High-speed loom brake system controlled by fuzzy PID algorithm based on cloud platform

Abstract

When a high-speed loom is suddenly stopped or is driven again in a faulty state, it is easy to cause defects such as brake marks and driving marks on the fabric. This is because the brake system of the loom has insufficient control of the accuracy of the parking angle. To improve the control accuracy of the braking system, this paper analyzes the dynamic process of the braking system when braking, builds a mathematical model of the electromagnetic clutch of the braking system, and proposes to regulate the excitation current of the system by fuzzy PID algorithm. The rule table of this PID controller is established by expert experience, and the center of gravity method is used for defuzzification. In addition, this article combines internet communication and storage technology to build a cloud platform for the brake system, and realizes the monitoring, storage and diagnosis of the brake system data. Finally, hardware testing and on-site braking experiments (including parking angle data acquisition experiment and spindle speed change experiment during braking) verify that the design can achieve high-precision parking angle positioning at different speeds, and has a fast dynamic response and a smooth braking process.

Keywords

Fuzzy PID cloud platform high speed loom brake system

1 Introduction

During the weaving process of the loom, there may be stopping marks when the warp or weft is broken, or when a malfunction causes an emergency stop. In the high-end processing field, once the fabric has quality problems such as stop marks or the starting marks, it will be regarded as waste directly. Starting marks are the phenomenon of uneven weft density in the fabric during the time from the start of the rapier loom to the smooth operation of its main shaft. There are many factors that cause starting marks. Through a large number of loom parking experiments, it is found that when the rapier loom brakes, the deviation of the position of the fabric and warp caused by the creep and relaxation of the yarn is the main reason for the driving marks. The position deviation of the weaving mouth will also cause defects such as thin and dense roads. A survey of the reasons for the formation of thin and dense roads is down in [1]. There is a certain relationship between the displacement of the weavers and the stopping time. The shorter the stopping time of the loom is, the smaller the movement of the position of the weave is, and the smaller the possibility of the fabric producing opening marks.

It can be seen from [2] that in the early loom field, rapier looms used tooth discs to mesh with each other to achieve braking. This method will cause severe wear on the sprocket. Frequent replacement of the chainring not only increases the overall cost but also brings inconvenience to the brakes of the loom. To solve this problem, Tetsuya Matsuyama proposes to use a high torque direct drive motor to directly connect the loom to the main shaft, and use a frequency converter to adjust the speed of the stepping motor to achieve relatively accurate braking [3]. If the direct drive motor is adopted, the brake system does not need to use the clutch. Both the starting force and braking force of the brake system can be achieved by adjusting the torque of the motor. The disadvantage of this method is that the cost is too high. Although the mechanical part is much simpler, the production method of the direct driven electric motors is more complicated, and the saved mechanical cost is not enough to offset the production and use cost of the direct drive motor [4]. Compare with the above two driving methods, the electromagnetic clutch drive has some following advantages: higher safety, stronger transmission system operability, easier maintenance, simpler control, and less power loss [5]. Therefore, a large number of high-speed rapier looms use electromagnetic clutches for transmission and braking. The electromagnetic clutch can control the action of the clutch by controlling the on and off of the excitation current, so as to realize the connection and transmission of the mechanical mechanism. This control method is described in [6].

In this article, the brake system of the rapier loom uses an electromagnetic clutch. In order to achieve smooth braking and ensure braking accuracy, a suitable control algorithm is needed to adjust the excitation current in the electromagnetic clutch.

Proportion integral differential (PID) control has the advantages of simple algorithm, good robustness, and high reliability. It is widely used in process control and motion control, and is especially suitable for systems that can establish accurate mathematical models. However, the actual industrial automation process often has the characteristics of non-linear, time-varying, and difficult to establish an accurate mathematical model. It requires manual adjustment of various parameters. The parameter setting is more difficult and difficult to change after the setting, which cannot meet the stability and rapidity at the same time. When the brake and clutch control system is in use, accurate mathematical models cannot be obtained, and there is a certain degree of non-linearity and hysteresis. Therefore, the use of traditional PID control cannot achieve good control effects. It is necessary to make certain improvements to the traditional PID controller. It meets the requirements of the control system for excitation current control. Since the end of the 20th century, fuzzy control has been applied in the field of industrial control. At present, some intelligent control algorithms with self-tuning PID parameters have made up for the shortcomings of traditional PID algorithms, such as fuzzy PID control algorithms, which effectively solve the non-linearity, time-varying and hysteresis existing in industrial control systems. [7] presents a survey on recent developments of fuzzy control systems focused on industrial applications. For example, in [8], V. Vichuzhanin designed a fuzzy PID controller with fuzzy dynamic correction. The fuzzy dynamic correction can reduce the overshoot and shorten the determination time of the controlled parameter. In [9, 10], Lu et al. designed a fuzzy neural network PID controller combined with neural network. In [11], Xiangyang Lu et al. proposed an adaptive proportional integral derivative (PID) controller based on fuzzy group analysis. The control convergence is more reliable than the conventional PID controller.

Aiming at the problems that the brake system of the loom cannot achieve high spindle accuracy and the brake speed change is not stable enough during high and low voltage conversion, the fuzzy PID control algorithm is used to adjust the excitation current in the brake system to make the brake system output stable voltage and ensure the brake accuracy. At the same time, the current data of the brake control system of the loom has insufficient storage and analysis. The brake data is only stored locally, and the fault diagnosis cannot be performed in a scientific way based on the historical operating parameters of the loom. This article addresses this problem and combines the Internet of Things communication technology. A cloud platform is designed for the brake system, which is used to save brake data in real time, predict and diagnose brake failures.

The overall system scheme of this paper is: analyze and simulate the electromagnetic clutch, obtain the relationship between output torque and excitation current, provide a theoretical basis for current regulation; analyze the magnetic circuit and dynamic characteristics, and establish a finite element simulation model. The electromagnetic clutch control method is researched, and the fuzzy PID control algorithm is applied to its excitation current adjustment. Cloud platform, internet, cloud computing, intelligent diagnosis and other technologies are applied to the remote monitoring of the loom brake system, and a networked and intelligent loom brake control diagnosis system is designed.

