefore, a method for high-precision measurement of web tension by a swing roller mechanism is urgently needed in the field of web printing equipment control technology. Summary of the invention

[0003] The purpose of the present invention is to provide a method for measuring the tension of the web of a web printing machine based on an expanded state observer, which aims to solve the problem of amplified interference in the process of obtaining the tension of the web using a tension system model of a swing roller mechanism, and greatly improve the accuracy of the swing roller mechanism in measuring the tension of the web. The method has the characteristics of simplicity, high efficiency, convenient calculation and good accuracy.

[0004] To achieve the above-mentioned purpose, the present invention provides the following technical solutions: a web printing press material belt tension measurement method based on an extended state observer, firstly, according to the mechanical relationship between the swing roller mechanism angle and the material belt tension to be measured, a mathematical model of the swing roller mechanism tension system is established; then, the swing roller angle and the first-order and second-order derivatives of θ(k) are estimated by using the extended state observer, and the interference in the swing roller angle collection process is filtered out, so as to solve the problem of amplifying the interference in the derivation process; finally, the estimated values ​​of the swing roller angle and its first-order and second-order derivatives are substituted into the swing roller mechanism tension system model to obtain a high-precision material belt tension value, and the specific steps are as follows:

[0005] Step 1: Establish a mathematical model of the tension system of the swing roller mechanism;

[0006] According to the actual working conditions, it is assumed that the swing roller mechanism rotation angle θ is small, the friction between the guide roller and the floating roller and the material strip is ignored, and the influence of the floating roller gravity on the dynamic performance of the swing roller is ignored. According to the torque balance equation, the mathematical model of the cylinder type swing roller mechanism tension system can be established as follows:

[0007]

[0008] In formula (1), T is the tension of the material strip in the swing roller mechanism, J D is the equivalent torque of the pendulum roller and the pendulum rod around the pendulum rod support point, θ is the angle of the pendulum roller mechanism deviating from the equilibrium position, B is the damping coefficient of the pendulum shaft, P is the cylinder pressure, A is the cylinder piston area, K is the cylinder spring elastic coefficient, d K is the length of the cylinder swing arm, d D is the length of the floating roller swing arm.

[0009] Step 2: Design the angle expansion state observer of the swing roller mechanism;

[0010] In order to filter out the interference in the process of collecting the swing roller mechanism angle θ, the extended state observer in the self-disturbance rejection control technology is used to estimate the collected swing roller mechanism angle θ and its first-order and second-order derivatives. According to the mathematical model of the swing roller mechanism tension system, the designed extended state observer is a second-order observer, and its discrete expression is as follows:

[0011]

[0012] In formula (2), e is the tracking error; z 1 、z 2 、z 3 is the output of the extended state observer, which is used to estimate θ, the first-order derivative of θ, and the second-order derivative of θ respectively; h is the sampling period; δ is the interval length of the linear segment, and its value is 0.01; β 1 , β 2 and β 3 is the gain parameter of the extended state observer, and β 1 The value is the reciprocal of the sampling period h; α 1 , α 2 is a power function parameter, and its values ​​are 0.6 and 0.3 respectively; fal(e,α,δ) is a power function, which can make the expansion observer converge quickly and smoothly and avoid the occurrence of high-frequency chattering. The specific algorithm is:

[0013]

[0014] Where sign(e) is the sign function;

[0015] Step 3: Calculate the tension value of the material strip in the swing roller mechanism;

[0016] Collect the swing roller mechanism angle θ(k) and cylinder pressure P(k) at time k, substitute θ(k) into the second-order extended state observer, and obtain the estimated value z for calculating θ(k) 1 (k+1), the first-order derivative estimator z of θ(k) 2 The second-order derivative estimator z of (k+1) and θ(k) 3 (k+1), z 1(k+1), z 2 (k+1), z 3 Substitute (k+1) into the tension system model of the swing roller mechanism, replace θ(k) and its first-order and second-order derivatives respectively, and substitute P(k) into the tension system model of the swing roller mechanism to obtain the tension value T(k) of the material strip at time k. The specific calculation formula is as follows:

