Research on integral separation control of warp tension based on fuzzy parameter optimization

Abstract

In textile machines, the stability of warp tension is one of the decisive factors for the reliability, stability and product quality of weaving process. In order to meet the improving requirement for weaving efficiency and fabric quality, it is proposed that a fuzzy optimization integral separation PID warp tension control scheme based on process sampling to improve the warp tension control level of loom. Aiming at the problems of time-varying, nonlinear and variable coupling in the warp tension control system of loom, the forming mechanism of warp tension is modeled and analyzed, and the sampling scheme of warp tension based on process is proposed. Based on the periodic change of warp tension at macro level and continuous fluctuation at micro level, the integral separation control and fuzzy optimization theory are introduced to optimize the control effect of the control system on the basis of classical PID control algorithm. Finally, the simulation and experiment show that the scheme can improve the tension controls performance and effectively reduce the tension error fluctuation.

Keywords

Rapier loom tension control closed loop control fuzzy optimization integral separation control

1 Introduction

With the continuous development of electronic technology and the sustained improvement of mechanical structure, the weaving speed of rapier loom is constantly increasing. However, higher weaving speeds would lead to larger warp tension fluctuation, which will increase the frequency of yarn breaks and interrupt the weaving process [1, 2]. Therefore, warp tension control is one of the main factors affecting weaving stability, reliability, fabric quality, and variety adaptability in high-speed rapier looms. Because the control system of rapier looms to warp tension are complex system of high-order, time-varying, nonlinear and multi-variable coupling, the research on it has always been a focus attention [1].

In high-speed rapier looms, electronic let-off and electronic coiler have been widely used, and it has been proved by practice that they have great advantages over the traditional mechanical warp delivery method [3]. At present, the main means to improve warp tension control’s performance are to study the influencing factors of warp tension in high-speed rapier loom, improve the hardware structure of the electronic warp delivery winding system, and develop more efficient control algorithms. Sung et al. measured warp tension and its variation, and conducted regression analysis on the influence of weft tension and loom sett parameters on warp tension. He concluded that warps tension was related to warp yarn density, weaving density coefficient, fabric texture, opening angle and winding speed [1]. Ben et al. used a fiber-optic sensor to directly measure the warp tension between the warp feeds shaft and the winding roller. They studied the yarn tension characteristics from two dimensions: the change of yarn tension during the weaving cycle and the change of yarn tension between the warp feed shaft and the winding roller [2]. To increase the production rate of 3D interlock weaving and deeply understand the interactions between the warp yarns, Carole et al. made in-situ measurements on a sequential weaving loom. The results show that higher peaks of tension and contact force will form when specific tow crossings [4]. Cao et al. introduced the direct memory access technology into the yarn tension measurement of looms, and proposed a virtual dynamic testing system. Experiments were carried out on looms and winders to prove that the scheme has the advantages of high sampling accuracy, fast sampling frequency, and good expansibility [5]. Li et al. proposed a multi-neuron adaptive PID control algorithm based on the let-off system of SAURER400 rapier loom to prevent excessive fluctuation of warp tension from adversely affecting fabric quality. SIMULINK simulation platform concerning the multi-neuron adaptive PID control algorithm and fuzzy PID control algorithm simulation comparison indicates that the multi-neuron adaptive PID control algorithm has the advantages of fast response speed, small overshoot [6]. Minna et al. proposed a fuzzy multi-attribute group decision-making method, which was used to find the best scheme among the numerous yarn tension detection and control schemes proposed by experts in the field. The decision-making results show the feasibility and effectiveness of the method [7]. Liu et al. established the dynamic model of let off system and take-up system of carbon fiber multi-layer diagonal loom, and applied adaptive fuzzy PID control to tension network control. Simulation proved that adaptive fuzzy PID control has a better control effect than PID control, and is more suitable for the tension network control system of carbon fiber multi-layer diagonal loom [8]. These models and methods have shortcomings: The research on warp tension measurement method and its characteristic analysis is mature, but it is difficult to meet the requirements of measurement cost, stability, parameter input of controller and real-time performance of the system in practical engineering application. In fact, virtual dynamic test is a kind of data model prediction, which depends on the accurate establishment of virtual model and powerful computing power of control system. What’s more, the predictive control is limited by the mapping quality between virtual entities and physical entities. Although fuzzy PID control has great application advantages, it also has some defects, such as subjectivity in the determination of membership function, lack of systematicness in system design, and improper fuzzy processing of information, which may lead to the decline of system control precision and dynamic quality [9]. The network structure of an artificial neural network needs to be made in advance or modified in the course of training by using heuristic algorithm, and excessively depends on learning samples. However, in practical application, training samples often need to be accumulated and tested for a long time. The The PID control is widely used in industrial process control because of its simple implementation, rich application cases and strong adaptability. However, the determination of the proportional coefficient (KP), differential coefficient (KD) and integral coefficient (KI) of classical PID control depends on the establishment of the accurate mathematical model. Besides, in the actual industrial site, the control quantity is often susceptible to external interference and deviates from the control target to a large extent. At this time, the classical PID control often leads to a decrease of control accuracy and control speed due to the accumulation of integral. Fuzzy optimization theory makes a macroscopic description of the problems to be optimized, and does not rely on accurate mathematical models. Instead, it only needs to provide the knowledge of domain experts, transform it into fuzzy language control rules, and use fuzzy reasoning to complete the correlation of input and output. At present, fuzzy optimization theory has achieved fruitful results, and also has a good performance in the application of controller optimization. A. et al. studied the definition of aggregation operator, the selection of membership function and the scoring method in fuzzy optimization. Aiming at the probleam of select fuzzy membership function, symbolic representation is used to consider each membership function, and the approximate value of fuzzy theory field length is determined according to its characteristics. In order to slove the ranking problem in group decision-making, a fuzzy optimization scoring method based on shape similarity is proposed, and some application examples are given in a variety of application scenarios [10 –14]. Charfeddine et al. solved the control problem of nonlinear perturbed polynomial system by fuzzy optimization of synovial

