Method for controlling unwinding tension of coating machine

Abstract

The invention discloses a coating machine unwinding tension control method which is characterized by comprising the steps that S1, parameters, operation data and tension data of a coating machine are collected, and a state-space equation of an unwinding tension control system is established; s2, constructing an obstacle function; s3, combining the obstacle function and constructing a non-singular sliding mode surface function; s4, solving an equivalent controller for controlling tension according to the non-singular sliding mode surface function; s5, optimizing key parameters of the equivalent controller by using an aurora optimization algorithm; s6, designing a self-adaptive control rate for improving the anti-interference capability of the unwinding tension control system; the adaptive control rate is combined with the equivalent controller, and a total control signal is output; s7, performing unwinding tension control on an unwinding tension control system according to the master control signal; according to the scheme, the speed of dynamic response can be adjusted, finite time convergence is enhanced, steady-state errors are eliminated, singularity is avoided, convergence is accelerated, and therefore high-precision control over an unwinding tension control system is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of tension control, and particularly relates to a method for controlling the unwinding tension of a coater. Background Art

[0002] As a key basic component in electronic devices, the production quality of multi-layer ceramic capacitors (MLCCs) is crucial for the performance of electronic devices. In the production process of MLCCs, the unwinding tension control link of the coater plays an important role; stable and accurate unwinding tension can ensure coating uniformity and avoid problems such as uneven coating thickness, wrinkles, and breaks, thereby improving the production quality and production efficiency of MLCCs.

[0003] Currently, the commonly used PID control in the field of coater unwinding control is difficult to accurately adapt to the dynamic characteristics of the system; it cannot adjust parameters in a timely manner when facing different web materials, thicknesses, and unwinding speed changes, resulting in low tension control accuracy. Fuzzy control usually relies on experience in rule formulation in practical applications, lacks systematic theoretical guidance, and is difficult to ensure the optimal control effect under various working conditions. Moreover, the parameter adjustment of fuzzy control is relatively difficult, and its adaptive ability in the face of complex system dynamic changes is limited, unable to meet the control requirements of high precision and fast response.

[0004] In order to achieve the precision and stable adjustment of the unwinding tension control of the MLCC coater, there is an urgent need for a method for controlling the unwinding tension of the MLCC coater based on the non-singular sliding mode with the aurora optimization algorithm and the barrier function. Summary of the Invention

[0005] Aiming at the above deficiencies of the prior art, the present invention provides a method for controlling the unwinding tension of a coater to solve the technical problems mentioned in the above background art.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] Provide a method for controlling the unwinding tension of a coater, characterized by comprising the following steps:

[0008] S1: Collect the parameters, operation data, and tension data of the coater, and establish the state space equation of the unwinding tension control system;

[0009] S2: Construct a barrier function for restricting the tension within a set range;

[0010] S3: Combine the barrier function and construct a non-singular sliding mode surface function for ensuring the convergence of the tension state within a finite time;

[0011] S4: Solve the equivalent controller for controlling the tension according to the non-singular sliding mode surface function;

[0012] S5: Optimize the key parameters of the equivalent controller using the aurora optimization algorithm;

[0013] S6: Design an adaptive control rate for enhancing the anti-interference ability of the unwinding tension control system; Combine the adaptive control rate with the equivalent controller and output the total control signal;

[0014] S7: Perform unwinding tension control on the unwinding tension control system according to the total control signal.

[0015] Furthermore, the unwinding tension control system includes an unwinding roller for unwinding the material tape. The material tape passes through a traction roller and a coating roller in sequence, and pressure rollers are arranged on both the traction roller and the coating roller. The unwinding roller, the traction roller, and the coating roller are respectively connected to an unwinding motor, a traction motor, and a coating motor in a transmission manner. A first tension sensor is arranged between the unwinding roller and the traction roller, and a second tension sensor is arranged between the traction roller and the coating roller. Both the unwinding motor and the first tension sensor are electrically connected to an unwinding controller, and both the traction motor and the second tension sensor are electrically connected to a traction controller.

