Constant tension control method for winding system

Abstract

The invention provides a winding system constant tension control method based on an improved inversion nonsingular fast terminal sliding mode controller, and the method comprises the steps: employing an observer to estimate system state values, such as the rotating speed of a system and the tension of a coil stock, introducing a constant-speed approaching rate as the approaching rate of a sliding mode controller, introducing a nonlinear function into a sliding mode surface, and carrying out the control of the constant tension of a winding system. An improved nonsingular terminal sliding mode surface is designed, so that tension tracking errors converge to zero more quickly in finite time. According to the method, a sliding mode control method and an inversion control method are combined, the problems that decoupling is difficult and robustness is poor due to strong coupling of a winding system are solved, and constant control over tension is achieved. The method is easy to implement, the robustness of a tension control system is improved, and the method has a good application prospect.

Description

Technical Field

[0001] The present invention belongs to the field of tension control of winding systems, and relates to a constant tension control method for winding systems based on an improved inverse nonsingular fast terminal sliding mode controller. Background Art

[0002] In recent years, winding systems have been widely used in production industries such as papermaking, printing, textile, and cold plastic materials. In practical applications, the control objective of the winding system is to improve the winding efficiency while ensuring the stable tension of the winding and unwinding materials. As the thickness of the material on the winding shaft increases during the working process of the winding system, the tension on the material will change, and too large or too small winding tension often leads to material breakage or shaft detachment. Therefore, the research on tension control technology has important practical significance.

[0003] The nonsingular fast terminal sliding mode controller can achieve fast global convergence of errors. By combining the inverse control method with the sliding mode control, constant control of tension can be achieved. Its basic principle is that the system ensures that the system state can quickly converge to the equilibrium state when it is far from the equilibrium state according to the nonlinear term of the sliding mode surface, and the linear term enables the system state to quickly converge when it is close to the equilibrium state of the system; moreover, due to the existence of the nonlinear term, it can ensure that there is no singularity problem in the control law, but the traditional nonsingular fast terminal sliding mode surface has problems of slow convergence time and poor robustness, and the time for the tension error to converge to zero is relatively long in practical applications. Summary of the Invention

[0004] The purpose of the present invention is to improve the traditional nonsingular fast terminal sliding mode controller, introduce a nonlinear function into the traditional fast terminal sliding mode surface, design a sliding mode surface with a faster error convergence speed, and combine the inverse control and the sliding mode control to enhance the robustness of the tension control system while improving the convergence speed of the tension tracking error, so as to achieve constant control of tension. The specific verification scheme is as follows:

[0005] The improved nonsingular fast terminal sliding mode surface is designed as follows:

[0006]

[0007] where: κ = g / h, γ = p / q, κ > γ, 1 < γ < 2, and g, h, p, q are the power term coefficients of the sliding mode surface and are all odd numbers; α and β are the coefficients of the sliding mode surface respectively, α > 0, β > 0.

[0008] The traditional nonsingular fast terminal sliding mode surface is:

[0009] s = δ1 + αδ1 κ + βδ2 γ (2)

[0010] Solve the system state convergence time \(t\) on the sliding mode surface (1) and the sliding mode surface (2). r1 and \(t\) r2 :[[]]END]]

[0011]

[0012]

[0013] When \(\delta_1 \gt 0\), then \(t\) r2 \(\gt t\) r1 . That is, the system state convergence speed on the improved non - singular fast terminal sliding mode surface of Equation (1) is faster than that on the traditional non - singular terminal sliding mode surface described in Equation (2).

[0014] The improved backstepping non - singular fast terminal sliding mode controller designed by the present invention has the following beneficial effects: By the backstepping method, the complex winding system is decomposed into two independent systems, an improved sliding mode surface is designed, and a sliding mode controller is constructed, so that the system tension tracking error quickly converges to zero within a finite time, improving the convergence speed of the tension error and the robustness of the winding system, and realizing the constant control of the tension; The method of the present invention is simple to implement, has high tension control accuracy and strong reliability, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Block diagram of the tension control system using the improved backstepping non - singular fast terminal sliding mode controller;

[0016] Figure 2 Working principle diagram of the winding system

[0017] Figure 3 Simulation diagram of the change tracking of the winding tension;

[0018] Figure 4 Simulation diagram of the change of the winding speed of the winding material; DETAILED DESCRIPTION OF THE INVENTION

[0019] The present invention will be further described below with reference to the drawings:

[0020] Figure 1 Figure []]END]] is the block diagram of the tension control system using the improved backstepping non - singular fast terminal sliding mode controller. The system mainly consists of an asynchronous motor, a tension observer, a tension controller, etc. After observing the winding tension through the observer, the given tension and the observed winding tension are subtracted, and the error value is input into the tension controller. The output current is used as the control current of the asynchronous motor to adjust the speed of the motor to achieve the real - time control of the winding tension.

[0021] Among them, the improved backstepping non - singular fast terminal sliding mode controller is the technology disclosed by the present invention.