controller [15]. In this paper, the mechanism of warp tension of high-speed rapier loom is analyzed, and the warp tension control model is established. The feasibility of the method is analyzed by the simulation platform and the hardware testing platform. The results show that the method has the advantages of high precision, fast response, strong anti-interference ability and certain adaptive ability, and it is suitable for warp tension control of high-speed rapier loom.

The rest of the paper is organized as follows: The second section analyzes the working mechanism of the warp tension control system of high-speed rapier loom, establishes the warp tension control model, and proposes a way of warp tension sampling base on the weaving process. Based on the second section, in the third section, the integral separation PID control system is set up, and the fuzzy optimization algorithm is used to optimize the parameters of the integral separation PID algorithm. In the fourth section, MATLAB simulation platform and hardware experiment platform is established to verify the proposed scheme, and compares the control effects of traditional PID, integral separation PID and fuzzy optimization integral separation PID, and verifies the effectiveness of the scheme. The fifth section summarizes the article.

2 Warp tension control system

2.1 Generation mechanism of warp tension

With the rapid development of rapier looms, the traditional way of let-off and winding using mechanical structure is challenging to ensure the stable control of tension and a specific weft density, which can not meet the market demand for high-quality fabrics. Therefore, electronic let-off and electronic coiling devices have become mainstream. As shown in Fig. 1, the arrow indicates the direction of warp yarn or fabric movement. Friction roller B is driven by the coiling motor and the corresponding reduction device. The transmission belt connects the coiling shaft C with friction roller B to wind the sent fabric into rolls. Driven by the let-off motor, the warp shaft A continuously sends out the warp yarn, to compensate the length of the friction roller B and guarantee the continuity of weaving [3, 16].

Fig. 1

Schematic diagram of let-off and take-up structure.

In the continuous weaving process, the weft density of the same fabric is a fixed value, which is recorded as λ, and a weft yarn is introduced for each rotation of the main shaft, the movement distance of the fabric along the motion direction in each weaving cycle should be 1 /λ(unit cm). If the spindle speed is taken as n₀ (unit rpm), and the radial elongation of the fabric is not taken into account, the distance L(unit cm) of fabric movement per unit time (1 s) can be expressed by Equation (1). $L = \frac{n_{0}}{60 λ}$ (1)

It means that the linear velocity of the fabric motion, which are recorded as v is defined, after the weft density and spindle speed are determined. As shown in Fig. 2, the active coiling part of the fabric is friction roller B, and the radius of the roller r _B is fixed, so the rotational speed of friction roller ω_B can be show by Equation (2).

