Modeling and frequency response of web tension with a pendulum dancer, and comparison of load-cell and dancer based tension control systems

In web processing lines, web tension is typically regulated using an outer loop that provides a trim to the velocity reference of the inner velocity loop. The feedback signal for the outer tension loop is either a position signal from a dancer or tension signal from load cells mounted on a roller. Both these strategies are used extensively in the web processing industry, but a systematic analysis, based on mathematical models and experimental observations, on the benefits and limitations of the strategies is lacking. The paper will report two investigations. First, a model that describes the action of a pendulum dancer on web tension will be developed, and frequency response of web tension in the presence of the pendulum dancer will be discussed. Second, a comparison of tension control strategies based on force feedback from load cells and position feedback from dancer motion will be given.Mechanical and Aerospace Engineerin

Recent advances in web longitudinal control

Stable web transport through processing machinery is critical in the web processing industry. Demands for improved performance under a wide variety of dynamic conditions and web materials are placing additional emphasis on developing new advanced control techniques. Further, technological advances in areas such as drive hardware, microprocessors, and sensors, are opening up new possibilities for implementing advanced control methods that are robust to a number of process and material variations and result in superior performance over existing industrial control methods.Mathematical models of fundamentals elements in a web process line are presented. A systematic procedure for computing the equilibrium inputs as well as reference velocities of all rollers based on the master speed reference is given. Recently developed robust control methods for web longitudinal control are described. Implementation of the controllers on two experimental platforms is given, and a sample of the experimental results is presented. Finally, some potential new directions and future research topics are discussed.Mechanical and Aerospace Engineerin

Web line resonant frequencies

The goal of this paper is to investigate the resonant frequencies of a system of idle rollers and web spans. Of particular interest is the determination of the minimum resonant frequency as a function of the number of idle rollers, web span lengths between idle rollers, web properties such as the modulus of elasticity and area of cross-section, and inertia and radius of the idle rollers. Any conclusions from the analysis that can provide insights into maximizing the minimum resonant frequency by choosing particular web paths or span lengths are of benefit to the web machine designer as well as the control system engineer. Knowledge of the minimum resonant frequency and the factors that influence it can assist the machine designer in reconfiguring web paths and/or number of idle rollers between two driven rollers such that the machine induced vibrations do not excite resonances. Further, the knowledge of the minimum resonant frequency will assist the control engineer to better select the bandwidth of the closed-loop system as well as the crossover frequency of the controller.A simple linear model that describes the dynamics of tension in a web span is considered. It is shown with experimentation on a web platform that the simple model is able to predict resonant frequencies in an idler roller system. Therefore, the simple model is used to investigate the behavior of the minimum resonant frequency as a function of the number of idle rollers and span lengths. Analytical solutions for computing the minimum resonant frequency for one idler (one idle roller and two spans) and two idler (two idle rollers and three spans) systems are given. Numerical analysis and discussions on how to maximize the minimum resonant frequency for two, three, and four idler systems are also given. An analytical approximation of the minimum resonant frequency for equal span lengths and any number of idle rollers is derived. This approximation tends to converge to the actual minimum resonant frequency with increase in the number of idle rollers. This is useful in getting a quick and reliable estimate of the minimum resonant frequency in festoons/accumulators that contain many idle rollers and equal span lengths.Mechanical and Aerospace Engineerin