2 Characteristic analysis of electromagnetic clutch

2.1 Structure of electromagnetic clutch

The electromagnetic clutch used in the high-speed rapier loom studied in this paper is a dry two-plate electromagnetic clutch, and the structure is shown in Fig. 1.

Fig. 1

Structure of the electromagnetic clutch of the rapier loom.

In Fig. 1, A is the central drive disc, B is the brake magnet, C is the clutch magnet, D is the clutch rotor, P1 and P2 are two pulleys, and M is the main motor. Among them, the clutch magnet C and the central drive disc A form an electromagnetic clutch; the central drive disc A and the brake magnet B form a brake; the pulley P1 and the main motor M are connected by a hard shaft; the two pulleys are connected by a V-belt; The clutch rotor D is connected with the pulley P2 through a hard shaft. The two pulleys, the clutch rotor and the motor rotate at the same time. The basic principles of frictional clutches and brakes is described in [12]. The parking process of the loom is: press the parking button, the coil of the clutch magnet C will quickly lose power, the coil of the brake magnet B will be energized and generate a magnetic field, so that the central drive disc A is close to the brake magnet B, and the brake magnet B is fixed on the base. On the upper side, a frictional resistance distance is generated between the central transmission disc A and the brake magnet B, so that the main shaft of the rapier loom is quickly stopped and the loom is braked.

2.2 Analysis of dynamic characteristics of electromagnetic clutch during braking

The electromagnetic brake is also a kind of electromagnetic clutch, and its structure and torque characteristics are exactly the same as the electromagnetic clutch [13, 14]. The magnetic circuit and dynamic characteristics of the electromagnetic brake are analyzed below.

2.2.1 Magnetic circuit analysis

The magnetic circuit of the electromagnetic brake is shown in Fig. 2. [15] analyzed the dynamic characteristics of high speed electromagnetic brake during braking. In Fig. 2, δ represents the permeance, and F represents the magnetomotive force of the braking system, F = Ni, N is the number of turns of the excitation coil, and i is the excitation current. δ_A, δ_B1, δ_B2 are electromagnet permeability, δ_G1, δ_G2 are air-gap permeability, δ_C1, δ_C2 are the magnetic permeability of the brake disc, and F is the magnetic potential of the braking system.

Fig. 2

Electromagnetic brake equivalent magnetic circuit.

According to electromagnetic theory [16], the air-gap permeability δ can be given by: $δ = \frac{μ S}{l}$ (1)

In equation (1), μ is the permeability of the material in the magnetic circuit; S is the cross-sectional area of the magnetic circuit; l is the effective length of the magnetic circuit.

When the electromagnetic brake brakes, the length of the air gap changes with the movement of the friction disc, and the air-gap permeance δ also changes, it can be expressed as $δ (x) = \frac{μ S}{x}$ (2)

In Equation (2), δ (x) is the air gap permeability during braking, μ is the permeability of the material in the magnetic circuit, S is the cross-sectional area of the magnetic circuit, and x is the dynamic air gap length during braking.

The inductance L (x) and electromagnetic force F of the electromagnetic brake dynamic process can be expressed as $L (x) = N^{2} δ (x) = N^{2} \frac{μ S}{l}$ (3)

$F = \frac{N^{2} i^{2} μ_{0} S}{2 x^{2}}$ (4)

In Equation (3) and (4), x is the dynamic air gap length; N is the number of turns of the coil; δ is the air-gap permeability; μ is the permeability of the material in the magnetic circuit; i is the excitation current.

2.2.2 Mathematical model

The equivalent circuit of the internal structure of the electromagnetic brake is an RL loop. The inductance has an obstructive effect on the current. It is a process of increasing from zero. The voltage at both ends of the excitation coil is U and the excitation current is i, then the differential equation of the internal circuit of the electromagnetic brake can be expressed as: $U = Ri + \frac{d φ}{dt}$ (5)

In Equation (5), R is the coil resistance, φ is the flux linkage in the coil, and the calculation equation of φ can be expressed as: $φ = Li$ (6)

Among Equation (6), L is the inductance.

Equation (7) can be derived from equation (5) and equation (6). $U = Ri + L \frac{di}{dt} + i \frac{dL}{dt}$ (7)

The inductance L is related to the air gap δ of the electromagnet, then the Equation (7) can be expressed as: $\begin{matrix} U = Ri + L \frac{di}{dt} + i \frac{dL}{d δ} \cdot \frac{d δ}{dt} \\ = Ri + L \frac{di}{dt} + i \frac{dL}{d δ} \cdot ν \end{matrix}$ (8)

When the inductance coil just has a current, because the current is small, that is, the electromagnetic attraction is not enough to make the electromagnet move. At this time, the inductance L is equivalent to a constant. Define the inductance at this time as a constant L₀, then the Equation (8) can be expressed as: $U = Ri + L_{0} \frac{di}{dt}$ (9)

The expression of excitation current i can be derived from Equation 9. $i = {Ce}^{\frac{R}{L_{0}} t} + \frac{U}{R}$ (10)

In Equation (10), C is a constant. From the function of current, it can be found that the excitation current changes exponentially, but when the electromagnetic force overcomes the pressure of the spring on the brake disc at the initial stage, the electromagnet starts to move, and the air gap δ will gradually change small. From equation (8), we can see that in order to conservation of momentum, the excitation current i in the circuit will also gradually decrease. When the electromagnet stops moving, the current returns to an exponential form, and finally reaches a steady state. The dynamic waveform of the coil excitation current i is shown in Fig. 3.

Fig. 3

Dynamic current waveform of excitation current.

In Fig. 3, the electromagnetic brake did not brake due to the small excitation current during the time period t1-t2; from time t0, the friction disc began to move, and the current continued to increase; during the time period t1-t2, the friction disc and The brake disc begins to contact and the braking process begins; the friction disc is in full contact with the brake disc at time t2. The length of time used in the time period t0-t2 is the lag time value of the electromagnetic brake.