Fig. 2

Schematic diagram of warp yarn elongation at the opening.

$ω_{B} = \frac{n_{0}}{60 λ r_{B}}$ (2)

If the transmission ratio between the coiling motor and the friction roller is fixed at i₂, the speed n₂ of the coiling motor should be $n_{2} = \frac{i_{2}}{120 π λ r_{B}} n_{0}$ (3)

Equation (3) indicates that the speed of the winding motor is only related to the spindle speed, and there is a linear relationship between them, after the weft density and spindle speed are determined. Therefore, in the weaving process, the spindle motor speed is usually used to control the coiling motor speed.

Figure 1. Schematic diagram of let-off and take-up structure. For the coiling shaft C, it’s rotational speed is linearly related to friction roller B. However, the radius r_c(t) of coiling shaft C increases gradually with the weaving process. If the transmission ratio between coiling shaft C and friction roller B is i₃, then the cloth length L_j(t) of the coiling shaft within time t can be written as $L_{j} (t) = \int 2 π i_{3} ω_{B} r_{C} (t) dt$ (4)

For the let-off mechanism, if the tension factor is not taken into account and the elongation of warp yarn is ignored for the moment, in order to maintain the continuity of weaving, the warp length measure L_s(t) delivered by the warp shaft A in a unit time should be the same as the fabric length L taken by the coiling roller B. $L_{S} (t) = L$ (5)

As the warp shaft radius r_A(t) decreases with time during let-off, it can be illustrated in Equation (6). $L_{S} (t) = \int \frac{2 π}{i_{1}} n_{1} (t) r_{A} (t) dt$ (6)

Where, ω_A(t) is the angular velocity of the feed beam shaft, i₁ is the transmission ratio between the let-off motor and the diameter of the feed beam shaft, and n₁(t) is the speed of the let-off motor. Combining Equation (1), Equations (5) and (6), it can be seen that the speed of the let-off motor needs to change constantly during the let-off process to ensure the same let-off amount and coiling amount in unit time.

In conclusion, the speed of the take-up motor is only related to the spindle speed, and there is a linear relationship between the two, after the weft density and spindle speed are determined. Therefore, the speed of the take-up motor is usually regulated by the spindle motor speed in the weaving process. However, the speed of the let-off motor needs to change constantly during the let-off process to ensure the same let-off amount and coiling amount in unit time, it maintains stable warp tension.

2.2 Warp tension control scheme

During weaving, warp tension is affected by let-off, winding, opening, weft insertion and beating etc [1, 2]. If only consider the main factors, there are the following provisions. Each warp is consistent and satisfies Hooke’s Law, its cross-sectional area and thickness are considered unchanged during normal stress and deformation. The beam feeding shaft moves uniformly. No mechanical deformation for machinery or transmission parts. According to the above agreement, Hooke’s Law indicate that the tension F_t exerted by the warp yarn should be $F_{t} = n \frac{A_{0} E}{L_{0}} [Δ L_{0} + \int (v_{B} v_{A}) dt]$ (7)

Among them, the F_t for the warp tension, n to bypass the number of a yarn tension roller, A₀ to cross-sectional area, single yarn for yarn elastic modulus E, L₀ for sending beam with A point of contact, and friction roller B yarn and fabric yarn length between the tangent point, ΔL₀ for tension yarn after initialization setting variables, V_A for sending beam tangent point A and yarn linear velocity, V_B for the friction roller and fabric B tangent point of linear velocity. Therefore, in order to maintain the stability of warp tension, it is necessary to adjust the linear velocity V_A between the warp feed shaft A and the yarn cutting point, in other word, it need to control the speed of the let-off motor. $K = \frac{Δ L_{0} + \int (v_{B} - v_{A}) dt}{L_{0}}$ (8)

K is a constant in Equation (8).

