Tension Control for High Quality Take-up of Yarn Transport Machine

Ulugbek R. Umirov, Seong Hyun Jung, Chang Wook Han, Jung Il Park

School of Electrical Engineering and Computer Science Yeungnam University, Gyeongsan, 712-749, Korea

ulugbek.umirov@gmail.com, jipark@yu.ac.kr

Abstract – Although researchers have studied dynamics of the spinning yarn balloon for over hundred years, tension control for this system due to its complexity has only recently been addressed. Tension control of a ballooning yarn has the potential to improve productivity of unwinding process. The Active Disturbance Rejection Control (ADRC) method was introduced for yarn tension regulation. This actively compensates the dynamic changes of the system and the unpredictable external disturbances. Experiment results show the effectiveness of the proposed method under dynamic variations of plant.

1. Introduction

Yarns are fundamental for production of many consumer and industrial textiles. During their manufacture and subsequent use, they are transported from one cylindrical package (bobbins, cones included) to another in order to either improve their quality performance characteristics(evenness, texture, strength integrity) or improve performance of the subsequent processing steps (e.g. warping, weaving). In a number of these situations, the optimal mechanism(high speed and productivity) to accomplish the task is over-end unwinding. However, in case of high transport speed, balloon is formed by spinning yarn between package and guide-eye, causing nonlinearity in yarn tension, which even can cause breakage of yarn. Because of importance of tension problem, it has drawn the attention of many researchers. Main problem is the establishment of a proper mathematical model. A comprehensive investigation of the dynamics of over-end unwinding has been reported by Padfield [1] and subsequently Kothari and Leaf [2] reported extensive numerical calculation based on Padfield’s analyses. Other researchers like Goswami [3] continued investigations of nonlinear dynamics of over-end unwinding, but there is still no exact mathematical model of this process and even in case of simplified mathematical model, its parameters are quite dependent on many conditions.

Thus dynamics of the spinning yarn balloon has been investigated for a long time, however its control has only recently been addressed, due to complex model and number of uncertainties in the process. It’s obvious, that proportional-integral-derivative (PID) control strategy, usually used in industry, is not applicable here, ‘cause of lot of variable parameters. Tension in over-end unwinding process depends on a lot of parameters, like transport speed, modulus of

elasticity of yarn, package winding density. It could be possible to use PID controller with variable gains for this problem, but for better performance we need to derive more or less accurate model of process, what by itself is not simple problem. And also in case of PID controller we would need to have input of transport speed, what is not always possible, especially in case of developing stand-alone controller. So we need another strategy to control yarn tension, which could be able to adjust plant model automatically, thus having ability to estimate and reject disturbances.

One of such strategies is using the active disturbance rejection control (ADRC) concept proposed by Y. Hou [4] for yarn tension control. According to this concept, the disturbances are estimated using an extended state observer (ESO) and compensated during each sampling period. The ADRC control system consists of the ESO and a nonlinear PD controller. It is designed without an explicit mathematical model of the plant. The controller is designed to be intrinsically robust against plant variations. Once it is set up for a class of problems within a predetermined range of variation in system variables, no tuning is needed for start up, or to compensate for changes in the system dynamics and disturbance. This method, because of its robustness and disturbance rejection capabilities, is particularly suitable for yarn tension regulation applications.

This research is motivated by the complex control problem, encountered in yarn twisting equipment. It is necessary to provide equal fixed tension for each of twisting yarns, which tensions are variable due to the reasons described above. Our goal is to modify existing mechanical-only tension control device in order to provide desired tension.

2. The Yarn Tension Regulation Problem

Processing line for single yarn is shown in Figure 1. Yarn unwinds from the package, passes through guide-eye and tension control device, and finally winds up to spool. In order to provide desired tension, yarn tension control device (dancer) is usually used. It includes first and second plate members having adjacent inner faces positioned on opposite sides of the running yarn with one of the plate members being resiliently urged toward the other plate member and in engagement with one side of the running yarn to thereby apply tension to the running yarn passing

therebetween. The inner faces of both plates are substantially smooth and flat.

