Research on the tension control method of lithium battery electrode mill based on GA optimized Fuzzy PID

Abstract

In the industrial field, the lithium battery industry has a long history and a large market scale. Lithium battery electrode strip rolling mill belongs to the high-end production equipment in the lithium battery industry. However, due to its complex structure, the tension of lithium battery electrode mill is prone to large fluctuation. This will lead to the phenomenon of wrinkle and looseness, which will affect the quality of the electrode strip. At present, the tension control method of lithium battery electrode mill mostly adopts traditional Proportional-Integral-Differential(PID) control. Under this control mode, the production speed and precision of lithium battery electrode mill need to be improved. In this paper, the fuzzy PID tension control method of lithium battery electrode mill based on genetic optimization is studied. Based on fuzzy theory and PID control method, a tension fuzzy PID model is established for experimental verification, and the initial parameters and fuzzy rules of fuzzy PID are optimized by Genetic Algorithm(GA). This method has better stability, can improve the precision of strip tension control, make the tension more stable when the rolling mill is running, and help to improve the quality of electrode strip production.

Keywords

Fuzzy theory genetic algorithm lithium battery electrode mill PID tension

1 Introduction

Lithium battery industry is developing rapidly and has a broad market prospect. It has a huge demand in all walks of life in the world. In order to adapt to the growth of lithium battery demand, the product quality and production efficiency of lithium battery are also facing higher requirements. The electrode mill of lithium battery is responsible for the electrode strip rolling in the production process of lithium battery, and the production precision of the electrode strip is directly related to the output and life of lithium battery and many other important factors. As one of the core parts of the rolling mill, tension control system directly determines the overall operation state and precision of the rolling mill. Therefore, it is particularly important to study the tension control method of lithium battery mill for improving the production efficiency and production accuracy of lithium battery [1].

For the tension control of lithium battery electrode mill, it was realized by traditional simulator and motor at first. Due to the lack of precise detection and feedback device, the production accuracy of products is low in the initial strip rolling. With the continuous development and improvement of the electronic manufacturing industry, the performance of the detection system and the computer processing ability are gradually improved. The traditional simulator is replaced by the existing high-precision sensors and controllers. The tension is adjusted and controlled by outputting control signal or adjusting current. This provides hardware support for the implementation of this method.

At present, in small enterprises, there are still many traditional lithium battery electrode mills being put into use. Most of the traditional tension control methods of lithium battery electrode strip mill are to receive control signals directly to complete the actuator drive, or combined with the real-time monitoring signal data, after comparing with the set value, drive the actuator according to the difference value to complete the rolling mill control. But in the actual tension control, there are nonlinear and multivariable coupling problems. Moreover, there are a lot of interferences in different links and the external industrial environment, so it is difficult to guarantee the rolling accuracy of the electrode strip effectively by using the traditional tension control method under multiple disturbances. With the requirement of the precision of the electrode strip is higher and higher, we need to comply with the trend of the times and study the new tension control method which can improve the precision of the electrode strip production. At present, no one has done in-depth research in the field of tension control of lithium battery electrode mill. This method is of great significance to improve the tension control theory and rolling precision of lithium battery electrode mill, and can effectively improve the production precision and speed of lithium battery, and fill the blank of tension control method research of lithium battery electrode strip rolling mill.

In previous studies, some scholars have done some research on tension controls: Carrasco et al. proposed two tension estimators for the winding process and unwinding process. After combining the basic equipment dynamic, friction and inertia change effects, the linear operation cycle of the winding equipment was evaluated, which was used as feedback to realize the stable and accurate control of paper tension [2]. Ashour H et al. designed a variable-speed AC drive hardware system based on PLC and HMI for paper curling. The system calculates the pulse number at the pressure roller through the encoder, and obtains the change of the roll diameter of the crimping mechanism. Through these parameters, the reference torque and angular speed can be calculated, and the constant tension and linear speed winding and unwinding equipment can be operated without tension sensor [3]. C Jiang et al. combined the trend law of sliding mode control with the dynamic characteristics of the unwinding system to reduce the influence of measurement noise by increasing parameters, aiming at the difficult parts such as nonlinear and strong coupling characteristics of battery unwinding tension, friction uncertainty, and measurement noise [4]. To solve the problem of enameled wire vibration caused by the change of winding wire tension in the motor winding machine, Lu j s et al. combined the feed-forward control and iterative learning control into the tension control scheme, and reduced the interference of the winding process by taking the wire tension measured by force sensor as the feedback signal of the tension control loop [5]. Xu, YX, Niu, LC, et al. carried out in-depth analysis on the rolling process of lithium battery electrode sheet, and proposed a thickness control method based on GA-BP neural network. By analyzing the production process and system characteristics of lithium battery, the mathematical model of the control system for the thickness of lithium battery electrode was established. Combined with the causes of the electrode thickness fluctuation of lithium battery, BP neural network is introduced into the electrode thickness control system, and a prediction model of electrode thickness control based on neural network is proposed and optimized by genetic algorithm. However, this control method is mainly reflected in the thickness of the lithium battery electrode strip, and does not optimize the possible wrinkle, loose coil and other phenomena [6].

The existing tension control methods are robust control, adaptive control, fuzzy control, neural network and PID control. Among them, robust control has good performance in resisting the disturbance of system internal and external environment, but its control precision is slightly lower than other methods. Adaptive control has good performance in dealing with external random disturbance and mechanical equipment lag response method, but the lag of mill tension control is not high, and the interference is not particularly strong in the process of stable control, so this method is not selected in this paper. Neural network has strong performance in self-learning and self- optimization, and has good adaptability in the tension control of rolling mill, but it is not convenient to write the control system algorithm. The PID control method is simple and easy to operate and widely used in industry. With the fuzzy algorithm which does not need to establish accurate mathematical model and has excellent anti-interference ability, it can be well applied to the tension control process of rolling mill. At the same time, these two methods are easy to be converted into corresponding C language and other code forms to write into the control system. Therefore, this paper combines the two methods of PID control and fuzzy algorithm, studies the fuzzy PID control method, and optimizes it with genetic algorithm to further improve the control accuracy.

This method can produce the following beneficial effects on the existing lithium battery electrode mill:

Keep the electrode strip of lithium battery flat to avoid waves caused by uneven elongation of electrode strip.

Smooth and stable rolling of the electrode strip to avoid deviation of the lithium battery electrode strip in the rolling process.

Slightly adjust the thickness of the lithium battery electrode strip to meet the set thickness requirements.

Reduce the deformation resistance of the electrode strip, fine-tune the rolling force, and reduce the energy and material loss.

The structure of the rest of this paper is as follows: the second section studies and analyzes the mathematical model of tension control system. The third section studies the tension fuzzy PID control method, and establishes the simulation model. In the fourth section, the tension fuzzy PID control method is optimized by genetic algorithm. In the fifth section, experiments are carried out to verify the effectiveness of the method. The sixth section summarizes and discusses this paper.

2 Analysis and research of tension control system

This section starts from the causes of tension, analyzes the tension control method and completes the construction of tension control mathematical model, which provides theoretical basis and mathematical model for subsequent analysis of tension control algorithm [7].

2.1 Causes of tension

The tension control part of the lithium battery electrode strip mill can be divided into two parts: winding up and unwinding by taking the main role as the dividing point. The structure from the unwinding air expansion shaft to the main role is similar to that from the main roll to the winding air expansion shaft, and the causes of the tension are similar to the tension control method. Next, take the tension of the winding part as an example to analyze the tension generation mechanism and basic tension control method of the electrode strip when the rolling mill rolls the electrode strip [8].

In the process of electrode strip rolling, the tension on the strip is caused by the difference between the linear speed of the main role and that of the air expansion shaft. The mechanism of tension generation in the unwinding part of the lithium battery rolling mill can be simplified as Fig. 1.

Fig. 1

Causes of the tension of electrode strip.