For electromagnetic brakes, the smaller the lag time value, the better the electromagnetic force performance. Y. Yasa et al. describe a design approach for electromagnetic brakes in [17]. When the high-speed rapier loom is parking, the spindle parking accuracy is very high, and the spindle parking angle offset should be as small as possible, so it is necessary to use an electromagnetic brake with better electromagnetic force performance. At present, the electromagnetic brake applied to high-speed rapier looms has a pull-in lag time of about 15 ms. The spindle speed R of the loom controlled by this control system is 500rad/min, and the calculation equation of the angle θ that the spindle rotates within the lag time t is: $θ = R * Π * 1000 * t / 60$ (11)

In equation (11), R is the motor speed; t is the lag time of the electromagnetic brake.

Then the angle θ that the spindle rotates within 15 ms of lag is theoretically 45°. But in reality, through multiple parking experiments, the data we collected is 65°. In other words, the electromagnetic brake needs to be energized 65° in advance to stop the spindle within the specified angle range. This is because when the main motor is powered off, even if the brake does not output torque, the spindle speed will drop during this period of time. Secondly, when the spindle is positioned and braked, the spindle inertia, load and other unknown factors will also affect the parking accuracy.

3 Fuzzy PID control and cloud platform

3.1 Fuzzy PID

In this paper, fuzzy PID control algorithm is used to adjust the excitation current of the controlled object in real time.

3.1.1 Fuzzy controller

Fuzzy controller includes four parts: fuzzification, rule base, fuzzy inference and defuzzification [18]. The principle of fuzzy control is shown in Fig. 4.

Fig. 4

Block diagram of fuzzy control.

(1) Fuzzification

Fuzzification is the process of transforming physical quantities into fuzzy quantities through corresponding rules. For example, the input variable is divided into seven levels, namely PB, PM, PS, ZO, NS, NM, PB, each level includes seven subsets, and then the precise quantity is mapped to the fuzzy sub-set by selecting the appropriate membership function set.

(2) Rule base

The fuzzy rules of the controller are obtained based on previous work experience. In order to control the excitation current of the electromagnetic clutch well, a corresponding rule library is established in this paper.

(3) Fuzzy inference

Fuzzy inference is to map the fuzzy input set to the fuzzy output set, that is, the corresponding relationship between the input set and the output set is realized by establishing a rule base.

(4) Defuzzification

The corresponding fuzzy quantity is obtained by fuzzy inference. Since the actual fuzzy control rules require a non-fuzzy quantity, a suitable defuzzification method is selected to convert the obtained fuzzy quantity into an accurate quantity. The defuzzification in this paper uses the center-of-gravity method. That is, the centroid of the geometric figure enclosed by the membership function represents the fuzzy set [19].

3.1.2 Fuzzy PID controller

The fuzzy PID controller is composed of two parts, including the fuzzy controller and the traditional PID controller. Fuzzy control does not rely on accurate models, can simulate the way of thinking of people, and has strong stability [20]. The block diagram of the fuzzy PID controller is shown in Fig. 5.

Fig. 5

Block diagram of the fuzzy PID controller.

Fuzzy PID takes the deviation e between the expected value and the feedback value and the error rate of change ec as input, and obtains the setting values of K_P, K_I, K_D after fuzzification, fuzzy inference and defuzzification. [21] and [22] are examples of using fuzzy method to control electromagnetic clutch.

3.2 Cloud platform

The cloud platform part of this article mainly realizes the real-time data storage of the loom’s brake system, which can save the loom’s operating parameter information, operating status information, and fault information in the database in real time, as a basis for fault diagnosis and judging operating conditions.

The cloud platform needs to pay attention to information security when designing. The cloud security requirements, threats, vulnerabilities and countermeasures are analyzed in [23]. In terms of system security design, the cloud platform adopts the method of setting different operating permissions and different login passwords for people with different identities to prevent people with non-designated identities from misoperation of the system and causing losses. For example, the operator can only view the operating parameters. Information and fault information, but the administrator can not only view all the loom operating parameter information and fault information, but also set the loom operating parameters; in addition to the above functional requirements, the system also needs to consider the compatibility of the client, which should meet the requirements It can be accessed by different devices and different browsers. Since there are many interference sources in the environment of the system, the anti-interference of the system should also be considered.

The fault diagnosis part of the cloud platform uses information fusion technology. This method can make better use of each sensor and effectively improve the accuracy of the diagnosis results. Fault diagnosis uses rough set and Bayesian network as the loom fault diagnosis method. Firstly, the collected loom parameter information is simplified by rough sets, then the smallest decision table is obtained; secondly, the Bayesian network model is constructed according to the method of scoring the best. According to the conditional probability of the decision table and the connection relationship between the Bayesian network nodes, the network with the highest score is obtained. The cause of failure and the solution to the failure are determined by the above method and fed back to the remote client. The basic architecture of the cloud platform is shown in Fig. 6.

Fig. 6

The basic architecture of the cloud platform.

There are several aspects to pay attention to in the construction of the cloud platform. The first is the choice of data transmission communication methods between the local execution end and the cloud server, which generally include wired and wireless two methods [24]. The wired method mainly realizes the communication between the local execution end and the cloud server through communication methods such as network cable, CAN bus, RS485 bus, and RS232 bus. Wireless methods mainly include Bluetooth, Zigbee, WIFI, GPRS and other wireless communication connection methods. The second is the design of the software system. The client needs to display the operating status, operating parameters, faults and fault solutions of the loom in real time. Therefore, the software system should have high reliability, real-time performance, and rapid diagnosis.

The communication mode between the server and the remote client in the remote monitoring and fault diagnosis system has two development architectures: B/S (browser/server) and C/S (client/server). The B/S architecture uses the browser as a remote client, and its server is a Web server. It is a special and specific C/S architecture, and its working process is the concretization of the C/S architecture. Among them, the difference between C/S architecture and B/S architecture is shown in Table 1:

Table 1

Differences between C/S architecture and B/S architecture

Type	C/S architecture	B/S architecture
Hardware environment	Local area network, slow access	Wide area network, fast access
Information safety factor	High safety factor, difficult development	The safety factor is weak and development is easier
system maintenance	Need to install the client, the system upgrade is difficult, all the clients need to be updated and upgraded, and the overhead is high	No need to install, just use a browser, the system upgrade is easier, only need to upgrade the server, the cost is small
Operating environment	Need to install the client, the system upgrade is difficult, all the clients need to be updated and upgraded, and the overhead is high	No need to consider

The data transmission between the local execution end and the cloud server adopts Socket-based data transmission and the TCP/IP communication protocol is selected. In order to increase the interaction rate, when data is exchanged between the Web server and the client, only the changed loom operating parameter information is refreshed, instead of refreshing the entire page. Ajax (Asynchronous JavaScript And XML) is a technology that can realize asynchronous update of web pages. It can update part of the content of the web page without reloading the entire page. Therefore, this system uses Ajax technology for remote client and Web server data interaction.