[0016] The beneficial effects of the present invention are as follows:

[0017] The unwinding tension control system of this solution is a strongly coupled, parameter-time-varying non-linear complex system. First, establish the state space equation of the unwinding tension control system, limit the reasonable range of the tension through a barrier function, design a non-singular sliding mode surface function, and solve the equivalent controller to ensure that the system state converges within a finite time; And use the aurora optimization algorithm to optimize the key parameters C i , β i , α i of the sliding mode control, and perform a global search for the optimal parameter combination through "aurora elliptical walking". The purpose is to adjust the speed of the dynamic response, enhance the finite-time convergence, eliminate the steady-state error, avoid singularity and accelerate convergence, effectively improve the control accuracy and avoid falling into the misunderstanding of local optimum; Use adaptive control to approximate external interference and enhance the robustness of the control system, thereby achieving high-precision control of the unwinding tension control system. Description of the Drawings

[0018] Figure 1 It is the control flow chart of the unwinding tension control method for the coating machine.

[0019] Figure 2 It is the structural schematic diagram of the unwinding tension control system.

[0020] Among them, 1 - unwinding roller, 2 - first tension sensor, 3 - traction roller, 4 - second tension sensor, 5 - coating roller, 6 - unwinding motor, 7 - traction motor, 8 - coating motor, 9 - unwinding controller, 10 - traction controller, 11 - unwinding unit, 12 - traction unit, 13 - pressure roller. DETAILED DESCRIPTION

[0021] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0022] like Figure 1 As shown, the coating machine unwinding tension control method of the present scheme includes an unwinding tension control system, which includes an unwinding roller 1 for unwinding a material strip, the material strip passes through a traction roller 3 and a coating roller 5 in sequence, and the traction roller 3 and the coating roller 5 are equipped with a pressure roller 13, the unwinding roller 1, the traction roller 3 and the coating roller 5 are respectively connected to the unwinding motor 6, the traction motor 7 and the coating motor 8 by transmission, a first tension sensor 2 is arranged between the unwinding roller 1 and the traction roller 3, a second tension sensor 4 is arranged between the traction roller 3 and the coating roller 5, the unwinding motor 6 and the first tension sensor 2 are both electrically connected to the unwinding controller 9, and together with the unwinding roller 1 constitute an unwinding unit 11; the traction motor 7 and the second tension sensor 4 are both electrically connected to the traction controller 10, and together with the traction roller 3 constitute a traction unit 12.

[0023] The unwinding tension control method of this scheme comprises the following steps:

[0024] S1: Collect the parameters, operation data and tension data of the coating machine, and establish the state space equation of the unwinding tension control system; specifically, it includes:

[0025] Establish a nonlinear mathematical model of the unwinding tension control system:

[0026]

[0027] Wherein: T1 is the material strip tension monitored by the first tension sensor 2, T2 is the material strip tension monitored by the second tension sensor 4; R1 is the coil radius, R2 is the traction roller 3 radius, R3 is the coating roller 5 radius; ω1, ω2, ω3 are the angular velocities of the unwinding roller 1, the traction roller 3 and the coating roller 5, respectively, and ω3 is a preset constant value; L1 and L2 are the material strip lengths between the unwinding roller 1 and the traction roller 3, and between the traction roller 3 and the coating roller 5, respectively; A is the cross-sectional area of the material strip; E is the elastic modulus of the material strip;

[0028] Select state variables x1=T1, x2=T2, input variables u1=ω1, u2=ω2, u3=ω3 and organize the nonlinear mathematical model into state space equations:

[0029]

[0030] S2: Construct a barrier function for restricting the tension within a set range; among them, the barrier functions of T1 and T2 are respectively:

[0031] B1(T1) = ln(T max - T1 + ε / T1 - T 1min + ε)

[0032] B2(T2) = ln(T 2max - T2 + ε / T2 - T 2min + ε)

[0033] Among them, T 1max is the upper limit value allowed for T1, T 1min is the lower limit value allowed for T1, T 2max is the upper limit value allowed for T2, T 2min is the lower limit value allowed for T2; ε is a small positive number much smaller than the tension control accuracy to prevent the tension from approaching the preset upper and lower limits during the control process, resulting in the numerator or denominator tending to 0 and causing mathematical singularities.