With the control of the opening mechanism, the heald frame divides the warp yarns into two layers to form the shed, and it is assumed that the shed is symmetrical up and down, the yarn will often be deformed during the shed generation process. When the opening is at its maximum, as shown in Fig. 2, the following formula can represent the total shape variable ΔL $Δ L = \frac{h}{sin θ_{1}} + \frac{h}{sin θ_{2}} - L$ (9)

Where θ₁ and θ₂ are 1 / 2 of the opening angle on both sides respectively, h is the maximum opening height, and L is the yarn length when the angle of opening mechanism is 0 degrees. According to Hooke’s Law, the tension fluctuation ΔF at the maximum opening is $Δ L = \frac{h}{sin θ_{1}} + \frac{h}{sin θ_{2}} - L$ (10)

The weft insertion starts after the shed is formed. At this time, the weft insertion rapier with weft will cause slight fluctuation to the warp tension when passing through the shed. After the weft and warp yarns are interwoven, the reed performs the beating up process. The beating up process schematic diagram is shown in Fig. 3. The reed drives the warp yarn to move towards the weaver during beating up, resulting in a peak tension fluctuation.

Fig. 3

Schematic diagram of beating process.

The above analysis show that the warp tension is mainly caused by let-off and take-up motion, which causes yarn deformation and produces internal tension in the yarn. In the case of opening motion, if tension is sampled and adjusted in real time, the let-off amount in a single weaving cycle must be the same as the coiling amount in order to keep the tension stable. As mentioned above, the take-up in a single cycle is 1 /λ cm, but in fact Δ L> > 1 /λ in Equation (9), and the let-off motor will not reverse during continuous weaving. Therefore, the real-time sampling of tension is not suitable, and periodic interference is easy to be introduced into the sampling value, which is not conducive to control. In the weaving process, let-off and take-up motor are the main control objects, and they are in continuous motion. If the factors of shedding, weft insertion and beating up are removed, the control method will be relatively simple. Therefore, a special sampling time can be selected in each period to avoid the influence of opening and other factors on the sampling value. The opening is the maximum, and the opening is still when the spindle angle is between 45° and 57°. At this time, the weft insertion has just started, but the beating has not started, and the weft has not entered the shed, which has no effect on the warp tension. Therefore, the 10° range of 45° to 55° in each cycle can be taken as the angle interval of warp tension sampling, as shown in Fig. 4.

Fig. 4

Schematic diagram of warp tension sampling interval.

According to Equation (10), to ensure the warp tension is stable and within the error range of set tension, V_B = V_A should be made as far as possible. Combining Fig. 1 and Equation (2), the tangential velocity of the warp yarn and the friction roller can be obtained as follows $v_{B} = ω_{B} r_{B} = \frac{n_{0}}{60 λ}$ (11)

In combination with Equation (6), the tangential velocity V_A of warp and let off shaft is as follows $v_{A} = ω_{A} r_{A} = \frac{2 π}{i_{1}} n_{1} r_{A}$ (12)

Equations (11) and (12) shows that the speed n₁ of let-off motor can be obtained as follows $n_{1} = \frac{i_{1}}{120 π} \times \frac{n_{0}}{λ r_{A}}$ (13)

It can be seen from Equation (13) that the let-off motor speed n₁ is directly proportional to the loom spindle speed n₀, and inversely proportional to the product of warp shaft radius r_A and weft density.

From the above analysis, with the limited conditions, the transfer function model of warp tension control system illustrated in Equation (14). $G (s) = \frac{n A_{0} E (Δ Ls + 1)}{L_{0} s^{2}}$ (14)

the number of yarn s bypassing the tension roller is n, A₀ is the cross-sectional area of single yarn, e is the elastic modulus of yarn, L₀ is the yarn length between let off shaft a and yarn tangent point, friction roller B and fabric tangent point, and ΔL₀ is the yarn linear variable after tension initialization.

3 Control algorithm of warp tension

3.1 Integral separation PID

According to the analysis of the research status of tension control algorithm in the previous paper, the classical PID control is widely used in industrial process control because of its simple implementation mode, rich application cases, and strong adaptability. As shown in Equation (15), In the classical PID control, the deviation signal of the control quantity is processed by proportion, integral and differential, and then acted on the follow-up actuator as the output of the controller to complete the regulation of the control quantity. $u (t) = k_{p} • e (t) + k_{i} \int_{0}^{t} e (t) dt + k_{d} \frac{d e (t)}{dt}$ (15)

k_p is the proportional coefficient, k_i is the integral coefficient, k_d is the differential coefficient, e_(t) is the deviation of the control signal, u_(t) is the output of the controller.

