Synchronized online simulation at field level for virtual sensing of web tension

Abstract

In industrial automation, online simulation should reflect a real mechatronic system as accurate as possible. However, the simulation could drift away from the real manufacturing process due to imprecise modeling or changing system behavior. While in literature, some methods are already used to synchronize digital twins or online simulations of processes to their real counterpart, this article systematically describes the comprehensive field of synchronizing online simulations of manufacturing systems by defining several types of synchronization, explaining their functions, and indicating exemplary realization methods in this context. Subsequently, the concepts are applied to a newly presented use case of online simulation at field level for the demonstration of the proposed concepts. In particular, an exemplary synchronized online simulation is implemented that serves as a virtual sensor for web tension in an imitated web transport system. For this use case, an individual synchronization strategy based on the described methods is presented. The results are validated and discussed based on an experiment, where the behavior of the web transport system is rapidly changing and the synchronized online simulation is adapting accordingly. The findings of this research contribute to the aim of using existing simulation models for online simulation in the operation phase of manufacturing systems.

Article Highlights

A comprehensive overview of synchronization for online simulation is presented.

Online simulation is used beneficially as a virtual sensor for web tension control.

Synchronized online simulation proves to be robust against changing dynamics.

Introduction

The importance of simulation technologies in industrial automation is steadily increasing. Simulation models and tools that are used mainly in the design and commissioning phase of a manufacturing system can be reused during the operation phase beneficially, for example, for online simulation [1]. Online simulation means that a manufacturing system is simulated in parallel to its operation, whereat the simulation system is coupled to the manufacturing system [2, 3]. An online simulation usually considers the same system state and real-time inputs that affect the real system and feeds back simulation results to improve the manufacturing system’s operation [2].

Usually, an online simulation should represent the actual state of the real manufacturing systems. In many cases, the simulation has to consider changing behavior due to wear, reconfiguration, or malicious manipulation [4]. To solve this, some concepts were already presented for the process industry [5, 6], but there are also examples regarding discrete manufacturing systems [7]. However, these approaches were mainly applied to online simulations relying on process models, while reusing complex machine models, for example, from virtual commissioning, for online simulation is an upcoming technology in discrete manufacturing [8].

An example, where an online simulation would be beneficial, are web transport systems for webs consisting of paper, metal, polymer films, or fabric, which is a common application in the printing and converting industry. The main challenge is to be able to control the web tension, while machine operators require high machine speeds and complex web paths in a machine. Maintaining a stable web tension is important for the primary process, like printing, and a high variation of the web tension could even lead to a web break or fold.

Usually, the web tension is controlled by electrically driven rollers within separate sections of the overall web path. As diverse disturbances are influencing the web tension, closed-loop web tension control is necessary, which needs the actual web tension as an input. Traditionally, mechanical measurement systems are used, which are influencing the web transport and suffering from high measurement noise that adversely affects the closed-loop control. Filtering the measurement noise leads to reduced reactivity and therefore a reduced control performance of the closed-loop control. Additionally, physical measurement, for example by a strain gauge, is coming with design, implementation, and hardware costs and sometimes there is no space for the integration of a measurement device. To overcome this, web tension observers have been state-of-the-art for many years, which enable to obtain the information about the web tension without the usage of mechanical measurement systems [9, 10]. However, the observers are facing disturbances due to the unknown and varying parameters of elasticity and friction. The web’s elasticity (described by Young’s modulus) of paper changes due to humidity, for example by the processing with color or due to other inconsistent environmental conditions, and the elasticity of foils is changing depending on the temperature.

Within this work, the concept of a synchronized online simulation is presented, which, among other use cases like monitoring or anomaly detection, is providing an improved solution for the problem of web tension control by virtual sensing. The focus of this article is on solving the problem of synchronizing an online simulation for discrete manufacturing systems in general, while demonstrating the proposed principles with the example of a web transport system. In section 2, the concept of synchronized online simulation is explained on an abstract level, distinguishing between temporal synchronization, model parameter synchronization, and state synchronization. Subsequently, the concept is demonstrated based on the example of a web transport system, where the synchronized online simulation is used as a virtual sensor for a closed-loop web tension control. An individual synchronization strategy is proposed for the specific example and validated based on the implementation on a demonstrator (see section 3). By this, the application of synchronized online simulation is illustrated and the required functionalities are proved. In conclusion, the results are discussed and an outlook on further possible applications of a synchronized online simulation is given.

Synchronized online simulation

Synchronized online simulation is a concept that ensures that an online simulation always reflects its real counterpart by using synchronization mechanisms. As synchronization in this context has multiple facets, this article defines several types of synchronization for online simulation at field level, which are described in the following sections.

Fig. 1 [Images not available. See PDF.]

Distinction between temporal synchronization, which only aligns the timespaces of simulation and reality, and model synchronization, which adapts the simulated behavior

Temporal synchronization

Temporal synchronization refers to the task of synchronizing the simulation time and the simulation’s execution speed with the actual progression of time (see Fig. 1a). If the simulation is not run within the same runtime environment as the real process control, there are different timespaces which have to be aligned to be able to compare the process data adequately. Additionally, the simulation may run with an inconsistent simulation speed and therefore lead or lag behind the actual process. For co-simulations, which are running multiple solvers in parallel, the problem is getting even more complex. Solutions for event driven simulations are the synchronization of the event list [11] or waiting for a simulated event to also occur in reality before the simulation is continued [12].