Effect of compliance and backlash on the output speed of a transmission system

Backlash is one of the most commonly encountered nonlinearities in drive systems employing gears or ball-screws and indicates the play between adjacent movable parts. Presence of backlash causes delays and oscillations and consequently gives rise to inaccuracies in the position and velocity of the machine. Coupled with this, if the drive system consists of compliant members, torsional oscillations may also occur. Though the presence of backlash may not be of utmost significance in the case of a general speed controlled drive system, web handling systems stand as a unique exception to this observation; any small change in the web speed causes large changes in the controlled tension and hence tight control of speed is an essential requirement in web handling systems. Also, it is of interest to know an estimate of the accuracy of speed achievable in a given closed-loop control system. This paper addresses the effects of compliance and backlash on the output speed of the transmission system.A model to include the effects of compliance and backlash is proposed under the assumption that the collisions due to backlash are sufficiently plastic to avoid bouncing. The proposed model considers the compliance (which may be either due to the elasticity of the shafts or belt in a belt-pulley transmission system) and backlash appearing in series in a drive system. In contrast to the classical backlash model which considers both input and output to the backlash as displacements, the proposed model considers (torque) force as input to the backlash and (angular velocity) velocity of the driven member as the output of the backlash. Thus, the proposed model does not assume that the load is stationary when contact is lost due to backlash width, i.e., momentum of the load is taken into account in the proposed model.From the proposed model, a bound on the speed error due to the presence of backlash is derived. To derive the bound on speed error due to backlash, two situations are considered: (i) closed-loop speed control system with a given backlash, and (ii) the same closed-loop system with no backlash. The difference between the outputs of these two systems indicates the error caused by the backlash and represents the achievable accuracy of the closed-loop system. Closed-loop experiments were conducted on a rectilinear system to obtain the error caused by different backlash widths. The bound obtained from the experimental results agrees with the theoretically computed bound.Mechanical and Aerospace Engineerin

Decentralized Control of Large-scale Interconnected Systems with Application to Web Processing Machines

The thesis investigates decentralized control of a class of large-scale nonlinear systems, which contain unmatched, linear and nonlinear interconnections between constituent subsystems. A large experimental platform, which mimics most of the features of an industrial web process line, is used for experimentation. It is shown that decentralized control schemes can be developed for a class of unmatched large-scale systems. Sufficient conditions are developed that will result in closed-loop stability. A model reference decentralized adaptive controller is developed for systems with unmatched, linear interconnections. To circumvent the unmatched problem, a new reference model that exchanges reference information between subsystems is proposed. Improved dynamic models for unwind/rewind rolls are obtained and bsed on that accurate inertia compensation terms are computed for on-line compensation. Extensive experiments with the proposed decentralized controllers and an often used industrial decentralized PI controller show substantial reduction in web tension error with the proposed decentralized controllers.Mechanical & Aerospace Engineerin

Role of active dancers in tension control of webs

This paper investigates the role of active dancers in attenuation of web tension disturbances in a web process line. A general structure of the active dancer is considered; an input/output model is developed for analysis and controller design. Three types of control designs were investigated for the active dancer: proportional-integral-derivative controller, internal model based controller, and linear quadratic optimal controller. An open-architecture experimental platform is developed for conducting real-time control experiments using the active dancer system. Data collected from an extensive set of experiments using the three control designs validate the usefulness of the active dancers in a web process line. We present a representative sample of the experimental data in this paper.Mechanical and Aerospace Engineerin

Modeling and identification of the source of oscillations in web tension

Although there has been much work in dynamic modeling of different web handling elements and web longitudinal behavior, efforts to systematically validate models by experimentation on a web platform are non-existent. Existing literature has extensively used dynamic models for numerical analysis and/or design of control systems without adequate experimental validation of the models. One of the well-known modeling techniques for creating a model for the entire web line is based on the concept of primitive elements. In this approach every primitive element of the web line is modeled separately using first principles approach, and then the entire web line model is obtained by appropriately combining the primitive element models. The goal of this paper is to present results from recent investigations on validation of key primitive element models. Model refinement and modifications are also considered when sufficient level of agreement between model and experimental data was not obtained.Since the dynamic model for web tension in a span is nonlinear, designing experiments for web line model validation is a formidable task. There are a few known model validation techniques for nonlinear systems but these do not provide any clear procedures that can be applied to the web line. Therefore, the approach taken in this study was to consider test cases of experimentation that mimic typical web line operations in the industry such as acceleration/deceleration of the line and running the line at a constant speed. A number of test cases for model simulations and experimentation were considered. A representative sample of the results is shown and discussed.Data from the simulations of existing models did not contain the oscillations found in measured tension signals. This study also considered refinement and modifications of dynamic models that would lead to better agreement between the model and experimental data. It was found that span length variations introduced by out-of-round and/or eccentric rollers are the direct cause of oscillations in the tension signal. A refined model for web tension that includes span length variations is given. Comparison of the data from simulations of the refined model and experimental data shows a high level of agreement. These results are shown and discussed.Mechanical and Aerospace Engineerin