[0034] S3: Combine the barrier function and construct a non-singular sliding mode surface function for ensuring the convergence of the tension state within a finite time; specifically, it includes:

[0035] Construct the sliding mode functions of T1 and T2, and their expressions are respectively:

[0036]

[0037] In the formula, x 1d and x 2d are the expected reference values of T1 and T2 respectively; (x 1d - x1), (x 2d - x2) are the tension errors e1 and e2 of the unwinding tension control system respectively; C1 and C2 are both constants determined by the pole placement method; α1 and α2 are the weight coefficients of the integral term; α1 > 0, α2 > 0, and α i << C i , i is 1 or 2;

[0038] Construct the non-singular terminal sliding mode surface functions of T1 and T2:

[0039]

[0040] Among them, β1 > 0, r1 = p1 / q1, p1 and q1 are positive odd numbers, and 1 < p1 / q1 < 2, p1 < q1; β2 > 0, r2 = p2 / q2, p2 and q2 are positive odd numbers, and 1 < p2 / q2 < 2, p2 < q2; α i + β i << Ci , where \(i = 1\) or \(2\), to avoid the integral term and the terminal term from prematurely dominating the dynamics and causing response oscillations;

[0041] The method for determining the constants \(C1\) and \(C2\) by the pole placement method in this scheme is as follows:

[0042] Linearize the state - space equation of the unwinding tension control system near the equilibrium point. Assume the equilibrium point is Perform a Taylor expansion on the above equation and neglect the highest - order terms to obtain the linearized state - space equation:

[0043]

[0044] where \(d(t)\) is the disturbance term of the system; Calculate the elements of matrices \(A\) and \(B\):

[0045]

[0046] Define the state - feedback control law: \(u=-Kx\), where:

[0047]

[0048] Substitute it into the linearized state equation to obtain the state equation of the closed - loop system:

[0049]

[0050] According to the performance requirements of the tension system, determine the desired closed - loop pole positions; assume the desired closed - loop poles are \(\lambda1\) and \(\lambda2\), and the desired characteristic equation is:

[0051] (s - \(\lambda1\))(s - \(\lambda2\)) = s 2 + a1s + a0 = 0

[0052] The characteristic equation of the closed - loop system is:

[0053] det(SI-(A - BK)) = S 2 + b1S + b0 = 0

[0054] where \(S\) and \(s\) are both Laplace operators, \(a1\) and \(a0\) are the coefficients of the desired characteristic equation; det is the determinant calculation, \(b1\) and \(b0\) are the coefficients of the closed - loop system characteristic equation, and \(I\) is the identity matrix;

[0055] Let the coefficients of the desired characteristic equation and the closed - loop system characteristic equation be equal, i.e., \(a0 = b0\), \(a1 = b1\) to obtain a set of linear equations about the elements of \(K\), and solve the system of equations to find the feedback gain matrix \(K\);

[0056] Let The constants C1 and C2 can be determined accordingly.

[0057] S4: Solve the equivalent controller for controlling the tension according to the nonsingular sliding mode surface function. Specifically, it includes:

[0058] Derive σ1(t) and σ2(t) of the nonsingular terminal sliding mode surface function, and the comprehensive formula can be obtained as:

[0059]

[0060] Substitute and let The expression of the equivalent controller can be obtained as:

[0061]

[0062] where f i (x) and g i (x) are the system nonlinear dynamic term Ax and the control gain matrix B respectively, and i is 1 or 2.

[0063] S5: Optimize the key parameters C i , β i , α i of the equivalent controller by using the aurora optimization algorithm. Specifically, it includes:

[0064] Initialize the population and randomly generate a group of particles containing the parameters C i , β i , α i of the equivalent controller. Each particle represents a group of parameter combinations;

[0065] Define the fitness function and select the integral of the system tracking error as the fitness function to evaluate the quality of each solution. The expression of the fitness function is:

[0066]

[0067] where e x1 , e x2 are the errors of x1 and x2 respectively, t s is the time when the system reaches the stable state, M P is the overshoot, and ω 11 -ω 55 are the weight coefficients;

[0068] Particle update operation: Update the particle positions by simulating the rotational motion, elliptical walking, and particle collisions in the aurora phenomenon, so that the particles search for better parameter combinations in the solution space;

[0069] Iteration and termination judgment: Calculate the fitness value of each particle, update the global optimal particle and the individual optimal particle, and determine whether the maximum number of iterations is reached or the fitness value meets the preset accuracy requirement. If it is satisfied, stop the iteration and output the sliding mode controller parameters corresponding to the optimal particle; otherwise, continue with the particle update operation.