During the operation of high-speed rapier loom, due to the deviation of sampling point, external interference and other factors, the warp tension often fluctuates greatly. Even the tension deviates too much from the set value of warp tension. In this case, large integration accumulation will occur in a short time due to the existence of integration, and the controller output may oscillate[17 –20]. To avoid the influence of integral link on control system when control deviation is large, this paper introduces integral separation control method based on classical PID control. The stability of the system is improved by removing the integral link when warp tension deviation crosses. At this time, the control quantity can be quickly returned to the target control value by increasing the proportion coefficient. When the deviation signal is near the control target value, the integral link control is introduced to eliminate the warp tension control system’s static error. The operation process is shown in Fig. 5.

Fig. 5

Operation flow of integral separation.

Eliminate an integral part in PID control and set a large proportional coefficient when the controlled quantity exceeds the set value too much. Deviation is greater than the set deviation threshold. Conversely, when the controlled quantity is close to the set value and less than the set deviation threshold, the integral link is re-introduced to complete the proportional integral differential control and switch back to the original proportional coefficient. After the introduction of integral separation control method, the PID control method can be expressed as $β = {\begin{matrix} 1 | e (t) | \leq ω \\ 0 | e (t) | > ω \end{matrix}$ (16) $u (t) = k_{p} e (t) + β k_{i} \int_{0}^{t} e (t) dt + k_{d} \frac{de (t)}{dt}$ (17)

3.2 PID parameter optimization

Searching for the global optimal solution of PID parameters is the critical problem in applying the PID control algorithm. In practical engineering, the most widely used method is to carry out parameter correction through continuous debugging in the industrial field. However, this method is challenging to ensure that these parameters fit well in the closed-loop tension control system of the high-speed rapier loom. The determined parameters are based on specific control objects. Once the parameters of the control system change or other errors are introduced, the existing PID controller will be affected and the control accuracy and efficiency will be reduced.

In this paper, a fuzzy optimization algorithm is introduced on the basis of integral separation PID algorithm, and the online setting of k_p, k_i and k_d parameters in PID control is realized by using relevant expert knowledge. This method can not only effectively improve the precision and anti-interference ability of closed-loop feedback control link in warp tension control system of high-speed rapier loom, but also make the system adaptive [21, 22].

According to Fig. 6, in order to realize the optimization of the proportion, integral, differential coefficient by fuzzy algorithm, these parameters was classified into initial value and the revised value. The initial value, which is give by experts or obtained through the experimental debugging determines the overall performance of the closed-loop control. The revised value obtained by fuzzy controller is used to optimize PID control performance and reduce all kinds of disturbance and error in the warp tension control. The calculation method is shown in Equation (18). ${\begin{matrix} k_{p} = k_{p}^{'} + Δ k_{p} \\ k_{d} = k_{d}^{'} + Δ k_{d} \\ k_{i} = k_{i}^{'} + Δ k_{i} \end{matrix}$ (18)

Fig. 6

Application flow of fuzzy optimization integral separation PID algorithm.

k_p’, k_i’, k_d’ are the initial values of PID parameters, k_p, k_i, k_d are the output values of the fuzzy controller, and k_p, k_i and k_d are the final values of the PID parameters [23 –28]. The specific creating process of the fuzzy reasoning mechanism as follows.

Three parameters of PID are optimized by the fuzzy algorithm to control warp tension in closed-loop feedback system. Therefore, the input parameters are deviation signal e and the rate of change e_c of deviation signal, and the output parameters are k_p, k_i, k_d of the three parameters of PID controller. Taking the set tension of 110 kg and tension fluctuation range within <5%as an example, and combining with the actual range of other parameters, the basic domain of input and output parameters is set and certain quantification factors are selected. The corresponding fuzzy domain of each parameter was show in Table 1.

The five parameters are divided into seven parts according to different quantitative levels, seven fuzzy subsets corresponding to the fuzzy domain: NB (negative large), NM (negative middle), NS (negative small), ZO (zero), PS (positive small), PM (positive middle), PB (positive large).

According to the performance of the warp tension control system and the variation range of input and output parameters, the membership function is selected as shown in Figs. 7 8.

