Conference Papers

Hedging Point Policies for Multi State Failure Prone Manufacturing Systems

In this paper we consider a single-product single-machine manufacturing system, with the machine characterized by multiple working modes. A cost is associated both with inventory surplus and demand backlog and the policy which minimizes the overall long-run expected cost, which based on previous work in literature is known to be a multiple hedging point policy, is analyzed. This paper derives a condition on system parameters for the optimality of just-in-time (JIT) policies and investigates the dependence of hedging points on the ratio among inventory surplus and backlog cost parameters. Some numerical examples are included to illustrate the effectiveness of the achieved results.

Adaptive Feedforward Based Control Strategy for Attenuation of Periodic Tension Oscillations in Roll-to-Roll Manufacturing

Periodic oscillations in the tension signal are frequently observed in roll-to-roll manufacturing due to the presence of many rotating elements which are often non-ideal, such as out-of-round material or eccentric rolls. In certain situations the amplitude of the oscillations is large enough to affect normal operation of the web line. The proportional-integral-derivative (PID) feedback control algorithms that are commonly used for tension regulation do not have the dynamic complexity to compensate for such periodic disturbances. In this paper we investigate a two-degree-of-freedom controller which has two control actions, feedback and feedforward. The feedforward part is adaptive and is designed to provide control actions to compensate for periodic oscillations. Several issues must be considered when designing a control algorithm for the attenuation of periodic oscillations. First, since the control algorithm is executed in real-time using a real-time system which may have restrictions on the sampling period, the complexity of the algorithm must be such that the control action can be computed in a time period that is less than the sampling period, and the sampling period for most systems is typically in the range of tens of milliseconds. Second, it is desirable to have a feedforward algorithm that can be implemented in parallel with an existing feedback control scheme for tension and speed regulation without the need to retune and redesign the existing scheme. Further, it is desirable to have an algorithm that is understandable to practicing engineers who may have limited or no advanced controls background other than an undergraduate course in control systems. Considering the aforementioned issues, an adaptive feedforward (AFF) algorithm that can work in parallel to an existing feedback control systems is developed for control of web tension and to attenuate periodic oscillations. The essential ingredient of the AFF algorithm is the estimation of amplitude and phase of the periodic oscillations based on which a feedforward compensating control action is generated. The action of the AFF algorithm is such that retuning or redesign of the existing feedback controller is not required. Several different configurations of the AFF for different scenarios in terms of where to apply the feedforward action in the control system are investigated. Extensive experiments are conducted on a large web platform with different scenarios and by transporting two different web materials at various speeds. Results from these experiments are presented and discussed. Experimental results show the effectiveness of the proposed AFF algorithm to attenuate tension oscillations.

On the Governing Equation for Web Tension with Out-of-Round Rolls

In roll-to-roll (R2R) manufacturing the presence of non-ideal elements, such as out-of-round or eccentric rolls, induces periodical oscillations in the web tension signal. Model simulations based on ideal elements do not exhibit these tension oscillations but can only follow the measured tension signal in an average sense. In order for the models to predict these measured tension oscillations due to non-ideal elements, the derivation of governing equations must consider a mechanism to include the correct behavior of the non-ideal transport elements. Continuing with our previous work on this topic presented at previous IWEBs, we present additional results that provide improvements to the web span tension governing equation which can better predict measured tension signals. In particular, this work is useful for tension control in the unwind section of the web line when the unwind material roll is often out-of-round. The governing equation for web span tension is typically derived using the law of conservation of mass by considering a control volume enclosing the web span, i.e., at any instant of time the variation of web mass in the control volume is equal to the difference of the incoming and outgoing material flow rates. If the web span is between two ideal elements the only way to induce changes in web span tension is with an imbalance in the web material flow. For ideal elements it is easily shown that the material flow rate is proportional to the difference of the peripheral velocities of the web on the surface of the rolls adjacent to the web span. When an out-of-round roll is at one end of the web span, two aspects make the derivation of the web tension governing equation different from the ideal case. First, because of the out-of-roundness of the roll, the span length adjacent to the roll is time-varying; variations in the span length induce web tension variations that are not associated with an imbalance in material flow. Second, the material flow rate is not proportional to the peripheral velocity of the web on the out-of-round roll and must be computed explicitly. Given a measure of out-of-roundness of the roll, due to the complexity of the problem it is difficult to derive a closed form expression for the material flow rate as a function of the roll position and velocity. A numerical algorithm for the computation of the material flow rate is presented in the paper. Based on the computation of the material flow rate and the algorithm for the computation of the span length adjacent to an out-of-round roll which was presented in the previous IWEB, a new governing equation for web tension is developed. Using this new governing equation a dynamic model for an experimental web line is developed and model simulations are conducted. To corroborate the model, experiments are conducted on the web line with an out-of-round unwind material roll. Comparison of the results from model simulations and experiments are presented and discussed.

A Hierarchical Optimization Algorithm for Cooperative Vehicle Networks

In this paper, we combine model predictive control (MPC) and mixed integer linear programming (MILP) into a hierarchical optimization framework capable of solving a class of coordination problems in multi-vehicle networks. A critical issue in MPC/MILP applications is that the underlying optimization problem must be solved on-line. This introduces a time constraint that is hard to meet when the number of vehicles and the number of obstacles increase. To alleviate this problem, we implement some heuristics that significantly improve the efficiency of the proposed hierarchical, decentralized optimization scheme. Numerical simulations verify the scalability of the algorithm to the number of vehicles and complexity of the environment.