4 Design of fuzzy PID controller for excitation current regulation system

This paper uses the output excitation current error e of the control system and the current error rate of change ec as the input of the fuzzy controller, transforms the basic domain of e and ec into the corresponding fuzzy domain, and establishes the rules of the fuzzy control theory through expert knowledge Then, the three coefficients ΔK_P, ΔK_I, ΔK_D of the PID controller are adjusted through the fuzzy universe, and finally defuzzification is performed. In the process of defuzzification, the center of gravity method is used to obtain the real-time values of the three coefficients ΔK_P, ΔK_I, ΔK_D, and the control parameter Δu (k) of the controlled object is obtained through the PID calculation equation [26 –28].

4.1 Establishment of membership function

The input error e is the excitation current error of the electromagnetic clutch, that is, the difference between the expected excitation current and the actual excitation current, ec is the rate of change of the electromagnetic clutch excitation current error, and the expression of ec is: $ec = e (k) - e (k - 1)$ (12)

In the excitation current adjustment system of the brake and clutch control system, according to previous experiments, the universe of the excitation current error e is [–0.3, 0.3], and the universe of the excitation current error change rate ec is [- 0.03, 0.03], the fuzzy universe of e and ec are both [- 0.3 - 0.2 - 0.100.10.20.3]. It can be determined that the quantization factor K_e = 0.3/0.3 = 1 corresponding to the excitation current error, then the quantization factor K_ec = 0.3/0.03 = 10 corresponding to the excitation current change rate ec. The fuzzy universe of output ΔK_P and ΔK_I is defined as [- 3, 3], and the fuzzy universe of output ΔK_D is set to [- 0.030.03].

Set the excitation current error e, error rate of change ec, and the fuzzy universe of output variables ΔK_P, ΔK_I, ΔK_D to 7 levels, namely {PB, PM, PS, ZO, NS, NM, NB}, the fuzzy sets of input and output variables are represented by gaussmf and trimf membership functions. The membership functions of e, ec, ΔK_P, ΔK_I, ΔK_D are shown in Fig. 7.

Fig. 7

Membership function of each variable.

4.2 Establishment of fuzzy control rules

When calibrating each parameter of PID, it is necessary to consider the interaction relationship between the three parameters in different working conditions and different sampling moments [29]. Under fuzzy PID control, the output response curve of the brake and clutch control system is shown in Fig. 8.

Fig. 8

Output response curve.

According to Fig. 8, the excitation current adjustment principle can be obtained as follows:

Section I and V: The excitation current error e is relatively large at the beginning, e (k) > 0, ec (k) < 0, and the control quantity needs to be increased.

Section II: The actual excitation current is greater than the expected excitation current and the adjusted volume has an increasing trend. e (k) < 0, ec (k) < 0, the control amount should be reduced more to reduce the error.

Section III: The actual excitation current is greater than the expected excitation current and the adjusted amount tends to decrease. e (k) < 0, ec (k) > 0, should comprehensively consider the situation of e (k) and ec (k), and determine to reduce, maintain or increase the control quantity, so that the actual excitation current tends to the expected excitation current.

Section IV: The actual excitation current is less than the expected excitation current and the adjusted amount has a tendency to increase. The current error e is small, e (k) > 0, ec (k) > 0, the control amount should be increased greatly.

e (k) and ec (k) are the projections of e and ec in the fuzzy universe respectively. When establishing fuzzy rules, it is necessary to consider three aspects: fuzzy correction of proportional link, fuzzy correction of integral link, and fuzzy correction of differential link.

Fuzzy correction of proportional link:

When the value ofΔK_P is appropriately reduced, it can effectively avoid excessive overshoot and oscillation problems in the system, but if the value of ΔK_P is too small, the system will appear slow response; when the value of ΔK_P is appropriately increased, it can be the response time and steady-state error of the electromagnetic clutch are reduced, and the system excitation current adjustment accuracy can be improved at the same time. However, if the value of ΔK_P is too large, the system will have excessive overshoot and oscillation.

When the electromagnetic clutch is working, the output excitation current will change due to changes in external conditions. In the two intervals of I and V in Fig. 8, if the value of ΔK_P is appropriately increased, the system response speed can be improved; when the system reaches the desired excitation current, in order to achieve the accuracy of the electromagnetic clutch excitation current adjustment and the stability of the operating state, the value of ΔK_P can be reduced. In the interval II, if the value of ΔK_P is appropriately reduced, the system accuracy can be improved; in the interval III and IV, the value of ΔK_P should be increased, decreased or unchanged according to the values of e and ec. ΔK_P fuzzy rules are implemented, and the ΔK_P fuzzy rules are shown in Table 2.

Table 2

ΔK_P Fuzzy Rule Table

ec\ΔK_P\e	NB	NM	NS	ZO	PS	PM	PB
NB	PB	PB	PM	PM	PS	ZO	ZO
NM	PB	PB	PM	PS	PS	ZO	NS
NS	PM	PM	PM	PS	ZO	NS	NS
ZO	PM	PM	PS	ZO	NS	NM	NM
PS	PS	PS	ZO	NS	NS	NM	NM
PM	PS	ZO	NS	NM	NM	NM	NB
PB	ZO	ZO	NM	NM	NM	NB	NB

Fuzzy correction of integral link:

In the electromagnetic clutch excitation current adjustment control, ΔK_I is mainly used to eliminate the static deviation of the controller. Take the intervals of I and V as examples. When the excitation current of the electromagnetic clutch increases to the expected excitation current value, a smaller value of ΔK_I can be used to avoid the problem of excessive overshoot and integral saturation in the system; When the electromagnetic clutch excitation current value is close to the expected current value, in order to avoid the undesirable effect of the integral link on the system, ΔK_I can be set to a moderate value; when the electromagnetic clutch excitation current returns to the expected current, the value of ΔK_I can be increased in order to improve the response speed of the system. To speed up the system response speed. In section II, the system response speed can be improved by taking a larger value of ΔK_I. In section III and IV, the value of ΔK_I must be judged comprehensively according to the values of e and ec, which can be implemented in accordance with the fuzzy rules of ΔK_I, ΔK_I The correction rules are shown in Table 3.