In the ideal case, the influence of the change of the winding diameter of the winder is ignored, and the tension of the strip is solved by force analysis. Set the linear velocity at the winding point to be v_b, the outgoing velocity of the main role to be v_a, and the length of the electrode strip between the roller and the winding to be L. To ensure the winding operation to be completed smoothly, it is necessary to ensure that the linear velocity of the winding gas expansion shaft is greater than the rotational linear velocity of the main role, namely v_b > v_a. At this point, the difference in velocity leads to elastic deformation of the electrode strip, which can be regarded as a displacement of ΔL occurring when the electrode strip moves faster toward the velocity of the electrode strip. The displacement of ΔL can be converted into an expression of velocity and time:

$d (Δ L) = (v_{b} - v_{a}) dt$ (1)

Integrate Equation (1) to get:

$Δ L = \int (v_{b} - v_{a}) dt$ (2)

At this time, the strain ɛ of the electrode strip is obtained: $ɛ = \frac{Δ L}{L}$ (3)

According to Hooke’s law, the linear stress σ on the strip is the ratio of the tension T of the strip to the sectional area S of the strip, and the linear stress σ is proportional to the strain ɛ of the strip: $σ = \frac{T}{S} = E ɛ$ (4)

In the formula, E is the elastic modulus.

By combining Equations (3) and (4), the tension T in the electrode strip can be obtained: $T = ES ɛ = ES \frac{Δ L}{L} = \frac{ES}{L} \int (v_{b} - v_{a}) dt$ (5)

The Equation (5) shows that the elastic modulus E, electrode strip with cross-sectional area S, and electrode strip with length L in a sheet rolling process are valued, won’t produce change, therefore, lithium battery electrode strip take tension is due to an electrode strip rolling pressure points, winding wire gassing axis point rolling into the gassing axis line and point exist, as a result of the speed difference control of the sheet belt tension can be converted into the mill main roll down the volume and inflatable shaft speed and torque control.

When the tension of the electrode strip in the winding part is too large, too small, or fluctuates violently, it will cause fold or tear in the transmission process of the electrode strip, and the inner ring or outer ring of the electrode strip may also be loosened. Among them, the folding of the electrode strip and the looseness of the inner ring of the winding electrode strip is shown in Fig. 2.

Fig. 2

(a) Fold phenomenon of electrode strip; (b) looseness of the inner ring.

2.2 Tension control method

The tension control mode of rolling mill can be divided into open-loop control and closed-loop control according to different processes. The open-loop control lacks the corresponding feedback link. By analyzing the tension change law of the winding and unwinding part in advance, the fixed rolling mill control strategy is set up. Due to the lack of actual control of rolling process, the anti-interference ability and rolling accuracy of this method are slightly insufficient. The closed-loop control is to add a tension feedback link. The tension information of the electrode strip is collected in real time through the tension sensor. Through the real-time analysis of the deviation between the collected tension value and the set tension value, the controller drives the motor or frequency converter to drive the mechanical transmission mechanism to complete the tension adjustment.

In this paper, the tension closed-loop control method is selected, which can timely feedback control the motor speed and torque of the take-up air expansion shaft through the detected tension change, which can effectively avoid excessive tension fluctuation during the electrode strip rolling, so as to improve the rolling accuracy of the electrode strip. The tension control link of electrode strip rolling mill can be roughly divided into tension detection, tension control and motor drive.

The tension detection link needs to collect the tension information in real time through the tension roller and tension sensor, collect and transmit it to the control system for subsequent algorithm analysis; the tension control link analyzes and calculates the real-time values of the tension and winding diameter, and obtains the tension moment and inertia moment compensation, and obtains the driving power by combining the friction torque and the electrode strip bending moment compensation The speed and torque of the machine, and then output the motor drive signal; the motor drive link is through the received motor drive signal, completes the servo motor drive, drives the mechanical transmission mechanism, changes the speed and torque of the air expansion shaft of the winding, and completes the real-time tension adjustment. In order to facilitate the algorithm analysis of the subsequent electrode strip tension control link, the tension detection part and coil diameter calculation part are calculated and analyzed. At the same time, the torque model and transmission mechanism model of the drum are established to complete the mathematical model construction of the tension control part of the electrode strip mill.

2.3 Tension detection model

The tension detection structure in the overall structure of the rolling mill is shown in Fig. 3. It can be seen from the figure that the tension detection mechanism is composed of a force measuring roll, two guide rolls, and a tension sensor.

Fig. 3

Structural drawing of tension detection.

The electrode strip is fed in from the guide roller 1, bypasses the force measuring roller, and leads out from the guide roller 2. Therefore, the tension of the electrode strip can be converted into the pressure value collected by the tension sensor. Since the two guide rollers are symmetrical according to the vertical line of the tension roller, the tension value on the electrode strip is symmetrical concerning the vertical line of the tension roller. If the pressure collected by the tension sensor is F and the angle between the electrode strip and the vertical line is θ, then the tension T on the electrode strip can be obtained:

$T = \frac{F}{2 cos θ}$ (6)

electrode strip rolling require before set as the standard values of electrode strip belt tension, need to take into account at this time for the rolling sheet with the cross-sectional area, the material, the width and thickness, and so on many factors, so the actual mill rolling different specifications of the lithium-ion batteries were extremely need to set different tension values, but overall, the tension adjustment range between 0.5 to 3.5 kgf.

2.4 Coil diameter calculation

In the process of winding and unwinding of the strip by the gas expansion axis, the coil diameters of the winding part and unwinding part of the strip will change continuously with the feed and feed of the strip. To prevent the increase or decrease of the tension caused by the change of the coil diameter, it is necessary to measure the value of the coil diameter in real-time and adjust the tension fluctuation caused by the coil diameter. In this paper, according to the winding speed of the electrode strip, the area on the side of the electrode strip was analyzed by the micro-element method to realize the measurement of the winding diameter. Because the electrode strip was thin, the side of the electrode strip was regarded as a standard circular structure. Before the real-time calculation of the drum radius, it is necessary to clarify the variation law of the drum radius, as shown in Fig. 4.

Fig. 4

Drum radius change diagram.

When there is no electrode strip involved in the drum, the minimum radius of the drum is R_min, when the upper electrode strip is fully loaded, the maximum radius of the drum is R_max, and the real-time radius of the drum is R; when the electrode strip operates stably, the linear velocity is V, and the thickness of the electrode strip is H; then, after t, the cross-sectional area produces changes in the size of ∫vdt.

In the winding process of the electrode strip, the radius of the drum gradually increases. The side area of the drum is the sum of the cross-sectional area with the minimum radius of the drum and the side area of the coiled electrode strip: $π R^{2} = π R_{min}^{2} + H \int vdt$ (7)

Since the rolling speed is constant when the rolling mill is working, the linear speed V is the fixed value set in advance, so the real-time rolling diameter during the rolling process can be obtained as follows: $R = \sqrt{R_{min}^{2} + \frac{Hvt}{π}}$ (8)

During the winding process, the radius of the reel gradually decreases, and the side area of the reel is the difference between the sectional area of the smallest radius of the reel and the side area of the strip: $π R^{2} = π R_{max}^{2} - H \int vdt$ (9)

In the same way, the real-time winding diameter of the electrode strip unwinding can be calculated as: $R = \sqrt{R_{max}^{2} - \frac{Hvt}{π}}$ (10)

2.5 Analysis of moment of inertia

In the process of electrode strip tension control of rolling mill winding and unwinding, the main control method is to adjust the motor speed under the premise of ensuring the stability of the moment of inertia of the winding drum and to complete the tension adjustment by forming the speed difference with the main roller. With the rotation of the gas expansion axis, the material of the electrode strip is released and entered into the line, which will cause the constant change of the radius of the electrode strip and the change of the moment of inertia of the electrode strip. Therefore, to ensure the stability of tension, in addition to changing the motor speed, the motor’s moment of inertia also needs to be compensated.