[0017]

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] The present invention provides a method for measuring the web tension of a web printing press based on an extended state observer. On the basis of establishing a mathematical model of the tension system of a swing roller mechanism, a second-order extended state observer is used to estimate the collected swing roller mechanism rotation angle and its first-order and second-order derivatives, thereby effectively filtering out the interference in the process of collecting the swing roller mechanism rotation angle, solving the problem of amplifying the interference in the derivation process, greatly improving the accuracy of measuring the web tension of the swing roller mechanism of the web printing press, and laying a foundation for high-precision tension control. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the structure of the tension system of the swing roller mechanism in the present invention;

[0021] Figure 2 It is a schematic diagram of the principle of obtaining the tension of the material strip in the swing roller mechanism in the present invention;

[0022] Figure 3 It is a flow chart of the algorithm for obtaining the tension of the material strip in the swing roller mechanism in the present invention;

[0023] Figure 4 In the present invention, when θ generates a step disturbance, only the established tension system model of the swing roller mechanism is used to output the tension response curve;

[0024] Figure 5 It is the tension response curve output by the material strip tension measurement method invented in the present invention when θ generates step interference;

[0025] Figure 6 In the present invention, when θ generates random fluctuations, only the established tension system model of the swing roller mechanism is used to output the tension response curve;

[0026] Figure 7 It is the tension response curve output by the material strip tension measurement method invented when θ in the present invention produces random fluctuation interference. DETAILED DESCRIPTION

[0027] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] The present invention provides a web printing press material belt tension measurement method based on an extended state observer. First, according to the mechanical relationship between the swing roller mechanism angle and the material belt tension to be measured, a mathematical model of the swing roller mechanism tension system is established; then, the swing roller mechanism angle and its first-order and second-order derivatives are estimated by using the extended state observer, and the interference in the swing roller angle collection process is filtered out to solve the problem of amplifying the interference in the derivation process; finally, the estimated values ​​of the swing roller angle and its first-order and second-order derivatives are substituted into the swing roller mechanism tension system model to obtain a high-precision material belt tension value. The specific steps are:

[0029] Step 1: Establish a mathematical model of the tension system of the swing roller mechanism;

[0030] like Figure 1 As shown in the figure, the swing roller mechanism is mainly composed of two guide rollers, a cylinder, a swing arm floating roller and a material belt, among which an angular displacement sensor is installed at the hinge of the swing arm floating roller to collect the rotation angle of the swing roller mechanism. The pressure of the cylinder is set according to the material belt tension control requirements. When the material belt tension is stable, the swing arm of the swing roller mechanism does not deflect, and the swing arm is in a balanced position. At this time, the torque between the cylinder thrust and the material belt tension is balanced; when the material belt tension fluctuates, the torque balance between the cylinder thrust and the material belt tension is broken, resulting in the swing arm deflecting at an angle of θ. This angle is collected by the angular displacement sensor, and then the material belt tension value at this moment can be calculated through the swing roller tension model, and finally the real-time detection of the material belt tension is completed.

[0031] In order to simplify the structure of the swing roller model and facilitate the mathematical modeling of the tension system of the swing roller mechanism, it is assumed that the swing roller mechanism rotation angle θ is small according to the actual working conditions, the friction between the guide roller and the floating roller and the material strip is ignored, and the influence of the floating roller gravity on the dynamic performance of the swing roller is ignored. According to the torque balance equation, it can be obtained:

[0032]

[0033] In formula (1), J D is the equivalent torque of the pendulum roller and the pendulum rod around the pendulum rod support point; θ is the angle of the pendulum roller mechanism deviating from the equilibrium position; M K is the elastic moment of the cylinder, M B is the damping torque of the swing roller, M T is the strip tension moment, and M K 、M B 、M T They are:

[0034]

[0035] In formula (2), T is the tension of the material strip in the swing roller mechanism, B is the damping coefficient of the swing shaft, P is the cylinder pressure, A is the cylinder piston area, K is the cylinder spring elastic coefficient, and d Kis the length of the cylinder swing arm, d D is the length of the floating roller swing arm.