Table 3

ΔK_I Fuzzy Rule Table

ec\ΔK_I\e	NB	NM	NS	ZO	PS	PM	PB
NB	NB	NB	NM	NM	NS	ZO	ZO
NM	NB	NB	NM	NS	NS	ZO	ZO
NS	NB	NM	NS	NS	ZO	PS	PS
ZO	NM	NM	NS	ZO	PS	PM	PM
PS	NM	NS	ZO	PS	PS	PM	PB
PM	ZO	ZO	PS	PS	PM	PB	PB
PB	ZO	ZO	PS	PM	PM	PB	PB

Fuzzy correction of differential link:

ΔK_D can predict the imminent large error change of the electromagnetic clutch excitation current. The selection of ΔK_D requires comprehensive consideration of the proportional link and the integral link. If the value of ΔK_D is too small, the system response time will increase, braking will be slow, and overshoot and oscillation will occur. Therefore, if the value of ΔK_D is increased, the stability and response speed of the system can be improved and the overshoot will be reduced. If the value is too large, the anti-interference ability of the system will be weakened. In the two intervals of I and V, when the electromagnetic clutch excitation current error is at the beginning to decrease, ΔK_D needs to be increased appropriately; when the actual current is close to the expected current, the system response is sensitive, and the ΔK_D should be stabilized at a small value; When the current is stable, ΔK_D can be appropriately reduced to avoid slow initial braking of the system. In the II interval, when the error e is in the initial increasing stage, ΔK_D should be appropriate to make the actual current close to the expected value. In the interval of III and IV, the value of ΔK_D should be comprehensively judged according to ΔK_I and ΔK_I, which can be implemented according to the fuzzy rules of ΔK_D. The time-varying nonlinearity of electromagnetic clutches is pointed out in [30]. According to the non-linear characteristic of electromagnetic clutch time-varying, the ΔK_D correction rule is formulated. The specific correction rule of ΔK_D is shown in Table 4.

Table 4

ΔK_D Fuzzy Rule Table

ec\ΔK_D\e	NB	NM	NS	ZO	PS	PM	PB
NB	PS	NS	NB	NB	NB	NM	PS
NM	PS	NS	NB	NM	NM	NS	ZO
NS	ZO	NS	NM	NM	NS	NS	ZO
ZO	ZO	NS	NS	NS	NS	NS	ZO
PS	ZO	ZO	ZO	ZO	ZO	ZO	ZO
PM	PB	NS	PS	PS	PS	PS	PB
PB	PB	PM	PM	PM	PS	PS	PB

The initial parameters of the PID can be obtained by trial and error, and the specific values of the parameters can be obtained by real-time tuning of the system. [31] proposed a nonlinear fuzzy PID controller that used the center of gravity defuzzification, and this paper also used this method to realize the defuzzification. At K time, the three PID parameters are: $K_{P} = K_{P} + Δ K_{P}$ (13) $K_{I} = K_{I} + Δ K_{I}$ (14) $K_{D} = K_{D} + Δ K_{D}$ (15)

Through the above equations, the various parameters of PID at time K can be calculated, then the control quantity Δμ (k) of the controlled object can be expressed as: $\begin{matrix} Δ μ (k) = K_{P} (k) [e (k) - e (k - 1)] \\ + K_{I} (k) e (k) \\ + K_{D} (k) [e (k) - 2 e (k - 1) - 2 e (k - 2)] \end{matrix}$ (16)

4.3 Fuzzy reasoning and defuzzification

This system has two input variables, each of which has 7 fuzzy subsets, so 49 fuzzy rules are designed. The form of the fuzzy conditional statement is as follows:

if (e is NB) and (ec is NB) then (K_P is PB) (K_I is NB) (K_D is PS)

if (e is NB) and (ec is NM) then (K_P is PB) (K_I is NB) (K_D is NS) ⋯⋯

if (e is PB) and (ec is PB) then (K_P is NB) (K_I is PB) (K_D is PB)

After formulating the fuzzy rules, this paper uses the “ General Fuzzy Min-Max “ method to sum up the fuzzy rules to complete the fuzzy calculation.

Taking ΔK_P as an example, the fuzzy relationship established by e, ec and ΔK_P is R, then: $R = \cup A_{i} \times B_{i} \times C_{i}$ (17)

In Equation (7), “×” represents the Cartesian product, and the membership function of the fuzzy relationship is: $μ_{R} (abc) = \begin{matrix} n \\ \lor \\ i = 1 \end{matrix} μ_{A_{i}} (a) \land μ_{B_{i}} (b) \land μ_{C_{i}} (c)$ (18)

Among them, ∀a ∈ A, ∀ b ∈ B, ∀ c ∈ C; A, B, and C are the discourse domains of e, ec, and ΔK_P, respectively. If a = a₀, b = b₀, then ΔK_P can be given by: $Δ K_{P} = (A \times B) \circ R$ (19)

In the above equation, “∘” means composite operation. The proportional control amount of the controlled object which called μ_{ΔK_P} (c) can be expressed as: $\begin{matrix} μ_{Δ K_{P}} (c) = \lor_{a \in Ab \in B} μ_{A} (a_{0}) \land μ_{B} (b_{0}) \land \\ μ_{C} (c_{0}) \land μ_{R} (a, b, c) \end{matrix}$ (20)

In this paper, the defuzzification method adopts the center-of-gravity method. The calculation equation is: $u = \frac{\int_{\min}^{\max} x μ (x) dx}{\int_{\min}^{\max} μ (x) dx}$ (21)

In the equation, u is the output of defuzzification; x is the output variable; μ is the membership function of the fuzzy set; min and max are the upper and lower limits of defuzzification in equation (20).