However, in the case of reusing real-time capable Hardware-in-the-Loop (HiL) simulation models and tools, for example, from virtual commissioning, and integrating the simulation via a real-time capable fieldbus, the task of temporal synchronization is already accomplished by the HiL simulation platform, as it manages the execution of the simulation steps on a real-time capable simulation device. By using the existent fieldbus, the simulated process data is automatically aligned to the real process data at the control system and does not need further synchronization. As online simulation at field level usually relies on this kind of configuration, temporal synchronization is already widely solved by the simulation platforms, here.

Model synchronization

As the online simulation model should represent the real system behavior as accurate as possible at any time and simulations could be inaccurate in the beginning or get inaccurate because of a changing system behavior, an online model adaption is reasonable, which tracks the actual behavior and therefore accomplishes the task of model synchronization (see Fig. 1b).

Models of manufacturing systems comprise the logical behavior of devices, the dynamical behavior of the manufacturing processes including the mechanics, and geometrical models of the manufacturing system. If the considered mechatronic system changes fundamentally, like due to the reconfiguration of a plant, the adaption of the model structure and replacement of submodels is necessary. This applies to the logical and dynamical behavioral models as well as to geometrical models and data models. To synchronize data models of mechatronic components during the life cycle of a manufacturing system, Talkhestani et al. [13] presented a concept based on the anchor-point method.

Model parameter synchronization

For slight changes of the system behavior, which occur, e.g., due to a changing process environment or degradation of the hardware, an adaption of the dynamic models’ parameters is suitable. As the system behavior is depending on both, its current state and the model parameters, defining whether a quantity is a model parameter or a state variable is reasonable. The classification of a quantity depends on whether the system model includes a specification of how this quantity changes. If the quantity is changing dynamically according to a modeled behavior, it is a state variable. If a quantity is assumed to be a constant within the system model, it is a model parameter.1 As the quantities considered as model parameters nevertheless are changing in reality, the adaption of model parameters within an online simulation is a reasonable technique to synchronize the simulation with the actual manufacturing system.

Based on the state variables and model parameters, there are system outputs, which correspond to the quantities that are measured in the real system. These outputs could directly represent certain system states or model parameters but could also require a transformation of these quantities.

Fig. 2 [Images not available. See PDF.]

Basic principle of model synchronization in the form of model parameter adaption

Basic principle of model parameter adaption

There are diverse options to systematically adapt the model parameters, while most of them are relying on the principle, which is depicted in Fig. 2. The online simulation processes the system inputs and determines an output based on the model parameters and the system state. In parallel to this, the inputs are affecting the real process of the manufacturing system, where the outputs are extracted in form of measurements. These measurements could determine a model parameter directly, for example in the case of a humidity sensor, if humidity would be a model parameter in the online simulation. If model parameters are not measured, they can be estimated based on the comparison of the simulated outputs with the real outputs. If the outputs are corresponding well, no adaption of the parameters is necessary. Otherwise, a parameter estimation algorithm or systematic recursive adaption should adapt the model parameters.

Note that generally, model parameter adaption could be any adjustment of model parameters, so model parameter adaption is not necessarily related to minimizing the discrepancy between simulated and real outputs. However, for the synchronization of online simulation it is the prevalent principle.

Model parameter adaption with optimization algorithms Fitting the model parameters to the actual process behavior can be done by using an optimization algorithm to determine parameters which optimally reproduce the progress of previously recorded dynamic output variables. To always determine the current system behavior, moving-window based approaches are reasonable, which are selecting recent data points for the optimization algorithm.

As the used models usually are non-linear, gradient-based algorithms like the Levenberg-Marquardt algorithm are prevalent [6, 14, 15], which minimize a cost function based on the difference between the parameter dependent simulation outputs and the real outputs. For complex models, stochastic optimization algorithms have the advantage that they are not prone to get stuck in local optima [16].

Alternatively, also evolutionary algorithms are suitable. For online model adaption, the population consists of different sets of parameters, which are recombined and selected by using their accuracy as a fitness criterion. As the determination of the parameters’ accuracy requires the simulation with each set of parameters, evolutionary algorithms are computationally expensive.

Non-linear optimization algorithms usually work iteratively and therefore are transformed to recursive approaches, which only process one new data point at one step, to reduce the computational load for each adaption. To consider changing system behavior, a forgetting factor should be included, which down-weights the influence of a data-point the older it gets.

Model parameter adaption with tracking simulation Another possibility is the so-called tracking simulation, which was firstly presented by Nakaya et al. [5] as a dynamic process simulator, which works simultaneously with a target plant. To minimize the discrepancy between the simulated outputs and the real outputs, certain outputs are compared directly in each time step and a correction of a relating model parameter is determined based on the discrepancy. This is resulting in a recursive adaption and leading to converging outputs if the correction policy is suitable. A basic correction policy for a parameter correction $\mathrm{\Delta }\mathrm{\Lambda }$ based on a deviation e is:

1

$$\begin{array}{c}\hfill \mathrm{\Delta }\mathrm{\Lambda }=K_P·e+K_I·\int edt,\end{array}$$where $K_P$ and $K_I$ are feedback gains, which have to be chosen empirically. This correction policy bases on the principle of PI control, while also diverse other closed loop controllers could be the basis for a tracking simulator [5, 17, 18]. Tracking simulation based on closed loop controllers for certain model parameters are lightweight, easy to implement and adjustable to their particular application. However, this synchronization method has to be tuned manually by system experts and only works for single model parameters mapped to a single output variable.