The moment of inertia of the roller is analyzed by taking the unwinding part of the electrode strip as an example. The moment composition of the unwinding roller is shown in Fig. 5. In the unwinding process, the torque of the drum part will reach a balance, that is, the electrode belt tension torque, frictional resistance torque, the torque of the drum inertia, and the output torque of the motor will work together to reach a balance, at this point, it can be obtained: $M_{D} = M_{T} + M_{f} + M_{J}$ (11)

Fig. 5

Moment balance diagram of unwinding roll.

In the formula, M_D is the output torque of the motor, M_T is the tension moment of the electrode plate, M_f is the frictional resistance moment, and M_J is the inertia moment of the drum.

M_T is the product of the strip tension value and the radius of the rewinding drum: $M_{T} = F_{T} R$ (12)

The moment of inertia J and angular velocity ω changes continuously when the electrode strip is reeling and unwinding. Since the electrode strip is transported smoothly when the rolling mill is running, both J and ω are functions of time T. therefore, the moment of inertia M_J of the drum can be transformed into: $M_{J} = \frac{\partial (J ω)}{\partial t} = J \frac{\partial ω}{\partial t} + ω \frac{\partial J}{\partial t}$ (13)

The part J of the moment of inertia in Equation (13) can be divided into two parts according to the material composition of the electrode strip belt drum: the core part of the drum and the hollow drum part of the electrode strip belt. The core part of the drum can be regarded as a solid cylinder, and the moment of inertia of the core part can be obtained as:

$J_{1} = \frac{1}{2} m_{1} R_{min}^{2}$ (14)

Where m₁ is the mass of the core and the core is solid with uniform density: $m_{1} = π ρ_{1} {lR}_{min}^{2}$ (15)

In the formula, ρ₁ is the density of the core material, l is the length of the retractable reel, and R_min is the cross-section radius of the core.

By analyzing the above formula, the moment of inertia of the core part can be obtained as: $J_{1} = \frac{π}{2} ρ_{1} {lR}_{min}^{4}$ (16)

The electrode roll wound by the electrode strip can be regarded as the hollow drum, and the formula for calculating the moment of inertia is: $J_{2} = \frac{1}{2} m_{2} (R^{2} + R_{min}^{2})$ (17)

Where m₂ is the mass of the electrode strip, similarly, it can be obtained: $m_{2} = π ρ_{2} l (R^{2} - R_{min}^{2})$ (18)

In the formula, ρ₂ is the electrode band density and R is the radius of the reel measured in real time.

Through Equations (17) and (18), it can be obtained that the moment of inertia of the wound part of the electrode strip is: $J_{2} = \frac{π}{2} ρ_{2} l (R^{4} - R_{min}^{4})$ (19)

The moment of inertia of the core and the coil of the electrode strip can be obtained by summation: $\begin{matrix} J = J_{1} + J_{2} = \frac{π}{2} ρ_{1} {lR}_{min}^{4} + \frac{π}{2} ρ_{2} l (R^{4} - R_{min}^{4}) \\ = \frac{π}{2} {lR}_{min}^{4} (ρ_{1} - ρ_{2}) + \frac{π}{2} ρ_{2} {lR}^{4} \end{matrix}$ (20)

According to Equation (20), except the real-time drum radius R, all are constants, so the overall rotational inertia of the drum is only related to the drum radius R. Combination formula (10), under the condition of constant online speed, the rotational inertia can be transformed into a function of time t, and the rotational inertia of the winding part is shown in Equation (21): $J = \frac{π}{2} {lR}_{min}^{4} (ρ_{1} - ρ_{2}) + \frac{π}{2} ρ_{2} l {(R_{min}^{2} + \frac{Hvt}{π})}^{2}$ (21)

The moment of inertia of the unwinding part is shown in Equation (22): $J = \frac{π}{2} {lR}_{min}^{4} (ρ_{1} - ρ_{2}) + \frac{π}{2} ρ_{2} l {(R_{min}^{2} - \frac{Hvt}{π})}^{2}$ (22)

Taking the winding part as an example, except R, the other elements of the moment of inertia J are fixed values, so the two variables in M_J are respectively: $ω \frac{\partial J}{\partial t} = 2 π ρ_{2} {lR}^{3} ω \frac{\partial R}{\partial t}$ (23) $J \frac{\partial ω}{\partial t} = [\frac{π}{2} {lR}_{min}^{4} (ρ_{1} - ρ_{2}) + \frac{π}{2} ρ_{2} {lR}^{4}] \frac{\partial ω}{\partial t}$ (24)

And because: $\frac{\partial ω}{\partial t} = \frac{\partial (\frac{v}{R})}{\partial t} = \frac{1}{R^{2}} (R \frac{\partial v}{\partial t} - v \frac{\partial R}{\partial t})$ (25)

Therefore: $ω \frac{\partial J}{\partial t} = ρ_{2} {lHRv}^{2}$ (26) $J \frac{\partial ω}{\partial t} = \frac{J}{R^{2}} (R \frac{\partial v}{\partial t} - \frac{{Hv}^{2}}{2 π R})$ (27)

Then the drum inertia moment M_J is: $M_{J} = ρ_{2} {lHRv}^{2} + \frac{J}{R} \frac{\partial v}{\partial t} - \frac{{JHv}^{2}}{2 π R^{3}}$ (28)

In addition to the above analysis of tension torque M_T and inertia torque M_J, M_f is the frictional resistance torque, which can be regarded as a constant. During the equipment debugging of lithium electric rolling mill, the torque value under different rolling speeds can be acquired by making the winding or unwinding mechanism perform no-load rotation. The curve is drawn by analyzing the data. In the actual operation of the rolling mill, the corresponding friction resistance torque under the rolling speed can be set through the curve call. M_D is the motor output torque, which can be determined by setting the winding or unwinding motor torque parameters and combining with the transmission ratio of mechanical structures such as coupling and winding core [9].

The torque balance equation of the winding part of the drum is: $F_{T} R = M_{D} - (ρ_{2} {lHRv}^{2} + \frac{J}{R} \frac{\partial v}{\partial t} - \frac{{JHv}^{2}}{2 π R^{3}}) - M_{f}$ (29)

Similarly, the moment balance equation of the unwinding part of the drum can be calculated as: $F_{T} R = M_{D} + (- ρ_{2} {lHRv}^{2} + \frac{J}{R} \frac{\partial v}{\partial t} - \frac{{JHv}^{2}}{2 π R^{3}}) + M_{f}$ (30)

Through the analysis of the above two formulas, it can be seen that in the process of starting or stopping the strip mill, the linear speed v has acceleration and deceleration stages, and $\frac{\partial v}{\partial t}$ is not zero at this time. There is an obvious relationship between the strip tension and the linear speed, linear acceleration, drum radius, and motor output torque. When the rolling mill runs stably, the roll rotates stably and the rolling line speed is constant, then $\frac{\partial v}{\partial t}$ is zero. At this time, the tension of the electrode strip is related to the radius of the drum and the input torque. By establishing the mathematical model, the output torque of the motor is adjusted according to the real-time value and changes the rule of the coil diameter, which provides model and parameter support for the subsequent tension control system [10].

3 Research on tension fuzzy PID control method

3.1 Research on fuzzy PID control method

In order to avoid the phenomenon that the tension value exceeds the set value too much in the process of start-up, stable operation and stop of the electrode strip rolling mill, the integral control method is introduced in the PID control process, and the system stability is improved by removing the integral link in the PID control when the tension deviation signal is large When the tension deviation signal decreases and is close to the set value, the integral link is introduced again to eliminate the static error in the tension control [11 –13].

The method involves the determination of K_P, K_I and K_D parameters in application. The determination methods of these parameters are given by experienced experts or adjusted in industrial field. However, the determined parameters are based on the specific control object. Once the parameters of the electrode strip change or other errors are introduced, the existing PID controller will be affected and the control accuracy and efficiency will be reduced. Therefore, this paper introduces fuzzy algorithm on the basis of this algorithm, and realizes the on-line adjustment of K_P, K_I and K_D parameters in PID control by using relevant expert knowledge, which can effectively improve the precision and anti-interference ability of the closed-loop feedback control link in lithium battery electrode rolling mill [14 –16]. The structure of Integral Separated PID controller with fuzzy algorithm is shown in Fig. 6.

