Roll-to-roll (R2R) printing shows great potential for high-throughput and cost-effective production of flexible electronics, including solar cells, wearable sensors, and so on. In roll-to-roll process, precise control of the web speed and tension is critical to ensure product quality, since improper web speed and tension would lead to severe damages to the substrates. In this chapter, we will focus on the advanced control algorithms of web tension and speed control in roll-to-roll system. Two concepts of control algorithms will be presented, which are model-based control and data-based control. For model-based control algorithms, the modeling of web dynamics and an application of robust H∞ controller will be reviewed; for data-based control algorithms, two methods of neural network control learning methods will be introduced, and the application of neural network control in web tension and speed control will be presented. Moreover, performances of different control algorithms are compared.
- roll-to-roll system
- tension control
- speed control
- model-based control
- neural network control
Flexible electronics offer lightweight, thin form factor and unbreakable foldability with maximum design freedom and easy affordability, bringing the world of consumer electronics to a new age. Research works have been carried out to explore its use for a wide range of applications, from simple low-power electronic circuity for conventional logics and mobile devices, smart and paperlike displays, efficient energy harvesting and storage capability, disposable label-free biosensors, and smart skins to autonomous wearable electronics.
In order to realize such a huge potential, appropriate mass production technologies need to be developed. The roll-to-roll (R2R) printing process as a low-cost and fast-throughput patterning, and fabrication technique on flexible substrates is the current focus. Several kinds of printing technologies, such as inkjet printing , microcontact printing , and gravure printing , have been successfully applied on roll-to-roll system to fabricate flexible electronics. The print resolution has achieved 50–100 nm at lab scale, which makes high-resolution flexible devices available. This high-resolution printing process requires high demands on the control of web speed and web tension, as the printed patterns would be destroyed by the fluctuation of the web speed and web tension, even the web itself may be broken or sagged. As a result, web tension and speed are two key variables that affect the quality of the manufactured products.
This chapter is aimed at introducing different methods of web tension and web speed control. The control algorithms are classified into two large groups: model-based control and data-based control. For model-based control, first, the dynamic model of the web handling system is developed. After that, two major control algorithms, PID and decentralized control, are presented. For data-based control, the application of neural network control will be discussed. Moreover, performances of the above control algorithms are compared.
2. Model-based control
Model-based control mentioned here refers to plant modeling based on physical laws. The mathematical model conceived is used to identify dynamic characteristics of the plant model. Controllers can be synthesized based on these characteristics. The main steps in model-based method are:
Plant modeling. Plant modeling is based on physical laws, where a model consists in connected blocks that represent the real physical elements of the plant. Usually, certain parameters are hard to measure, such as the model of load cells and motors in roll-to-roll system. In this situation, parameter optimization could be applied. It is done in several steps in order to reduce the number of parameters to identify at each step.
Controller analysis and synthesis. Based on the model of the plant, differential-algebraic equations can be derived which governs plant dynamics. Different control algorithms can then be designed.
2.1 Dynamic model
A typical roll-to-roll system can be divided into two parts: web handling part and printing part. Here, we will focus on the web handling part. Web handling refers to the physical mechanics related to the transport and control of web materials through processing machinery. It is common to divide a process line into several tension zones by denoting the span between two successive driven rollers as a tension zone in web handling. Since the free roller dynamics influences the web tension only during the transients due to acceleration/deceleration of the web line and negligible effect during steady-state operation, the assumption that the free rollers do not contribute to web dynamics during static operation is reasonable. This assumption will be used in developing dynamic model. Also it is assumed that there is no slip between the web and rollers, and the web is elastic.
Figure 1 shows a web line with three tension zones. It consists of four motorized rollers and three load cells. Load cells are mounted between each pair of rollers which are used to measure the web tension. The driving motors are donated by
The speed dynamics of the unwind roll can be written as
The speed of the web coming off the unwind roll is related to the angular speed of the unwind roll by
The rate of change of radius,
This is because the thickness affects the rate of change of the radius of the roll only after each revolution of the roll; the continuous approximation is valid since the thickness is generally very small. Hence, Eq. (6) can be simplified to
To derive the dynamic behavior of the web tension as shown in Figure 3, we need three laws:
Hooke’s law, which models the elasticity of the web
Coulomb’s law, which gives the web tension variation due to the fraction and to the contact force between web and roll
Mass conservation law, which expresses the cross-coupling between web velocity and web strain
For Hooke’s law, the tension t of an elastic web is the function of the web strain
Coulomb’s law: The study of the web tension on a roll can be considered as a problem of friction between solids. On the roll, the web tension is constant on a sticking zone which is an arc of length
The tension change occurs on the sliding zone, while the web speed is equal to the roll speed on the sticking zone. A sliding zone can also appear at the roll entry if the tension varies at high rate.