Tracking simulation is a form of adaptive filtering. Other forms of adaptive filters are the Least-Mean-Square algorithm or adaptive forms of the Kalman Filter, which usually are less suitable for the application on online simulation systems as they are traditionally meant for simple linear models [16].

State synchronization

In contrast to the model parameters, the state variables are calculated by the online simulation based on the system model. If the behavior of a manufacturing system is not modeled sufficiently accurate, the system state is not changing the same in the simulation as it changes in reality. Especially for quantities, which are integrating over other quantities that are imprecisely reflected in the simulation, this is leading to an increasing deviation between the simulated and real system state. As an example, if the velocity of a conveyor is modeled imprecisely, the resulting position of an object on this conveyor is diverging between simulation and reality over the time of movement of the conveyor. Hence, a synchronization of the system state variables is necessary in these cases to adjust the online simulation towards the actual state of the manufacturing system.

If state variables are measured reliably in the real system (see outputs in section 2.2.1), they can be directly transferred to the simulation. Within the example of the conveyor, a light barrier might detect, whether the object reached a certain position. At this point, the position of the object can be corrected in the simulation.

Fig. 3 [Images not available. See PDF.]

Basic principle of state synchronization by the adaption of the simulated system input

Alternatively, the simulation can be synchronized by adapting the simulated system input in a way that the discrepancy of the system outputs is minimized. Zipper et al. [7] use an optimization algorithm to choose a suitable adapted input. However, the correction of a system state only works if there is a sufficient relation between the concerned state and a considered output variable. The mechanism is depicted in Fig. 3 and assumes that the online simulation uses black-box models, which could not be adapted. Referring to the conveyor example, the control input could be changed so that the movement stops earlier or later in the simulation than it stops in reality, leading to the same resulting position of the object.

Online model parameter adaption methods which minimize the output discrepancy also lead to a synchronization of the state variables if the concerned state variables have a suitable relation to the considered output variables or the adapted model parameters. In the conveyor example, adapting the velocity parameter in the simulation to be more precise also leads to a more precise positioning behavior and therefore the resulting position of the moved object is reflected more accurately in the simulation. Therefore, online model parameter adaption methods which minimize the output discrepancy perform model parameter synchronization and state synchronization at once.

Virtual sensing of web tension

To demonstrate the principle and abilities of synchronized online simulation at field level, the proposed approaches are applied on an exemplary imitated web transport system, which could be used in a printing machine, for example. The application demonstrates the web tension control of a section in the web transport system. The web tension control is important for the reliable operation of web processing machines. For this, a synchronized online simulation is used to determine the actual web tension by simulation to substitute a physical sensor. The synchronized online simulation includes a high-fidelity drive model and a dynamic process model to reflect the real process accurately. However, the behavior of a web transport system is depending on the elasticity of the moved substrate. The elasticity can change significantly during the machine operation due to changing humidity, temperature or the processing of the substrate, for example, by printing it differently. Hence, the synchronized online simulation should also detect the changing elasticity of the substrate to be able to provide a precise and reliable estimation of the actual web tension. For this, the actual torque of a real servo axis is used for a comparison between simulation and reality.

System modeling

The considered part of a web transport system consists of a section between two consecutive rollers (see Fig. 4). Each roller is driven by a servo drive, which is controlling a servo motor. To simulate this system in parallel to its operation, it has to be modeled sufficiently. The overall model inputs are the master data of the simulated servo drives, which are consisting of control words, configuration parameters, and command values for the drive’s operation. The drive’s behavior is simulated by combining high-fidelity drive models with dynamical models for the axes’ movement and the dynamic web tension behavior.

Fig. 4 [Images not available. See PDF.]

Web transport between two consecutive rollers

Servo axes model

To model the behavior of the servo axes, a high-fidelity drive model, including the drive’s logic behavior, control loops and the servo motor is used. The output of this drive model is the actual torque resulting from the motor current (see Fig. 5). For each axis, the actual torque $\tau$ is multiplied with the gear ratio $k_{\mathit{gear}}$ and then transformed into a translational force by multiplying it with the roller’s radius. In addition to the driving force of the servo motor, the rollers are affected by the web tension forces of the previous and following sections $F_{\mathit{prev}}$ and $F_{\mathit{fol}}$, which are calculated according to the web tension model described in section 3.1.2.

Fig. 5 [Images not available. See PDF.]