4.4 Fuzzy PID parameter tuning

During the operation of the system, the actual excitation current of the clutch coil is collected by the current sensor, combined with the expected excitation current value to calculate e (k), and then ec (k) is obtained by the calculation equation of the deviation change rate, and then enters the fuzzy control PID controller to obtain PID parameters setting values K_P, K_I, K_D. The parameter setting process is shown in Fig. 9.

Fig. 9

Fuzzy PID parameter tuning process.

It can be seen from Fig. 9 that the adjustment and control of the excitation current need to be developed from two aspects: current acquisition and duty cycle modulation. In this paper, the data collected by the closed-loop Hall current sensor is converted into a voltage signal of no more than 3.3V through a sampling resistor and sent to the main controller. The main controller obtains the excitation current of the electromagnetic clutch coil through conversion calculation.

In order to verify the control effect of the fuzzy PID controller in the electromagnetic clutch current regulation system, Matlab software was used to simulate the control effect of the traditional PID controller and the control effect of the fuzzy PID controller, and the control results were analyzed and compared. The simulation model of the current regulation system is shown in Fig. 10.

Fig. 10

Simulink simulation.

Figure 10 (b) is a fuzzy adaptive PID control simulation model. Compared with the traditional PID simulation model in Fig. 10 (a), it adds a two-input three-output fuzzy controller. The three share gain feedback is changed to five share gain feedback in the gate signal control of the IGBT drive. In the fuzzy adaptive PID simulation model, the excitation current output by the system first passes a time delay, and then the two input parameters e(k) and ec(k) required by the fuzzy PID are calculated, and then processed by the fuzzy PID controller module get the three parameters K_P, K_I, K_D used to control the brake. Figure 10 (c) is the internal diagram of the fuzzy adaptive PID controller module package. The initial parameters of the fuzzy PID controller in this module, K_P is 80, K_I is 20, and K_D is 0.0002. The specific process of fuzzy PID parameter tuning is shown in Fig. 9.

After building the simulation model, select the ode23tb algorithm, and set the initial simulation time to 0s to obtain the response curves of the coil current and voltage when the electromagnetic clutch is working under the traditional PID control and fuzzy PID control. As shown in Fig. 11. Since this control system needs to control three electromagnetic clutches and one electromagnetic brake, the principles are exactly the same, and the output control high voltage is different. Therefore, this section only simulates the voltage and current of one of the main clutches.

Fig. 11

Electromagnetic clutch response curve.

As shown in Fig. 11(a), under traditional PID control, the time it takes for the excitation current to rise to the maximum value and reach a stable value is about 45ms, and the current fluctuates more when the excitation current of the coil reaches the desired value. However, in Fig. 11(b), under the fuzzy PID control of the electromagnetic clutch, the time required for the excitation current to rise to the maximum value and reach a stable value is about ten milliseconds or so, and the output curves of voltage and current are More stable, smaller overshoot and higher accuracy. Therefore, through the above comparison, it can be determined that the braking effect of the system under fuzzy PID control is better.

For the electromagnetic clutch, it has been modeled and simulated to prove that the output torque is proportional to the current, that is, the faster the excitation current increases, the faster the pull-in speed is, and the output torque reaches a stable value. The faster the speed, the better the braking effect when the loom is braking, so as to improve the braking quality [31].

5 Test verification and result analysis

After the various functional modules of the hardware platform were tested, we debugged the hardware platform on the spot, and then conducted multiple parking experiments and collected the actual parking angle of the spindle. The parking experiment mainly includes the positioning parking experiment and the emergency parking experiment.

5.1 High voltage action time debugging

The electromagnetic clutch of the controlled object of the system requires the system to output high pressure to achieve pull-in. If the high-pressure action time is too short, the clutch cannot be pulled-in. If the high-pressure action time is too long, the electromagnetic clutch coil will be burned. In this paper, by collecting data on the downtime and high-pressure action time of the loom, the corresponding curve is obtained. The relationship curve between the downtime and the high-pressure action time is shown in Fig. 12.

Fig. 12

Relationship between downtime and high voltage action time.

As shown in Fig. 12, there is a certain hysteresis for the electromagnetic clutch to pull in. During the high-voltage debugging, the clutch did not pull in for the first 15ms, so the data on the time spent in stopping is collected only after 15ms. The longer the high-voltage action time, the shorter the time required for the loom to stop. If the high-voltage action time exceeds 45ms, the time value of the loom stopping will hardly change. When the high-voltage action time is 45ms, the electromagnetic clutch does not get hot. Field experiments show that if the high-voltage is applied for too long, the electromagnetic clutch will have heating problems. In order to ensure that the electromagnetic clutch can be closed and the coil is not burnt out, this paper has collected and analyzed data from hundreds of high-voltage action time experiments, and finally set the high-voltage action time to 45ms.

5.2 Parking process analysis

The parking experiment is carried out on the industrial site, and the spindle speed data collected by the encoder during the braking process is sent to the braking and clutch control system through the main control system, and the curve of the speed change with time is obtained. As shown in Fig. 13, the first scheme is a control scheme that the output high voltage of the control system gradually drops to low pressure, and the algorithm is used to adjust the excitation current in real time, and the second scheme is a control scheme without current adjustment.

Fig. 13

Spindle brake process speed curve.

It can be seen from Fig. 13 that the electromagnetic brake has a hysteresis of about 15ms. During this period of time, the electromagnetic brake has no output torque, and the speed of the loom’s main shaft changes very little. From 15ms to 30ms, the brakes are gradually engaged. During this period, the output torque of the clutch and brake changes slowly, so the spindle speed changes relatively smoothly in the two schemes without major fluctuations. Starting from 30ms, the brakes are fully engaged, and the difference in the control effect of the two schemes begins to be obvious. For the second scheme, since the excitation current cannot be adjusted in real time, the output torque is uncontrollable. The output torque will increase to the maximum as the excitation current increases. At this time, the spindle speed is still at a relatively large value. Under the action of torque, the spindle speed will drop rapidly, which cannot achieve smooth speed reduction, and it is easy to cause the spindle to shake. For scheme 1, in the braking process, the duty cycle modulation is used to realize the continuous adjustment of the voltage, and the fuzzy PID algorithm is used to adjust the excitation current in real time. When the excitation current changes greatly, the excitation current is adjusted in real time by the algorithm. The adjustment of the output torque ensures that the output torque can change steadily after the brake is engaged, so that the spindle can ensure a smooth decrease in the speed when the speed value is large and the torque gradually increases.