[0022] According to Figure 2 Analyze the dynamic characteristics of the winding system and establish a second-order nonlinear model of the winding system based on the mechanism model:

[0023]

[0024] where: F0 is the tension of the material between the discharge port and the traction roller; F1 is the tension of the material between the traction roller and the coiling roller; V0 is the linear velocity of the material between the discharge port and the traction roller; V1 is the linear velocity of the material between the traction roller and the coiling roller; L is the length of the wound material between the take-up shaft and the drive shaft; R is the real-time radius of the coiling roller; J is the total rotational inertia on the take-up side; E is the elastic modulus of the material, S is the cross-sectional area of the wound material; ε = ρ·b·δR 2 ; ρ is the material density of the hot-rolled strip; b is the width of the material; δ is the thickness of the material; b f is the material friction coefficient;

[0025] Design an improved non-singular fast terminal sliding mode surface according to the second-order nonlinear model of the winding system as follows:

[0026]

[0027] where: κ = g / h, γ = p / q, κ > γ, 1 < γ < 2, g, h, p, q are the power term coefficients of the sliding mode surface and are all odd numbers; α, β are the coefficients of the sliding mode surface respectively, α > 0, β > 0. Among them, z1 is the tension tracking error, and h2 is the change rate of the tension error;

[0028] Define where c1 > 0, z2 is the virtual control quantity, that is Combined with this sliding mode surface, introduce the backstepping control method. Taking the derivative of the Lyapunov function, we can get:

[0029]

[0030] where,

[0031] The reaching law adopts the constant velocity reaching law: Solve out the backstepping sliding mode control law u:

[0032]

[0033] where, x d is the given tension of the wound material; E is the elastic modulus of the material; L is the length of the wound material; J0 is the initial rotational inertia of the take-up shaft; R0 is the initial radius of the take-up shaft; g2 is the non-linear change quantity observed by the observer;

[0034] Substitute Equation (8) into Equation (7), we get where c2 is a constant greater than zero. It can be seen that the designed non-singular terminal sliding mode controller based on the inversion algorithm is stable;

[0035] The present invention uses the backstepping control method to decompose the complex non-linear winding system into two subsystems. By designing the Lyapunov function and the virtual control quantity, the control quantity required by the system is gradually deduced, and then the control law of the whole system is obtained, which greatly enhances the robustness of the winding system. Combining the designed non-singular global terminal sliding mode controller with the backstepping control method to construct a backstepping sliding mode controller and design a tension control system, which improves the robustness and control accuracy of the system;

[0036] According to Figure 1 Establish a simulation platform for the tension control system of the improved backstepping non-singular fast terminal sliding mode controller;

[0037] Figure 3 It is the simulation diagram of the winding tension change tracking. When the winding system starts, the given tension is set to 10N. Comparing the control effects of the two controllers, after the system starts, the tension of the conventional sliding mode controller stabilizes at 3.5s, and the tension of the controller designed by the present invention stabilizes at 1.6s. Compared with the conventional sliding mode controller, the adjustment time of the control method designed by the present invention is reduced by 57%;

[0038] Figure 4 It is the simulation diagram of the winding speed change of the coil. It can be seen that the designed controller can accurately track the change of the winding speed.

Claims

1. A constant tension control method for a winding system based on an improved inversion nonsingular fast terminal sliding mode controller, characterized in that, The method introduces a nonlinear function into the sliding mode surface, designs an improved nonsingular terminal sliding mode surface, and combines the backstepping control and sliding mode control methods to achieve constant control of the tension, improving the convergence speed of the tension error and the robust performance of the tension control system at the same time.

2. The constant tension control method for the winding system based on the improved inversion nonsingular fast terminal sliding mode controller according to claim 1, characterized in that It is constructed by the following method: According to the dynamic characteristics of the winding system, a second-order nonlinear model of the winding system based on the mechanism model is established: Where: F0 is the tension of the material between the discharge port and the traction roller; F1 is the tension of the material between the traction roller and the coiling roller; V0 is the linear velocity of the material between the discharge port and the traction roller; V1 is the linear velocity of the material between the traction roller and the coiling roller; L is the length of the coiled material between the take-up shaft and the drive shaft; R2 is the real-time radius of the coiling roller; J is the total moment of inertia on the take-up side; E is the elastic modulus of the material, S is the cross-sectional area of the coiled material; ε = ρ·b·δR 2 ; ρ is the material density of the hot-rolled strip; b is the material width; δ is the material thickness; b f is the material friction coefficient; Define x1 as the tension F1 on the winding material, x3 as the linear velocity V1 of the material between the traction roller and the coiling roller, z1 as the tension tracking error, and h2 as the tension error change rate; design the following improved nonsingular fast terminal sliding mode surface s according to the second-order nonlinear model of the winding system: In the formula: κ = g / h, γ = p / q, κ > γ, 1 < γ < 2, and g, h, p, q are the power term coefficients of the sliding mode surface and are all odd numbers; α and β are the coefficients of the sliding mode surface respectively, α > 0, β > 0; Definition where \(c1>0\), \(z2\) is a virtual control quantity, that is Combined with this sliding surface, an inversion control method is introduced; taking the derivative of the Lyapunov function gives: Among them, The reaching law adopts the constant velocity reaching law: Solve for the inverse sliding mode control law u: where x d is the given tension of the coil stock; E is the elastic modulus of the material; L is the length of the coil stock; J0 is the initial moment of inertia of the take-up reel; R0 is the initial radius of the take-up reel; and g2 is the non-linear variation observed by the observer.

Images