Overview of the model for a web transport section including two servo axes

These forces are summed up and divided by the inertia of the rollers (transformed to a point-mass m) to receive the acceleration $\ddot{x}$ (see Fig. 4):

2

$$\begin{array}{c}\hfill \ddot{x}=\frac{1}{m}\left(F_{\mathit{motor}},+,F_{\mathit{prev}},+,F_{\mathit{fol}}\right)=\frac{1}{m}\left(\tau ,·,k_{\mathit{gear}},·,r,-,F_{\mathit{prev}},+,F_{\mathit{fol}}\right)\end{array}$$The inertia of the web is assumed to be very small in relation to the rollers’ inertia, so it is not included here. The integrated actual position x is fed back to the drive model, after transforming it according to the gear ratio.

Web tension model

Assuming ideal elastic behavior, the web tension F is calculated based on Hooke’s law, which models the elasticity of the web:

3

$$\begin{array}{c}\hfill F_{\mathit{tension}}=E·S·ϵ,\end{array}$$where E is the Young’s modulus expressing the elasticity, S is the web’s cross-sectional area, and $ϵ$ is the strain, which is defined based on the nominal web length $L_0$ and the actual length under stress L.

4

$$\begin{array}{c}\hfill ϵ=\frac{L-L_0}{L_0}\end{array}$$The ideal elastic behavior of Hooke’s law is holding for a small strain $ϵ\ll 1$. Depending on the contact of the web to the rolls, it is distinguished between a sticking zone, where the roll velocity is equal to the web velocity, and a sliding zone, where the friction is not sufficient to compensate the web force. Within this work, the web is assumed to remain in the sticking zone, which is the case for propperly deisgned mechanics [19]. This means that there is no slip in the considered model. Furthermore, the mass density and the web’s section are assumed as constant, as the web is not processed in the considered section. Consequently, by applying the mass conservation law, the behavior of the web strain depending on the roll velocities (${\dot{x}}_1$ and ${\dot{x}}_2$), the web strain previous to the first roll ${ϵ}_{\mathit{prev}}$ and the variation of the web length L is derived as [19]:

5

$$\begin{array}{c}\hfill \frac{d}{\mathit{dt}}ϵ=\frac{1+ϵ}{L}\left({\dot{x}}_2,+,\frac{d}{\mathit{dt}},L,-,{\dot{x}}_1,\frac{1+ϵ}{1+{ϵ}_{\mathit{prev}}}\right)\end{array}$$The velocities are taken from the axis models, which means that none of the model inputs is suffering from measurement noise. Usually, this model is further linearized, for example, to be used in a linear state-space representation [9, 10]. This is not necessary for online simulation, as the model types are only restricted by the possibilities of the simulation platform.

Implementation

Fig. 6 [Images not available. See PDF.]

Overview of demonstrator for imitated web transport section

To demonstrate the applicability of the proposed methods, the application is implemented with components from industrial automation. However, no real mechanics but a demonstrator consisting of an industrial control system and several servo drive axes with coupled motors for a realistic load imitation is used (see Fig. 6). Imitating the mechanics enables to systematically adapt the actual system behavior by a changing load imitation instead of the intentional adaption of a real web transport system’s mechanic behavior, which is reasonable for the demonstration of model synchronization for online simulation.

The Bosch Rexroth ctrlX COREplus X3 control system includes a Programmable Logic Control (PLC) program that runs a closed-loop web tension control determining the suitable velocity command value for the first axis, while the second axis is kept at constant speed. This principle is known as upstream control [19]. The servo axes (ctrlX DRIVE XMD1-W1616 double axis inverter with a MSK050B-600 synchronous servo motor and a MSK030B-0900 servo motor by Bosch Rexroth) run in the velocity control operation mode, while the motor of the second servo axis is coupled to a load motor (VEM K21R 71 G 2) applying the load torque, which is controlled by a ctrlX DRIVE XMS1-W0036 and calculated based on a load model at the control system. By this, the second servo axis runs with a realistic load so that it can be used for feedback to the synchronization of the online simulation.

For the load imitation, rollers with a 20 cm radius and 1.167 ${\text{kg/m}}^2$ coupled to the motors with 1:5 gears are assumed. The web transport system is inspired by a printing machine [20] with a 0.5 m wide and 65 $\mu \text{m}$ thin 80 ${\text{g/m}}^2$ paper having a modulus of elasticity of 8700 ${\text{N/mm}}^2$. The web with an exemplary nominal length of 1 m is moving by 3 m/s. The web tension of the previous section is 80 N and the web tension of the following section is 70 N. Both values are assumed to be fixed, which could be due to a separate closed-loop control or an ideal dancer, which are guaranteeing nearly fixed web tensions also in practice.

Besides the real servo drives, also the simulation device, an ISG real-time target, is integrated via the EtherCAT fieldbus, which is running with a cycle time of 2 ms, for the exchange of cyclic process data. The real servo drives are reflected by high-fidelity drive models, which include a motor model and are simulated together with a comprehensive process model (see section 3.1). The drive models have individual EtherCAT addresses so they also receive separate EtherCAT datagrams. To provide the online simulation with the same inputs as the real system, the master data is copied from the datagram for the real servo drives to the datagram of their virtual counterparts. Additional process data, like the value of the simulated web tension, are exchanged by using virtual input and output (I/O) modules, which are integrated into the simulation.