Modeling and Analysis of a Rotating Turret Winder in Roll-to-Roll Manufacturing Systems

The process of manufacturing products using roll-to-roll (R2R) methods involves unwinding of thin, flexible material in rolled form into machinery for processing and winding of the processed material into a roll. This paper describes modeling and control of a rotating turret winder in the rewind section of a R2R printing press. Governing equations for web speed and web tension within the rewind section are described by taking into consideration the motion of the rotating turret winder. Data from production runs of an industrial R2R printing press are analyzed to determine web behavior during a wound roll change sequence accomplished by the rotating turret. Model simulations are conducted and data from these simulations are compared with typical data from production runs. The key challenges associated with controlling web speed and web tension in a rewind section containing a rotating turret winder are discussed along with recommendations for machine and control design to achieve improved regulation of process parameters.

A New Laser-based Sensing System for Monitoring and Control of Webs

A new laser based sensing system for measuring the velocity of the web is proposed in this paper. The doppler shift between the incident light and scattered light from a moving particle contains information about the velocity of the particle. A collimated laser source is incident on the web edge and scattered light is collected. The proposed sensing system measures the true velocity of the web by measuring the doppler shift. The doppler shift is measured by heterodyning the scattered light and incident light. The sensor is capable of measuring the web velocity in all three directions, longitudinal, lateral, and transverse. The measurement of the three true velocity components will be highly beneficial for both monitoring and control of webs. The theory of operation of the sensing system is developed based on the reference beam technique. The methods that will be used for processing various signals are given. The architecture of the sensor is described and construction of the sensing system is underway. The experimental platform developed thus far is discussed in detail.

Optimal Control of Web Guides Using a New Fiber Optic Edge Sensor

This paper discusses the development of a linear quadratic optimal control algorithm for web guides, and implementation of the control algorithm using web lateral position feedback from a new, experimental fiber optic sensor. The lateral dynamic model of the web and the measurement characteristics of the fiber optic sensor are conducive for a linear quadratic regulator design. The performance of the optimal control algorithm with web lateral position feedback from the fiber optic edge sensor is evaluated by conducting experiments on a web platform. Experiments were also conducted using the same controller but with an existing industrial infrared sensor for web lateral position measurement. Results from a series of comparative experiments indicate that the optimal control algorithm with feedback from the fiber optic sensor provides accurate lateral position regulation in the presence of disturbances, at various web transport speeds, and with web materials with different mechanical, physical and geometric properties. Based on the analysis of the web lateral dynamic model, recommendations for proper guide operation and selection of appropriate web transport conditions for good guiding performance are also discussed.

A New Sensor for Web Flutter Measurement

A new sensor for web flutter measurement is proposed in this paper. The sensor is based on the principle of scattering of light and directional properties of optical fibers. A collimated beam of light is incident on the web edge and scattered light from the web edge is collected using a linear array of optical fibers. As the web flutters the point of scattering moves. Due to the directional property of the optical fibers, each fiber collects scattered light that is incident on it at certain angles. The motion of the scattering point as the web flutters is directly related to which fibers are being illuminated within the fiber array. The other end of the fiber array is terminated onto a linear array of photodiodes (pixels). Based on which fibers in the array are receiving scattered light and the amount of light received, the transverse displacement (web flutter) of the web can be determined. This paper describes the construction and working of the new sensor for web flutter measurement. Experiments conducted on a web platform show that the sensor is capable of accurately measuring web flutter. The frequency response of the sensor is limited only by the scanning rate of the pixel array and not by the flutter measurement method. A dedicated signal processing circuit can be used to obtain a desired scanning rate, thus, a desired frequency response.

Interaction in Decentralized Control Systems: Application to Roll-to-Roll Systems

A procedure to analyze interaction in an experimental roll-to-roll system that uses a decentralized control strategy is presented in this paper. A Perron root based interaction metric is employed for the analysis. Experiments conducted on a roll-to-roll system are used to evaluate the interaction between different subsystems of the roll-to-roll system. To minimize interaction between subsystems of the roll-to-roll system, a procedure for designing pre-filters based on the Perron root of the system is also discussed in the paper. Experimental results with and without pre-filter clearly indicate the effectiveness of the pre-filter in minimizing interaction. Discussions regarding the roll-to-roll application, stability considerations and insights on using the Perron root based interaction measure for decentralized control applications are also given.

Design of Delay Independent State Feedback Control for Roll-to-Roll Printing Applications

Control of print quality (registration) in roll-to-roll (R2R) printing is challenging because of the presence of transport delays involved in the printing process. In this work we present a delay-independent state feedback control design to stabilize a R2R printing press by considering all the significant dynamics involved in the printing process. State feedback control design using past state measurements (controllers with memory) are discussed first. Since controllers with memory are less desirable in industrial applications, we investigate and discuss the feasibility of designing a simple, memoryless, delay-independent state feedback controller for printing applications. The feasibility is shown by the use of a control design procedure that exploits the structure information in the system matrix to find a stabilizing controller. The design procedure is also extended to other common industrial R2R control strategies, such as decentralized control and state feedback with integral action for R2R printing applications.