Cross-directional Research Articles

Data Reconstruction Method for CD Basis Weight Analysis of Paper by using Compressed Sensing Technology

The control of the cross-directional (CD) basis weight of paper is very challenging. The actuator of the system needs to control the properties of the entire sheet according to a set of restricted data measured by a scanning sensor. The scanning sensor measures the sheet in the cross direction of the paper. For the moving sheet, CD variations were those along an axis perpendicular to the motion of the sheet, while MD (machine direction) variations were those along the axis of motion. One of the problems that make the CD control difficult is data sampling, which is obtained by continuously measuring the CD basis weight of paper through multiple scanning sensors. As the paper moves vertically, the scanning sensor can only measure the “Z” shape area on the paper. When the scanning frequency was not at least twice the maximum frequency of the paper variation, it was difficult to estimate the sheet profile. According to the sparse characteristics of paper signal, a novel approach to accurately reconstruct the sheet properties by a random sampling protocol was proposed by using compressed sensing technology. Compared with the simple bandwidth based uniform sampling theory, it could accurately reconstruct the real process variations from less measurement data. Based on the reconstructed data and actual industrial process data, the CD response model was identified and the reconstruction effect was verified. The CD and MD basis weight data were separated by the predictive separation algorithm, which ensured the basis for CD control. The approach of the compressed sensing technology was found to be effective.

Model-plant mismatch detection for cross-directional processes

This paper presents a two-component framework to detect model-plant mismatch (MPM) in cross-directional (CD) processes on paper machines under model-predictive control. First, routine operating data is used for system identification in closed loop; second, a one-class support vector machine (SVM) is trained to predict MPM. The iterative identification method alternates between identifying the finite impulse response coefficients of the spatial and temporal models. It converges, and the parameter estimates are asymptotically consistent. Coefficient estimates drawn from normal operation are used to train a one-class SVM, which then detects model-plant mismatch in subsequent routine operation. This approach applies to routine operating data without requiring external excitations. It can also distinguish mismatches in the process model from changes in the noise model. Examples of CD processes on paper machines are provided to verify the effectiveness of both components.

Multidimensional Interpolation Decoupling Strategy for CD Basis Weight of Papermaking Process

With a focus on the multivariable coupling characteristics in a cross-directional (CD) basis weight control system, we study the coupling characteristics of a CD control system and decoupling control, and we propose a novel multivariable interpolation decoupling control strategy and a real-time decomposition algorithm in this paper. Based on a model of the CD basis weight profile, a system non-square interaction matrix of high-dimensional data is analyzed by experimental studies and numerical simulation. Along the diagonal of the interaction matrix, the matrix block method is adopted to reduce the system dimension and convert it into a square system. A multivariable control system with high dimensionality is divided into several subsystems. For the high-dimensional Toeplitz symmetric subsystem with small-scale coupling characteristics, an interpolation decoupling algorithm is proposed. Then, a decoupling compensator with the structure of a symmetric Toeplitz matrix was obtained. Compared with the conventional diagonal decoupling matrix, the branch number of the new decoupling network is reduced from 2408 to 186, which realizes the fast decoupling of multivariable systems. The results were even better when we used a double size interaction matrix obtained by interpolation between actual values. By designing the diagonalized controller for the new decoupled system, a decouped CD control system for corrugated paper with a basis weight of 133 g/m2 was implemented in an actual project in a paper mill.

Decoupling control method of paper cross‐directional basis weight based on sparse decomposition

With a focus on the coupling problems of multivariable control for the paper cross‐directional (CD) basis weight caused by a hydraulic headbox, a novel approach of multivariable decoupling control based on sparse decomposition is proposed. The model function of the CD basis weight control for a single dilution water branch valve is used as the basis of a sparse atomic library. Then, according to the deviation curve of the CD basis weight, the particle swarm optimization (PSO) algorithm is used to obtain atoms corresponding to each control unit (the multiple dilution water branch valves) to form a sparse atomic library. As each atom in the atomic library contains the control information of the corresponding dilution water branch valve, the decoupling control of paper CD basis weight can be realized via mining control information. The essence of this method is to solve the coupling problems of multivariable control by using optimization theory. Experimental results demonstrate that this method achieves a remarkable decoupling control effect.

