Physical modelling and control of lateral web position for wallpaper making processes

https://doi.org/10.1016/j.conengprac.2004.02.014Get rights and content

Abstract

This paper presents a modelling and control algorithm for the lateral movement of web using a pivoting guider, where an accurate lateral positioning is important for web conveyor systems so as to achieve a high productivity and improve the product quality. The process considered is the hot embosser for the polyvinyl chloride-based materials where a steering guide is used for the in-register embossing. A new theoretical model is developed by regarding a moving web as a beam with a very small, but finite thickness. This leads to a transfer function that has four complex poles and two zeros with a time delay. This model has been validated through real experiments. The design of a Smith predictive control scheme has been made that shows, from a number of real-time applications, a high potential in speeding up the response of the pivoting guider and reducing the lateral variations of the moving web.

Introduction

The wallpaper industry converts a unique natural resource into everyday consumer products. The conversion processes are, in general, continuous and exhibit a complicated dynamical behaviour. Indeed, the environmental requirements, product quality and competitive pressures have increased the needs for better process management practices, including advanced process control implementations such as improved control systems for web transports. A ‘web’ is defined as a very long but thin, continuous sheet of flexible material. This definition includes materials processed in a web form by various industries, such as papers, metal strips, metal foils, plastic films, woven and not-woven fabrics, etc. Most of the products used today have as their origins a web form. Examples include all forms of paper, coated plastic wraps for food items, electronic storage media such as floppy disks, all forms of fabrics including steel strips used for automobile bodies and appliances. The moving of materials in the web form is called web handling.

As a web is being processed, it is conveyed through a system of rollers that supply support, transport and control. Ideally, the motion of the web should be only in the longitudinal direction (i.e., in the machine direction). However, this is not the case for many real web conveyance systems due to unexpected roller's misalignment and lateral disturbances. An added difficulty is that the variations of web physical properties can also result in its lateral movements. As this lateral motion causes an inferior product quality, it is important to model and control the lateral positioning of the web so as to minimise the lateral movements.

In web handling, the lateral web position at a certain location is often pre-specified. To keep a moving web at its desired position, guiding devices are required to effectively control the lateral web position. In order to make the control accurate and stable, the dynamics of lateral web motion should be well understood.

Fig. 1 shows a web handling process, where the entering span is the free span of web immediately before the first shifting roller of a guide assembly. The exiting span is the free span of web between the last roller on a guide assembly and the next roller or rewind roll. The entering roller is the roller located just before the entering span, and after the pre-entering span, which is the free span of web just previous to the entering roller. The wrap angle of a roller is the angle between the ingoing and outgoing tangent of a web on a roller, or equivalently, the angle the web deflects as it goes over a roller.

This paper is focused on the interaction between the intermediate guiding and the lateral web movement. An intermediate guide can be classified as a steering guide or a displacement guide, as shown in Fig. 2. When the steering guide roller moves at an angle from the entering roller, it displaces the web with a large bending angle. The displacement guide roller consists of two parallel rollers. When these rollers move and form an angle with the entering roller, they displace the web with a small bending angle. The advantage of using a displacement guide is that the entering span can be relatively short as there is a less severe web distortion in the entering span. However, the expensive structure of a displacement guide discourages its usage. As the model in this paper only applies to steering guides, the word ‘guider’ will always be used to refer to a steering guider.

Research into the establishment of models that can describe lateral web dynamics can be backdated to the early work of Campbell (1958), where the model was derived based on the assumption that the web behaves like a string that is subjected to sharp brakes at every roller. This basic assumption led to an inaccurate first-order model. To improve this model, Shelton and Reid (1971) developed a second-order model by assuming the web as an Euler beam. Young and Reid (1993) further summarised the formulation of the lateral movements by a set of partial differential equations without considering the line mass density, where a historical perspective on longitudinal dynamics and control was also discussed. In parallel to these developments, practical approaches to the problem have also been investigated. For example, Erhardt and Leimer 1990, Erhardt and Leimer 1991 presented a wide range of tailor-made guiding systems for convey belts. A consequence of this development is that most web handling systems use a PID controller with control gains determined by a set of trail and error methods. In this context, the PID controllers used on the machines do not take advantage of any model-based control design methods. Sorsen (1996) analysed an end-pivoted steering guide system, but incorrectly specified the transfer function that governs the response of the web to the position of the guide roller as a simple integration rather than a first-order dynamics with a time lag.