The rule is connected to the input deviation signal and the output PID correction parameters base in the knowledge base, which is established in the form if A and B then C. For the fuzzy control structure with two inputs and three outputs, a total of 147 fuzzy rules need to be constructed for subsequent reasoning. Taking the relationship between deviation e, deviation change rate eC and the correction value of proportional coefficient ΔkP as an example, there are 49 empirical rules (Table 2).

One of them is: “if the deviation is small and the variation rate of deviation is small, the correction value of proportional coefficient should be reduced", according to the empirical rule, the fuzzy relation matrix R_C1 can be obtained as show in Equation (19). $Rc 1 = [\begin{matrix} 0.95 & 0.5 & . . . & 0 \\ 0.5 & 0.5 & . . . & 0 \\ . . . & . . . & . . . & 0 \\ 0.5 & 0.5 & . . . & 0 \\ 0.5 & 0.5 & . . . & 0 \\ . . . & . . . & . . . & 0 \\ 0 & 0 & . . . & 0 \end{matrix}]$ (19) In the same way, the corresponding fuzzy relation matrix can also be obtained through other 48 empirical rules. By combining 49 fuzzy relation matrices, a total fuzzy relation matrix R with 49 rows and 7 columns can be obtained. The matrix represents the corresponding relationship between deviation e, deviation change rate e_c and the correction value Δk_p.

If the input parameter e is 4.167 and e_c is 1, the correction value Δk_p can be obtained by the following steps:

The fuzzy subset of input deviation e is T_e = 0, 0, 0, 0, 0.25, 0.75, 0.8176.

The fuzzy subset of input deviation change rate ec is: T_ec = 0, 0, 0, 0, 0, 0.5, 1, 0.5.

Fuzzy reasoning T_Δ _k_P = 0, 0, 0, 0, 0.25, 0.75, 0.75.

The center of gravity method is used to solve the ambiguity, and the result is: Δ k_p = 0.457.

Table 1

Domain correspondence table of input and output parameters

parameters	fuzzy domain	quantification factor	basic domain
e	[–3, –2, –1,0,1,2,3]	(a_e-b_e)/6	[b_e, a_e]
e_c	[–3, –2, –1,0,1,2,3]	(a_ec-b_ec)/6	[b_ec, a_ec]
Δ K_p	[–3, –2, –1,0,1,2,3]	(a_p-b_p)/6	[b_p, a_p]
Δ K_i	[–3, –2, –1,0,1,2,3]	(a_i-b_i)/6	[b_i, a_i]
Δ K_d	[–3, –2, –1,0,1,2,3]	(a_d-b_d)/6	[b_d, a_d]

Fig. 7

Membership function of e.

Fig. 8

Membership function of e_c,k_p,k_i and k_d.

Table 2

Domain correspondence table of input and output parameters

Δk_p/Δk_i/	e_c
Δ k_d	NB	NM	NS	ZO	PS	PM	PB
e	NB	NB/NB/PM	NB/NB/PM	NB/NB/PB	PB/NB/PB	PB/NB/PB	PM/NB/PM	ZO/NM/PS
	NM	NB/NB/PS	NM/NM/PS	NM/NM/PM	PM/NB/PM	PM/NS/PM	PM/NM/PM	PS/NM/PS
	NS	NM/NM/NM	NS/NS/NM	NS/PS/NS	PS/NS/ZO	ZO/PS/NS	ZO/NS/NM	NS/NS/NB
	ZO	NB/ZO/NB	NB/ZO/NB	NM/PM/NM	ZO/PB/ZO	NM/PM/NM	NB/ZO/NB	NB/ZO/NB
	PS	NB/NS/NB	NS/NS/NS	ZO/PS/ZO	PS/NS/ZO	NS/PS/NS	NS/NS/NM	NM/NM/NM
	PM	PS/NS/PS	PM/NM/PM	PM/NS/PM	PM/NB/PM	NM/NM/PM	NM/NM/PS	NB/NB/PS
	PB	ZO/NM/PS	PM/NB/PM	PB/NB/PB	PB/NB/PB	NB/NB/PB	NB/NB/PM	NB/NB/PM

In this paper, using the Simulink design environment of MATLAB, a closed-loop simulation model combining fuzzy algorithm and integral separation PID control method is established, and the speed and overshoot of the corresponding warp tension adjustment process in the simulation process are analyzed and optimized. On this basis, the fuzzy optimization integral separation PID algorithm code is written in C language by the embedded control system. The industrial field experiment of rapier loom warp tension control is carried out to verify the performance of the control strategy and optimize the parameters.