Fig. 6

Schematic diagram of application flow of integral separation fuzzy PID algorithm.

As shown in the figure above, in order to optimize the proportional, integral and differential coefficients of PID controller by fuzzy algorithm, these parameters are divided into initial value and modified value after optimization of fuzzy algorithm [17, 18]. The initial value determines the overall performance of closed-loop control, and the modified value is obtained by fuzzy controller to optimize PID control performance [19]. The calculation method is as follows:

$\begin{matrix} K_{P} = K_{P}^{'} + Δ K_{P} \\ K_{I} = K_{I}^{'} + Δ K_{I} \\ K_{D} = K_{D}^{'} + Δ K_{D} \end{matrix}$ (31)

In the formula: $K_{P}^{'}$ , $K_{I}^{'}$ and $K_{D}^{'}$ are initial values of PID parameters. ΔK_P, ΔK_I and ΔK_D are output values of fuzzy controller. K_P, K_I and K_D are final values of PID parameters.

In this paper, the fuzzy algorithm is used to optimize the three parameters of PID to realize the tension control. Therefore, the deviation signal e and the change rate e_c of the deviation signal are taken as the input parameters, and the regulating values of the three parameters of the PID controller ΔK_P, ΔK_I and ΔK_D are taken as the output parameters. In order to transform the above parameters from the precise input and output variables to the universe corresponding to the fuzzy set, it is necessary to determine the fuzzy universe corresponding to the quantization factors in fuzzy control. Seven fuzzy subsets of these five parameters are fuzzified according to different quantity levels: NB (negative large), NM (negative middle), NS (negative small), Z (zero), PS (positive small), PM (positive middle), PB (positive large). The centroid method is used in the fuzzification and defuzzification of these parameters, which is widely used in industrial control.

In the process of database establishment in the knowledge base, different membership functions should be established according to different input and output. The main membership functions are as follows:

The spline curve of Z-type membership function is Z-shaped, which is determined by x₁ and x₂ parameters in the calculation formula. The calculation method is as follows (32). $μ_{A} (x, x_{1}, x_{2}) = {\begin{matrix} 1, & x < x_{1} \\ 1 - \frac{2 (x - x_{1})^{2}}{(x_{2} - x_{1})^{2}}, & x_{1} ⩽ x < \frac{(x_{1} + x_{2})}{2} \\ \frac{2 (x_{2} - x)^{2}}{(x_{2} - x_{1})^{2}}, & \frac{(x_{1} + x_{2})}{2} ⩽ x < x_{2} \\ 0, & x_{2} ⩽ x \end{matrix}$ (32)

The spline curve of anti-Z-type membership function is in inverse Z-shape, and its calculation method is symmetrical with Z-type, as shown in Equation (33). $μ_{A} (x, x_{1}, x_{2}) = {\begin{matrix} 0, & x < x_{1} \\ \frac{2 (x - x_{1})^{2}}{(x_{2} - x_{1})^{2}}, & x_{1} ⩽ x < \frac{(x_{1} + x_{2})}{2} \\ 1 - \frac{2 (x_{2} - x)^{2}}{(x_{2} - x_{1})^{2}}, & \frac{(x_{1} + x_{2})}{2} ⩽ x < x_{2} \\ 1, & x_{2} ⩽ x \end{matrix}$ (33)

The shape of the spline curve of the triangular membership function is determined by the three parameters x₁, x₂ and x₃ in the calculation formula. The calculation method is as follows [20, 21]. $μ_{A} (x, x_{1}, x_{2}, x_{3}) = {\begin{matrix} 0, & x < x_{1} \\ \frac{(x - x_{1})}{(x_{2} - x_{1})}, & x_{1} ⩽ x < x_{2} \\ \frac{(x_{3} - x)}{(x_{3} - x_{2})}, & x_{2} ⩽ x < x_{3} \\ 0, & x_{3} ⩽ x \end{matrix}$ (34)

3.2 Research on a tension control method of electrode strip unwinding

3.2.1 Research on membership function of unwinding fuzzy control

In combination with the change of tension in the actual unwinding control process of the electrode strip, a certain quantitative factor is selected to complete the transformation of the theoretical domain of the tension deviation and deviation change rate of the electrode strip as well as the optimal change range of the modified parameters in the PID control process. The rules for the specific parameters are shown in Table 1.

Table 1
Fuzzy theory and quantitative factors of unwinding tension

Input and output parameters Fuzzy domain Quantification factor Basic domain

Unwinding tension deviation e [–6, –4, –2, 0, 2, 4, 6] 1/2 [–12, 12]

Variation rate of deviation e_c [–3, –2, –1, 0, 1, 2, 3] 1/2 [–6, 6]

ΔK_P [–6, –4, –2, 0, 2, 4, 6] 3 [–2, 2]

ΔK_I [–6, –4, –2, 0, 2, 4, 6] 3 [–2, 2]

ΔK_D [–6, –4, –2, 0, 2, 4, 6] 6 [–1, 1]

Input and output parameters	Fuzzy domain	Quantification factor	Basic domain
Unwinding tension deviation e	[–6, –4, –2, 0, 2, 4, 6]	1/2	[–12, 12]
Variation rate of deviation e_c	[–3, –2, –1, 0, 1, 2, 3]	1/2	[–6, 6]
ΔK_P	[–6, –4, –2, 0, 2, 4, 6]	3	[–2, 2]
ΔK_I	[–6, –4, –2, 0, 2, 4, 6]	3	[–2, 2]
ΔK_D	[–6, –4, –2, 0, 2, 4, 6]	6	[–1, 1]

Taking the unwinding tension deviation e as an example, the membership function of unwinding tension control is constructed as shown in Fig. 7. The input and output five parameters use Z-type and anti-Z-type membership functions to form the left and right boundaries, which are used to represent the concepts of “positive big” and “negative large”, and the membership degree at the boundary can realize the smooth transition from 0-1 or 1-0. Due to the slow running speed of the rolling mill, the tension is relatively stable when it is not disturbed by the outside, so the triangular membership function is evenly distributed in the middle of the five grades, and the structure is symmetrical [22, 23]. When the input changes, the sensitivity of trigonometric membership functions is higher than that of the normal distribution, and the output can be obtained in time.

3.2.2 Research on fuzzy control rules for unwinding tension

When establishing the fuzzy rules for the control of unwinding tension, the influence of such factors as the reel diameter, moment of inertia, and rolling speed on the change of unwinding tension is combined with field debugging to formulate the fuzzy inference rules. The specific rules are as follows:

In the start-up stage of the lithium mill, the unwinding device is disturbed by various mechanical parts, which may cause the tension fluctuation or large deviation of the electrode strip. At this time, the deviation value e of the tension of the electrode strip is large. To prevent the deviation from leading to output integral saturation and deviation value overshooting, it is necessary to appropriately reduce the value of ΔK_P and ΔK_I and increase the value of ΔK_D.

When the rolling mill enters the working state normally and runs stably, the tension will not deviate greatly in a short time. At this time, the change rate of tension deviation e and deviation e_c of the electrode strip is small, so that ΔK_P and ΔK_I can be steadily increased, and the value of ΔK_D can be stable within a small range.

In the process of transmission, the tension value may change greatly in a short time due to equipment reasons or some environmental factors. At this time, the rate of change of tension deviation e_c is large, and ΔK_I should be appropriately increased and ΔK_P reduced. At the same time, ΔK_D should be small to avoid overshoot and vibration caused by the differential link.

According to the expert knowledge summarized above, combined with the relevant data, fuzzy rules can be established, as shown in Table 2.