The purpose of this research is to investigate an effective modelling and control strategy for the wall paper making processes where a guiding is required so as to improve the lateral position control of the process under consideration by using a pivoting guider.

Section snippets

Process description

The printing of wallpaper is carried out by a set of gravure printing presses. From there on, the printed paper is ready to go through the hot embossing process. A simple example of embossing is to stamp an address on a notepaper. The embosser consists of two rollers and on one of them the required pattern is raised. Between the two rollers the paper is drawn and stretched under an applied pressure. The quality of the paper and its thickness has to be accurately related to the degree of the

Physical modelling

In this section, an attempt is made to physically model the lateral and longitudinal dynamics of a moving web. The main purpose is to use possible theoretical models to improve the control of the current embosser register. The mechanical properties of a web used in this paper are tabulated in the appendix (Table 2). Since there is a short distance between the exit guider and the sensor head as shown in Fig. 6, there is a small time delay between the input and the output of the system. However,

First-order approximation model

The model in Section 3 can be further simplified and in this section a first-order approximation model will be formulated. Indeed, the time factor indicates that the web system vibrates at one or more of its natural frequencies, which are related to the properties of the dynamical system established by its mass and stiffness. A lower bound on natural frequency can be calculated by considering a perfectly flexible string stretched between two points x=0 and l with a uniform tension T. Using the

Control of lateral web position

In a guiding process, it is important to hold the lateral web position on a pre-specified location r. The process of holding the system output close to the reference is generally referred to as regulation.

Conclusions

In this paper, a physical modelling for the lateral position system of a wallpaper machine is developed. The model is obtained by taking the moving web as a beam supported by two points, where the Hamilton's principle has been used to produce a set of partial differential equations that characterise the dynamic behaviour of the system. Using the data from the real machine, a fourth-order transfer function model is obtained and validated against the real system response. An alternative control

Acknowledgements

The work reported here was funded jointly by Emerson & Renwick Ltd and European Social Fund (ESF). This is gratefully acknowledged.

References (16)

  • Campbell, D. P. (1958). Process control (pp. 113–156). New York:...
  • F. Charlton

    Textbook of dynamics

    (1986)
  • D.A. Daly

    Factors controlling traction between webs and their carrying rolls

    Tappi Journal

    (1965)
  • D. Erhardt et al.

    Pivoting roller guider for conveyor belts

    International Textile Bulletin, Dyeing/Printing/Finishing

    (1990)
  • D. Erhardt et al.

    Web guider for accurate control of conveyor belts

    International Textile Bulletin, Dyeing/Printing/Finishing

    (1991)
  • J.M. Gere et al.

    Mechanics of materials

    (1990)
  • T. Kenjo et al.

    Stepping motors and their microprocessor controls

    (1994)
  • J.S. Rao

    Advanced theory of vibrations

    (1982)
There are more references available in the full text version of this article.

Cited by (13)

  • Dynamics modeling and deviation control of the composites winding system

    2017, Mechatronics
    Citation Excerpt :

    A dynamic matrix controller is designed in [9] to rectify the deviation, which doesn't need the mathematical model. A mathematical model is established in [10] for the moving tape and a novel controller with Smith prediction is proposed to eliminate influence of the nonlinearities and uncertainties. In [11], a fuzzy controller is designed to rectify deviation of the moving tape.

  • Dynamics of axially moving continua

    2014, International Journal of Mechanical Sciences
    Citation Excerpt :

    In addition, modeling and control of multiple web spans is studied in [79]. Using the date from the real wallpaper machine, the mathematical model is obtained and validated against the real system response in [70]. To facilitate the Lyapunov analysis for the vibration regulation in [54], a control strategy for an axially moving web system is presented.

  • Theories and Control Technologies for Web Handling in the Roll-to-Roll Manufacturing Process

    2020, International Journal of Precision Engineering and Manufacturing - Green Technology
View all citing articles on Scopus
View full text