[0036] Combining the above two equations, the mathematical model of the tension system of the cylinder type swing roller mechanism can be established as follows:

[0037]

[0038] According to the tension system model of the swing roller mechanism, the swing roller mechanism is a second-order differential system, and its material tension value T is obtained by the linear combination of the swing roller mechanism rotation angle θ and its first-order and second-order derivatives. The swing roller mechanism rotation angle θ has interference in the measurement process of the angular displacement sensor. Directly using it to obtain the material tension value T will introduce and amplify interference, resulting in a decrease in measurement accuracy.

[0039] Step 2: Design the state observer of the swing roller mechanism angle expansion

[0040] like Figure 2 As shown in the figure, in order to filter out the interference in the process of collecting the swing roller mechanism angle θ, the extended state observer in the self-disturbance rejection control technology is used to estimate the collected swing roller mechanism angle θ and its first-order and second-order derivatives. According to the mathematical model of the tension system of the swing roller mechanism, the designed extended state observer is a second-order observer, and its discrete expression is as follows:

[0041]

[0042] In formula (4), e is the tracking error; z 1 、z 2 、z 3 is the output of the extended state observer, which is used to estimate θ, the first-order derivative of θ, and the second-order derivative of θ respectively; h is the sampling period; δ is the interval length of the linear segment. Appropriate adjustment can make the ESO have a good filtering function, and its value is 0.01; β 1 , β 2 and β 3 is the gain parameter of the extended state observer, and β 1 The value is the reciprocal of the sampling period h; α 1 , α 2 is a power function parameter, and its values ​​are 0.6 and 0.3 respectively; fal(e,α,δ) is a power function, which can make the extended state observer converge quickly and smoothly and avoid the occurrence of high-frequency chattering. The specific algorithm is:

[0043]

[0044] In formula (5), sign(e) is the sign function.

[0045] Step 3: Calculate the tension value of the material belt in the swing roller mechanism

[0046] like Figure 3 As shown, the steps for obtaining the tension value of the material strip in the swing roller mechanism include:

[0047] Step 3.1: Collect the swing roller mechanism rotation angle θ(k) and cylinder pressure P(k) at time k.

[0048] Step 3.2: Substitute θ(k) into the second-order extended state observer to obtain the estimate z for calculating θ(k) 1 (k+1), the first-order derivative estimator z of θ(k) 2 The second-order derivative estimator z of (k+1) and θ(k) 3 (k+1), the specific calculation formula is:

[0049]

[0050] In formula (6), β 2 and β 3 According to the specific model parameters of the swing roller mechanism, the adjustment principle is to make z 2 (k+1), z 3 (k+1) tracks the first and second derivatives of θ(k) without overshoot, respectively.

[0051] Step 3.3: z 1 (k+1), z 2 (k+1), z 3 Substitute (k+1) into the tension system model of the swing roller mechanism, replace θ(k) and its first-order and second-order derivatives respectively, and substitute P(k) into the tension system model of the swing roller mechanism to obtain the tension value T(k) of the material strip at time k. The specific calculation formula is as follows:

[0052]

[0053] The performance of the web tension measurement method for a web printing machine based on an extended state observer was simulated and verified in MATLAB software, and finally the high-precision measurement of the web tension in the swing roller mechanism was achieved. Specifically, the swing roller mechanism tension system model was built using the Simulink module in the software, and the effect of the invented web tension measurement method was verified by comparing the tension output by only the established swing roller mechanism tension system model with the tension output by the web tension measurement method based on the extended state observer. When using Simulink for the above simulation, the selected steady-state tension was 50N, and the effect of the invented web tension measurement method was verified by applying a disturbance to the swing roller mechanism angle θ(t). The simulation time was set to 30s, and at the 5th second, θ(t) produced an angle step of 0.01, Figure 4 , Figure 5The tension response curves are respectively the tension output by the established swing roller mechanism tension system model and the tension response curve output by the invented material belt tension measurement method; θ(t) continuously produces a random fluctuation of ±0.01. Figure 6 , Figure 7 The tension response curves are respectively the tension output by the established swing roller mechanism tension system model and the tension response curves output by the invented material belt tension measurement method. It can be seen that the invented material belt tension measurement method effectively filters out the interference in the swing roller mechanism rotation angle acquisition process, and greatly improves the accuracy of the swing roller mechanism in measuring the material belt tension.