The principle of the applied closed-loop web tension is depicted in Fig. 7. Instead of a physical measurement, the web tension controller receives feedback from the online simulation, which is synchronized to the real system. The synchronization is also included in the control system in this implementation, as the control system has access to all process data and simulation results. However, the synchronization could possibly also be included in the simulation system, if the necessary process data are distributed.

ISG-virtuos, which is known as a tool for virtual commissioning, was chosen as simulation platform as it provides a lot of functionalities that are beneficial for online simulation [21]. The models run within a real-time capable runtime environment with a simulation step size of 1 ms and ISG-virtuos provides the mapping of the fieldbus data into the simulation. A drawback of the particular simulation method is a limitation of the real-time capability for large systems with numerous servo axes and complex process models due to limited computational power and memory at the simulation device. However, there are already approaches like distributed co-simulation and increasing computational performance, which are able to solve this problem.

Fig. 7 [Images not available. See PDF.]

Closed-loop web tension control based on a synchronized online simulation as virtual sensor

The demonstrator is based on the setup of [8] and enables to apply the principles of a synchronized online simulation on a real mechatronic system using actual components from industrial automation, while the disadvantages of using real mechanics of the complex use case are avoided.

Synchronization strategy

To accurately reflect the actual system behavior in the simulation and ensure reliable information for the web tension control as a virtual sensor, the online simulation is synchronized to the real process. As the online simulation runs on a real-time capable simulation system and receives its inputs in every deterministic fieldbus cycle, a further alignment of the timelines between simulation and real devices is not necessary. Both systems are initialized with the same stable state and the tension control is ramped up simultaneously as the simulated drives are receiving the same command values and control words in the same fieldbus cycle during the whole operation.

As the problem of temporal synchronization is already solved by the online simulation’s particular architecture using HiL models and a HiL simulation platform, model synchronization is remaining. The overall concept for model parameter synchronization and state synchronization is depicted in Fig. 8. The drive models are based on the real drives’ firmware and mainly consist of logical behavior, which is assumed to be modeled optimally and receives exactly the same inputs as the real servo drives. Hence, only the dynamical process model is considered for the model synchronization. Within the process model (see section 3.1.2), the system state is mainly defined by the following quantities:

• Actual velocities of the first and second servo axis

• Actual web strain at the previous section

• Actual web strain at the considered section

• Actual web tension at the considered section

• Actual web tension at the following section

The actual velocities of the first and second servo axis do not have to be synchronized, as the simulated drives run in a closed-loop velocity control with the same velocity command values as the real drives. As the control loops are designed well, the actual velocities are also corresponding well. A synchronization would only be necessary, if the closed-loop controllers could not manage to reach the velocity command value fast enough.

The actual web strain at the previous section and the actual web tension at the following section are assumed to be available by physical or virtual measurement. In the particular case of this demonstrator, they are taken from the load model at the control system so they could be synchronized by directly transferring them from the real system into the simulation.

Fig. 8 [Images not available. See PDF.]

Model synchronization for a web transport system

The actual web tension is not detected by a real sensor in this example, as the simulation is used as a virtual sensor for this quantity, so it has to be determined by the simulation. Virtual sensing of the web tension requires low noise, as the value is used for the web tension control loop. Hence, determining the web tension from the actual torque at the second servo axis and the known web tension of the following section (see Eq.(2)) is not suitable, as the measurement of the actual torque is very noisy. Nevertheless, the actual torque at the second axis can be used as an output that is used as feedback for a model parameter synchronization, which also leads to a synchronization of the web tension because of its decisive impact on the simulated motor torque, which is converging to the actual motor torque due to the model parameter synchronization.

The model parameter synchronization has to focus on the elasticity of the transported web that changes over time due to varying humidity and temperature, varying impacts of the web processing and inconsistent characteristics of the web. In other examples, also the web length could be a varying parameter for accumulator systems or moving rollers in general. The approach of tracking simulation is chosen to synchronize the elasticity, as only one variable has to be synchronized and the model adaption mechanism should be lightweight to meet the real-time requirements of the simulation and the control system in this application. In particular, a PID controller is implemented that manipulates the elasticity E in a way that the simulated motor torque ${\tau }_{\mathit{sim}}$ and the real motor torque ${\tau }_{\mathit{real}}$ converge. For this, E is changed by a correction $\mathrm{\Delta }E$ depending on the error $e={\tau }_{\mathit{sim}}-{\tau }_{\mathit{real}}$:

6

$$\begin{array}{c}\hfill \mathrm{\Delta }E=K_P·e+K_I·\int edt+K_D·\frac{d}{\mathit{dt}}e\end{array}$$By adjusting the controller gains $K_P$, $K_I$ and $K_D$, the characteristics of the tracking simulation can be chosen depending on the requirements and intended use of the tracking simulation. For example, if the synchronization should respond to rapid changes fast, $K_P$ and $K_I$ should be increased. However, this also comes with an increased sensitivity to noise and disturbances of the actual torque signal. Conversely, if the synchronization of the elasticity should be more stable and it is sufficient to slowly react to the rapid changes and to mainly track gradual changes, then $K_P$ and $K_I$ should be decreased. To avoid overshooting after a slow reaction to a rapid change, the error integral is limited.