Mass conservation law: Consider a web of length
Based on these three laws, web tension between two successive rolls can be obtained. The equation of continuity applied to the web transport system gives
If the web section is constant,
Using Eq. (11) and assuming that
Rearranging equation and using Eq. (1) gives
Hence, dynamic behavior of the web tension
Master speed roller: The dynamics of the master speed roller are given by
Sometimes there are idler rolls in processing section; in that case, we can ignore the torque generated by the motor in Eq. (24).
Equations (9) and (21)–(26) represent the dynamics of the web handling. Extension to other web lines can be easily made based on this model. However, it is necessary to emphasize all the assumptions when using this model:
The length of contact region between the web material and a roller is negligible compared to the length of free web span between the rollers (i.e., the strain variations in the contact region are negligible).
The thickness of the web is very small compared with the radius of rollers over where the web is wrapped.
There is no slippage between the web material and the rollers.
There is no mass transfer between the web material and the environment (i.e., no humidification or evaporation).
The strain in the web is small (much less than unity).
The strain is uniform within the web span.
The web cross section in the unstretched state does not vary along the web.
The density and the modulus of elasticity of the web in the unstretched state are constant over the cross section.
The web is perfectly elastic.
The web material is isotropic.
The web properties do not change with temperature or humidity.
2.2 Model-based robust control
To synthesize the controllers, we need a linearized model of the plant. The linear model is obtained by linearizing the simplified form of the equations around the nominal web tension and velocity, by assuming slow variations of the radius and inertia. Let
Using Eqs. (14), (22), (24), (26), and (28), the state-space representation of the nominal model around an operation point,
Here, model Eq. (29) is called nominal model
Robust control is a powerful tool to synthesize multivariable controllers with interesting properties of robustness and disturbance rejection. The robust controller is designed according to nominal model
The frequency-weighting functions
The frequency-weighting function
3. Data-based control
From the physical model of the web handling part, we can see that the model is nonlinear and time-variant, which leads to difficulties in monitoring the dynamics. Besides, in order to implement controllers, the model is linearized by dropping the high-order terms. Thus, the designed controller can’t follow closely enough the dynamics of the system during all the winding process. Moreover, up to 11 assumptions are made to derive the model. However, we can’t guarantee that all the assumptions are satisfied, which may cause a large difference between the performance of the model and the real plant. To overcome these disadvantages of model-based control, data-based control was carried out. In data-based control, the identification of the plant model and/or the design of the controller are based entirely on experimental data collected from the plant. The controlled plants in data-based control are treated as black-boxes, which the dynamics of plants can be learned using a large amount of sensory data.
The standard approach in data-based control system design has two steps:
Model identification: The basic idea of data-based control is to make use of the wealth of data obtained from sensors to learn the dynamics of the plant. These data are also called training data.
Controller design: The controller design could be done in the same way as in model-based control, such as neural generalized predictive control (GPC). Meanwhile, training method can also be applied for training the controller, like neural network control.
In this section, we will introduce an application of one data-based control algorithm, i.e., neural network control, in web tension and speed control of roll-to-roll system.
3.1 Neural network
Neural network is a universal approximator, which is capable of approximating any measurable function to any desired degree of accuracy. Hence, we could use neural network to learn the dynamics of plants. Here, we use the classical definition of neural network in Ref. . Neural network consists of networks of artificial neurons in which the data flows through and their weights are changed to reduce the error in the learning process. A one-layer neural network is typically presented by a network diagram as in Figure 6. Derived features
The activation function is usually chosen to be the sigmoid:
For output function
The units in the middle of the network are called hidden units as the values
ANN encompasses various types of learning algorithms, the most popular of which include feedforward neural network and recurrent neural network.
In feedforward neural network, the data flow is one directional, which is from the input layer through hidden layers to the output layer without loop and feedback.
In recurrent neural network, some of the outputs are fed back to the input layer. One of the applications of recurrent neural network is time series prediction, which then can be applied in predictive control .
After a certain neural network is built, it needs to get training, which is to find a set of weights to minimize the error between the real outputs and predicted outputs. Backpropagation is a method used in neural networks to calculate a gradient that is need in the calculation of the desired weights based on mean squared error loss function . This method has two steps: first data are fed into the network from input layer, and the activations for each layer of neurons are cascaded forward; then based on the loss, we calculate the gradient from the output layer to the input layer and update the weights.