Therefore, compared with the second solution, the rotation speed of the first solution drops more smoothly, which can effectively avoid the spindle shaking due to the too fast speed change during the braking process.

5.3 On-site parking angle collection

When the latitude and longitude is broken, the parking angle is collected when the spindle is positioned and stopped, and the collected spindle parking angle data is sent to the upper computer for display on the touch screen. At the same time, the upper computer saves the historical data as a.CSV file,.CSV The file contains the actual stopping angle of the loom when the spindle speed is within the range of 450rad/min–500rad/min at different times. In the two positioning parking situations, the touch screen displays the spindle parking angle offset. One hundred sets of data were collected for the two parking processes on site. Due to the large amount of historical data, only part of the data is shown in the attached drawings. The data of the broken weft parking are shown in Table 5 and Table 6. Figure 14 is the data diagram of the angle offset of the spindle when the weft is broken.

Table 5
The first ten sets of data to stop the weft

Number Speed Parking corner Offset Parking time

1 500 39 –6 08 : 33 : 29

2 500 50 5 08 : 40 : 41

3 500 37 –8 08 : 49 : 33

4 500 41 –4 08 : 57 : 42

5 500 52 7 09 : 16 : 41

6 500 53 8 09 : 29 : 19

7 500 49 4 09 : 36 : 57

8 500 52 7 09 : 49 : 37

9 500 36 –9 10 : 01 : 07

10 500 38 –7 10 : 19 : 11

Number	Speed	Parking corner	Offset	Parking time
1	500	39	–6	08 : 33 : 29
2	500	50	5	08 : 40 : 41
3	500	37	–8	08 : 49 : 33
4	500	41	–4	08 : 57 : 42
5	500	52	7	09 : 16 : 41
6	500	53	8	09 : 29 : 19
7	500	49	4	09 : 36 : 57
8	500	52	7	09 : 49 : 37
9	500	36	–9	10 : 01 : 07
10	500	38	–7	10 : 19 : 11

Table 6

The last ten sets of data to stop the weft

Number	Speed	Parking corner	Offset	Parking time
91	500	45	0	13 : 41 : 20
92	500	51	6	13 : 50 : 04
93	500	47	2	13 : 53 : 16
94	500	53	8	14 : 01 : 24
95	500	52	7	14 : 10 : 47
96	500	53	8	14 : 13 : 36
97	500	54	9	14 : 32 : 53
98	500	40	–5	14 : 44 : 41
99	500	36	–9	14 : 52 : 02
100	500	39	–6	15 : 00 : 53

Fig. 14

Data diagram of spindle angle offset during weft stop.

As shown in Fig. 14, if the loom has a weft break and needs to be stopped, the loom’s main shaft will stop in the range of 35° to 55°, and the slip cannot be reached to zero. There are two main reasons for the amount of slip. First of all, the external voltage that controls the three-phase asynchronous motor is sometimes unstable, causing the actual speed of the loom’s main shaft to deviate from the theoretical value. At the same time, the vibration of the motor itself also has a certain impact on the main shaft speed; secondly, the loom positioning brake When the loom mechanism has its own kinematic inertia during operation, the dynamic load loaded on the main shaft changes irregularly. Therefore, the equivalent moment of inertia on the main shaft during the rotation also changes with the change of the main shaft angle. It has a certain impact on the parking accuracy of the spindle.

When the slip is within the range of 10°, it meets the system accuracy index and does not affect the quality of textile processing products. In the actual weaving process, there are dozens of times a day for fault location and stop of broken warp and weft. This control system can realize that no angle search is required when driving again, which directly improves the efficiency of textile processing and the quality of fabrics.

6 Conclusion

This paper studies the brake and clutch system of high-speed rapier looms, analyzes the internal structure, magnetic circuit, and dynamic characteristics of the electromagnetic brake, and lists the mathematical model of the brake system. We found that the electromagnetic clutch of the brake system has a certain time lag. Adjusting the excitation current of the brake system can change the main shaft angle of the loom when it stops. Therefore, it is proposed to achieve accurate parking angle positioning by braking in advance and adjusting the excitation current. The advance time of the braking action is determined by calculating the angle that the spindle has rotated during the lag time, and the real-time adjustment of the excitation current of the braking system is controlled by a suitable algorithm to achieve faster and accurate braking angle positioning. In addition, it analyzed the remote control requirements of the brake system, combined with cloud platform technology to build a complete brake control and analysis system for the loom, realized real-time monitoring and fault analysis and even prediction of brake system data, making the control function of brake system more completed.

The algorithm for calculating the regulation value of the excitation current of the system uses the fuzzy PID algorithm. The rule base of fuzzy control theory is established through expert knowledge, and finally, the center of gravity method is used for defuzzification. The simulation and experiment show the applicability of the fuzzy PID algorithm in the brake control system of the loom. To explain the control effect better, we use simulation to compare the traditional PID controller and the fuzzy PID controller. The simulation results show that the fuzzy PID controller designed in this paper can improve the dynamic response of the system effectively, reduce the overshoot and improve the accuracy. The designed control system was tested on an industrial field loom. The experiment showed that the controller can achieve more precise control of the brake spindle angle of the loom. The spindle slip is reduced from 20° to less than 10°. The response speed is faster and the braking time is shorter.

The control method proposed in this paper improves the positioning accuracy and dynamic response of the brake system. However, due to the limited time and experimental conditions, the system still has certain problems. For example, there are many electromagnetic interference sources in the industrial field, which will affect the stability of the system. The electromagnetic compatibility needs to be paid attention to in the future.

It is hoped that this research can provide some references in engineering for the scholars who design the precise brake system for high-speed looms and the scholars who design the fuzzy PID controller. When developing controllers for some systems with non-linear parameters, strong time-varying parameters, and difficult to establish precise mathematical models, the fuzzy control method used in this article can be used. People’s manual control experience is described in words to form control rules so that the designed controller can simulate the way of thinking of people, obtain better control accuracy, smaller overshoot, and thus achieve better control effects.