Active scanner control on paper machines

ABSTRACT The cross-directional (CD) basis weight control on paper machines is improved by optimizing the path of the scanning measurement. The optimal path results from an LQG problem and depends on how the uncertainty of the present estimate of the basis weight and the intensity of process noise vary in CD. These factors are assessed by how accurately the CD basis weight estimate predicts the measured optical transmittance with a linear adaptive model on synchronized basis weight and transmittance data. Simulations on optimized scanner path in disturbance scenarios are presented, and the practical implementation of scanner control is discussed.

Performance Assessment of Cross-Directional Control for Paper Machines

The minimum variance controller has been extensively used as a benchmark in the performance assessment of both univariate and multivariate control loops when time delay is the fundamental performance limitation. In this paper, the spatial and temporal performance limitations in the cross-directional (CD) control of paper machines are analyzed. The idea of minimum variance benchmarking is extended to the CD process based on these performance limitations. Based on an industrial CD controller, a user-specified benchmark, which is more practical and less aggressive, is also proposed. In addition, several related performance indices are proposed for the CD process based on both the minimum variance benchmark and the user-specified benchmark. Illustrative examples from a paper machine simulator and industrial data sets are provided to show the effectiveness of the proposed performance indices.

Automatic tuning of robust constrained cross‐direction controllers

SummaryThe paper machine cross‐directional (CD) process is a large‐scale spatially distributed system. It is known to be severely ill‐conditioned as the gain rolls down to zero for some of the process directions. Model uncertainties in the process are inevitable resulting in a challenging robust control design problem. CD actuators are subject to min–max constraints while slice lip actuators are subject to additional bending moment limits. Because of the large number of input constraints, the industrial practice is to tune the CD controller assuming inactive constraints. The robustness of CD feedback loops to model uncertainties under constrained internal model control satisfies an integral quadratic inequality. This work develops an automatic tuning algorithm that guarantees robust stability and performance of the constrained CD feedback loop. Spatial response models are identified in a prediction error frame delivering bounds on the CD process pseudo‐singular values. The CD controller is synthesized online through a linear matrix inequalities feasibility problem taking into consideration the modal space uncertainty rising from the uncertainties in the estimated parameters and the expected variations in the dynamic response. The developed tuning technique is suitable for paper machines producing different grades of paper as the CD process spatial and dynamic responses change for each grade. The performance of the tuned constrained internal model control controller is validated through comparing it to an industrial CD controller that has been implemented in paper mills as part of a commercial product. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling and Control of a Plastic Film Manufacturing Web Process

This paper is concerned with the modeling of a plastic film manufacturing process and the development and implementation of a model-based Cross-Directional (CD) controller. The model is derived from first-principles and some empirical relationships. The final validated nonlinear model could provide a useful offline platform for developing control and monitoring algorithms. A new controller is designed which has a similar structure to that of Internal Model Control (IMC) with the addition of an observer whose gain is designed to minimize process and model mismatch. The observer gain is obtained by solving a multiobjective optimization problem through the application of a genetic algorithm. The controller is applied to the nonlinear model and simulation results are presented demonstrating improvements that can be achieved by the proposed controller over two existing CD controllers.

Iterative adaptive robust control of multivariable CD processes

AbstractIn this paper we present a novel adaptive robust control approach to the multivariable cross‐directional (CD) process of continuous web manufacturing. The common assumption of spatial frequency decomposition (SFD) is used to allow the process analysis in terms of a family of single‐input single‐output (SISO) transfer functions across the spatial frequencies. We then apply discretized Windsurfing adaptive robust control to each individual separated spatial frequency, starting with a stable initial model and a robust stabilizing controller at each spatial frequency. This approach allows the 2D bandwidth of the closed‐loop system to be increased progressively at each spatial frequency through an iterative relevant system identification and control design procedure. The method deals with both model uncertainty and measurement noise issues. Simulation results are given to illustrate the performance of the applied method. Copyright © 2009 John Wiley & Sons, Ltd.