Web tension behavior in the presence of eccentric rollers: Modeling and validation

Since rotating machinery is used to transport the web on rollers, it is common to observe periodic oscillations in measured signals such as web tension and web transport speed. These periodic oscillations are more prevalent in the presence of non-ideal machine elements such as eccentric rollers and out-of-round material rolls. One of the main objectives in transport of webs is to maintain tension at a prescribed value. Tension regulation affects almost all key aspects of web transport including printing, registration, wrinkle formation, winding, etc. Therefore, models of web tension and web transport velocity in the presence of non-ideal rollers which can accurately predict measured behavior will be beneficial to the analysis of web transport under various dynamic conditions and in the design of suitable control systems.The focus of this paper is on modeling the effect of eccentric rollers on web tension. The governing equations for web velocity on an eccentric roller and web tension in spans adjacent to the eccentric roller are presented and discussed. To solve these governing equations, one requires the knowledge of the entry and exit point of the web on the eccentric roller as it rotates and the length of web spans adjacent to the eccentric roller; a method in obtaining this information is described. To corroborate the models and the developed approach, data from experiments on a web platform are compared with model simulations and results are presented and discussed.Mechanical and Aerospace Engineerin

Design of fixed structure controllers for web tension control

It is a common practice in industry to design a Proportional-Integral (PI) velocity feedback controller cascaded with a PI outer tension loop to regulate web velocity and tension to their desired values. The controller gain tuning is often heuristic and does not explicitly account for process variations, and often fails to provide adequate performance in the presence of uncertainties. To address these issues, one can pose two key questions: (1) How does one systematically obtain controller gains for a given controller structure and a set of operating conditions? (2) Is it possible to systematically choose controller gains to satisfy some pre-defined performance specifications for the closed-loop system when the operating conditions and web material properties have variations?The goal of this paper is to investigate methods to address the above two questions. Methods from robust control theory are used to investigate and develop techniques to systematically design fixed structure controllers that satisfy pre-specified performance criterion. Although the design procedure allows for choosing controller structures with different number of gain parameters, emphasis will be given to controller structures that contain two or three gain parameters (The PI controller structure has two gain parameters). The objective is to use parametric methods whose end result is a region of controller gains which will satisfy the specified performance criteria. Although emphasis is given to tension control, the proposed techniques can be used for other control loops such as velocity or dancer or lateral position control systems. Since the methods used are an outgrowth of classical time and frequency response methods, it is expected that a control engineer with an understanding of classical techniques will be able to comprehend the design procedures discussed in the paper.Mechanical and Aerospace Engineerin

Comparative study on active and passive dancers used for attenuation of web tension disturbances

A dancer mechanism, used in most of the web process lines, consists of a roller which is either connected to a fixed support by passive elements such as springs and dampers or is force loaded in opposition to the web tension. Dancer mechanisms are commonly used to attenuate web tension disturbances caused by uneven wound rolls, eccentric rollers, mis-alignment of idle rollers, and slacks in webs. A dancer mechanism is also used as a feedback element in a number of web tension control systems. The tension control system is driven by the variations in the position of the dancer mechanism as opposed to the variations in actual tension from the desired tension.Since a substantial number of web process lines in web handling industries use dancer mechanisms, there is a need for a systematic comparative study of different types of dancer mechanisms and their applicability; the focus of this paper will be on such a study. Active and passive dancers will be compared using analytical models; a representative sample of the most common dancer mechanisms will be considered. The results of this analysis will assist in the selection of the dancer mechanism and its components, design of the dancer mechanism, and the effectiveness of a particular dancer mechanism to reject different types of web tension disturbances. Also, to substantiate the fundamental analysis, results from experiments, for certain situations, will be shown and discussed.Mechanical and Aerospace Engineerin