References

Zeng

, Research on the Scheme of Eliminating Sparse and Dense Roads, MA thesis, Donghua University, 2004.

Choogin

V.V.

, Bandara

, Chepelyuk

E.V.

, 9 – Weaving machine drives: mechanisms and types, in Mechanisms of Flat Weaving Technology : Woodhead Publishing, 2013, pp. 145–a2.

Matsuyama

, Tomigashi

, Yoshimoto

, Inoue

and Morimoto

, Discretization Error Compensation Method in High-Speed Motor Drive System by using Direct Torque Control, Electrical Engineering in Japan 201(4) (2017), 45–54.

Biček

, Pepelnjak

and Pušavec

, Production aspect of direct drive in-wheel motors, Procedia CIRP 81 (2019), 1278–1283.

Steinberger

, Rehrl

, Kirchengast

, Reichhartinger

and Laimgruber

, Observer design for an electromagnetically actuated dry clutch, IFAC PapersOnLine 48(11) (2015), 53–58.

Yang

, Design of an electric vehicle electromagnetic clutch and its controller, master, Beijing Jiaotong University, 2018.

Precup

R.E.

and Hellendoorn

, A survey on industrial applications of fuzzy control, Computers in Industry 62(3) (2011), 213–226.

Vichuzhanin

, Realization of a fuzzy controller with fuzzy dynamic correction, Central European Journal of Engineering 2(3) (2012), 392–398.

Xiaodan

and Cinan

, Design and Simulation of Improved Fuzzy Neural Network PID Controller, Journal of Data Acquisition and Processing 36(02) (2021), 365–373.

10.

Weiwei

and Tongxiang

, Compound control strategy based on fuzzy neural network PID, Instrumentation 28(01) (2021), 90–93.

11.

Lu, Xiangyang et al., Intelligent Rail Lubrication System Based on Fuzzy Group Analysis, 1 Jan. 2021, 1137–1146.

12.

Childs

P.R.N.

, 8 – Clutches and Brakes, in Mechanical Design (Third Edition), P.R.N. Childs, Ed. Butterworth-Heinemann, 2021, pp. 289–336.

13.

, Permanent Magnet-Electromagnetic Clutch Magnetic Field Analysis and Characteristic Research, master, Hefei University of Technology, 2008.

14.

and Wang

, Application of electromagnetic clutch brake for flexible rapier loom, Textile Accessories 47(06) (2020), 41–44.

15.

, Cui

and Lu

, Analysis of dynamic characteristics of a high-speed electromagnetic brake during braking, Transactions of China Electrotechnical Society (08) (2007), 131–135.

16.

Guangzheng

and Xiuying

, Numerical calculation of engineering electromagnetic field, Machinery Industry Press, 2010.

17.

Yasa

, Sincar

, Ertugrul

B.T.

and Mese

, A multidisciplinary design approach for electromagnetic brakes, Electric Power Systems Research 141 (2016), 165–178.

18.

Huo

, Research on Unmanned Ship Control System Based on Fuzzy PID, Journal of Physics: Conference Series 1852(2) (2021), 022066.

19.

Elhosseini

M.A.

, et al., Heat Recovery Steam Generator (Hrsg) Three-Element Drum Level Control Utilizing Fractional Order Pid and Fuzzy Controllers, ISA Transactions, 2021. doi:https://doi.org/10.1016/j.isatra.2021.04.035.

20.

Jalali

, Razmi

and Doagou-Mojarrad

, Optimized fuzzy self-tuning PID controller design based on Tribe-DE optimization algorithm and rule weight adjustment method for load frequency control of interconnected multi-area power systems, Applied Soft Computing 93 (2020), 106424.

21.

Claudia-Adina

, Radu-Emil

, Marius

, Stefan

, Emil

and and

, R.M.-Bogdan, An Approach to Fuzzy Modeling of Electromagnetic Actuated Clutch Systems, International Journal of Computers Communications & Control (3) (2013), 395–406.

22.

Kirchengast

, Steinberger

, Laimgruber

, Prix

and Horn

, Identification and Position Control of an Electromagnetic Clutch Actuator, IFAC-PapersOnLine 48(11) (2015), 59–64.

23.

Kumar

and Goyal

, On cloud security requirements, threats, vulnerabilities and countermeasures: A survey, Computer Science Review 33 (2019), 1–48.

24.

M.S.M, Wireless Networks Technology and Cybersecurity. Mercury Learning & Information, 2020.

25.

Turc

, AJAX Technology for Internet of Things, Procedia Manufacturing 32 (2019), 613–618.

26.

Gao

, Gao

, Li

, Lin

and Wu

, Design and experiment of tea charcoal roasting machine based on fuzzy PID control, Food & Machinery 37(03) (2021), 96–101.

27.

Wang

, Zhang

, Zhou

and Yan

, Simulation Research on Fuzzy Control of Steam Temperature of Lignite Boiler, Journal of Engineering Thermophysics 38(01) (2017), 27–32.

28.

Wang

, Chen

, Yang

and Li

, Research on Control Algorithm of Air Pressure Simulation System Based on Fuzzy PID Iterative Learning, China Measurement & Test 47(04) (2021), 77–82+112.

29.

Sain

and Mohan

B.M.

, A simple approach to mathematical modelling of integer order and fractional order fuzzy PID controllers using one-dimensional input space and their experimental realization, Journal of the Franklin Institute 358(7) (2021), 3726–3756.

30.

Bojan-Dragos

C.A.

, Precup

R.E.

, Preitl

, Roman

R.C.

, Hedrea

E.L.

and Szedlak-Stinean

A.I.

, GWO-Based Optimal Tuning of Type-1 and Type-2 Fuzzy Controllers for Electromagnetic Actuated Clutch Systems, IFAC-PapersOnLine 54(4) (2021), 189–194.

31.

Sain

and Mohan

B.M.

, Modeling, simulation and experimental realization of a new nonlinear fuzzy PID controller using Center of Gravity defuzzification, ISA Transactions 110 (2021), 319–327.