Figure 1: Experimental yarn transport system

Structure of dancer is shown in Figure 2a. To adjust

tension, different weight load is applied. We proposed to use control input instead of weight load, as shown in Figure 2b, so that there is no need for manual adjusting of load.

a b

Figure 2: Tension control device: (a) conventional; (b) modified – instead of load, control input is applied

We define as plant part of the system shown in Figure 3. It includes path of yarn from unwinding point to the sensor position. As stated above, there is no explicit mathematical model of tension during over-end unwinding process, so we have to estimate inner model of the plant during process. It was experimentally verified that it is acceptable to represent plant as second-order system.

Plantu

oT

Control BoardrT

Sensor

Motor

Figure 3: Schematic diagram of yarn transport system

Most recently derived formulae for yarn tension in balloon is given by

( ){ } FVRRkkRkR ++=××+×+ ')''(2 200

2 TDDm ωω (1) where: ( ) ( ) s∂∂= /' ; and ),( tsT is the tension in the yarn. More on eq. (1) and its parameters can be found at [5]. We are interested in order of that equation. It is second order, so it is possible to estimate plant as second-order system.

Thus we can write tension dynamics as buwyytfy += ),,,( &&& (2)

where, y is tension, u is motor control input, and w is disturbance. Here, ),,,( wyytf & is generally a time-varying nonlinear function that represents the true system dynamics. The difficulty in tension control is mainly due to the fact that the function ),,,( wyytf & changes significantly during operation. Thus, self-adapting control method is needed for that kind of problem.

3. The Active Disturbance Rejection Controller (by Hou [4])

The fundamental idea of ADRC is that in order to formulate a robust control strategy, one should start with the original problem in eq. (2), not its linear approximation.

Instead of following the classic design path of modeling and linearizing ),,,( wyytf & and then designing a linear controller, the ADRC approach seeks to actively compensate for the unknown dynamics and disturbances in the time domain. This is achieved by using an extended state observer (ESO) to estimate y , dtdy and ),,,( wyytf & iteratively. Once ),,,( wyytf & is estimated, the control signal is then used to actively compensate for its effect and reduce eq. (2) to a double integration, which in turn becomes a relatively simple control problem. A brief introduction of this novel control concept is given below.

3.1 The Extended State Observer (ESO) In order to estimate ),,,( wyytf & without knowing its

analytical form, the plant in eq. (2) is augmented as

==

=+==

1

3

21332

21

)(),,,()(,

xythx

wxxtftxbuxxxx

&

&

&

(3)

where, )(th is the derivative of ),,,( wyytf & and is unknown. The reason for increasing the order of the plant is to make

),,,( wyytf & a state set such that a state observer can be used to estimate it. One such observer is given as

−−=+−−=

−−=

),),((),),((

),),((

331033

02210232

1110121

δαβδαβ

δαβ

tyzfalzubtyzfalzz

tyzfalzz

&

&

&

(4)

where, 01β , 02β and 03β are observer gains, 0b is normal value of b and )(⋅fal is defined as

≤

>=

−1 δεδ

εδεεε

δαεα

α

,

,)(),,(

signfal (5)

This observer is denoted as the extended state observer (ESO) and is the corner stone of the ADRC method.

Nonlinear function in eq. (5) is derived heuristically by Hou [4] to make observer more efficient.

3.2 The Control Law

Profile Generator

Nonlinear PD Plant

ExtendedState Observer

(ESO)

0b01 b

)(tr)(2 tv

)(1 tv

)(1 tz

)(2 tz)(3 tz

)(0 tu )(tu

)(tw

)(ty

Figure 4: Structure of the ADRC

The architecture of the ADRC is shown in Figure 4. It consists of three components: the Profile Generator which provides the desired transient trajectory for tension to follow from the initial value to the reference one; the ESO which is described above, and the control law which is defined as

030 )()()( btztutu −= (6) This control law reduces the plant to a double integration and is controlled by the nonlinear PD controller:

),,(),,()(0 DDDDPPPP falKfalKtu δαεδαε += (7) In tension control applications, 11 zvP −=ε , 22 zvD −=ε , are “tension” and “derivative of tension” error, respectively,

PK and DK are the gains of the PD controller, and )(⋅fal is the nonlinear function defined in eq. (5).