[0054] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope described in the claims.

Claims

1. A method for measuring web tension of a web printing press based on an expansion state observer, characterized in that: Firstly, according to the mechanical relationship between the swing roller mechanism angle and the measured material strip tension, a mathematical model of the swing roller mechanism tension system is established; then, the swing roller angle and its first-order and second-order derivatives are estimated using the extended state observer, and the estimated values ​​of the swing roller angle and its first-order and second-order derivatives are substituted into the swing roller mechanism tension system model to obtain a high-precision material strip tension value, which specifically includes the following steps: Step 1: Establish a mathematical model of the tension system of the swing roller mechanism; Step 2: Design the angle expansion state observer of the swing roller mechanism; Step 3: Calculate the tension value of the material strip in the swing roller mechanism; Step 1: Establish the mathematical model of the tension system of the swing roller mechanism: （1） In formula (1), T is the tension of the material strip in the swing roller mechanism, J D is the equivalent torque of the pendulum roller and the pendulum rod around the pendulum rod support point, θ is the angle of the swing roller mechanism deviating from the equilibrium position, B is the damping coefficient of the pendulum shaft, P is the cylinder pressure, A is the cylinder piston area, K is the elastic coefficient of the cylinder spring, d K is the length of the cylinder swing arm, d D is the length of the floating roller swing arm; Step 2: Design the angle expansion state observer of the swing roller mechanism as follows: According to the mathematical model of the tension system of the swing roller mechanism, the designed expansion state observer is a second-order observer, and its discrete expression is as follows: （2） In formula (2), e is the tracking error, z1, z2, z3 are the outputs of the extended state observer, which are used to estimate θ , θ The first-order derivative of θ The second derivative of h is the sampling period, δ is the interval length of the linear segment, β 1. β 2 and β 3 is the gain parameter of the extended state observer, α 1. α 2 is the power function parameter, fal( e , α , δ ) is a power function, and the specific algorithm is: （3） In formula (3), sign( e ) is a symbolic function.

2. The web tension measurement method of a web printing press based on an expansion state observer according to claim 1, characterized in that: The value of δ is 0.01, the value of β1 is the inverse of the sampling period h; the values ​​of α1 and α2 are 0.6 and 0.3 respectively.

3. The web tension measurement method of a web printing press based on an expansion state observer according to claim 1, characterized in that: The step 3: calculating the tension value of the material strip in the swing roller mechanism, the specific steps are: Step 3.1: Collection k The swing roller mechanism angle at the moment θ ( k ), cylinder pressure P ( k ); Step 3.2: θ ( k ) is substituted into the second-order extended state observer, and the calculation is obtained θ ( k ) z 1( k +1), θ ( k ) is the first-order derivative estimator of z 2( k +1), θ ( k ) is the second-order derivative estimator z 3( k +1), the specific calculation formula is: （4） In formula (4), β 2 and β 3 is obtained by adjusting the specific model parameters of the swing roller mechanism. The adjustment principle is to make z 2( k +1), z 3( k +1) respectively no overshoot tracking θ ( k )’s first and second derivatives; Step 3.3: z 1( k +1), z 2( k +1), z 3( k +1) Substitute into the tension system model of the swing roller mechanism and replace θ ( k )and θ ( k ) first and second order derivatives, and P ( k ) is substituted into the tension system model of the swing roller mechanism to obtain k Material belt tension value at the moment T ( k ), the specific calculation formula is as follows: （5）。

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