[0070] S6: Design an adaptive control law for enhancing the anti-interference ability of the unwinding tension control system; Combine the adaptive control law with the equivalent controller and output the total control signal; Specifically, it includes:

[0071] Define the adaptive law as:

[0072]

[0073] Add the adaptive control term as:

[0074]

[0075] Obtain the total control input as:

[0076] u i = u ieq + u isw

[0077] Where is the estimated value of the upper bound of the interference, γ i is the adaptive gain coefficient, and i is 1 or 2.

[0078] S7: Perform unwinding tension control on the unwinding tension control system according to the total control signal.

[0079] This solution can also prove the stability of the control system by constructing a Lyapunov function and combining it with the system state space equation. Specifically, it includes:

[0080] For the subsystem related to x1, construct a Lyapunov function: For the subsystem related to x2, construct a Lyapunov function: Where respectively represent γ1>0 is the adaptive gain coefficient.

[0081] By taking the time derivative of V1 respectively, we get , where adaptive rate Substitute into the derivative to obtain: After further simplification: Since and η1≥D1, finally we get Similarly, we can get:

[0082] Total Lyapunov function: V = V1 + V2, and its derivative is According to the Lyapunov stability theorem, the system states σ1 and σ2 will converge to zero; further, from the design of the sliding mode surface, it can be seen that when σ1 = 0, the introduced terminal term accelerates the convergence of the error e1; similarly, σ2 = 0 ensures the convergence of e2 within a finite time.

[0083] To sum up, the unwinding tension control system of this scheme is a strongly coupled, parameter-time-varying non-linear complex system. First, establish the state space equation of the unwinding tension control system, limit the reasonable range of the tension through the barrier function, design the non-singular sliding mode surface function, and solve the equivalent controller to ensure the convergence of the system state within a finite time; and use the Aurora optimization algorithm to optimize the key parameters C i , β i , α i to find the optimal parameter combination globally through "Aurora elliptical walking", aiming to adjust the speed of the dynamic response, enhance the finite-time convergence, eliminate the steady-state error, avoid singularity and accelerate the convergence, effectively improving the control accuracy and avoiding falling into the misunderstanding of local optimality; use adaptive control to approximate external disturbances and enhance the robustness of the control system, thus achieving high-precision control of the unwinding tension control system.

Claims

1. A method for controlling the unwinding tension of a coater, characterized in that, The following steps are involved: S1: Collect the parameters, operation data and tension data of the coating machine, and establish the state space equation of the unwinding tension control system; S2: constructing a barrier function to limit the tension within a set range; S3: Combine the barrier function and construct a non-singular terminal sliding surface function to ensure that the tension state converges in a finite time; S4: Solve the equivalent controller for controlling tension based on the non-singular terminal sliding surface function; S5: Optimize the key parameters of the equivalent controller using the Aurora optimization algorithm; S6: Design an adaptive control rate to improve the anti-interference ability of the unwinding tension control system, combine the adaptive control rate with the equivalent controller, and output the total control signal; S7: Control the unwinding tension of the unwinding tension control system according to the total control signal.

2. The unwind tension control method of the coater according to claim 1, characterized in that The unwinding tension control system includes an unwinding roller for unwinding a material strip, the material strip passes through a traction roller and a coating roller in sequence, and the traction roller and the coating roller are equipped with a pressure roller, the unwinding roller, the traction roller and the coating roller are respectively connected to the unwinding motor, the traction motor and the coating motor by transmission, a first tension sensor is arranged between the unwinding roller and the traction roller, a second tension sensor is arranged between the traction roller and the coating roller, the unwinding motor and the first tension sensor are both electrically connected to the unwinding controller, and the traction motor and the second tension sensor are both electrically connected to the traction controller.