3.2 Neural network control
In control system, in order to implement an effective algorithmic controller, we must have a thorough understanding of the plant that is to be controlled, which is very difficult in practice. A neural network controller performs a specific form of adaptive control, as it has nonlinear network and adaptable parameters. The learning process gradually tunes the weights so that the errors between the desired outputs and actual plant outputs are minimized. Here we introduce two learning structures to minimize the error signal, which are both simple and easy to understand and implement .
Figure 7 shows the general learning method for training the neural network controller that does minimize the overall error. The training sequence is as follows. A plant input
Figure 8 shows the specialized learning method for training the neural network controller to operate properly in regions of interest only. The desired output
3.3 Neural network control application in web tension and speed control
Figure 9 presents the prototype of our roll-to-roll system. Here, we only use the web handling part to test the neural network controller. The web handling part consists of one unwind roll, one rewind roll, one idler roll, and one tension-measuring roll. The web unwinds at unwinder and passes through the idler roll and tension-measuring roll and rewinds at rewind roll. A ring encoder and a readhead (RENISHAW MF100F and LM10) are mounted on the idler roll, which the diameter is 3 inches, to measure the linear web moving speed with a resolution of 1,310,720 CPR. The tension-measuring roll (FMS RMG1922) is used to measure the tension of the web with 1 kHz sampling rate and 0.25 N resolution. The unwind roll and rewind roll are driven by two servo motors (YASKAWA SIGMA-7). The rewind roll is used to control the web speed according to the measured speed from the encoder. The unwind roll is used to control the tension based on the feedback signals from the tension-measuring roll. The diameter of unwind roll and unwind roll are both 3.25 inches after installing the core. The web we used here is MYLAR type A film with 5 mil thickness and 4 inches width.
The data acquisition, A/D conversion, data processing, and control algorithm are all carried out using NI CompactRIO (NI CompactRIO 9049). The motor control is done by LabVIEW SoftMotion Module. The integrated field-programmable gate array (FPGA) in CompactRIO is used to receive the encoder signals and tension signals with up to 40 MHz sampling rate.
A single-layer feedforward neural network with time-delayed structure is generated to learn the plant using generalized learning method. The structure is shown in Figure 10. The inputs to this network consist of external inputs,
The building and training of the neural network are both done in MATLAB. In Ref. , the trained neural network is called in LabVIEW through MATLAB scripts. However, we find that this implementation would consume a rather long time, which is about 100 ms in our application. Since this delay is caused by the communication between MATLAB program in personal computer and LabVIEW program in NI CompactRIO, if we put the neural network into the CompactRIO directly, the delay could be eliminated entirely. Therefore, we complied the MATLAB code into a shared objects file (.so) which can be integrated to CompactRIO directly. The resulted time to call the neural network is reduced to 20 μm, which is fast enough for real-time application.
Figure 11 shows the results of using neural network to control web speed and tension. The reference speed and tension are set to 3 inch/second and 20 N, respectively. We have recorded the web tension and speed during the whole process. The maximum deviation (ΔT/T) of measured tension is 7 and 4% for speed (ΔV/V). The standard deviation is 0.2% for tension and 0.1% for speed. The tension requirement in roll-to-roll fabrication is error within 10%. Thus, the neural network controller meets the requirements. Moreover, using neural network to control web speed and tension saves lots of work and time in identifying the mathematical motel of roll-to-roll system. We should mention that, during the starting phase, the variation of speed and tension is both larger than the other phases. The possible reason is that the training data from PID controller doesn’t cover the region of interest in this phase, so that the interpolation of neural network is not accurate. Our future work will include investigating this issue.
Roll-to-roll fabrication is known as a cost-effective method in producing electronic devices on flexible substrates. However, improper tension and speed may cause manufacturing defects of the substrate, including web wrinkling, edge cracks, and web misalignment, which lead to damages and wastes of the products. Hence, the study and control of web handling systems are carried out for decades. In this chapter, we introduce the two set of control algorithms in web handing field, model-based control and data-based control. In model-based control, a mathematical model of web tension and speed is derived. Based on the model, a robust H controller is applied. In data-based model, neural network control is discussed in detail. Two major learning methods are compared. A real application of neural network control in web handling is realized in roll-to-roll system. Both control algorithms have advantages and disadvantages. For model-based control, the physical laws behind the dynamics of plant are clear; however, certain parameters of the model are difficult to identify, and some control algorithms are hard to realize in real life. For data-based control, the design of the controllers is simple and easy to implement, but we don’t know what happens inside the controller. Consequently, it is worth to explore different control algorithms for a certain roll-to-roll system and then choose the one with the best performance.
We also thank Mehdi Riza, Neel Prakashchandra, Mehta Jonathan Lombardi, and Patrick Caviston for their help in the setup of the roll-to-roll machine.
Conflict of interest
The authors declared that they have no conflicts of interest to this work.