Table 2
Fuzzy control rules of ΔKP, ΔKI and ΔKD for unwinding tension

e_c e

–6 –4 –2 0 2 4 6

–3 6/–6/2 6/–6/–2 4/–4/–6 4/–4/–6 2/–2/–6 0/0/–4 6/0/2

–2 6/–6/2 6/–6/–6 4/4/–6 2/–2/–4 2/–2/–4 0/0/–2 –2/0/0

–1 4/–6/–6 4/–4/–2 4/–2/–4 2/–2/–2 0/0/0 –2/4/2 –2/4/2

0 4/–4/0 4/–4/–4 2/–2/–2 0/0/0 –2/2/–2 –4/4/–2 –4/4/0

1 2/0/6 2/–2/0 0/0/0 –2/2/0 –2/2/0 –4/4/4 –4/6/0

2 2/0/6 0/0/4 –2/2/4 –4/2/4 –4/4/2 –4/6/2 –6/6/6

3 0/0/6 0/0/4 –4/2/2 –4/4/4 –4/4/2 –6/6/6 –6/6/6

e_c	e
–3	6/–6/2	6/–6/–2	4/–4/–6	4/–4/–6	2/–2/–6	0/0/–4	6/0/2
–2	6/–6/2	6/–6/–6	4/4/–6	2/–2/–4	2/–2/–4	0/0/–2	–2/0/0
–1	4/–6/–6	4/–4/–2	4/–2/–4	2/–2/–2	0/0/0	–2/4/2	–2/4/2
0	4/–4/0	4/–4/–4	2/–2/–2	0/0/0	–2/2/–2	–4/4/–2	–4/4/0
1	2/0/6	2/–2/0	0/0/0	–2/2/0	–2/2/0	–4/4/4	–4/6/0
2	2/0/6	0/0/4	–2/2/4	–4/2/4	–4/4/2	–4/6/2	–6/6/6
3	0/0/6	0/0/4	–4/2/2	–4/4/4	–4/4/2	–6/6/6	–6/6/6

3.2.3 Model construction of unwinding tension transfer link

By analyzing the causes of tension in the previous section, it can be seen that the tension of the unwinding part of the electrode strip is: $T = \frac{ES}{L} \int (v_{main} - v) dt$ (35)

In the formula, v_main is the running line speed of the main role of the mill, and v is the line speed at the outlet of the electrode strip of the unwinding roll.

By deriving Equation (35), we can get the following results: $\frac{dT}{dt} = \frac{ES}{L} (v_{main} - v)$ (36)

It can be seen from Equation (36) that the main factor affecting the electrode strip is the linear speed of unwinding. On the premise of stable and reliable torque, the linear speed is only related to the speed of the unwinding motor and the winding diameter of the unwinding roll. The motor speed and voltage transfer function in the simulation model is $\frac{3.5}{5 s^{2} + 0.8 s + 1}$ by selecting the signal conversion proportional coefficient appropriately. In the process of strip unwinding, it can be seen from the variation formula $R = \sqrt{R_{max}^{2} - \frac{Hvt}{π}}$ that the size of the strip is closely related to the speed and running time of strip rolling. In the process of rolling mill running smoothly, the transmission speed of the strip is stable and invariable. At this time, the real-time coil diameter can be converted into a function of time and motor output speed. Through Laplace transformation, it can be seen that the relationship between the unwinding line speed and the tension of the unwinding electrode is a first-order inertial link. so the unwinding tension transfer link model can be established, as shown in Fig. 8. In the figure, Step1 and Step2 are the linear speed of the electrode strip passing through the main roll. By selecting the simulation parameters properly, the real-time winding diameter is obtained by using the integrator, Fcn1, and Sqrt1 modules. Transfer Fcn1 is the transfer function of unwinding speed and tension.

Fig. 7

Membership function of unwinding tension deviation “e".

Fig. 8

Model of unwinding tension transfer link.

3.3 Research on a tension control method of electrode strip winding

3.3.1 Research on membership function and fuzzy rules of fuzzy control of winding tension

The input and output of fuzzy control of winding tension are also three parameters of tension deviation, tension deviation change rate and PID control. The fluctuation range and control method of each parameter are basically similar. In the construction of fuzzy rules, the overall design principle is similar to the unwinding tension, so the corresponding membership function and fuzzy rules of winding part in section 3.2.2 are referred to.

3.3.2 Construction of winding tension transfer link model

Although the construction principle of the winding tension is similar to that of the fuzzy inference part of the winding tension, the mathematical model will be different because of the variation trend of the winding diameter and the moment of inertia as the main factors of the two parts of the tension are different. The tension of the winding part of the electrode strip is: $T = \frac{ES}{L} \int (v - v_{main}) dt$ (37)

In the formula, v is the linear speed at the entrance of the electrode strip of the winding roller, and v_main is the running speed of the main role of the mill.

According to the above analysis method, the transfer model of the winding tension and output voltage of the electrode strip can be obtained by carrying out Laplace transform of the above formula and combining it with the speed and voltage transfer function of the motor and the calculation formula $R = \sqrt{R_{min}^{2} + \frac{Hvt}{π}}$ of the winding diameter. As shown in Fig. 9, except motor transfer function and electrode strip speed of the main roller, the rest parts are different from unwinding tension, and Transfer Fcn9 is the transfer function of unwinding speed and tension.

Fig. 9

The model of tension transfer in windingGenetic algorithm optimization.

4 Genetic algorithm optimization

In the process of fuzzy PID control algorithm research, it involves the selection of PID initial parameters and the construction of fuzzy rules. However, in the process of selecting these parameters, K_P, K_I and K_D may have some deviation from the optimal value [24]. There are also some useless rules, repetitive rules and unreasonable rules in fuzzy rules, which will reduce the accuracy of tension control. In this section, genetic algorithm is introduced to optimize the fuzzy PID control method [29]. Figure 10 shows the operation flow of genetic algorithm optimizing PID initial parameters and fuzzy rules.

Fig. 10

(a) Schematic diagram of optimization of PID initial parameter flow by genetic algorithm; (b) schematic diagram of optimization of fuzzy rule flow by genetic algorithm.

To ensure the efficiency of genetic optimization, it is necessary to set some key links in the application process of genetic algorithm [25]:

(1) The setting of population parameters is directly related to PID initial parameters. When setting the initial PID parameters of different tension control, it is necessary to expand the scope to cover the initial PID parameters. Therefore, K_P is 0–20, K_I is 0–5, and K_D is 0–5. In order to ensure the complexity of the population, the number of population samples is set to 100, which can not only improve the number of samples, but also ensure the operation speed. In this way, a 50*3 matrix is generated to represent the initial population, in which each element is a real number. The three values of the same horizontal axis of the matrix represent the three initial PID parameters contained in a single individual, and the vertical axis represents 50 different population individuals [26].

(2) Fitness function selection: In the selection of fitness function, in order to make the optimized rules adapt to the closed-loop control system, it is also necessary to introduce the transfer function of winding tension control, so as to introduce the PID control strategy. Therefore, the time error integral function is introduced in this section, and the deviation output value and time information of the tension model are introduced into the time error integral function. This is to compare and analyze the response speed, output error and overshoot of the closed-loop output corresponding to different individuals [27, 28].

(3) Selection, crossover, and mutation operation: Selection operation preserves the individual with higher fitness by sorting the fitness value. Here, the roulette method is adopted for operation; Crossover and mutation by setting corresponding crossover and mutation probability, and making fine adjustments for different fitness individuals, to ensure that excellent individuals are more likely to retain.

4.1 Genetic algorithm to optimize tension PID initial parameters

4.1.1 Genetic algorithm optimized the initial PID parameters of unwinding tension

According to the model of unwinding tension obtained above, the winding speed of the unwinding drum is slow, and the thickness of the electrode strip of lithium battery is relatively thin in the actual rolling process, so the winding diameter of the unwinding drum changes slowly with time. To facilitate iterative calculation, the volume diameter is set as a fixed value in MATLAB to simplify and calculate the unwinding tension model and convert it into a third-order transfer function $\frac{7}{2.5 s^{3} + 40 s^{2} + 7 s + 8}$ . In this study, the MATLAB software version is 2018 (a), the GPU model of the computer running the software is GTX1080Ti, the CPU model is i7-7700, and the memory is 16 G.