3. The unwind tension control method of the coater according to claim 2, wherein Step S1 specifically includes: Establish a nonlinear mathematical model of the unwinding tension control system: Where: T1 is the material strip tension monitored by the first tension sensor, T2 is the material strip tension monitored by the second tension sensor; R1 is the coil radius, R2 is the traction roller radius, and R3 is the coating roller radius; ω1, ω2, ω3 are the angular velocities of the unwinding roller, traction roller, and coating roller, respectively, and ω3 is a preset constant value; L1 and L2 are the material strip lengths between the unwinding roller and the traction roller, and between the traction roller and the coating roller, respectively; A is the cross-sectional area of the material strip; E is the elastic modulus of the material strip; Select state variables x1=T1, x2=T2, input variables u1=ω1, u2=ω2, u3=ω3 and organize the nonlinear mathematical model into state space equations:

4. The coating machine unwind tension control method according to claim 3, characterized in that, The barrier functions of T1 and T2 in step S2 are: B1(T1) = ln(T max - T1 + ε / T1 - T 1min + ε) B2(T2) = ln(T 2max - T2 + ε / T2 - T 2min + ε) where T 1max is the upper limit value allowed by T1, T 1min is the lower limit value allowed by T1, T 2max is the upper limit value allowed by T2, T 2min is the lower limit value allowed by T2; ε is a positive number less than the tension control accuracy.

5. The unwind tension control method of the coater according to claim 4, characterized in that Step S3 specifically includes: Construct the sliding mode functions of T1 and T2, whose expressions are: Wherein, x 1d and x 2d are the expected reference values of T1 and T2 respectively; (x 1d -x1) and (x 2d -x2) are the tension errors e1 and e2 of the unwinding tension control system respectively; C1 and C2 are both constants determined by the pole placement method; α1 and α2 are the weight coefficients of the integral term; α1>0, α2>0, and α i <<C i , where i is 1 or 2; Construct the non-singular terminal sliding surface function of T1 and T2: where, β1 > 0, r1 = p1 / q1, p1 and q1 are positive odd numbers, and 1 < p1 / q1 < 2, p1 < q1; β2 > 0, r2 = p2 / q2, p2 and q2 are positive odd numbers, and 1 < p2 / q2 < 2, p2 < q2; α i + β i << C i , and i is 1 or 2.

6. The unwinding tension control method of the coater according to claim 5, characterized in that, The method for determining constants C1 and C2 by pole placement is: The state-space equation of the unwinding tension control system is linearized near the equilibrium point. Assume the equilibrium point is The above equation is Taylor-expanded and the highest-order term is ignored, resulting in the linearized state-space equation: where d(t) is the disturbance term of the system; Calculate the elements of matrices A and B: Define the state feedback control rate: u = -Kx, where: Substituting it into the linearized state equation, we get the state equation of the closed-loop system: The characteristic equation method is used to solve the feedback gain matrix K. Let The constants C1 and C2 can be determined.

7. The unwind tension control method of the coater according to claim 6, characterized in that Step S4 specifically includes: By taking the derivative of the non-singular terminal sliding surface function σ1(t) and σ2(t), we can get the comprehensive formula: Substitute and let The expression of the equivalent controller can be obtained as follows: where f i (x), g i (x) are the system nonlinear dynamic term Ax and the control gain matrix B respectively, and i is 1 or 2.

8. The unwind tension control method of the coater according to claim 7, characterized in that, The key parameters of the equivalent controller in step S5 include C i , β i , α i , and its optimization methods include: Initialize the population and randomly generate a set of particles containing the equivalent controller parameters C i , β i , α i , where each particle represents a set of parameter combinations; Define the fitness function and select the system's tracking error integral as the fitness function to evaluate the quality of each solution. The fitness function expression is: Among them, are the errors of x1 and x2 respectively, and t s is the time for the system to reach the steady state, and M P is the overshoot, and ω 11 -ω 55 is the weight coefficient; Particle update operation updates the particle position by simulating the rotational motion, elliptical movement and particle collision in the aurora phenomenon, so that the particles can search for a better parameter combination in the solution space; Iteration and termination judgment, calculate the fitness value of each particle, update the global optimal particle and the individual optimal particle, judge whether the maximum number of iterations is reached or the fitness value meets the preset accuracy requirement. If it is satisfied, stop the iteration and output the sliding mode controller parameters corresponding to the optimal particle; otherwise, continue with the particle update operation.

9. The unwind tension control method of the coater according to claim 8, characterized in that Step S6 specifically includes: Define the adaptation law as: Add the adaptive control term as: Obtain the total control input as: u i = u ieq + u isw Among them, is the estimated value of the interference upper bound, and γ i is the adaptive gain coefficient, and i is 1 or 2.

Images