Note that in Fig. 8, only the most relevant state variables for the synchronization are included in the figure. Besides the quantities that are relevant for the synchronization of the dynamic process, the system state also comprises the logical state of the servo drives as well as the actual velocities and the model parameters include the drives’ configuration.

Validation and discussion

For the validation of the synchronized online simulation that serves as a virtual sensor for the web tension in a web transport system, the web tension control was run, using the simulated web tension as feedback value (see section 3.2). The goal was to verify, whether the synchronization mechanism is able to detect the changing system behavior and to correct the online simulation model accordingly, which is important for the accuracy of the web tension control.

The changing dynamics behavior is assumed to be caused by a changing modulus of elasticity of the web. As a dynamics model is used for the load imitation in the demonstrator, the corresponding parameter for the modulus of elasticity serves as a ground truth, while the corresponding parameter in the online simulation should converge to this value to prove the functionality of the synchronization mechanism. The functionality of the virtual web tension sensor is proven by showing that the closed-loop controller manages to keep the actual web tension at the desired value by using the virtual sensor as feedback. The accuracy of the used dynamics model was not validated by the experiment, as the model was used for both, the load imitation and the online simulation. However, apart from this, the proposed system is facing real-world conditions, as real components from industrial practice are used with a dynamic load in the demonstrator.

Experiment results

Fig. 9 [Images not available. See PDF.]

Rapid change of elasticity tracked by the synchronized online simulation

During the experiment, the web tension control should keep the web tension in the considered section at 80 N, which corresponds to the same web tension that the previous section has for the initial modulus of elasticity of 8700 ${\text{N/mm}}^2$. As therefore, the initial web strain is equal to the previous section, also the roller velocities in the considered section are initially equal at the desired web transport velocity of 3 m/s. The result is depicted in Fig. 9. Note that the velocity values were smoothed by a moving average filter over 20 values, while the data was recorded every 20 ms.

Within printing machines, rapid changes of the elasticity of up to 20% are possible [20]. To replicate this, the modulus of elasticity in the imitated mechanics is increased instantaneously to 10,500 ${\text{N/mm}}^2$ in the experiment, which is depicted in Fig. 9c. This directly results in a higher web tension in the considered section (see Fig. 9d). As the web tension control relies on the virtual sensor, it does not react to this increase. However, the resulting motor torque at the second real servo axis also increases significantly due to the increased web tension (see Fig. 9b). Hence, the model synchronization mechanism is detecting a high discrepancy between the simulated and real motor torques at the second servo axis. This leads to an adaption of the modulus of elasticity in the online simulation, which is seen in Fig. 9c. After about 20 s, the estimated modulus of elasticity in the simulation already reaches the real modulus of elasticity with a discrepancy of less than 1%. As the modulus of elasticity is increasing successively in the simulation, also the simulated web tension would increase. However, the web tension control keeps the simulated web tension at 80 N by successively increasing the velocity of the first servo axis (see Fig. 9a). Hence, the simulated web tension remains constant, but the behavior of the web tension control is getting more suitable to the real behavior, because of the converging modulus of elasticity. By this, the real web tension also converges to its desired value (see Fig. 9d).

With the increased modulus of elasticity, the web strain is getting smaller to remain the same web tension. As the web strain of the previous section remains constant in this experiment, the roller velocities could not be equal anymore in the stable state (see Eq. (5)), which results in a higher velocity of the first axis (see Fig. 9a).

Discussion

This experiment shows that the implemented synchronized online simulation is able to automatically react to a changing system behavior through an online model adaption. By this, the synchronized online simulation is able to reflect the real system, ensuring reliable simulation results. In particular, the synchronization mechanism adapts the modulus of elasticity in a way that the simulated motor torque and the real motor torque at the second servo axis correspond. By this, the requirement of providing reliable estimates of the web tension with low noise as a virtual sensor for a closed-loop web tension control is met.

As the implementation is intended to demonstrate the principles of synchronized online simulation with an imitated web transport system as an example, the model synchronization mechanism was not optimized to fit to a particular scenario. In the evaluated experiment, the synchronization took a relatively long time, but the resulting estimation for the modulus of elasticity was relatively stable despite the inconsistent torque measurement. As indicated before, the synchronization gains could be chosen higher for a faster and more sensitive adaption, which conversely would also lead to higher instability towards noisy and inconsistent torque measurements. In practice, the gains have to be adjusted to meet the specific requirements optimally.

An alternative synchronization method would be to detect the changing system behavior by the comparison of the motor torques and trigger an optimization algorithm to find a suitable parameter adaption. However, this method is still not able to adjust the model parameters directly after the modification, as a sufficient set of data has to be collected for the new system behavior at first. Additionally, an optimization algorithm is computationally costly and a less frequent adaption could be insufficient for faster changes in the system behavior. In general, this means that a continuous synchronization is more suitable for small but frequent changes, whereas a stepwise synchronization is more suitable for an application with less but more drastic changes.

The use of imitated mechanics has the advantage that the system behavior of the real mechatronic system could be adapted systematically, while knowing the exact system parameters and without the need of an error-prone physical manipulation of real mechanics. However, this approach also has the disadvantage that the behavior of the real mechanics could not be fully replicated due to the limits of the load modeling. Hence, a more complex online simulation model could be necessary in practice and the system would be exposed to more disturbances than in the demonstrator. For this reason, evaluating the accuracy of the implemented virtual sensor is not reasonable at this point.