4 Simulation and experiment

Through the theoretical analysis and research on the warp tension control mechanism and control algorithm of high-speed rapier loom, the warp tension control model and control algorithm are completed. Taking polyester yarn as an example, the feasibility and effectiveness of the scheme are verified by simulation and experiment. Substituting the sample yarn parameters into Equation (14), the control transfer function of sample yarn tension is calculated as follows: $G (s) = \frac{2.3 s + 76}{1000 s^{2}}$ (20)

Firstly, the classical PID, integral separation PID and fuzzy optimization integral separation PID simulation models are built on Simulink, and their effects are compared [29, 30]. The initial proportional coefficient, integral coefficient and differential coefficient of PID are determined to be 2320, 1700 and 417, respectively by simulation model tuning method. The initial modified proportional coefficient of integral separation PID is 6000, the switching threshold of the proportional coefficient is 1, and the integral separation threshold of integral separation PID is 0.2. Firstly, the response rate and overshoot of the above control methods are compared and simulated with the step signal as the input. The initial step signal is set to 2 and 10 respectively, so as to compare the control performance of the three control methods in the case of small amplitude fluctuation and large amplitude fluctuation [31]. The simulation results of the two cases are shown in Figs. 9 10.

Fig. 9

(a) Response curve when step signal is 2, (b) Local graph of response curve.

Fig. 10

(a) Response curve when step signal is 10, (b) Local graph of response curve.

The analysis of Fig. 9 shows that when the tension fluctuates slightly, the overshoot and response time of the fuzzy optimization integral separation PID control algorithm is superior to the integral separation PID control algorithm and the traditional PID control algorithm.

Through the analysis of Fig. 10, when the tension fluctuates greatly due to interference and other factors, the fuzzy optimization integral separation PID control algorithm has obvious advantages in response time and overshoot compared with the traditional PID control algorithm and the integral separation PID control algorithm.

Based on Fig. 9, the proportional coefficient switching threshold is set to 0.6, and the integral separation PID integral separation threshold is 0.6. A interference signals with the amplitude of 2 and a duration of 1 and an interference signals with amplitude of 0.4 and duration of 2 are introduced to simulate and compare the traditional PID control algorithm, integral separation PID control algorithm and fuzzy optimization integral separation PID control algorithm. The results are shown in Fig. 11.

Fig. 11

(a) Simulation curve of small interference signal.

Parameter comparison table (Table 3) can be obtained by analyzing Fig. 11. Table 3 shows that after introducing the interference signal whose amplitude exceeds the integral separation threshold, the fuzzy optimization integral separation PID control algorithm control algorithm still maintain the dual advantages compared in overshoot and convergence speed at the rising edge of the interference. At the falling edge of the disturbance, the overshoot is slightly inferior to the integral separation PID control algorithm, but it is still superior to the traditional PID control algorithm. When the amplitude of tension fluctuation is below the integral separation threshold, the fuzzy optimization integral separation PID control algorithm has similar performance to the traditional PID control algorithm and integral separation PID control algorithm.

Table 3

Parameter comparison table

Point	Traditional PID		Integral separation PID		Fuzzy optimization integral separation PID
	Overshoot	Response(s)	Overshoot	Response(s)	Overshoot	Response(s)
A	0.25	–	0.11	–	0.08	–
B	0.10	3.62	0.05	2.51	0.06	2.46
C	0.05	2.52	0.05	2.54	0.05	2.52

In order to verify the practical application effect of the control method, the traditional PID control and fuzzy optimization integral separation PID control are tested respectively in the experimental platform as show in Fig. 12, and the computer is connected with the field touch screen online, and the relevant parameter settings and tension interface are saved. In the test, No.3 (11.30 tex×2) polyester yarn is used, and its strain range is required to be less than 1.6%(when the strain is greater than 1.6%, the polyester fiber will break gradually). At this time, the elastic modulus is 3.0 cn/tex (maximum), and the tension setting value is 110 kg (warp density is 108, width is 2.6 m), and the tension fluctuation range is [106, 114].