The transfer function was established and Z-transform was performed in MATLAB. The sampling time was set to 0.05 s. The discrete molecular coefficients were 1.0e-06*{0, 0.057 2, 0.224 2, 0.054 9}, and the denominator coefficients were {1.000 0, –2.923 0, 2.846 2, –0.923 1}. It is replaced into the unwinding PID control, the sampling time is 0.005 s, the cycle is 1200 times, and the response within 6 s is obtained. At this time, the unwinding tension control is stable.

100 genetic iterations are carried out through MATLAB, and the variation of the optimal individual fitness value in each generation of the genetic process is shown in Fig. 11. It can be seen from the figure that after the 20th generation, the adaptive ability of the optimal individual is stable. In the subsequent genetic operation, although the adaptive ability can be slightly improved, the change is no longer obvious. To ensure the output of the optimal initial PID parameter of unwinding tension, the optimal individual after 100 genetic iterations are selected here as the final solution.

Fig. 11

Genetic algorithm of unwinding tension with the best individual fitness of 100 generations.

In the process of genetic algorithm optimization of unwinding tension PID parameters, 10 groups of K_P, K_I, and K_D parameters are obtained through multiple iterations. The specific values are shown in Table 3:

Table 3

The optimal solution of unwinding tension PID parameters after 100 genetic iterations

Groups number
	1	2	3	4	5	6	7	8	9	10
K_P	7.615	8.179	8.025	8.023	7.828	8.054	8.152	8.215	8.052	8.264
K_I	3.015	2.785	3.403	2.706	3.184	3.196	3.930	3.616	3.668	3.528
K_D	4.693	4.923	4.903	4.746	4.752	4.822	4.979	4.983	4.869	4.957
Fit value	329.375	328.777	328.870	329.392	329.082	328.999	328.763	328.665	328.862	328.741

By averaging the parameters in the table, the final initial PID parameters of unwinding tension control are K_P = 8.041, K_D = 4.863, K_I = 3.303.

4.1.2 Genetic algorithm optimized the initial PID parameters of winding tension

The optimization process is similar to the genetic algorithm for unwinding tension control. First, the unwinding tension model is simplified to some extent to obtain the third-order transfer function $\frac{7}{5 s^{3} + 10 s^{2} + 2.5 s + 1.8}$ . The transfer function was established in MATLAB and Z-transformation was carried out. The sampling time was set as 0.01 s, and the discretized molecular coefficient was 1.0e-06*{0, 0.232 2, 0.924 1, 0.229 9}, and the discretized denominator coefficient was {1.000 0, –2.980 1, 2.960 3, –0.980 2}. It is substituted into the winding PID control, and the response condition within 10 s can be obtained through cyclic iteration for 1,000 times. At this time, the winding tension control reaches a stable state. According to the output of tension PID closed-loop control model and closed-loop control error in 1 000 cycles, the fitness values of different individuals are obtained. The numerical variation of fitness value of the optimal individual in the 100 iterations is shown in Fig. 12.

Fig. 12

Genetic algorithm of winding tension with the best individual fitness of 100 generations.

In the process of genetic algorithm optimization of winding tension PID parameters, 10 groups of K_P, K_I, and K_D parameters are obtained through iterative optimization for many times. The specific values are shown in Table 4:

Table 4

Optimal solution of PID parameters of winding tension after 100 genetic iterations

Groups number
	1	2	3	4	5	6	7	8	9	10
K_P	3.788	3.861	3.782	3.703	3.641	3.935	3.521	3.861	3.564	3.859
K_I	0.838	0.937	1.711	0.611	1.364	1.204	0.918	1.103	1.052	0.839
K_D	4.975	4.871	4.794	4.990	4.984	4.944	4.938	4.870	4.849	4.885
Fit value	328.741	337.902	338.838	337.674	338.087	336.870	339.047	338.428	338.985	337.555

By calculating the average value of the three groups of values in the table, the final initial PID parameters of unwinding tension control are K_P = 3.752, K_D = 4.910, K_I = 1.058.

4.2 Genetic algorithm optimization tension control fuzzy rules

4.2.1 Genetic algorithm optimizes fuzzy control rules for unwinding tension

In the process of optimization of unwinding tension fuzzy rules, the PID initial parameters K_P = 8.041, K_D = 4.863, K_I = 3.003 obtained before being substituted into the fuzzy PID control algorithm of unwinding tension in MATLAB. The genetic algorithm is used to carry out 200 iterations of fuzzy rules [25]. The fitness value of the optimal individual in each generation is shown in Fig. 13(a). The optimal individual in the 200th generation is taken as the final optimization value of fuzzy rules. The optimal individual genome obtained after 200 iterations is transformed into a fuzzy rule code, and Fig. 13(b) is the histogram of the fuzzy rule gene code of the optimal individual.

Fig. 13

(a) 200 generation optimal individual fitness; (b) optimal gene histogram.

The unwinding tension fuzzy rules in Fig. 13(b) are extracted and divided into 3 sets of data containing 49 fuzzy rules in each set, corresponding to the fuzzy rules in the case of K_P, K_I, and K_D output in the fuzzy controller. The control table of fuzzy rules shown in Table 5 is obtained, which is the optimized unwinding tension fuzzy rules.

Table 5

Fuzzy control rule of unwinding tension optimized by genetic algorithm

e_c	e
	–6	–4	–2	0	2	4	6
–3	6/3/2	7/2/2	7/1/5	5/5/6	5/1/3	4/1/3	4/2/2
–2	4/5/5	5/3/4	5/3/3	6/6/4	2/5/4	5/4/6	6/5/6
–1	3/5/3	6/4/7	7/6/6	5/4/3	6/4/7	6/3/5	2/5/6
0	7/1/6	4/4/3	3/3/4	7/7/4	2/7/4	3/4/5	4/2/5
1	2/3/7	4/6/6	3/6/3	3/6/7	5/3/4	6/1/4	6/4/3
2	7/5/4	2/5/3	6/2/1	3/3/5	4/2/3	6/5/1	2/2/4
3	6/6/3	2/1/6	3/2/4	6/1/6	3/7/5	3/6/1	4/1/4

4.2.2 Genetic algorithm optimizes fuzzy control rules for winding tension

In the process of fuzzy rule optimization of winding tension, the optimized initial PID parameters K_P = 3.752, K_D = 4.910, K_I = 1.158 are substituted into the fuzzy PID control algorithm of winding tension in MATLAB. The genetic algorithm is used to iterate the fuzzy rules for 200 times. The fitness value of the optimal individual in each generation is shown in Fig. 14(a). After 200 iterations, the optimal individual genome corresponding to the fuzzy rule of winding tension obtained after 200 iterations is transformed into the fuzzy rule code. The histogram representation of the optimal fuzzy rule is shown in Fig. 14(b).

Fig. 14

(a) 200 generation optimal individual fitness; (b) optimal gene histogram.

The fuzzy rules of winding tension in Fig. 14(b) are extracted and transformed into corresponding quantization levels. Each group contains three groups of data with 49 fuzzy rules, corresponding to the fuzzy rules of K_P, K_I, and K_D. The fuzzy rule control table of optimal winding tension is obtained in Table 6.