The model was chosen as an optimum of complexity and accuracy, leading to some limitations due to simplifications. In practice, there exist many sources of disturbances on the web velocity, like roller non-circularity or web sliding [10], which were not included in the load model. In this work, only a changing web elasticity was considered as this is the major disturbance in well-designed web transport systems. In systems with moving rollers, like in accumulators, or in sections with dancers, also a changing web length has to be considered. For a changing cross-sectional area of the web and position-dependent material properties, the model has to be extended even further. Additional friction models are necessary in the case of sliding web transportation. For further validation, considering multiple coupled web sections should be the successive goal to further address real world problems.

Nevertheless, the implementation shows the applicability of the proposed methods and the potential of using synchronized online simulation as a virtual sensor for web tension. Although the demonstrated process was inspired by a printing machine, the results are applicable for all kinds of web transport systems and the concepts concerning synchronized online simulation are valid universally. The advantage compared to the measurement with a physical sensor is that physical measurement would be noisy and could negatively affect the web transport. Furthermore, the hardware costs of a physical sensor are saved and the web tension can be determined by simulation also at sections where it is not possible to establish physical sensing.

In comparison to existing observers or direct computation based on the rollers’ actual velocities, the synchronized online simulation benefits from low signal noise. While observers have to rely on the noisy measurements, it is possible to include high-fidelity drive models in the online simulation that are able to determine a good estimation of the actual velocities by being combined with dynamics models and directly processing the master data. However, also the models have an uncertainty, which is also known as process noise. A consideration of this uncertainty, like in a Kalman Filter, could lead to even better state estimations.

The consideration of the logical behavior of the field devices in the process simulation is becoming increasingly relevant as manufacturing processes are more and more diverse and vary depending on the logical state of the mechatronic components. This is especially important for anomaly detection, where online simulation is able to realize whether the behavior changed due to a logical reconfiguration or the behavior is unwanted. Conversely, traditional observers are very limited concerning the supported model types, which often leads to a simplification of the modeled system behavior.

Conclusion and outlook

Online simulation has the potential to extend the use of simulation from the design to the operation phase of manufacturing systems, where it may be used for monitoring, anomaly detection, or virtual sensing. However, there are many examples where the online simulation has to be synchronized to the actual behavior of the manufacturing system to be able to accurately reflect it. This article presents universal concepts for a synchronized online simulation and proposes specific methods for the practical realization. The principles are successfully validated by applying them on an exemplary online simulation for an imitated web transport system. In the particular example, a virtual sensor for a closed-loop web tension control was implemented and showed the practical applicability of synchronized online simulation.

Another application of a similar online simulation could be the detection of anomalies, like web slip or web break in the example of a web transport system. In this case, the synchronized online simulation would represent the ideal behavior and discrepancies of the motor torque could be used to decide, whether the real behavior is correct. This principle is applicable on various use cases. Furthermore, the synchronized online simulation as a digital twin of a real manufacturing system can be used to gather information about the manufacturing system. This information could be collected and used for multiple supporting services, like predictive maintenance. For example, the change of the mechanics behavior over time, which is tracked by a synchronized online simulation, is a valuable feature for determining mechanic degradation.

Due to the increasing use of simulation technologies in industrial automation, online simulation has a great potential to be used for many applications. To ensure a reliable and accurate reflection of the simulated manufacturing process, synchronized online simulation is an important concept, which should be further investigated by future research. Main existing challenges are the automated initialization of online simulation with the current state of the manufacturing system, comprehensive synchronization, and especially the application of the concept to many examples from industrial practice to show the applicability and possibilities for the implementation. While this paper focusses on the application of online simulation at field level, the application at higher levels in the automation pyramid and also in other domains, like the process industry, should be investigated further. Besides virtual sensing, the usage of online simulation for visualization, monitoring and anomaly detection, as well as predictive online simulation are promising.

Author contributions

All authors contributed to the study conception and design. In-depth conceptualization and implementation were conducted by Darius Deubert. The first draft of the manuscript was written by Darius Deubert and was reviewed by all authors.

Funding

Open Access funding enabled and organized by Projekt DEAL. The work presented in this paper has been partly funded by the German Federal Ministry for Economic Affairs and Climate Action (BMWK) under the project 13IK001ZF “Software-Defined Manufacturing for the automotive and supplying industry https://www.sdm4fzi.de/”.

Data availablity

Data sharing not applicable to this article as no datasets were generated or analysed during the current study

Declarations

Competing interests

The authors declare no competing interests

1

However, model parameters could be transferred to state variables by providing a model for it, which could be a constant change in the simplest case. Then, the variable would behave according to a model and be a state variable.

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References

1. Klingel L, Heine A, Acher S, Dausend N, Verl A. Simulation-based predictive real-time collision avoidance for automated production systems. In: 2023 IEEE 19th International Conference on Automation Science and Engineering (CASE), 2022;pp. 1–6. https://doi.org/10.1109/CASE56687.2023.10260637

2. Kain, S; Heuschmann, C; Schiller, F. Von der virtuellen Inbetriebnahme zur Betriebsparallelen Simulation. ATP Edition; 2008; 50, 08 pp. 48-52.