Fig. 12

Experimental platform of rapier loom.

In the traditional PID control, the PID parameters need to be adjusted manually to achieve better control effect. The tension curve of traditional PID was shown in Fig. 13(a). At this time, the speed of loom is 320 r/min, the PID proportional gain k_p is 100%, the integral time t_i is 500 ms, and the set PID sampling time is 200 ms, without differential control. In Fig. 13(a), The red line is the set value of tension, the black line is the real-time measured value of tension, and the blue line is the effective value of tension after applying the traditional PID, and the sampling interval is 45° to 55°. It can be seen from Fig. 13 (a) that the error range is about [–3.7, +3.6] when applying the traditinal PID.

Fig. 13

(a) The tension curve of traditional PID, (b) The tension curve of Fuzzy optimization integral separation PID.

To facilitate comparison, the parameters of the fuzzy optimal integral separation PID control are consistent with the traditional PID control. It shows the detected tension curve in Fig. 13(b). It can be seed that the effective value of tension after PID control by fuzzy optimization integral separation is more stable than that in Fig. 13(b), and the error range is about [–2.2, +1.5].

Compared with Fig. 12 (a) and Fig. 12 (b), it can be known that the two control methods both can make the warp tension stable near the set value. However, when using the traditional PID algorithm, the warp tension fluctuates violently, and various factors of loom equipment and external environment have obvious influence on the tension. Traditional PID controller has weak adaptability and slower response speed. At the same time, some tension sampling points are close to the set alarm boundary line in PID algorithm. Once the interference increases, the tension may be too large or too small, which will cause the alarm of advance equipment. However, when using the the fuzzy optimization integral separation PID algorithm, the fluctuation is small. The tension error comparison table (Table 4) can be obtained by extracting 7 groups of tension sampling data under different vehicle speeds.

Table 4

Comparison table of warp tension error

speed (r/min)	Set (kg)	Traditional PID		Fuzzy optimization integral separation PID
		Measure(kg)	Error(kg)	Measure(kg)	Error(kg)
60	110.00	112.92	2.92	107.82	–2.18
120	110.00	106.46	–3.64	111.43	1.43
240	110.00	110.36	0.36	110.31	0.31
360	110.00	108.61	–1.39	108.61	–1.39
400	110.00	113.54	3.54	109.57	–0.43
500	110.00	110.28	0.28	110.28	0.28
600	110.00	113.44	3.44	108.40	–1.60

According to the deviation of tension value in the Table 4, through the application of fuzzy optimization integral separation PID control method, the warp tension value stable near the set value, and the relative error is stable within 3%, less than the set requirements (8%). The stability of fuzzy optimization integral separation PID algorithm is better than traditional, which can effectively improve the accuracy of warp tension control, and make the loom tension more stable.

5 Conclusion

In this paper, the factors affecting the stability of warp tension in the weaving process of high-speed rapier loom are analyzed in detail, and a sampling method of warp tension associated with weaving process is proposed. On this basis, the integral separation control method is introduced into the traditional PID control method. The threshold value of proportional coefficient switching is set to overcome the large interference signal in the system control. The fuzzy optimization theory is introduced to optimize the parameter of traditional PID, which improves the control performance and enhances the adaptability of the control system. Finally, the simulation and experimental comparison between the fuzzy optimization integral separation PID control and the traditional PID control are carried out. The results show that the fuzzy optimization integral separation PID control algorithm can effectively reduce the fluctuation of warp tension and improve the quality of warp tension control.

Funding statement

This study is financially supported by Jiangsu Province training fund funded project (Grant No. BRA2020244); The National Natural Science Foundation of China (Grant No. 51675160).

Footnotes

Acknowledgments

First of all, I would like to express my gratitude to all those who helped me during the writing of this thesis. At the same time, I gratefully acknowledge the help of my supervisor, Mr. Xiao Yanjun, who has great contribution in conceptualization, funding acquisition and resources ect. Next, I would like to thank Mr. Liu Zhenhao for his work in data processing, software and investigation. Moreover, without the help of Professor Zhang, Professor Zhou and Professor Liu in form analysis and supervision of project management, I could not complete the work of writing and editing. Thanks again to all the people who helped me.

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