Detecting Mismapping in Cross-Directional Control Systems

Cross-directional (CD) control systems regulate product properties in industrial web processes by manipulating the inputs to arrays of actuators. In many of these processes, the product wanders or undergoes transformations such as stretching that introduce lateral shifts in the location of the actuator responses. The spatial position of the center of the response of each actuator is known as the actuator mapping and for CD controllers to operate effectively, it is important that this is known accurately. Actuator mapping is one of the main sources of uncertainty in the model that is used to design CD controllers and mismapping can lead to closed-loop instability, so CD controllers are often designed conservatively to provide robustness to this uncertainty. Because CD controllers can operate with a significant level of mismapping, both the dynamic and steady-state responses of the closed-loop system are often degraded. In practice, it is difficult to detect the presence of mismapping, but this brief describes an online diagnostic technique based on a vector auto regression (VAR) representation of the closed-loop response of the actuator inputs, which derives a statistic from existing plant data that can be used in a hypothesis test to detect the presence of mismapping. The performance of the technique is demonstrated by results from an implementation on a plastic film process.

A novel cross directional register modeling and feedforward control in multi-layer roll-to-roll printing

For the adaption of roll-to-roll printing method to the printed electronics, it is mandatory to increase the resolution of register control. Therefore, it is desired to derive a mathematical model for register and to develop a controller to reduce the register error. The cross direction register error was derived considering both the lateral motion of a moving web and the transverse position of a printing roll. And a feedforward control method was proposed to cancel out the disturbance of CD register from upstream span. The proposed controller could be used to improve the performance of the CD register controller in a large area roll-to-roll printing machine. The mathematical modeling and proposed control method were validated by numerical simulations and experimental verifications in various operating conditions using a multi-layer direct gravure printing machine. These results show that the proposed feedforward control scheme greatly improves the control performance of register control in overcoming the upstream disturbances.

Tensor-based blind alignment of MIMO CD processes

A key issue in paper–machine cross-directional (CD) control is alignment, i.e., accurate spatial mapping of the actuators to the scanning points. Typically, this mapping problem is a non-linear and slowly time-varying phenomenon. Most current methods require bump tests, in which a few actuators are excited, and the peaks in the observed scan data are assigned to the excited actuators. A major drawback of these methods is that they need to be manually initiated and thus require the CD control system to be in manual mode. This paper presents a novel, deterministic, tensor-based modeling of the CD process and an alignment method that works while the closed-loop CD controlled system is running. First, we link the CD data to the parallel factor (PARAFAC) model. Exploiting this link, we derive a deterministic blind PARAFAC decomposition as an alignment method with performance close to non-blind minimum mean-square error (MMSE). We show that blind alignment follows from simultaneous matrix decomposition. The proposed PARAFAC capitalizes on the physical location of the actuators, scanning databoxes and their temporal diversities. Its performance is verified in several simulations for different actuator models. The discussed algorithm is then tested on industrial paper–machine data and evaluated as an identification tool.

Iterative Feedback Tuning of Cross-directional Processes Controller

This paper studies the possible application of Iterative Feedback Tuning (IFT) to the paper machine cross-directional (CD) control. Although the CD control is naturally a multi-input-multi-output (MIMO) problem, by enforcing the circulant assumption, IFT for CD control is as simple as the single-input-single-output (SISO) case, i.e. only one gradient experiment is needed for estimating the gradient. Simulation of a simple disturbance rejection problem is included to demonstrate the main ideas.

Approximate steady-state performance prediction of large-scale constrained model predictive control systems

When tuning the parameters of a constrained model predictive controller (MPC), one usually will use closed-loop simulations in order to predict closed-loop performance. Closed-loop simulation can be very time-consuming and inconvenient for large-scale constrained MPC, such as paper machine cross-directional (CD) predictive control. Paper machine CD processes are two-dimensional (2-D) (temporal and spatial) systems with up to 600 inputs and 6000 outputs. It is very important to predict the steady-state values for the closed-loop CD MPC systems during the tuning process, as the variances of these values are used as the control performance indexes in paper making industry. This article proposes to use a direct one-step static optimizer for approximating the closed-loop steady-state performance of constrained CD MPC. The parameters of this static optimizer can be obtained through minimizing the difference of two closed-loop transfer functions. Experiments with industrial data demonstrate that the static optimizer is computationally much more efficient (up to two orders of magnitude) than closed-loop simulation while reliably and accurately predicting the steady-state performance.