Table 6

Fuzzy control rule of coiling tension optimized by genetic algorithm

e_c	e
	–6	–4	–2	0	2	4	6
–3	3/3/3	7/7/5	3/6/7	6/2/2	6/5/3	5/1/3	2/2/3
–2	5/7/2	5/6/5	1/5/4	1/3/5	4/7/7	3/2/6	3/5/5
–1	2/1/2	3/2/7	2/2/5	4/2/6	3/2/2	3/4/2	3/5/5
0	4/6/6	5/2/7	6/3/6	4/7/4	2/6/4	2/2/4	1/2/5
1	2/2/6	3/2/1	4/2/2	6/2/7	3/4/3	6/7/3	3/4/3
2	5/6/3	2/3/5	5/3/5	4/5/1	3/6/6	2/4/3	6/6/5
3	2/4/2	1/2/6	1/3/3	3/6/7	4/6/3	5/5/6	3/5/7

5 Simulation and experimental verification of tension control

5.1 Simulation analysis of tension control

5.1.1 Simulation analysis of unwinding tension control

The following three methods of unwinding tension control part PID, integral separation PID and integral separation fuzzy PID are compared and analyzed. The simulation results are shown in Fig. 15.

Fig. 15

Simulation of three methods of unwinding tension control.

Fig. 16

Simulation curve of interference signal introduced into unwinding tension control.

According to the formula of tension generation, after the introduction of the linear velocity of the electrode strip of the main roll, the speed difference can be obtained by subtracting the linear speed of the unwinding roll. Therefore, in the initial stage of the signal, there will be a weak vibration in the same direction as the step signal. In the simulation Fig. 15, because the step value is greater than the set threshold value which will cause integral separation, the two curves corresponding to PID and integral separation PID are no longer coincident. The curve response rate of the three methods is close, but the overshoot of PID and integral separation PID is obviously too high, and the time to reach steady state is longer than that of integral separation fuzzy PID.

The optimized PID parameters and fuzzy rules are put into the unwinding tension simulation model constructed above to conduct a comprehensive simulation analysis. Under the excitation of the step signal, the response curve before and after parameter optimization is obtained. At the same time, different types of abrupt interference signals are introduced at 15 ms and 30 ms. Finally, the response curve before and after parameter optimization is obtained, as shown in Fig. 15.

The interference signal is introduced into the simulation Fig. 15. When the interference signal occurrence point is set as t = 30 ms, the corresponding simulation curve is shown in Fig. 16.

It can be seen from the figure that after the interference signal occurs, three curves quickly track the response, among which the curve representing integral separation fuzzy PID is the fastest regression to the initial step value set, while the other two curves have certain oscillation. This proves that the stability and anti-interference ability of integral separation fuzzy PID are the best among the three methods.

Fig. 17

Comparison simulation of unwinding tension parameters before and after optimization.

It can be seen from the response curve in Fig. 17 that when the initial excitation signal is received, the curves corresponding to parameters before and after optimization can achieve a faster response speed and the slope of the curves is the same. However, in the subsequent process, the curve corresponding to the optimized parameters can be adjusted faster to reach a stable state, while the previous curve corresponding to the parameters will have a large overshoot. A new step input signal is introduced at the 15 ms. At this time, the change rule of the two curves is similar to that of the first response, and the performance of the curve corresponding to the optimized parameters is slightly better. A small interference signal with a size of 0.5 is introduced at the 30 ms. It can be seen from the subsequent changes of the curve that the corresponding curve of optimized parameters can return to a stable state faster in the face of interference and has a strong resistance to interference. Through the above comparison, the performance of the optimized initial PID parameters and fuzzy rules is slightly better than that before optimization, which plays a good role in promoting the control of unwinding tension.

5.1.2 Simulation analysis of winding tension control

The following three methods of winding tension control part PID, integral separation PID and integral separation fuzzy PID are compared and analyzed. The simulation results are shown in Fig. 18.

Fig. 18

Simulation of three methods of winding tension control.

In the initial stage of the signal, the speed difference is obtained by subtracting the linear speed of the main roll from the linear speed of the winding roll, so the weak vibration in the direction opposite to the step signal will be produced. In the simulation Fig. 18, the curve response rates of the three methods are basically the same, but the overshoot of the curves corresponding to PID and integral separation PID is obviously too high, and the time to reach the steady state is much longer than that of the integral separation fuzzy PID.

In order to show the resistance of the three methods to interference, the disturbance signal is introduced into the simulation Fig. 18, and the corresponding simulation curve is shown in Fig. 19.

Fig. 19

Simulation curve of interference signal introduced into winding tension control.

It can be seen from the figure that the integral separation fuzzy PID can adjust faster and reach steady state more quickly in the face of interference. Through the analysis and summary of the above situation, it can be seen that in the process of unwinding tension control, the three methods have a higher response rate and a certain anti-interference ability, but the integral separation fuzzy PID can achieve a stable state more quickly, the curve change is more smooth, and the performance is better for the stable control of tension. When there is signal interference, the resistance of integral separation fuzzy PID is stronger.

Similar to the simulation process of unwinding tension control, the optimized initial PID parameters and fuzzy rules are also introduced into the winding tension simulation model, and sudden change interference signals are introduced at 15 ms and 30 ms. the response curves before and after optimization are shown in Fig. 20.

Fig. 20

Comparison simulation before and after optimization of winding tension parameters.

Among the curves corresponding to PID parameters and fuzzy rules before and after optimization, the optimized curve has fast response, small overshoot, and strong anti-interference ability, while the curve response corresponding to original parameters has obvious hysteresis, with large overshoot and poor self-regulation ability. The curves before and after optimization respond to the input step signal at the same time, but when the curve rises, the peak value caused by an overshoot in the optimized curve is lower than that before optimization, and the two curves reach a stable state after 10 ms. Under the effect of the interference signal, the changing state of the curve is similar to that of the curve in the unwinding tension simulation. According to the overall simulation, the initial PID parameters and fuzzy rules of winding tension control can improve the control performance and efficiency to a certain extent after optimization.

5.2 Experimental verification of tension control

5.2.1 Sensitivity test

When the main roll speed is set at 30 m/min, the experimental equipment can run stably. When the roll speed is more than 40 m/min, the electrode strip will break and shake due to the excessive tension, which makes it impossible to control the tension accurately. When the roll speed is lower than 10 m/min, the strip will be relaxed and wrinkled due to the low tension, and the tension cannot be controlled accurately. Now in the actual industrial environment, the rolling speed of lithium battery is 15∼30 m/min, which can fully meet the experimental requirements.

5.2.2 Unwinding tension control test

In the process of lithium battery electrode sheet rolling, the tension will be set according to the requirements of the production electrode strip, usually set in the range of 0–200 N. Take the tension set value of 100 N as an example, the unwinding tension control test is carried out. Generally, the range of tension fluctuation should be within 10% of the set value in the process of plate rolling.

When the classical PID control method is adopted, the three parameters of K_P, K_I, and K_D in the algorithm are fixed and unchanged. At this time, the real-time acquisition and display interface of the electrode strip tension is shown in Fig. 21 (a). After introducing the integral separation fuzzy PID algorithm studied in this paper, the three parameters K_P, K_I, and K_D in the algorithm will be continuously adjusted according to the change of unwinding condition. The real-time acquisition and display interface of electrode strip tension is shown in Fig. 21 (b).

Fig. 21

(a) Tension curve of traditional PID; (b) Genetic optimization fuzzy PID tension curve.

Ten groups of sampling points are randomly extracted from the sampling data, and the tension error comparison table shown in Table 7 can be obtained.

Table 7

Comparison of unwinding tension error

Number	The setting the value of unwinding tension/N	Traditional PID tension acquisition value/N	Error/N	Relative error/%	Optimize PID tension acquisition value/N	Error/N	Relative error/%
1	100	93.88	–6.12	6.12	102.56	2.56	2.56
2	100	95.64	–4.36	4.36	101.37	1.37	1.37
3	100	103.91	3.91	3.91	98.08	–1.92	1.92
4	100	94.70	–5.30	5.30	103.45	3.45	3.45
5	100	101.68	1.68	1.68	101.28	1.28	1.28
6	100	107.43	7.43	7.43	102.88	2.88	2.88
7	100	99.41	–0.59	0.59	99.57	–0.43	0.43
8	100	104.37	4.37	4.37	101.78	1.78	1.78
9	100	102.25	2.25	2.25	100.92	0.92	0.92
10	100	96.77	–3.23	3.23	101.58	1.58	1.58

5.2.3 Winding tension control test

In the test of winding tension control, the tension set value of 100 N is also taken as an example. At the same time, the fluctuation range of tension is set within 10%, and the corresponding tension value and generation time are recorded when the tension is beyond the range. To collect the winding tension of the electrode mill during a period of stable operation, 10 groups of measured tension values are selected respectively under two control algorithms to form Table 8.