3. Cardin, O; Castagna, P. Using online simulation in holonic manufacturing systems. Eng Appl Artif Intell; 2009; 22, 7 pp. 1025-1033. [DOI: https://dx.doi.org/10.1016/j.engappai.2009.01.006]

4. Zipper H, Auris F, Strahilov A, Paul M. Keeping the digital twin up-to-date - process monitoring to identify changes in a plant. In: 2018 IEEE International Conference on Industrial Technology (ICIT);2018. pp. 1592–1597. https://doi.org/10.1109/ICIT.2018.8352419

5. Nakaya M, Fukano G, Onoe Y, Ohtani T. On-line simulator for plant operation. In: 2006 6th World Congress on Intelligent Control and Automation;2006. 2:7882–7885. https://doi.org/10.1109/WCICA.2006.1713505

6. Martínez GS, Karhela TA, Ruusu RJ, Sierla SA, Vyatkin V. An integrated implementation methodology of a lifecycle-wide tracking simulation architecture. IEEE Access 6, 2018;15391–15407 https://doi.org/10.1109/ACCESS.2018.2811845

7. Zipper H, Diedrich C. Synchronization of industrial plant and digital twin. In: 2019 24th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA);2019. 1678–1681. IEEE

8. Deubert D, Selig A, Verl A. Real-Time Online Simulation at Field Level in Industrial Automation. accepted at the Stuttgart Conference on Automotive Production (SCAP2024) (2024)

9. Patri T, Wolfermann W, Schroder D. The usage of decentralized observers in continuous moving webs. In: Conference Record of 2001 Annual Pulp and Paper Industry Technical Conference (Cat. No. 01CH37209);2001. pp. 147–154. IEEE

10. Koc, H; Knittel, D; De Mathelin, M; Abba, G. Modeling and robust control of winding systems for elastic webs. IEEE Trans Control Syst Technol; 2002; 10, 2 pp. 197-208. [DOI: https://dx.doi.org/10.1109/87.987065]

11. Manivannan S, Banks J. Real-time control of a manufacturing cell using knowledge-based simulation. In: 1991 Winter Simulation Conference Proceedings;1991. pp. 251–260. https://doi.org/10.1109/WSC.1991.185622

12. Cardin, O; Castagna, P. Proactive production activity control by online simulation. Int. J. of Simul Process Modell; 2011; 6, pp. 177-186. [DOI: https://dx.doi.org/10.1504/IJSPM.2011.044766]

13. Talkhestani BA, Jazdi N, Schlögl W, Weyrich M. A concept in synchronization of virtual production system with real factory based on anchor-point method. Procedia CIRP 67, 2018;13–17 https://doi.org/10.1016/j.procir.2017.12.168. 11th CIRP Conference on Intelligent Computation in Manufacturing Engineering, 19-21 July 2017, Gulf of Naples, Italy

14. Martínez GS, Karhela T, Ruusu R, Lackman T, Vyatkin V. Towards a systematic path for dynamic simulation to plant operation: OPC UA-enabled model adaptation method for tracking simulation. In: IECON 2017-43rd Annual Conference of the IEEE Industrial Electronics Society;2017. pp. 5503–5508. IEEE

15. Fagervik K, Konstari O, Schalien R. Control of batch evaporative crystallization of sugar by means of adaptive simulation. In: 1988 American Control Conference;1988. pp. 677–683. https://doi.org/10.23919/ACC.1988.4789805

16. Deubert D, Zhou Z, Selig A, Verl A. Towards Efficient Real-Time Model Adaption for Online Simulation at Machine Level. accepted at the 12th International Conference on Industrial Technology and Management 2024

17. Friman, M; Airikka, P. Tracking simulation based on PI controllers and autotuning. IFAC Proceed Vol; 2012; 45, 3 pp. 548-553. [DOI: https://dx.doi.org/10.3182/20120328-3-IT-3014.00093]

18. Pietilä, J; Kaartinen, J; Reinsalo, A-M. Parameter estimation for a flotation process tracking simulator. IFAC Proceed Vol; 2013; 46, 16 pp. 122-127. [DOI: https://dx.doi.org/10.3182/20130825-4-US-2038.00048]

19. Goeb M. Dynamisches Bahnzugkraft- und -geschwindigkeitsverhalten kontinuierlicher Fertigungsanlagen unter rheologischen, klimatischen und regelungstechnischen Aspekten;2012. PhD thesis, University of Erlangen-Nuremberg

20. Goeb M, Schultze S. Reduktion von durch Rollenwechsel verursachten Registerfehlern. In: VDD-Seminar, IDD, TU-Darmstadt;2017

21. Scheifele C, Scheifele D, Eger U, Daniel C, Buchal E, Röck S. ISG-virtuos–der Digitale Zwilling für die Praxis. InEchtzeitsimulation in der Produktionsautomatisierung: Beiträge zu Virtueller Inbetriebnahme, Digitalem Engineering und Digitalen Zwillingen;2024 pp. 61–74. Berlin, Heidelberg: Springer Berlin Heidelberg.