BAYESIAN METHODS FOR CONTROL LOOP PERFORMANCE ASSESSMENT IN CROSS-DIRECTIONAL CONTROL

The minimum variance (MV) lower bound has been applied to many multivariable control systems in order to assess their performance based on routine operating data. However, such analysis often depends on the selection of a suitable dynamic model of the data and for multivariable systems, there can be many candidate models. Also, uncertainty is often not considered, because standard approximations do not exist for the sampling distribution of these multivariable performance indices. This paper addresses these two issues by using the Bayesian approach to vector autoregression (VAR) modelling with Markov Chain Monte Carlo (MCMC) numerical methods. Dynamic model selection is carried out by using Reversible Jump (RJ) MCMC and it is shown that MCMC can be used to the estimate the non-standard distributions that exist in multivariable MV performance indices. The approach is applied to data from an industrial cross-directional (CD) control system by using a more general class of model than has previously been studied for these systems.

Two-dimensional frequency analysis for unconstrained model predictive control of cross-directional processes

This paper presents consistent criteria for evaluating the selection of tuning parameters for an industrial model predictive control of large-scale cross-directional (CD) processes using a two-dimensional (temporal and spatial) frequency analysis technique. The concept of rectangular circulant matrices (RCMs) and their properties are presented. It is shown that large-scale CD processes can be approximated as RCMs and then diagonalized by complex Fourier matrices, allowing analysis in terms of a family of SISO transfer functions across the spatial frequencies. Familiar concepts from control engineering such as bandwidth and stability margin are extended into the two-dimensional frequency domain, providing intuitive measures of closed-loop performance and robustness.

Identification tool for cross-directional processes

This paper considers an industrial identification tool for cross-directional (CD) process of continuous web manufacturing such as papermaking. A special focus is on identification of the mapping between CD actuators and measured profiles of the web properties from input-output process data. The developed algorithms are based on nonlinear parametric models of the CD response shape and mapping and minimize a model fit error for a two-dimensional array of data. The algorithms are deployed as a part of an automated process control support tool and have been successfully used over a period of time on many paper mills with various types of the CD actuators. The paper is illustrated by identification results from a real-life paper mill.

Feedback controller design for a spatially distributed system: the paper machine problem

This paper reports on the development and implementation of an algorithm for the design of spatially distributed feedback controllers for the wide variety of physical processes that are included in cross-directional (CD) control of industrial paper machines. The spatial and temporal structure of this class of process models is exploited in the use of the 2D frequency domain for analysis and 2D loop shaping design of feedback controllers. This algorithm forms the basis of a software tool that has recently been implemented in a commercial product and its use is illustrated for tuning CD controllers on two different industrial paper machines. The first example describes the use of the tool in stabilizing an unstable closed-loop system by retuning the distributed controller. The second paper machine example exposes an underperforming controller. Subsequent retuning of the controller resulted in a dramatic performance improvement.

Dual adaptive control of paper coating

The paper is concerned with the cross directional (CD) control of coat weight on industrial bent blade coaters. The coater is a coupled multivariable process whose gain drifts over time and often switches sign. Current industrial practice is to switch off automatic control when the loop becomes unstable due to gain sign reversal. Because of this, the standard industrial controller is rarely on for more than half of the blade life. The control strategy developed in the paper is based primarily on viewing the coater as a plant with uncertain linear characteristics. An active suboptimal dual controller minimizes a nonlinear performance index designed specifically to reflect the peculiarities of the process. Thus, no heuristic logic is needed. The controller, which takes into consideration the loading and bending limitations imposed by the actuators and the blade, is coupled with an adaptive Kalman filter for parameter estimation. An approximate analytical control law was derived to allow for easy implementation. The proposed strategy was successfully applied to an off-machine bent blade coater. The results of a series of trials show the advantages of including probing in the control signal, and that the adaptive Kalman filter was capable of tracking gain variations. The dual controller yielded substantial quality improvement and was able to control the process throughout the entire blade life. The developed strategy was well accepted by the company.

Cross‐directional Estimation and Predictive Control of Paper Machines Using DWT

AbstractThis paper proposes a novel approach for cross‐directional (CD) estimation, modeling and control on paper machines based on discrete wavelet transforms (DWT). The CD basis weight variations are approximated at various resolutions using wavelet multiresolution analysis (WMRA). The controllable component of CD variations can be extracted from the original samples by choosing a suitable threshold resolution. An acceptable response model describing the relationship between the settings of the slice‐screws to the basis weight profile is obtained. The controller synthesis, model prediction, optimization and parameter estimation are all performed in the DWT domain. The size of optimization and control problems associated with such large dimensions can be significantly reduced.