Table 8
Comparison of winding tension error

Number The setting the value of unwinding tension/N Traditional PID tension acquisition value/N Error/N Relative error/% Optimize PID tension acquisition value/N Error/N Relative error/%

1 100 104.24 4.24 4.24 103.77 3.77 3.77

2 100 103.68 3.68 3.68 101.59 1.59 1.59

3 100 102.51 2.51 2.51 102.23 2.23 2.23

4 100 97.70 –2.30 2.30 99.27 –0.73 0.73

5 100 98.53 –1.47 1.47 101.45 1.45 1.45

6 100 103.62 3.62 3.62 102.46 2.46 2.46

7 100 106.19 6.19 6.19 99.06 –0.94 0.94

8 100 104.43 4.43 4.43 97.19 –2.81 2.81

9 100 101.98 1.98 1.98 100.95 0.95 0.95

10 100 103.52 3.52 3.52 102.72 2.72 2.72

Number	The setting the value of unwinding tension/N	Traditional PID tension acquisition value/N	Error/N	Relative error/%	Optimize PID tension acquisition value/N	Error/N	Relative error/%
1	100	104.24	4.24	4.24	103.77	3.77	3.77
2	100	103.68	3.68	3.68	101.59	1.59	1.59
3	100	102.51	2.51	2.51	102.23	2.23	2.23
4	100	97.70	–2.30	2.30	99.27	–0.73	0.73
5	100	98.53	–1.47	1.47	101.45	1.45	1.45
6	100	103.62	3.62	3.62	102.46	2.46	2.46
7	100	106.19	6.19	6.19	99.06	–0.94	0.94
8	100	104.43	4.43	4.43	97.19	–2.81	2.81
9	100	101.98	1.98	1.98	100.95	0.95	0.95
10	100	103.52	3.52	3.52	102.72	2.72	2.72

5.3 Results and discussion

By observing Fig. 21, it can be found that in the control process of the two methods, the fluctuation degree of tension can be stabilized within 10% of the set value, and the tension changes between 90–110 N, which does not cause alarm phenomenon. However, through comparison, it can be seen that the tension fluctuation under PID algorithm is more severe, at this time, various factors of rolling mill equipment and external environment have obvious influence on tension. The traditional method has weak adaptability and longer adjusting period of tension value. Some tension sampling points in PID algorithm are close to the set alarm boundary line. Once the interference increases, the tension may be too large or too small, which will cause the alarm of the equipment in advance. However, under the control of the algorithm proposed in this paper, the fluctuation is small.

By analyzing the deviation of unwinding tension value in Table 7, it can be seen that this method is different from the traditional PID algorithm, the tension error is far less than 10% of the setting requirements, the sampled tension values change near the set value, far away from the set boundary line, and the relative error is stable within 4%. This shows that the stability of the algorithm is better, and the adjustment period of tension is shorter, which can effectively improve the precision of tension control of electrode strip, make the tension more stable when the rolling mill is running, and help to improve the quality of electrode strip production.

By comparing the two control methods of winding tension error Table 8, it can be seen that under the control of traditional PID algorithm, the tension value is generally stable within the set range, and the relative error is within 7%. However, under the control of this algorithm, the collected tension values are all within the set tension range, and the relative error is stable within 4%. At the same time, the tension value corresponding to the traditional PID algorithm is not stable within 90–110 N, and the control cycle and regulation speed are slow. However, the tension curve corresponding to this algorithm has less fluctuation and higher stability and control accuracy.

6 Conclusion

This method is based on the relatively mature sensing technology, information acquisition technology and motor drive technology in the current society. Combined with the related knowledge of mathematical modeling, the mathematical model of the tension control structure of the electrode strip in the lithium electric rolling mill is established. Then, the fuzzy PID tension control method optimized by genetic algorithm is studied. Combined with the established mathematical model, the accuracy, response speed and anti-interference ability of the method are verified by simulation analysis and experiment. This method can avoid the large tension fluctuation during the operation of the lithium battery electrode strip rolling mill, and prevent the electrode strip from wrinkling and loosening. This method improves the production quality of the electrode strip and fills the blank in the research field of tension control method of lithium battery electrode strip rolling mill. The following work has been done:

1. Firstly, the cause of tension generation is analyzed. According to the change law of real-time winding diameter and moment of inertia, the real-time winding diameter model, moment of inertia model, and tension control model in tension control are established.

2. The integral separation principle is introduced into the traditional PID control method, and the PID control parameters are divided into basic parameters and correction parameters. Through the fuzzy algorithm, the tension deviation value and its rate of change are taken as the input of the fuzzy controller, and the PID parameter correction value of the tension control is taken as the output. The integrated and separated fuzzy PID simulation model is established.

3. The population individuals corresponding to the initial PID parameters and fuzzy rules are introduced into the corresponding simulation model. By setting the sampling time and the number of sampling steps, the system output value is continuously collected, and the time error integral is used to compare different individuals. The optimal individual optimized by the genetic algorithm is the optimal initial PID parameter and fuzzy rule corresponding to tension control.

4. Through the data analysis of the tension curve collected, it is verified that the method has a good response rate, overshoot, and stable rate, and has practical application value.

The tension control method of lithium battery electrode strip mill studied in this paper is feasible and stable, but there are also shortcomings: in this study, part of the rolling situation is selected for analysis in the experimental part, but the actual electrode strip rolling, the production parameters of the electrode strip are various. With the increase of rolling time, the operation status of the closed-loop link of the rolling mill may also change. Therefore, when the parameters such as the rolling mill, the material and the precision requirements of the electrode strip of lithium battery change, the control accuracy of the method will be different. In the future, this method can be extended to introduce different materials, thickness and width of electrode strips to verify the effect of tension control from various angles.

This paper focuses on the combination optimization of fuzzy algorithm, PID algorithm and genetic algorithm. In addition, there are also some algorithms, such as Internal Model Control(IMC) and predictive control, which can be applied to tension control of strip mill. Therefore, on the basis of the research content of this paper, other algorithms can be studied to determine the best control strategy.

Footnotes

The notations of concepts in this paper

Notation	Definition	Notation	Definition
v_a	Linear velocity of main roll	H	Thickness of electrode strip
v_b	Winding line velocity	t	Smooth running time of electrode strip
L	Length of electrode strip between roll and winding	M_D	Motor output torque
ΔL	Displacement caused by strip deformation	M_T	Tension moment of electrode strip
ɛ	Strain force of electrode strip	M_f	Friction torque
σ	Line stress on electrode strip	M_J	Inertia moment of drum
T	Strip tension	J	Moment of inertia
S	Sectional area of electrode strip	m₁	Core quality
E	Elastic modulus	ρ ₁	Density of core material
F	Tension collected by tension sensor	l	Length of drum
θ	The angle between the strip and the vertical line	R _min	Core section radius
R_min	Minimum drum radius	m₂	Strip quality
R_max	Maximum drum radius	ρ ₂	electrode strip density
R	Real time radius of drum	v_main	Linear speed of main roll
v	Linear velocity at the exit of electrode piece

Acknowledgments

This work was supported by the National Key Instrument and Equipment Development of the National Key R&D Program of China (Grant No. 2017YFF0106404), the National Natural Science Foundation of China (Grant No. 51675160), the Hebei key research and development plan project (Grant No. 18214407D), and Jiangsu Province training fund funded project (Grant No. BRA2020244).

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