Note that the profile generator generates the desired tension trajectory, )(1 tv , and it’s derivative, )(2 tv . They are then compared to the filtered output, )(1 tz , and its derivative,

)(2 tz . Clearly, the differentiation of the error is obtained without taking the direct differentiation of the set point or the output. This makes the algorithm much less sensitive to noise in the output and discontinuities in the setpoint )(tr .

The critical component here is obviously the ESO. Its parameters need to be tuned properly for the ADRC to work. It is useful to get a rough linear model from test data of the real system, based on which the ESO parameters and feedback gains are tuned. It was discovered that once the ESO is properly set up, the performance is quite insensitive to the plant variations and disturbances.

4. Experiment

As yarn unwinds from the package, diameter of package decreases significantly. Also unwinding can take place at different rate with different type of yarns. Understandably, it poses a significant challenge for the controller to be designed for stability and performance over the entire operating range. In our case coefficients were found by trial-and-error method.

Experiment was conducted using control board based on 8051 microcontroller by Silicon Laboratories with sampling rate 500Hz. For motor control, pulse-width modulation (PWM) control signal is used. Data is transmitted to computer at 10Hz rate using serial communication. Yarn transport speed is 10m/sec; total length of transported yarn is 10km and reference tension is 14cN. Figure 5 depicts active dancer and sensor of experimental system. And there also can be seen passive dancers in the lower right corner.

Figure 5: Experimental setup – active dancer and sensor

Figure 6 shows yarn tension without control (passive

dancer with weight load, only first 2km, following 8km behavior is the same). It can be seen, that tension increases while diameter of package becomes smaller, what conforms to investigation of Goswami [3].

Figure 7 shows yarn tension with ADRC control applied. It can be seen, that variance of tension is about 2 times smaller than in case of uncontrolled tension and there is no increasing tension while operation. As far as ESO was tuned by trial-and-error, we suppose it is possible to improve performance of controller by investigating behavior of the system mathematically, especially of yarn balloon effect, so that we can define limits of plant variations and tune-up system more precisely.

0 20 40 60 80 100 120 140 160 180 20010

11

12

13

14

15

16

17

18

19

20

sec

cN

Figure 6: Yarn tension without control

0 20 40 60 80 100 120 140 160 180 20010

11

12

13

14

15

16

17

18

19

20

sec

cN

Figure 7: Yarn tension with control

Also it is possible to improve performance by using

higher sampling rates of control system. It was verified that ESO’s performance is dependent on the sampling rate. Firstly control system operated at rate 100Hz and results were worse – variance was about 1.5 times bigger than in case of 500Hz (unfortunately, due to complex calculations and ADC conversion it was impossible to set control rate higher than 500Hz).

5. Conclusions The Active Disturbance Rejection Controller (ADRC) in

digital form is applied to control yarn transport system, which is characterized by significant dynamic changes during process. Results of experiment show applicability of proposed method to yarn tension problems, even without knowledge of explicit mathematical model of plant. It is verified, that properly set up ADRC controller can deal with large range of dynamic changes, and thus we propose this is perspective solution for yarn applications.

References 1. D. G. Padfield, “The motion and tension of an unwinding

thread,” Proc. of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 245, No. 1242, (1958), pp.382-407

2. V. K. Kothari, G. A. V. Leaf, “The Unwinding of Yarns from Packages. Parts I, II and III,” Journal of Textile Institute., Vol. 5, No. 70 (1979), pp.89-172

3. B. C. Goswami, “Nonlinear Dynamics of High-Speed Transport for Staple Yarns,” National Textile Center Annual Report, November, 2002

4. Y. Hou, Z. Gao, F. Jiang, B. T. Boulter, “Active Robust Rejection Control for Web Tension Regulation,” Proc. IEEE Conference on Decision and Control, 2001, Paper No. 9

5. J. D. Clark, W. B. Fraser, D. M. Stump, “Modeling of tension in yarn package unwinding,” Journal of Engineering Mathematics, No. 40 (2001), pp.59-75