Design and implementation of adaptive PI control schemes for web tension control in roll-to-roll (R2R) manufacturing

Highlights

• Two adaptive PI schemes that automate the tension control systems in R2R manufacturing are designed and implemented.

• The adaptive PI schemes can significantly automate the existing fixed gain PI tension control schemes.

• Both adaptive schemes work well for different operating conditions and materials without the need of extensive tuning.

• The key feature of the two adaptive schemes is that the design and implementation is simple for practicing engineers.

Abstract

In this paper, two adaptive Proportional-Integral (PI) control schemes are designed and discussed for control of web tension in Roll-to-Roll (R2R) manufacturing systems. R2R systems are used to transport continuous materials (called webs) on rollers from the unwind roll to the rewind roll. Maintaining web tension at the desired value is critical to many R2R processes such as printing, coating, lamination, etc. Existing fixed gain PI tension control schemes currently used in industrial practice require extensive tuning and do not provide the desired performance for changing operating conditions and material properties. The first adaptive PI scheme utilizes the model reference approach where the controller gains are estimated based on matching of the actual closed-loop tension control systems with an appropriately chosen reference model. The second adaptive PI scheme utilizes the indirect adaptive control approach together with relay feedback technique to automatically initialize the adaptive PI gains. These adaptive tension control schemes can be implemented on any R2R manufacturing system. The key features of the two adaptive schemes is that their designs are simple for practicing engineers, easy to implement in real-time, and automate the tuning process. Extensive experiments are conducted on a large experimental R2R machine which mimics many features of an industrial R2R machine. These experiments include trials with two different polymer webs and a variety of operating conditions. Implementation guidelines are provided for both adaptive schemes. Experimental results comparing the two adaptive schemes and a fixed gain PI tension control scheme used in industrial practice are provided and discussed.

Introduction

In Roll-to-Roll (R2R) manufacturing of continuous materials, control of web tension is critical during transport of the materials through many processes such as printing, coating, and lamination. It plays an important role in ensuring the quality of the finished web products. During transport, many processes may require transport under different operating speeds and heating/cooling of the webs. Further, there are many process and machine induced disturbances which the tension control systems must compensate to achieve a good tension regulation performance. Tension variations cause a variety of product defects. For example, high web tension may result in wrinkles and tears while low tension may cause web slack, loss of traction on rollers during transport, and difficulty in guiding the webs on rollers. The consolidated effect of large web tension variations may result in disruption in production, diminishing product quality, and machine hardware damage.

Industrial web tension control systems typically employ a fixed gain PI controller. The PI controller gains are tuned to give a stable response for a given operating condition and material. This is typically done empirically on the machine because analytical tuning of PI controllers is a challenging task due to changing operating conditions and uncertainty in the knowledge of web material parameters and machine parameters. In practice, the PI tension controllers are tuned on-site based on real-time observation of the tension response performance. When operating conditions or material properties change, the fixed gain PI tension controllers do not provide adequate performance or in some cases render the closed-loop tension control system unstable. The better approach is to use an adaptive control scheme that facilitates the adjustment of controller parameters for such changing conditions. An adaptive controller can modify closed-loop system behavior by compensating for the changes in system parameters.

There are many approaches to design adaptive control schemes, such as gain scheduling, self-tuning regulators, and model reference adaptive control [1], [2], [8], [13]. The direct and indirect adaptive schemes are promising but the design and implementation of those controllers are cumbersome and provide many difficulties for practicing engineers. For example, since many of these schemes are model based and the web system dynamic model is involved, the designs are complicated and result in a large number of estimated parameters. Simple adaptive control structures which mimic most of the features of the fixed gain PI schemes are desirable. These schemes can provide the automation to circumvent tuning under a wide variety of system parameter changes, and yet provide the ease of design and implementation.

A R2R manufacturing machine is a large-scale system which can be simplified for analysis and control design purposes by decomposing it into a number of interconnected subsystems. There has been substantial reported work in the literature in modeling and control of R2R systems. The tension dynamic model that considers entering web span tension was first developed in King [10]. Brandenburg [5] and Shelton [19] assumed strain in the web to be very small and derived the governing equation for web tension in a span with the small strain assumption. An early overview of longitudinal and lateral dynamic behavior and tension control can be found in [21]. A self-tuning regulator for web tension regulation is given in [4]. A robust $H_{\infty }$ controller is designed and implemented in [6], [11]. Linearization of the web system dynamic model and development of a decentralized state feedback control scheme are given in [17]. A state space reference model based adaptive control technique is given in [15]; a special reference model is chosen based on the overall dynamics of the large-scale R2R system. Model reference direct and indirect adaptive schemes for web tension control are investigated and implemented on an experimental platform in [18]; the motivation for the design and development of simple adaptive PI schemes came from this work. Application of fault tolerant control to a winding machine is given in [14]. Tension control in the web is also critical in the presence of key primitive elements used in R2R manufacturing such as accumulators [16], [12] and print cylinders.

In this paper, first a simple direct model reference adaptive PI (MRA-PI) controller based on the gradient method is designed. Controller gains are estimated by matching the plant performance and desired characteristics provided by a reference model. The estimates of the controller parameters are initialized by considering the stability of the nominal closed-loop tension control system. Second, an indirect adaptive PI control scheme that would facilitate automatic initialization of estimated parameters based on the relay feedback technique is investigated. The indirect adaptive PI control algorithm is simple and initialization of controller parameter estimates does not need the knowledge of nominal plant parameters. There are several ways to initialize the estimated parameters. The application of the relay feedback technique in industrial controllers is given in [7]. This technique is alternative to the conventional continuous cycling method used to generate sustained oscillations. The relay feedback method is known to be effective in determining the ultimate gain and ultimate frequency (frequency at which the phase shift of the plant is 180 degrees) of a system. An algorithm to compute the estimate of ultimate frequency in real-time is considered to account for its change due to plant parameter changes; the method given in [3] is employed where a small sinusoidal oscillation is introduced into the closed-loop tension control system. The fixed gain PI controller gains are tuned by comparing the closed-loop speed transfer function characteristic equation with a standard second-order characteristic equation with design parameters as the damping ratio and natural frequency. These gains are further tuned in experimentation to obtain the best possible performance. For complex processes, gain tuning methods of PID controller can be found in [20], [9]. The two adaptive PI schemes together with an industrial fixed gain PI tension control scheme are implemented on a large experimental R2R platform containing multiple driven rollers and tension zones. The implementation guidelines together with the discussion of experimental results are provided.

The rest of the paper is organized as follows. Governing equations for web tension and transport speed are discussed in Section 2. The existing industrial tension control schemes are described in Section 3. The design of the MRA-PI controller is presented in Section 4. In Section 5, design of indirect adaptive PI based on the relay feedback technique is presented; estimation of plant transfer function around the ultimate frequency is also discussed. The experimental setup and guidelines to implement the MRA-PI and adaptive PI controller to any general web line are provided in Section 6. The performance of the adaptive PI control schemes is presented through experimental results in Section 7. Concluding remarks and future work are given in Section 8.